text:
\section{Introduction}
\label{sec:1Int}
It is now more than fifty years since the seminal theoretical work of Abrikosov wherein the superconducting vortex lattice (VL) was first shown to be expected in type-II superconductors.~\cite{Abr57} This pioneering work sparked the intense and continuing research efforts into the physics of vortex matter, which assumed even greater importance with the discoveries of High-$T_{\rm c}$ cuprate and other unconventional type-II materials with novel pairing symmetries. A full understanding of the properties of vortex matter is also crucial from the technological perspective because type-II superconducting materials are, for example, key constituents of high current-carrying applications. From the latter viewpoint, it becomes vital to understand the vortex properties of High-$T_{\rm c}$ cuprates that display superconducting critical temperatures above those of the 77~K boiling point of liquid nitrogen, since this is a much more economical cryogen than liquid helium.

Close to optimally-doped YBa$_2$Cu$_3$O$_{7-\delta}$ is a prototypical High-$T_{\rm c}$ cuprate with superconducting critical temperatures in the region of 90~K, the exact value being composition dependent.~\cite{Lia06} Indeed, the VL properties of YBa$_2$Cu$_3$O$_{7-\delta}$ have been the subject of numerous investigations over the years,~\cite{Gam87,Mag95,Sch96,Fis97,Son97,Son99,Aus08,Kie10,For90,Yet93a,Yet93b,Kei93,Kei94,For95,Joh99,Bro04,Sim04,Whi08,Whi09,Cam14} with the bulk probe of small-angle neutron scattering (SANS) playing an important role in revealing the effects of effective mass anisotropy, VL melting and pinning, and field-induced nonlocality.~\cite{For90,Yet93a,Yet93b,Joh99,Bro04,Kei93,Kei94,For95,Sim04,Whi08,Whi09,Cam14} Despite the large body of work, it is only in the last decade that SANS observations of the intrinsic magnetic field- and temperature-dependent VL structures could be achieved.~\cite{Whi09,Whi11,Cam14} The more recent achievements can be largely attributed to significant improvements in sample quality, since these observations were not complicated by twin-plane pinning effects which hampered the earlier efforts to unveil the intrinsic VL properties.~\cite{For90,Yet93a,Yet93b,Joh99,Bro04}

In particular, at low temperature in detwinned and lightly overdoped YBa$_2$Cu$_3$O$_{7}$, the field-evolution of the VL structure was recently studied for magnetic fields up to 16.7~T applied parallel to the crystal \textbf{c}-axis.~\cite{Whi09,Whi11,Cam14} The most striking observations include successive field-driven first-order reorientation transitions of the VL coordination at both 2.3(2)~T and 6.7(2)~T,~\cite{Whi09} and a smooth evolution of the high-field VL that passes \emph{through} the perfectly square VL coordination expected to be stabilised by a pure $d$-wave gap symmetry.~\cite{Cam14} In general, anisotropies in both the Fermi surface and the superconducting gap can be responsible for the field-dependence of the precise VL structure,~\cite{Aff97,Nak02,Suz10} and also cause VL structure transitions. However, and as discussed in Refs.~\cite{Whi11,Cam14}, YBa$_2$Cu$_3$O$_{7}$ remains a high-profile example of an unconventional $d$-wave superconductor in which the physical origins of the VL structure transitions are not completely understood.

Towards addressing this problem, here we present new SANS studies of detwinned and lightly underdoped YBa$_2$Cu$_3$O$_{6.85}$. Despite the light underdoping which introduces oxygen vacancies, and hence pinning centers, into the CuO chains, we nonetheless observe well-ordered VLs up to the highest magnetic field of 16~T applied parallel to the \textbf{c}-axis. We observe a sequence of VL structure transitions in this material that is analogous to that seen in YBa$_2$Cu$_3$O$_{7}$, though the transition fields are slightly modified. We also present extensive measurements of the VLs observed in YBa$_2$Cu$_3$O$_{6.85}$ as a function of angle of applied field to the \textbf{c}-axis. The VL structure transition fields are found to display a strong and characteristic angle-dependence, and we use this observation to provide new insights into the physical origin of the two field-driven VL structure transitions in YBa$_2$Cu$_3$O$_{7-\delta}$.

\section{Experimental Method}
\label{sec:2Exp}
Single crystals of YBa$_2$Cu$_3$O$_{6.85}$ were prepared by the flux growth method, and from a starting mixture of BaCO$_3$, CuO and Y$_2$O$_3$ powders molten in yttrium-stabilized ZrO$_{2}$ crucibles.~\cite{Lin91} The as-grown crystals are crystallographically twinned and also have an ill-defined oxygen content. The individual crystals were therefore detwinned at elevated temperature using a uniaxial stress applied along a $\langle 100\rangle$ axis. To obtain the YBa$_2$Cu$_3$O$_{6.85}$ composition, the crystals were subsequently annealed at 520$^{\circ}$~C in an O$_{2}$ atmosphere.~\cite{Hin07}

The sample used for the SANS measurements was a co-aligned mosaic of eight YBa$_2$Cu$_3$O$_{6.85}$ single crystals of total mass 85~mg. Using single crystal neutron diffraction to study the (200) and (020) nuclear reflections, the bulk twin-domain population ratio was determined for each individual crystal. The YBa$_2$Cu$_3$O$_{6.85}$ single crystals were found to be almost completely twin-free, and the entire mosaic displayed a detwinning ratio of $98.6(5)\%$. The superconducting critical temperature ($T_{\rm c}$) of each individual crystal was also measured using a Quantum Design physical property measurement system (PPMS). The overall sample displayed a $T_{\rm{c}}$ of 90.5(1.0)~K, where the error represents the spread in $T_{\rm{c}}$ amongst the crystals. Comparison between this $T_{\rm{c}}$ value and the data reported in Ref.~\cite{Lia06} gives a sample doping level of $\delta=0.15(1)$. The sample mosaic was co-aligned and mounted on a 1~mm thick Si plate with the crystal \textbf{c}-axis of the sample perpendicular to the plate.

The SANS experiments were conducted on the SANS-I instrument at the Swiss spallation neutron source (SINQ), Paul Scherrer Institut (PSI), Villigen, Switzerland, the D11 at the Institut Laue-Langevin (ILL), Grenoble, France, and the NG3-SANS instrument at NIST Center for Neutron Research, USA. The neutrons were collimated over 6-18~m (SANS-I), 5.5~m (D11) and 4.5-8m (NG3-SANS), and wavelengths between 4.5-10~\AA~were selected with a typical FWHM spread of $10\%$. A position-sensitive 2D multi-detector placed behind the sample was used to detect the scattered neutrons. At SANS-I, D11, and NG3-SANS, 11~T, 17~T and 9~T horizontal field SANS cryomagnets were respectively available. In each cryomagnet the sample was initially installed with the crystal \textbf{c}-axis parallel to the applied field direction, and approximately parallel to the neutron beam. For the 11~T magnet at PSI, an additional motor-head allowed rotation of the sample stick about the vertical axis inside the variable temperature insert (VTI) of the cryomagnet. This motor provided in-situ control of the direction of the magnetic field with respect to the \textbf{c}-axis, therefore enabling the systematic field-angle-dependent measurements of the VL structure presented in Section~\ref{sec:3Res_VL_Ang}.

At each SANS instrument the cryomagnet was placed on a goniometer table that enabled both rotation and tilt of the sample-magnet ensemble. The SANS measurements of the VL were done by rotating the sample and cryomagnet together through a range of angles that moved the VL diffraction peaks through the Bragg condition. By summing over all measurements at different angles, the SANS diffraction patterns shown in this paper are obtained, and wherein all the VL diffraction spots can be observed in a single image.

For all the low temperature measurements reported in this paper, the VL was prepared using the oscillation-field-cooling (OFC) method. By this method the sample is field-cooled through $T_{\rm{c}}$ until the measurement temperature in a time-dependent magnetic field that weakly oscillates around the target field. The oscillation amplitude used was typically 1~\% of the target field. The OFC method was used to prepare the VL since previous work on twin-free YBa$_2$Cu$_3$O$_{7}$ showed such an approach allows i) the VL to achieve an improved perfection, and ii) a preferred VL coordination due to a lower effective temperature than achieved when cooling in a static field.~\cite{Whi09} Additional SANS measurements not reported here confirmed that the OFC method produced a similar effect on the VLs observed in the present YBa$_2$Cu$_3$O$_{6.85}$ sample. Background SANS measurements were conducted at $T=95$~K and subtracted from the low temperature measurements in order to leave just the VL signal. SANS data visualization and analysis was carried out using the GRASP software.~\cite{Dew03}

\section{Results}
\label{sec:3Res}

\subsection{Vortex lattice structure for $\mu_{0}H\parallel$~c in YBa$_2$Cu$_3$O$_{6.85}$}
\label{sec:3Res_VL_Coord}
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{66989Fig1_rev.eps}
\caption{(Color online) SANS diffraction patterns obtained from the VL at 2~K and (a) $\mu_{0}H\parallel$~\textbf{c}$~=1$~T, (b) $\mu_{0}H\parallel$~\textbf{c}$~=4$~T, (c) $\mu_{0}H\parallel$~\textbf{c}$~=16$~T, and (d) $\mu_{0}H$~=1~T applied $10^{\circ}$ away from \textbf{c}. Panels (e) to (h) show schematic drawings of the results shown in (a) to (d), and which clarify the different VL domains present. Panels (e) and (f) each show VL domains, denoted TP1 and TP2, whose alignment is affected by pinning effects due to the small residual density of twin-planes. In contrast, structures B (panel (f)) and A (panels (g) and (h)) are aligned with the crystal axes and their alignment is considered to be intrinsic.}
\label{Fig:1}
\end{figure}

Figs.~\ref{Fig:1}(a)-(c) show a selection of VL SANS diffraction patterns obtained from YBa$_2$Cu$_3$O$_{6.85}$ at $T=$~2~K, and at different magnetic fields applied parallel to the crystal \textbf{c}-axis ($\mu_{0}H\parallel$~\textbf{c}). Fig.~\ref{Fig:1}(a) shows the diffraction pattern obtained at 1~T that is typical for fields up to 2.37(2)~T. As shown schematically in Fig.~\ref{Fig:1}(e), this VL is composed of two distorted hexagonal domains that each have two spots aligned with a $\{110\}$ plane. The alignment of VL domains along these directions is a clear indication that the VL orientation is not intrinsic, but instead controlled by the small volume of twin-planes remaining in the sample.~\cite{Bro04,Sim04,Whi08} Consequently, we refer to this two domain VL structure as structure TP. As illustrated for one of the two domains in Fig.~\ref{Fig:1}(e), the primitive cell opening angle $\phi_{1}$ is almost bisected by the horizontal \textbf{b}$^{\ast}$-axis, but not exactly.

In the field range between 2.37(2)~T and 5.37(2)~T, structure TP coexists with an additional single distorted hexagonal VL domain, which we call structure B. Fig.~\ref{Fig:1}(b) shows the typical SANS pattern for this field range, with a schematic illustration of all the VL domains present shown in Fig.~\ref{Fig:1}(f). In contrast to structure TP, structure B is aligned intrinsically with the crystal axes, and its primitive unit cell is bisected exactly by the vertical \textbf{a}$^{\ast}$-axis. Across this field range the VL domains of both structures TP and B are always observed to co-exist and neither exclusively populates the entire sample. By surveying the individual crystals of the sample mosaic, we confirmed the structure co-existence in all crystals, though the relative populations of each structure differed slightly. This observed variation could reflect small differences in either oxygen stoichiometry between the individual crystals, or a distribution in spacings between the residual twin planes.

Increasing the field beyond 5.37(2)~T leads to a suppression of both structures B and TP. Instead the VL structure becomes composed of a different intrinsic and single VL domain aligned with the crystal axes that we call structure A. Structure A prevails until the highest measured field of 16~T, the SANS diffraction pattern of which is shown in Fig.~\ref{Fig:1}(c). This structure is sketched in Fig.~\ref{Fig:1}(g), and we define the primitive unit cell to be bisected exactly by the horizontal \textbf{b}$^{\ast}$-axis. A general feature of the data obtained in the high-field range is that the high-field diffraction pattern is dominated by a rhombic VL coordination characterized by four intense Bragg spots, in contrast to the hexagonal VL domains observed at lower fields.

\begin{figure}[t]
\centering
\includegraphics[width=0.46\textwidth]{66989Fig2.eps}
\caption{(Color online) The VL opening angles of the various VL primitive cells for $\mu_{0}H\parallel$~\textbf{c} and at $T=$~2~K. The dashed line is a guide for the eye. The shaded region denotes the field-range of co-existence for structures TP and B. Inset: the $\mu_{0}H\parallel$~\textbf{c}-$T$ VL structure phase diagram. The symbols denote the transition fields between the different VL structure phases, as determined by tracking the VL structures in the vicinities of the phase boundaries. The melting line was obtained from Ref.~\cite{Ram12}.}
\label{Fig:2}
\end{figure}

Fig.~\ref{Fig:2} shows the $\mu_{0}H$-dependence at $T=2$~K of the primitive cell opening angles for structures TP, B, and A. For the TP structure, $\phi$ is an average taken over the two constituent domains. Overall, with increasing $\mu_{0}H$ there is a smooth evolution of the opening angle of the TP structure, before a first-order re-orientation transition which occurs at 5.37(2)~T into the high-field phase where only structure A exists. At higher field, the primitive cell of structure A evolves smoothly with increasing $\mu_{0}H$ up to 16~T, and at 10.6(2)~T it passes through the value of 90$^{\circ}$ expected for a perfectly square coordination. The co-existence of structures TP and B between 2.37(2)~T to 5.37(2)~T is also seen clearly, while for fields outside this field range just a single VL structure type populates the sample.

Bearing in mind the similarity between the primitive cell orientations for both structures TP and A, structure A can be expected to be the \emph{intrinsic} structure that would be present at lower fields in the absence of an orientational effect due to twin-plane pinning. This assumption can be readily tested, since it is well-known that in lightly-twinned YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ samples, twin-plane pinning effects can be suppressed by rotating the sample so that all twin-planes form a small angle of $\sim$5-10$^{\circ}$ with respect to the field direction.~\cite{Bro04,Whi08} After rotating the present YBa$_{2}$Cu$_{3}$O$_{6.85}$ sample by 10$^{\circ}$ around the vertical \textbf{a}$^{\ast}$-axis with respect to a 1~T field, we find that such a rotation is indeed sufficient for the VL to overcome the twin-plane pinning. This is seen in Fig.~\ref{Fig:1}(d) which shows that in the rotated condition the VL diffraction pattern is composed of just a single distorted hexagonal domain aligned with the crystal axes, and not the $\{110\}$ planes. As illustrated in Fig.~\ref{Fig:1}(h), the primitive cell for this VL structure can be treated in the same way as structure A, with the denoted primitive unit cell bisected by the horizontal axis.

Returning to $\mu_{0}H\parallel$~\textbf{c}, another important feature seen in Fig.~\ref{Fig:2} is the broad field co-existence range of the TP and B structures. Such a co-existence exemplifies the near degeneracy between the two structure-types, and also shows that at 2.37(2)~T a first-order-type of VL structure transition occurs between a \emph{fraction} of the TP structure and structure B. Since such a `partial' transition occurs within \emph{all} crystals of the sample mosaic, it could be argued that the particular oxygen doping displayed by the sample appears to be close to a critical level for the occurrence of a complete phase transition. We also point out that this coexistence phase appears not to be a property of twin-plane pinning. As will be shown later, by again rotating the sample with respect to the field direction to suppress the pinning, the broad co-existence region survives, and is between structures A and B instead of structures TP and B.

The inset of Fig.~\ref{Fig:2} shows the $\mu_{0}H\parallel$~\textbf{c}-temperature VL structure phase diagram deduced from measurements where we tracked the VL transition fields. Here it is seen that the VL structure phase boundaries are only very weakly $T$-dependent, and so the field-width of the co-existence region remains essentially unchanged until the melting temperature. This behavior is similar to that reported for YBa$_{2}$Cu$_{3}$O$_{7}$ in Ref.~\cite{Whi11} with the same discussion presented there applicable also here for YBa$_{2}$Cu$_{3}$O$_{6.85}$.

\subsection{Vortex lattice structure for $\mu_{0}H$ not parallel to c in YBa$_2$Cu$_3$O$_{6.85}$}
\label{sec:3Res_VL_Ang}

\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{66989Fig3_rev.eps}
\caption{(Color online) Sketches to illustrate the expected effect on the observed VL structures for SANS measurements done with the field applied at an angle to the crystal \textbf{c}-axis. In (a) the sample is rotated relative to the $\mu_{0}H$ axis by an angle $\alpha$ around \textbf{a}$^{\ast}$. In (b) the sample is rotated by an angle $\beta$ around \textbf{b}$^{\ast}$. On the right side of each panel are sketches of the expected SANS VL diffraction patterns for the different $\alpha$/$\beta$, and where directions $q_{x}$ and $q_{y}$ respectively denote the horizontal and vertical directions on the detector. The filled circles denote the Bragg peaks due to structure A, while empty circles those of structure B.}
\label{Fig:3}
\end{figure}

\begin{figure}
\includegraphics[width=0.3\textwidth]{66989Fig4.eps}
\caption{(Color online) The VL structures observed at $T=$~2~K, and for $\mu_{0}H=$~4~T for (a) $\alpha=30^{\circ}$, (b) $\alpha=10^{\circ}$ and (c) $\beta=20^{\circ}$.}
\label{Fig:7}
\end{figure}

To provide further insight into the $\mu_{0}H$-dependent behaviour of the VL observed for $\mu_{0}H\parallel$~\textbf{c}, we conducted measurements of the VL structure for a range of angles between the applied field and the crystal \textbf{c}-axis. As illustrated in Fig.~\ref{Fig:3}, we explored two directions of sample rotation relative to $\mu_{0}H$: a) rotating the field by an angle $\alpha$ around the \textbf{a}$^{\ast}$-axis (towards $[010]$), and b) a rotation by an angle $\beta$ around the \textbf{b}$^{\ast}$-axis (towards $[100]$).

In Fig.~\ref{Fig:3} we also illustrate the change in distortion of hexagonal VL structures expected from anisotropic London theory as a consequence of the sample rotation. For $\mu_{0}H\parallel$~\textbf{c}, i.e. $\alpha=\beta=0^{\circ}$ we have seen in Sec.~\ref{sec:3Res_VL_Coord} that, although the orientation is determined by pinning, the low field hexagonal VLs are distorted along the \textbf{a}$^{\ast}$-axis away from an isotropic hexagonal coordination. Anisotropic London theory provides the simplest interpretation of the distortion in terms of an effective mass anisotropy since, $\eta=\gamma_{ab}=\lambda_{a}/\lambda_{b}\propto\sqrt{m_{a}^{\ast}/m_{b}^{\ast}}$,~\cite{Kog81,Cam88,Thi89} where $\eta$ is the axial ratio of the ellipse that overlays the six Bragg spots in a hexagonal VL domain. Since $\eta$ is related geometrically to the VL opening angles defined in Fig.~1, it is readily seen that $\eta>1$ at low field where London theory is most valid. In the zero-field limit we find $\eta=1.25(3)$ for YBa$_{2}$Cu$_{3}$O$_{6.85}$, which indicates a lower effective mass, and hence higher super-current density, along the \textbf{b}$^{\ast}$-axis compared with the \textbf{a}$^{\ast}$-axis; an observation consistent with the expected existence of superconducting CuO chain states.~\cite{Atk95,Xia96,Atk99} This suggestion is further supported by noting that the value of $\eta=1.25(3)$ for YBa$_{2}$Cu$_{3}$O$_{6.85}$, which has oxygen vacancies in the CuO chains, is less than that of $\eta=1.29(2)$ found for YBa$_{2}$Cu$_{3}$O$_{7}$ which has completely filled CuO chains,~\cite{Whi09,Whi11} and significantly less than the value of $\eta=2.57(5)$ reported for the stoichiometric double-chain compound YBa$_{2}$Cu$_{4}$O$_{8}$.~\cite{Whi14}

By increasing either $\alpha$ or $\beta$ the supercurrent response in the plane orthogonal to the field includes a contribution due to $m_{c}^{\ast}$. Since $m_{c}^{\ast}$$\gg m_{a}^{\ast}$ and $m_{b}^{\ast}$, increasing either $\alpha$ or $\beta$ always leads to an increase of the effective mass in the horizontal direction. Therefore, and as shown in Fig.~\ref{Fig:3}, increasing $\alpha$ causes the hexagonal VL distortion to decrease, and so a reduction of angle $\phi$ characteristic of structure A, or an \emph{increase} in angle $\rho$ characteristic of structure B. The converse is realised for increasing $\beta$ since the VL distortion will increase, with $\phi$ increasing and $\rho$ decreasing. It should be noted that even while anisotropic London theory provides a handy guide for understanding the angle-dependence of the VL distortion, no field-driven VL structure \emph{transitions} are expected within the theory for fields applied away from perpendicular to the basal plane. Therefore, any observed VL structure transitions still can only be understood as a consequence of higher-order anisotropies beyond those included in local anisotropic London theory. In what follows, it is observed that the $\mu_{0}H$-dependence of VL structure transitions are indeed strongly dependent on the direction of crystal rotation with respect to the field.

The usefulness of VL measurements with $\mu_{0}H$ at an angle to the crystal \textbf{c}-axis is exemplified by the data shown in Fig.~\ref{Fig:7}. Here we present VL diffraction patterns all obtained in $\mu_{0}H$=4~T but for different values of $\alpha$ and $\beta$. Beginning at $\mu_{0}H\parallel$~\textbf{c}, Fig.~\ref{Fig:1}(b) showed the VL at 4~T to be composed of structures TP and B. In contrast, with $\alpha=10^{\circ}$, an angle where pinning to twin-planes is suppressed, we observe the coexistence of structures A and B [Fig.~\ref{Fig:7}(b)]. Further increasing $\alpha$ to $30^{\circ}$ [Fig.~\ref{Fig:7}(a)] leads to a suppression of structure A, and structure B becomes the only VL structure type in the sample. On the $\beta$ side the inverse tendency with angle is observed. Fig.~\ref{Fig:7}(c) shows that for $\beta=20^{\circ}$, structure B is entirely suppressed, and structure A is the only structure-type in the sample. Therefore, at a constant field of 4~T we observe an angle-driven first-order VL structure transition between structures A and B. From the most general perspective, this observation is in agreement with the expectations of the `hairy-ball' theorem as applied to VLs, and which states that at any field discontinuous VL transitions must exist as the angle of the field to the crystal is varied.~\cite{Lav10,Kaw13}

\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{66989Fig5.eps}
\caption{(Color online) Magnetic field-$\alpha$/$\beta$ VL structure phase diagram at $T=2$~K. Each symbol denotes where the VL structure was measured by SANS. The phase boundary lines are estimated from the data. The dotted line close to zero angle ($\mu_{0}H\parallel$~\textbf{c}) and for fields below 5~T indicates the approximate region where vortex pinning can determine the VL orientation.}
\label{Fig:8}
\end{figure}

In Fig.~\ref{Fig:8} we show an overall angle-$\mu_{0}H$ VL structure phase diagram for YBa$_2$Cu$_3$O$_{6.85}$ that extends out to both $\alpha$ and $\beta=45^{\circ}$, and 10~T in applied field. Strongly contrasting $\mu_{0}H$-dependent behavior is observed for the two explored rotation directions. In general increasing $\alpha$ enhances the field stability range of structure B. Furthermore, for sufficiently large $\alpha$ the $\mu_{0}H$-dependent behavior evidences two \emph{complete} first-order transitions that separate structure B from structure A at both lower and higher field. Increasing $\beta$ leads to very different behavior, since any sign of structure B is quickly suppressed, and completely gives way to structure A at all fields by $\beta\geq17.5^{\circ}$.

\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{66989Fig6_rev.eps}
\caption{(Color online) The $\mu_{0}H$-dependence of the VL opening angle of (a) structure A and (b) structure B over a range of $\alpha$ and $\beta$ rotation angles. All data were obtained at $T$=2~K, and all dashed lines are guides for the eye. The legend shown in (b) applies to both panels.}
\label{Fig:13}
\end{figure}

The phase diagram shown in Fig.~\ref{Fig:8} was constructed by tracking the $\mu_{0}H$-dependence of the opening angles of both structures A and B for the range of explored $\alpha$ and $\beta$ angles. These data are presented in Fig.~\ref{Fig:13}. The overall observed behavior is generally consistent with the expectation of anisotropic London theory illustrated in Fig.~\ref{Fig:3}. For structure A [Fig.~\ref{Fig:13}(a)], by increasing $\beta$, the value of $\phi$ at a particular field increases, which is consistent with an increase of the effective superconducting anisotropy in the plane orthogonal to the applied field. At low field, increasing $\alpha$ leads to a reduction in $\phi$ as the VL tends towards a more isotropic distortion. Fig.~\ref{Fig:13}(b) shows that angle $\rho$ of structure B also generally obeys the expected behavior as a consequence of the sample rotation.

Interpreting these angle-dependent measurements in terms of effective mass anisotropy incorporated into local London theory provides at least a qualitative understanding of why the VL opening angle, and hence distortion, changes as a consequence of rotating the crystal with respect to $\mu_{0}H$. Nonetheless, similarly as for $\mu_{0}H\parallel$~\textbf{c}, the most important aspects of the observations, the $\mu_{0}H$-dependence of both $\phi$ and $\rho$, and the transitions observed between structures A and B, require a theoretical explanation that goes beyond the local approximation inherent to the London theory.

\section{Discussion}
\label{sec:4Discussion}
The purpose of this study is to shed new light on the sequence of $\mu_{0}H$-driven and first-order VL structure transitions observed at low temperature in close to optimally-doped YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ with $\mu_{0}H\parallel$~\textbf{c}. Using SANS we have studied the VL in a detwinned and lightly underdoped sample of YBa$_{2}$Cu$_{3}$O$_{6.85}$. By underdoping we aimed to controllably alter the electronic structure compared with the case of lightly overdoped YBa$_{2}$Cu$_{3}$O$_{7}$, both in terms of the precise Fermi surface morphology and the superconducting density of states (DOS). In theory, tuning these properties can lead to a variation in the $\mu_{0}H$-dependence of the VL structure between the two compounds.

First we establish the experimental observations. For $\mu_{0}H\parallel$~\textbf{c} and at $T$=2~K the following sequence of VL structure transitions has been reported in detwinned YBa$_{2}$Cu$_{3}$O$_{7}$:~\cite{Whi09,Whi11}
\begin{equation}
\mu_{0}H_{\rm{c1}} < \textrm{A} < 2.3(2)~\textrm{T} < \textrm{B} < 6.7(2)~\textrm{T} < \textrm{A} \nonumber
\end{equation}
where A/B denote VL structure types defined in the same way as in Sec.~\ref{sec:3Res}. This $\mu_{0}H$-dependent behavior is analogous to that reported here for YBa$_{2}$Cu$_{3}$O$_{6.85}$ which for $\mu_{0}H\parallel$~\textbf{c} and $T$=2~K is:
\begin{equation}
\mu_{0}H_{\rm{c1}} < \textrm{TP} < 2.37(2)~\textrm{T} < \textrm{TP}+\textrm{B} < 5.37(2)~\textrm{T} < \textrm{A}. \nonumber
\end{equation}
The principal differences between the two sequences concern the low and intermediate field phases. In the lowest field phase of YBa$_{2}$Cu$_{3}$O$_{6.85}$, measurements with $\mu_{0}H$ applied at an angle to the \textbf{c}-axis, allow us to deduce that structure TP arises due to residual twin-plane pinning in the sample. In a truly twin-free sample, structure A is expected to be present instead of structure TP, with this being the same low field VL structure-type seen in YBa$_{2}$Cu$_{3}$O$_{7}$.

In the intermediate field phase, both YBa$_{2}$Cu$_{3}$O$_{6.85}$ and YBa$_{2}$Cu$_{3}$O$_{7}$ display structure B, yet only in the latter compound does structure B occupy the entire sample for $\mu_{0}H\parallel$~\textbf{c}. In YBa$_{2}$Cu$_{3}$O$_{6.85}$, it remains unclear precisely why structures B and TP, which are spatially-separated in the sample, display such a broad range of field-coexistence. Since measurements at finite $\alpha$/$\beta$ show that the co-existence of structures TP and B becomes replaced by a co-existence between structures A and B, this allows us to rule out an obvious influence of the twin-plane pinning. Instead, the co-existence may reflect an extreme sensitivity of the VL structure to local variations in stoichiometry and homogeneity within the individual crystals of the sample. Whatever the true explanation, the general observation is that in terms of absolute field, the propensity for structure B falls with underdoping, since it occupies a narrower field range in YBa$_{2}$Cu$_{3}$O$_{6.85}$ compared with YBa$_{2}$Cu$_{3}$O$_{7}$. Future measurements on further underdoped samples may reveal a complete suppression of structure B for all $\mu_{0}H\parallel$~\textbf{c}.

It is also informative to re-write the transition sequences in terms of magnetic fields normalised to values of $H_{c2}(T=0)$, quantitative estimates of which have recently become available.~\cite{Gri14} For YBa$_{2}$Cu$_{3}$O$_{7}$, $H_{c2}$ is estimated to be 150(20)~T, and the transition sequence written in terms of normalized field is:
\begin{equation}
\mu_{0}H_{\rm{c1}} < \textrm{A} < 0.015(2) < \textrm{B} < 0.044(6) < \textrm{A} \nonumber
\end{equation}
For YBa$_{2}$Cu$_{3}$O$_{6.85}$, we use the value of $H_{c2}$=70(10)~T reported for YBa$_{2}$Cu$_{3}$O$_{6.86}$, and the transition sequence is:
\begin{equation}
\mu_{0}H_{\rm{c1}} < \textrm{TP} < 0.034(5) < \textrm{TP}+\textrm{B} < 0.077(11) < \textrm{A}. \nonumber
\end{equation}
This shows both VL structure transitions to occur at a higher fraction of $H_{c2}$ in the more underdoped compound, even though the absolute transition fields are similar. We also point out that while our experiments made use of the highest magnetic fields presently available for SANS, these fields extend only up to limited fractions of $H_{c2}$; for YBa$_{2}$Cu$_{3}$O$_{7}$ the highest applied field of 16.7~T corresponds to $\sim$0.11~$H_{c2}$,~\cite{Cam14} while for YBa$_{2}$Cu$_{3}$O$_{6.85}$ the highest applied field of 16~T corresponds to $\sim$0.23~$H_{c2}$. From this viewpoint, while the observations in the two compounds are comparable to one another on an absolute field scale, the measurements on the more underdoped compound cover a larger portion of the superconducting phase diagram.

Next we discuss the physical origin of the VL structure transitions seen in both compounds for $\mu_{0}H\parallel$~\textbf{c}. The vast majority of theoretical work on VL structure transitions has been developed on model systems with $\mu_{0}H$ perpendicular to a fourfold symmetry plane, since this provides the simplest system in which to treat the expected effects of either (or both) of a Fermi surface anisotropy and $d$-wave nodal gap symmetry.~\cite{Ber95,Xu96,Aff97,Fra97,Kog97a,Shi99,Ich99,Nak02,Hia08,Suz10} For $\mu_{0}H$ perpendicular to a twofold symmetry plane as appropriate for orthorhombic YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, the available theory is limited~\cite{Kog97a,Hir10} and, as far as we are aware, completely non-existent for the case where $\mu_{0}H$ is perpendicular to a twofold plane that includes a nodal gap anisotropy. We further mention that, since field-driven and still unexplained VL transitions have also been observed in other unconventional superconductors for fields applied perpendicular to a twofold symmetry plane,~\cite{Esk97b,Das12} understanding the observed VL transitions for such a symmetry setting assumes an added importance from the more general perspective. In what follows we interpret the observations in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ in terms of the expectations of available theory.

As mentioned previously, local London theory provides a useful starting point for understanding the coupling between the VL and the crystal anisotropy in high-$\kappa$ superconductors.~\cite{Kog81,Cam88,Thi89} In this approach, an effective mass anisotropy is incorporated into the free energy via a second rank tensor $m_{ij}$. The inclusion of $m_{ij}$ can lead to distortions of isotropic hexagonal VL structures at no energy cost, and thus local theory can provide an explanation for the distortions of the hexagonal VL domains that we observe at low field in YBa$_{2}$Cu$_{3}$O$_{6.85}$. However, local theory has well-noted shortcomings since no preferred VL orientation is expected for $\mu_{0}H\parallel$~\textbf{c}, and consequently no $\mu_{0}H$-induced transitions in the VL coordination can be expected. Since in all real materials the VL displays a preferred orientation at all fields, it is necessary to consider higher-order effects beyond local theory, i.e. nonlocal effects, to explain the observations.

The inclusion of nonlocal corrections in VL theory provides a means for the host system anisotropies, such as the Fermi velocity and superconducting gap, to couple to the VL properties. Consequently, nonlocal theory can be used to explain both observed preferred VL orientations, and $\mu_{0}H$- and temperature-driven VL structure transitions. Extensive theoretical work has been conducted exploring the role of nonlocality on the VL structure that involves varying degrees of approximation. Common approaches have involved developing nonlocal corrections or higher-order gradients into analytic phenomenological London and Ginzburg-Landau models, respectively.~\cite{Ber95,Xu96,Aff97,Fra97,Kog97a,Shi99,Hia08} The most desirable theoretical approach for calculating the VL properties are first-principle calculations within the framework of quasiclassical Eilenberger theory.~\cite{Eil68,Ich99,Nak02,Suz10} In this approach nonlocality is catered for by default, and the Fermi surface and superconducting gap anisotropies can be treated in equal measure. Furthermore, calculations can be done that are valid at any field or temperature. From such calculations it is well-established that for $\mu_{0}H$ perpendicular to a four-fold symmetry plane, anisotropies arising from both the Fermi velocity and a nodal superconducting gap can determine both the VL orientation, and explain $\mu_{0}H$-driven VL structure transitions.~\cite{Ich99,Nak02,Suz10}

In detail, the more recent quasiclassical Eilenberger calculations reported in Ref.~\cite{Suz10} compared the expected $\mu_{0}H$-dependence of the VL structure for cases where \emph{only} a four-fold Fermi surface anisotropy, or \emph{only} a $d$-wave gap anisotropy influences the VL structure. The calculations show that a `generic' low $\mu_{0}H$-dependent behavior of the VL structure can be expected regardless of the origin of the anisotropy. Briefly, the expectation is that with increasing field a first-order transition between a low field hexagonal VL and a 45$^{\circ}$ rotated hexagonal VL occurs at intermediate field. Further increase of the field causes the intermediate field VL to distort smoothly before a second-order lock-in transition occurs into a square VL. The orientation of the square VL is determined by the symmetry of the anisotropy included in the model, with nearest neighbours aligned along the direction of the Fermi velocity minima, or the nodal direction of the gap. This generic expectation has good support from experiments, and can describe the evolution of the low field VL in V$_{3}$Si,~\cite{Yet05} borocarbides (Er,Y,Lu)Ni$_2$B$_2$C systems,~\cite{Esk97,Pau98,Lev02,Dew05} and heavy-fermion CeCoIn$_{5}$.~\cite{Esk03,Bia08}

From the above discussion, it is clear that when the directions of the Fermi velocity minima and gap nodes are close or coincide, attributing either source of anisotropy as controlling the VL orientation is challenging; just such a situation arises for the case of two-fold symmetric YBa$_{2}$Cu$_{3}$O$_{6.85}$ and YBa$_{2}$Cu$_{3}$O$_{7}$. In Fig.~\ref{Fig:10} we show the Fermi surfaces of each compound calculated within the local-density approximation (LDA) that is strictly valid only for zero-field. Each Fermi surface is dominated by large quasi-cylindrical bonding and antibonding bands arising from the CuO$_{2}$ planes, and a quasi one-dimensional CuO chain band dispersing along $\Gamma-$X that touches the anti-bonding band. The anisotropy of the dominant bonding and antibonding bands in the Brillouin zone is expected to yield Fermi velocity minima along $\langle 110\rangle$ directions. However, a contribution due to superconducting chain states will shift the zone-averaged Fermi velocity minima towards $\langle 100\rangle$. Concerning the gap symmetry, both phase-sensitive~\cite{Kir06} and tunnelling~\cite{Smi05} measurements done on YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ show that the zero-field superconducting gap is of $d_{x^{2}-{y}^{2}}+s$ symmetry. The $d_{x^{2}-{y}^{2}}$ component with nodes along $\langle 110\rangle$ dominates, yet the finite $s$-wave component induced by the crystal orthorhombicity causes an observed shift in the nodal positions also towards $\langle 100\rangle$. Therefore, by itself each of Fermi surface and gap anisotropy are expected to dictate a similar field-dependence of the VL structure in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$.

\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{66989Fig7.eps}
\caption{(Color) In-plane Fermi surfaces of (a) YBa$_{2}$Cu$_{3}$O$_{6.85}$ and (b) YBa$_{2}$Cu$_{3}$O$_{7}$ obtained from standard LDA calculations using the DMol$^{3}$ code.~\cite{Per92,Del90,Del00} The standard settings included DND numerical local orbital basis sets, and a 4 4 2 $\Gamma$ centered $k$-points mesh. The Fermi surface contours were evaluated on a 50 x 50 mesh in the quarter plane. The calculations for the O$_{6.85}$ stoichiometry was simulated in the YBa$_{2}$Cu$_{3}$O$_{7}$ cell, but with a partial band-filling corresponding to 0.3 holes per unit cell. (c) and (d) show the calculated Fermi surface cuts in the plane perpendicular to $\mu_{0}H$ for YBa$_{2}$Cu$_{3}$O$_{6.85}$, and for the cases of $\alpha$=45$^{\circ}$ and $\beta$=45$^{\circ}$ respectively. In all panels, direction $\Gamma$-X is parallel to the crystal \textbf{a}$^{\ast}$-axis, while $\Gamma$-Y is parallel to the crystal \textbf{b}$^{\ast}$-axis. The black lines denote Fermi energy contours, while the blue (red) lines denote energy contours at $E_{\rm{F}}$-1~mHa ($E_{\rm{F}}$+1~mHa), where 1~mHa is 0.001~Hartree (Ha) units.}
\label{Fig:10}
\end{figure}

Bearing in mind the expected similar influences of the Fermi surface and gap anisotropies on the $\mu_{0}H$-dependent VL structure, it is difficult to reconcile the observation of \emph{successive} first-order reorientation transitions like those observed in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ with the expectation of any theory. As mentioned above, according to the calculations presented in Ref.~\cite{Suz10} each type of anisotropy by itself could cause the expected \emph{generic} field-evolution of the VL structure that displays a \emph{single} low field first-order reorientation transition, and a higher field second-order lock-in transition. In the case of a two-fold symmetry in the Fermi velocity, a similar generic sequence was found from a nonlocal London theory,~\cite{Kog97a} although it was shown later that the high-field continuous transition expected within the model must become forbidden on grounds of symmetry and in reality likely becomes replaced by a smooth crossover.~\cite{Whi11} Indeed, as shown in Fig.~2 for YBa$_{2}$Cu$_{3}$O$_{6.85}$, the field-dependence of the opening angle for structure A, $\phi$ varies smoothly over the high-field range, and above 90$^{\circ}$ tends toward a saturation orientation at the very highest fields.

On considering the above discussion, here we propose that the high field first-order transition seen in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ corresponds to the ``generic'' first-order transition expected in theory that can in principle be driven by either the Fermi surface or gap anisotropy.~\cite{Suz10} In contrast, we suggest that the low field transition arises instead as a consequence of a $\mu_{0}H$-dependence of the in-plane electronic structure particular to YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, namely the superconducting DOS associated with the CuO chains.

Theoretical work aimed at exploring the role of the chains in the vortex state of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ included calculations of the magnetic-field dependence of the coherence length, and hence vortex core size, in a bilayer model composed of plane and chain layers.~\cite{Atk08} The calculations revealed that at very low field, the vortex core shape in the chain layer is orthorhombically distorted so that it is two times longer along the chain direction (\textbf{b}-axis) than the \textbf{a}-axis. On the other hand, there is little orthorhombicity of the vortex core shape in the CuO$_{2}$ plane. Nonetheless, the net core shape is significantly longer along the \textbf{b}-axis than the \textbf{a}-axis. By increasing the field, both the core size in the chains, and hence the net core anisotropy, are expected to reduce with increasing field up to a critical field denoted $B^{\ast}$. The authors estimated $B^{\ast}\sim1.5$~T as denoting a critical field above which the vortex cores in the chains overlap. Physically this amounts to the quenching of a component of a small superconducting gap on the chains, and hence a modification in the superconducting DOS. We note that $B^{\ast}$ is in reasonable agreement with the low VL structure transition field seen in both YBa$_{2}$Cu$_{3}$O$_{6.85}$ and YBa$_{2}$Cu$_{3}$O$_{7}$, leading us to expect that this transition is driven by a $\mu_{0}H$-dependent suppression of the core anisotropy. Verification of this expectation requires careful numerical calculations that make use of realistic material parameters for YBa$_{2}$Cu$_{3}$O$_{7-\delta}$. In particular, calculating the spatial distribution of the local DOS near the Fermi energy, and its $\mu_{0}H$-dependence, are key for exploring the stability of the possible VL structures. On the experimental side, verification could be obtained from a direct measurement of the low-field-dependent vortex core anisotropy by using scanning tunnelling microscopy.~\cite{Mag95,Sud14}

The proposal that the low field transition is driven by a $\mu_{0}H$-dependent core anisotropy can be shown as consistent with the SANS measurements at finite $\alpha$/$\beta$. From Fig.~\ref{Fig:8} we see the tendency for the low field transition to shift to lower fields for increasing $\alpha$, and higher fields for increasing $\beta$. Qualitatively this behavior can be understood by considering how the angle evolution of the Fermi surface morphology affects the effective core anisotropy in the plane perpendicular to the applied field. To put this on a firmer footing, Figs.~\ref{Fig:10}(c)-(d) show further LDA calculations of the Fermi surface cuts in planes perpendicular to the applied field for $\alpha$ and $\beta$=45$^{\circ}$. As expected, at finite $\alpha$ and $\beta$ the bonding and antibonding bands become elongated along the direction perpendicular to the rotation compared with the case $\alpha=\beta=0$. On the $\alpha$ side, the increase in the effective mass along the direction including the chain Fermi surface will lead to a reduction in the net coherence length along this direction, and hence result in a reduction of the core anisotropy compared with the case of $\alpha=\beta=0$. Consequently, in accordance with the expectation of Ref.~\cite{Atk08}, a reduced core anisotropy favors the observed reduction in the transition field for finite $\alpha$. On the $\beta$ side, the converse effect is observed because the effective mass increases in the direction \emph{perpendicular} to the chains. This can then be expected to lead to the observed enhancement of the low field-stability of structure A.

The angle-dependent measurements also shed light on the underlying nature of the high field transition for $\mu_{0}H\parallel$~\textbf{c}. Were the high-field transition driven solely by a nodal gap anisotropy, increasing $\alpha$ and $\beta$ would be expected to have a largely similar effect on the transition field since each rotation plane includes an anti-nodal direction. In particular, by rotating the in-plane gap anisotropy away from the field direction it can be expected that a higher magnetic field, and so shorter intervortex distance, is required for the relevant nonlocal interaction to drive the structure transition. Since like the low transition field, the high transition field shifts in opposite directions for the two rotation directions, this confirms that the Fermi surface morphology plays a key role in the high-field transition in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$. It also shows that a significant twofold electronic anisotropy in the superconducting DOS, likely arising from persistent CuO chain superconductivity,~\cite{Atk95,Xia96,Atk99,Atk08} survives until the high-field region.

Having established that the Fermi surface morphology influences strongly the observed VL structure transitions in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ for $\mu_{0}H\parallel$~\textbf{c}, we finally discuss the role of the nodal gap anisotropy. This anisotropy is generally expected to become increasingly important at higher fields due to the increasing prevalence with vortex density of the vortex lattice effect (VLE).~\cite{Ich99,Suz10} This physical mechanism, which describes the tunnelling of quasiparticles between vortices, is a peculiarity of the intervortex interaction in a superconductor with an in-plane nodal gap, and is most efficient when vortex nearest neighbours are aligned along the nodal directions. In the theory of a fourfold symmetric and purely $d$-wave superconductor, the VLE is expected to lead to the stabilization of a perfectly square VL structure for fields above $\sim$0.15$H_{c2}$.~\cite{Ich99} Note that this expected transition field as a fraction of $H_{c2}$ is significantly higher than the transition fields observed by SANS in either YBa$_{2}$Cu$_{3}$O$_{6.85}$ or YBa$_{2}$Cu$_{3}$O$_{7}$. This therefore brings into question any involvement of the nodal gap anisotropy in driving the high field transition.

Nonetheless, since in our SANS experiments on YBa$_{2}$Cu$_{3}$O$_{6.85}$ we have explored the VL for applied fields up to $\sim$0.23~$H_{c2}$, we can expect that the observed VL properties in the high field range are indeed sensitive to the gap symmetry, even if it is does not drive the high field transition. From this viewpoint, it is therefore interesting to note that, as in YBa$_{2}$Cu$_{3}$O$_{7}$,~\cite{Cam14} at the highest fields the opening angle for structure A extends beyond the 90$^{\circ}$ value expected for a perfectly square coordination. If the very high field VL coordination is indeed determined by the nodal gap anisotropy, then the nodal directions at high field can be concluded to have shifted to the opposite sides of the $\langle110\rangle$ directions compared with the zero-field case.~\cite{Kir06,Smi05} Full clarification of this intriguing high field behavior of the VL structure in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ would certainly benefit from both new theoretical work and high field experiments.

\section{Summary}
\label{sec:5Summ}
In summary, using the small-angle neutron scattering (SANS) technique we have studied the magnetic field-dependence at 2~K of the VL structure in a sample of detwinned and lightly underdoped YBa$_{2}$Cu$_{3}$O$_{6.85}$. For magnetic fields applied parallel to the crystal \textbf{c}-axis ($\mu_{0}H\parallel$~\textbf{c}), measurements were conducted for fields up to 16~T, and we observed two field-driven and first-order VL structure transitions at 2.37(2)~T and 5.37(2)~T. These transitions are analogous to those reported in detwinned and lightly overdoped YBa$_{2}$Cu$_{3}$O$_{7}$ at 2.3(2)~T and 6.7(2)~T, and it can be expected that the physics behind the transitions in the two compounds is largely similar. In YBa$_{2}$Cu$_{3}$O$_{6.85}$ further measurements at 2~K, and up to 10~T in applied field were done after rotating the direction of applied field away from the \textbf{c}-axis. Dependent on whether the field is rotated around the orthogonal \textbf{a}$^{\ast}$- or \textbf{b}$^{\ast}$-axes, we observed a strong and opposing angle-dependence of the two transition fields, and consequently markedly different VL structure phase diagrams as functions of both field and rotation angle.

From our observations, and in conjunction with available theory, we have argued here that the low-field VL structure transition in both YBa$_{2}$Cu$_{3}$O$_{6.85}$ and YBa$_{2}$Cu$_{3}$O$_{7}$ arises as a consequence of a strong low field-dependence of a vortex core anisotropy that arises from the CuO chain superconducting density of states. Due to the proposed involvement of the chain states, this low field transition can be considered as particular to YBa$_{2}$Cu$_{3}$O$_{7-\delta}$.

In contrast, and once the pronounced low-field core anisotropy is suppressed on increasing the field, we propose that the high-field VL structure transition in both compounds more likely corresponds to the `generic' first-order VL reorientation transition expected in theory to be driven either by an anisotropy in the Fermi surface or a nodal gap. Although we are unable to unambiguously assign a particular anisotropy as driving the high field transition, the contrasting angle-dependences of the transition fields on the direction of field-rotation away from the \textbf{c}-axis allow us to demonstrate that this transition is indeed dependent on the Fermi surface morphology. By again comparing our experimental results to those of theory, we expect that the clearest evidence for an influence of the nodal gap structure on the VL properties is most likely away from the second transition field, and instead more in the range of the highest accessible fields. This can be checked by further field-angle SANS VL measurements done for very high fields above 10~T.

Finally, and perhaps most strikingly, on the approach to the highest explored fields in YBa$_{2}$Cu$_{3}$O$_{6.85}$ with $\mu_{0}H\parallel$~\textbf{c}=16~T, the precise field-evolution of the VL coordination is observed to tend towards a saturation orientation. This very high field VL coordination is not consistent with being stabilized by either the established superconducting gap or Fermi surface anisotropies at zero-field. This ultimately demonstrates the strong magnetic field-dependence of the superconducting density of states in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ that is reflected by the VL structure phase diagram. Overall it can be stated that the accumulated SANS observations on YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ illustrate the richness of the VLs in even `prototypical' unconventional superconductors, but which still call for further experimental and theoretical studies aimed at clarifying the mechanisms that dictate the novel field-dependent properties.

\section{Acknowledgements}
SANS experiments were performed at the Institut Laue-Langvein, Grenoble, France, the Swiss spallation neutron source (SINQ), Paul Scherrer Institut (PSI), Switzerland, and the NG3-SANS instrument at the NIST Center for Neutron Research, Gaithersburg, USA. We thank S.~Pheiffer, P.~Butler, D.~Dender, and R.~Dimeo for support at NIST, and especially A.~Jackson for providing a hand with the experiments there. J.-T.~Park is acknowledged for assistance with the sample preparation at MPI Stuttgart. We further thank J.~Kohlbrecher and Ch.~R\"{u}egg for support at PSI, and K.~Machida and I.~Maggio-Aprile for discussions. We acknowledge financial support from the EPSRC of the UK, the University of Birmingham, the Swiss NCCR and its program MaNEP, the Swiss National Science Foundation, and from the European Commission under the 6$^{th}$ Framework Programme though the Key Action: Strengthening the European Research Area, Research Infrastructures, Contract No. RII3-CT-2003-505925. This work constitutes part of the PhD thesis of NGL.


As far as we can tell, Camp Creek has not been included in past StatCan census counts, so there is no population information for this community.
<1> Unless noted otherwise, the population counts we use should be considered estimates. Our population values for Camp Creek were taken from various sources and although they can be traced back to Statistics Canada (StatCan), they should not be considered official.
<2> Our distances are not driving distances, but are calculated as a 'straight-line' (or point-to-point) distance. A straight line distance ignores obstructions like rivers, canyons, lakes, et cetera - it's truly a line from Point A (ie- Camp Creek) to Point B.
Our distance measurements begin at a specific point in Camp Creek. The point we use is located at these GPS coordinates - Latitude: 54.2500, Longitude: -114.5827 [Map].


text:
Guia de Isabel
Schilthorn
To get to the Schilthorn from the valley floor, a series of cable cars must be taken. The cable cars begin in Stechelberg leaving to Gimmelwald and then onto Mürren. From Mürren another cable car is taken to Birg, which is the final change before the Schilthorn. This cable airway is the longest and was the most technically challenging airway to be built. The other way up is to take the cable car from Lauterbrunnen to Grütschalp and a train to Mürren, from where the cable car must be taken. Between Birg and the summit, the cable car passes over Grauseeli, a small lake. It is also possible to hike to the peak, along the myriad of small, but well-marked paths to the top. The hike to the top takes roughly five hours from Gimmelwald for a fit walker. The panoramic revolving restaurant at the summit, Piz Gloria, was featured in the 1969 James Bond movie On Her Majesty's Secret Service. A black ski run featured in the film starts at the summit and leads down to the Engetal below Birg. The restaurant revolves a full 360 degrees in 45 minutes, slightly faster than the minute hand of a clock. The view includes Titlis, along Eiger, Mönch and Jungfrau to Mont Blanc. After considering a number of locations, the stalled construction of the sports bar atop the Schilthorn was chosen when the film's producer financed the completion of the famous revolving platform for the right to use the facility for his next film, the first and only Bond film starring George Lazenby. A number of scenes in the film were photographed by cameraman John Jordan hanging below a speeding helicopter. Jordan had previously lost a foot to a helicopter rotor while filming the previous Bond movie You Only Live Twice. Within a year and fitted with a prosthetic limb, Jordan lost his footing and fell 600 metres (2,000 ft) to his death when filming similar aerial imagery used in the film.
personas locales recomiendan
¿Te parece útil?
From Interlaken Ost station to Lauterbrunnen or Grindelwald via the Bernese Oberland Railway. Change to the Wengernalp rack railway and go to Kleine Scheidegg. Ride the Jungfrau Railway directly from there to Jungfraujoch – Top of Europe. Journey time from Interlaken-Ost: 2 hours. Icy air streams across your face, snow crunches under your feet, and the view nearly takes your breath away: on one side the view of the Mittelland up to the Vosges, on the other the Aletsch glacier, bordered by four thousand metre peaks. Standing on the Jungfraujoch 3,454 metres above sea level, you can feel it with your first step: this is a different world. It's one you have to experience. Jungfraujoch Bernese Alps.jpg The Bernese Alps with Jungfrau in the middle, and Jungfraujoch, its saddle, to the right, and the Jungfraufirn; as seen from east Highest point Elevation 3,466 m (11,371 ft) [1] Coordinates 46°32′50″N 7°58′50″E Naming English translation Virgin Yoke Language of name German Geography Jungfraujoch is located in SwitzerlandJungfraujochJungfraujoch Location in Switzerland Country Switzerland Cantons Bern and Valais Parent range Bernese Alps Topo map Swiss Federal Office for Topography - swisstopo Climbing First ascent traversed by Leslie Stephen and party (1862) Since 1912, the Jungfraujoch has been accessible to tourists by the Jungfrau line, a railway from Interlaken and Kleine Scheidegg, running partly underground through a tunnel through the Eiger and Mönch. The Jungfraujoch railway station, at an elevation of 3,454 metres (11,332 ft) is the highest in Europe. It lies east of the saddle, below the Sphinx station, and is connected to the Top of Europe building, which includes several panoramic restaurants and a post office. Several tunnels lead outside, where secured hiking trails on the crevassed glacier can be followed, in particular to the Mönchsjoch Hut. The Sphinx Observatory, one of the highest astronomical observatories in the world, provides an additional viewing platform at a height of 3,572 metres (11,719 ft). It can be reached by an elevator from the Jungfraujoch. The observatory houses one of the Global Atmosphere Watch's atmospheric research stations. The Jungfraujoch radio relay station, which is not accessible to the public, is installed west of the Jungfraujoch, on the Jungfrau ridge. It is Europe's highest radio relay station.
Eiger Trail
The notorious Eiger stands at 3970m above Grindelwald and has been enthralling visitors to the valley for decades, most notably since 1858 when local Mountain Guides Christian Almer and Peter Bohren together with their guest Charles Barrington, reached the summit for the first time. The Eiger began attracting a wealth of aspiring mountaineers from all over Europe wishing to tackle its steep north face – known as the 'last problem of the Alps' in north face climbing terms. It was finally conquered in 1938 by Anderl Heckmair, Fritz Kasparek, Ludwig Vörg and Heinrich Harrer, in a battle waged over 4 days. Inspired by the myth of the Eiger, the trail running event Eiger Ultra Trail was launched in 2013. The race routes take in the most breath-taking viewpoints this area has to offer, passing through Grosse Scheidegg, First, Faulhorn (2680m), Schynige Platte, Wengen, Männlichen and Kleine Scheidegg, before tackling the awesome traverse along the base of the Eiger North Face itself. This Ultra Trail is a truly spectacular alpine experience for trail runners and all spectators. The E101, a race of 101km and 6700m height difference is a mighty challenge to even the most seasoned of trail runners. The E51 winds its wicked way to the Faulhorn at 2680m, where competitors are rewarded for their efforts with stunning panoramic views of the surrounding peaks as the route continues on towards Schynige Platte. This route also has a Couples category for those wishing to test their strength -and friendship- as a team of 2. The E35 race delivers a great challenging route, while the E16 is suitable for all newcomers to trail running or as a fast tempo run for more ambitious runners. With the Trail Surprise on Friday a new concept was created for the relatives and supporters.
Trummelbach
The magnificent glacier fed Trümmelbach Falls (Trümmelbachfälle), a series of 10 waterfalls in a cave-like environment, is hidden inside a mountain in the Lauterbrunnen Valley. It's a natural UNESCO World heritage site, and rightly so. A tunnel elevator takes the edge off an otherwise steep climb. The lift leads up to a platform from where the uppermost waterfalls are accessed. The path leads over a small bridge, up a few flights of stairs and walkways and partly through dimly lit tunnels to the highest waterfall. Freezing spray makes path and stairs slippery and the caves damp. Spray and droplets from above won't let you get away dry. Melt water flowing down from Eiger, Mönch and Jungfrau form a powerful raging torrent that carries 20'000 liter water per second through the caves. The torrent carved its way through solid rock and debris over thousands of years and sculpted elegant and impressive shaped of rock formations. The result is spectacular and the thunder from crashing waters deafening. Small lookouts and cutouts along the way provide viewing points to the ten chutes that fall into foaming pools and disappear into darkness. It's a spectacle of milky glacier water twisting, tumbling and pirouetting its way down over sculpted rocks and hitting the walls of the narrow slot canyon. Once the last chute is reached one backtracks down to the lift platform from where one can take the elevator or continue to walk back down to the entrance to see the last two of the ten chutes tumble into the Trümmelbach River. It's steep and the stairs 'go straight to the knees' but the view over the Lauterbrunenn valley is gorgeous. It's not easy to make good photos , and mine certainly don't do justice to the impressive waterfalls. What's more, a friend lent me a camera and the battery died half way into my journey. Yeah, I know :) Instead of returning by post bus to Lauterbrunnen, one can hike back through lush and flat farm meadows along the famous Staubbach Falls (Staubbach Fälle) that cascade down from sheer rock faces. At the edge of the village, a steep gravel footpath branches off from the country road and leads up to one of the falls. A short tunnel ends at a viewing platform where one can see sheets of water crash down right in front of visitors.
Puerto de Susten
The architecturally spectacular Susten Road mainly serves tourism and is therefore one of the last to be cleared of snow, often remaining closed from the beginning of November until June. The route begins in Wassen on the Gotthard axis, where it negotiates the jagged estuary gorge of the Meienreuss River via several tunnels. At the beginning one sees the Swiss Federal Railway's (SBB) boldly designed Gotthard line, which runs through several switchback tunnels to overcome the steep climb. At the head of the valley the Sustenen Road leads to Meien Valley, where the characteristic peaks of the Fünffingerstock come into view. Near the rear of the valley, the road climbs again in several tight curves to the top of the Pass in the short summit tunnel. Shortly before the tunnel, a sweeping view extends over the vast basin of the Meien valley to the Sustenhorn. On the Bernese side of the tunnel, a large parking lot and the Susten Hospiz, located a few meters above the Pass road, invites you to rest awhile. During the ride through the valley the stunning panorama of the Gadmen Valley and the Steinen Glacier comes into view. During the two-hour hike on the glacier trail one can glean interesting information from the thematic markers. The starting point is the Hotel Steingletscher on the Pass road. With occasionally tight curves, the road leads down to Gadmen Village with its beautiful old houses. After the village of Nessental, a tiny road on the right hand side climbs to Engstligennalp, and to the mountain lake of the same name. This is the starting point of a popular hiking tour, which includes a spectacular cable car ride over the Jochpass to Lake Trübsee and further on in the direction of the holiday resort of Engelberg in Central Switzerland. Near Innertkirchen the Susten Pass road meets the Grimsel Pass road. At this juncture we recommend an excursion to the Aare Gorge that breaks through a mighty rock wall - a vestige of the Ice Age. Over thousands of years, the waters of the young Aare River pushed deeper and deeper through the rock until the spectacular canyon was created.
Wengen was first mentioned in official documents 751 years ago in 1268, and the origin of the name is unknown. Primarily an alpine farming community, the village began to be visited by tourists in the early 19th century. Mary and Percy Bysshe Shelley's History of a Six Weeks' Tour and Byron's Manfred, in which the scenery of the area is described, were published in 1817. This literature became the advent of the modern tourism industry for the village.[1] Felix Mendelssohn, to whom there is a memorial above the village, also visited in the early nineteenth century. Guesthouses and hotels began to be built in the mid-19th century, with the opening of the Launerhaus in 1859, with accommodation for 30 guests, and in 1880 the Pension Wengen was available to 100 guests.[1] The building and opening of the Wengernalpbahn in the 1890s made the village more accessible to tourists who previously had to walk up the steep slopes to the alpine village, opening the area for an expansion of tourism and the beginning of the ski industry.[2] In the early 20th century, British tourists started ski-clubs in the area, beginning in the nearby village of Mürren. By 1903 Wengen had an Anglican Church and two years later, Sir Henry Lunn formed the Public Schools Alpine Sports Club with Wengen as a destination ski area for the members.[1] A British Methodist minister, Lunn first visited the area to organize a meeting of Protestant churches in nearby Grindelwald where he learned about winter sports such as skiing. He returned to the area in 1896 with his son Arnold, who quickly learned to ski, and both father and son realized the potential in the future of winter sports. The club was established a few years later. Members of the Public Schools Alpine Sports Club were required to have attended an English public school or one of the "older universities".[3] Wengen's Curling Club was established in 1911.[1] The first ski races were held in the early 1920s with the British downhill championship held in 1921; the following year a ski race was held between Oxford and Cambridge.[4] These events were the first to have downhill races as opposed to Nordic races, which were held in other Swiss resorts. In Wengen, skiers requested use of the train system for access to the slopes; for some years trains were the earliest ski-lifts in the area.[5] Arnold Lunn used the natural terrain of the mountains for the courses; the downhill event followed the slopes above Wengen and was called the "straight down": skiers went straight down the mountain. Also during this period, Lunn invented, and introduced in Wengen, the first slalom race, in which skiers followed the terrain through the trees, replaced with ski gates in later years. These events are considered the birth of modern ski racing and Alpine skiing.[6] From August 1944 to the end of World War II, Wengen served as a sort of open-air internment camp for allied prisoners, mostly US bomber crews. Since the only practical way in or out of Wengen was via the cog railway, it was difficult for internees to escape.
Lauterbrunnen lies at the bottom of a U-shaped valley that extends south and then south-westwards from the village to meet the 8 kilometers (5.0 mi) Lauterbrunnen Wall. The Lauterbrunnen Valley (Lauterbrunnental) is one of the deepest in the Alpine chain when compared with the height of the mountains that rise directly on either side. It is a true cleft, rarely more than one kilometre in width, between limestones precipices, sometimes quite perpendicular, everywhere of extreme steepness. It is to this form of the valley that it owes the numerous waterfalls from which it derives its name. The streams descending from the adjoining mountains, on reaching the verge of the rocky walls of the valley, form cascades so high that they are almost lost in spray before they reach the level of the valley. The most famous of these are the Staubbach Fall, less than one kilometre from the village of Lauterbrunnen. The height of the cascade is between 800 and 900 feet (240 and 270 m), one of the highest in Europe formed of a single unbroken fall.[5] The river Weisse Lütschine flows through Lauterbrunnen and overflows its banks about once a year. The source of the river comes from melting snow high in the mountains, thus making it a very pure and clean source of water. It is common practice in the camp sites to chill drinks in the water. Trummelbach Falls is 3 km (1.9 mi) from Lauterbrunnen, connected by bus from the station.[6] The municipality of Lauterbrunnen extends a considerable distance beyond the village and valley, with an area of 164.51 km2 (63.52 sq mi). It reaches as far as the peaks of the Eiger, Mönch and Jungfrau to the east, the Gletscherhorn, Mittaghorn, Grosshorn, Breithorn and Tschingelhorn to the south, and the Gspaltenhorn and Schilthorn to the west. The Kleine Scheidegg Pass crosses over to Grindelwald to the east, whilst the Sefinenfurgge Pass crosses to Griesalp and Reichenbach im Kandertal to the west; both passes carry hiking trails that form part of the Alpine Pass Route, a long-distance hiking trail across Switzerland between Sargans and Montreux. Besides the village of Lauterbrunnen, the municipality also includes the villages of Wengen, Mürren, Gimmelwald, Stechelberg, and Isenfluh.[7][8][9]
The city of Thun, which is located at the lower end of Lake Thun, is the gate to the Bernese Oberland. The historic Old Town is situated about one kilometer from the shore of the lake, on the river Aare. There is a castle in the center of the Old Town that dates back to the 12th century and boasts a museum. The first settlement arose on today's site of the city as early as 2,500 BC. The mighty castle was constructed by the Dukes of Zähringen. It has a fortification tower built between 1180 and 1190. The halls of the tower house a historical museum that exhibits artifacts from prehistory and early history as well as medieval objects, weapons and uniforms from the 18th and 19th century. The castle's most splendid exhibit is the restored Knights Hall, dating to the 12th century. Further sights in the Old Town include the town church with its tower dating back to about 1330, the town hall from the 16th century, the Old Town itself and the numerous restaurants and cafés along the Aare River. Winter The Eiger, Mönch and Jungfrau rise majestically across Lake Thun, over which glides a historic paddle steamer. The castle and city church proudly dominate the late-medieval Old Town. Summer The Eiger, Mönch and Jungfrau rise majestically across Lake Thun, over which glides a historic paddle steamer. The castle and city church proudly dominate the late-medieval Old Town. News The news listed here is maintained by the regional / local tourist offices, which is why Switzerland Tourism can not guarantee the content. GUIDED TOUR OF THE OLD TOWN Discover Thun with us! Come on a guided tour through the Thun Old Town and solve the riddle of this Zähringer town. Thun is fascinating - its culture has a wealth of tradition, its history goes back to the stone age, and its unique setting between the lake and the Alps has left its mark on the historic and modern townscape. Come and discover Thun with us!
Interlaken is a fantastic base for seeing the best of central Switzerland's magnificent scenery while enjoying the comforts of a chic lakeside resort. Tourist attractions are all around it, with boat tours on Lakes Thun and Brienz at either side of the town and thrilling train and funicular rides to the spectacular surrounding mountain peaks. Interlaken is one of the oldest, best known, and most popular summer holiday resorts in Switzerland. The first visitors arrived in the 17th century, and as transport facilities improved with the coming of the railroad, boat services on the lakes, and most recently the expressway, Interlaken became the major tourist center of the Bernese Oberland. Day or night, you'll find plenty of things to do in and around Interlaken. Along with the almost endless variety of walks, climbs, and outdoor excursions, there are many other sports available for active travelers. On the right bank of the Aare, opposite the Kursaal, is a swimming pool, and visitors will find a golf course in Unterseen, as well as sailing and windsurfing on the lakes,
Harder Kulm
The views over Interlaken and both lakes from the Harder are spectacular. Beyond the bridge over the Aare River, next to the Harder Alpine Wildlife Park, the Harder-Kulm funicular climbs at a 64-degree gradient up the Harder to an altitude of 1,322 meters. From the Art Nouveau-style Panorama Restaurant at its top are magnificent views of the Jungfrau area, Interlaken, and the lakes. You can return along forest paths via the Hardermannli lookout pavilion at 1,116 meters and the Hohbühl pavilion, where there is a memorial to the composers Mendelssohn, Wagner, and Weber. Stop at the Harder Alpine Wildlife Park to see marmots and ibexes. The latter, once a common denizen of the Alps, had become extinct in Switzerland by the early 1900s. This park was created to re-introduce the ibex, and the breeding was so successful that within a few years they were able to begin reintroducing these beautiful creatures into the wild.
Höhematte
An area of 14 hectares in the heart of Interlaken that belonged to the Augustinian convent was acquired in 1860 by a group of 37 hotel owners and private citizens to be left as an open space, a remarkable example of farseeing town planning. Through its length runs the Höheweg, a splendid avenue between the east and west rail stations that affords a magnificent view of the Jungfrau, surrounded by hotels and flower-beds. Alongside it is the Kursaal, with a theater and a café and beautiful gardens with a flower clock, as well as a number of hotels, including the 150-year-old Victoria Jungfrau Hotel, itself a local landmark. Next to the Hotel Interlaken, you'll find the small Garden of Friendship, the first Japanese garden in Switzerland, a peaceful spot with flowering plants, water, and koi carp.
Schynige Platte
From Wilderswil, a five-minute walk from the Interlaken Ost railway station, you can take a rack-railroad that has been carrying sightseers up to the Schynige Platte since it opened in 1893. The hour-long ride is a series of ever-changing Alpine panoramas, and at the top, you'll find one of the finest panoramic views of the Alps, encompassing the Eiger, Mönch, and Jungfrau peaks as well as Lake Thun. You can enjoy these from a 45-minute panoramic walk along an easy trail, which also leads to an excellent alpine garden with 600 species of flowers and high-altitude plants. If you're lucky there may be locals playing traditional Swiss Alphorns at the Schynige Platte station.
Unterseen
The Marktgasse runs northwest from the Interlaken post office and across the Spielmatten islands and the river to the little hamlet of Unterseen, at the foot of Mt. Harder. This is one of several villages that form Interlaken, and in this old part of town is the 1471 parish church, with a Late Gothic tower. Here, you'll find some beautiful wooden chalets of the kind you'd expect to see in tiny mountain villages, not in a busy resort center like Interlaken. Set in green gardens, these may even have farm animals grazing on the lawns. Small restaurants around the pretty Stadthausplatz serve traditional Swiss dishes.
Cuevas de San Beato
More than one kilometer of walkways lead through the chambers and passageways of these hillside caves, where legend holds that a dragon took shelter when hunted by the monk, Beatus, whose hermitage was nearby. But the geology is no legend, and you can tour these underground caverns to see mirror lakes, underground waterfalls, stalactites, and stalagmites accompanied by a guide or at your own speed using a descriptive app. The entire area is quite beautiful, with a series of waterfalls cascading down the cliffs. You can get here by bus from Interlaken (it's about a 10-minute walk from the bus stop) or by boat from Interlaken West station, but it's quite a steep climb from the lake to the caves. Address: Sundlauenen, Interlaken
Grindelwald in Switzerland (in the Bernese Oberland region) is a large resort with 30 lifts (10 chair lifts, 13 surface lifts) that offers skiers an incredible 1528 metres (5013 feet) of vertical descent. Grindelwald has 125 acres of terrain over 51 pistes with a total length of 157 kilometers (98 miles). Grindelwald is best suited to intermediate skiers and snowboarders with some terrain for beginners but little of interest for advanced skiers. There are 20 kilometers (12 miles) of cross country ski trails at Grindelwald. For snowboarders, there is a terrain park and 5 half pipes. About one quarter of the pistes at Grindelwald are covered by snowmaking. The nearest airport is at Bern / Berne and the nearest train station to Grindelwald is at Grindelwald. There is accommodation located close to the pistes but we would welcome additional information about any hotels or chalets in Grindelwald.
Lindt Chocolate Shop Kilchberg
Kilchberg, October 15, 2019 – The Swiss premium chocolate brand LINDT & SPRUNGLI makes a bold move in the Chinese market by launching a new campaign featuring world-class tennis champion Roger Federer and popular Chinese actress Xin Zhilei. As one of the greatest tennis players in history, Roger Federer symbolizes the Swiss perfection and, as a professional actress, Xin Zhilei masters in her every role with passion and dedication. Together, they represent LINDT's core values of quality and premium, and open the world's door of premium Swiss chocolate to Chinese consumers. The first video launch achieved an astonishing 12 million views in less than 1 hour. CHOCOLADEFABRIKEN LINDT & SPRÜNGLI AG Seestrasse 204, 8802 Kilchberg Switzerland
58 Pilgerweg
La Maison du Gruyère is a village cheese dairy providing the opportunity of viewing the hand-made production of the cheese "Le Gruyère AOP" and much more… Do you know the history, century-old expertise and the different production stages of a Gruyère AOP? The specifications, with their quality and traceability requirements? The ageing periods and the cellar treatment during its minimum 5 months of ripening? The interactive display « Gruyère AOP, a journey to the heart of the senses » plays on the five senses to plunge visitors into the world of Gruyère AOP and reveal all its secrets. Thanks to his dexterity and experience, the cheesemaker imparts to Gruyère AOP its particular character and individuality. Between 9:00 am and 11:00 am or 12:30 pm and 2:30 pm, the high point is of course the opportunity of observing the expertise of the cheesemakers. A tip: between 9:00 and 10:15 am all the principal phases can be observed on several vats, or at 9:55 am and 11:00 am or 2:25 pm, the draining and placing in the moulds. The visit, lasting some 30 to 45 minutes, takes place with headphones, and it's in the company of the friendly cow « Cerise » that one explores the world of Gruyère AOP. The audio information is available in thirteen languages and written translations are also provided in eight languages. The Restaurant of La Maison du Gruyère offers the opportunity of prolonging the experience in tasting numerous dishes with Gruyère AOP as well as typical local dishes. Le Marché gruérien (Gruyère Market) features the products of our cheesemakers, local products, crafts and souvenirs.
Mürren
Mürren is a very special place Mürren is one of those picture perfect villages in the Swiss Alps: there are no cars, mountains all around, and green slopes and forests. You'll find many hiking trails here. In winter, there are many options for skiing, snowboarding and tobogganing. The Jungfrau region offers more than 200 km of pistes. Wengen, on the other side of the valley, offers a similar, but not identical experience. Like many popular villages, Mürren is pretty touristy, but not in a disturbing way. It is one of the best places to enjoy the Swiss Alps, away from traffic, shopping centers and other distractions. There are quite some hotels and restaurants. There aren't many shops, but it's enough for all the basic needs: you'll find a supermarket there, as well as various sports shops and a bakery. Murren is a charming village with magnificent views and no traffic noise. It is perched on a shelf of Alpine pasture forming a balcony overlooking the steep cleft of the Lauterbrunnen Valley. Destinations like Murren are hard to find – alpine scenery, mountain culture, and exciting activities! It is a great place for hiking enthusiasts who wish to enjoy the natural beauty of Switzerland. And in winter you will find skiing for all levels. Murren is the highest altitude ski resort in the Bernese Oberland and faces a series of giant peaks carved out of rock or ice: from left to right the view encompasses the Eiger, the Monch, the Jungfrau, the Breithorn and the Gspaltenhorn range. Book your Murren, Switzerland vacation to experience one of the most beautiful places in Switzerland! This beautiful village is completely cut off from car traffic, and the sporting character account for the popularity of the resort. Being car free will make for an exceptional vacation that will create long lasting memories. From Murren a cable car takes its breathtaking ride up to the Mt. Schilthorn summit. From up there you can enjoy exceptional panoramic views and sip cocktails in the revolving Piz Gloria summit restaurant. Mt. Schilthorn was featured in the James Bond film "On Her Majesty's Secret Service" and is also referred to as the James Bond Mountain. The development of tourism in the area was largely due to the British, who came here at the turn of the century to indulge in their favorite winter sports and who succeeded in recreating a cozy, congenial atmosphere that reminded them of England. It was Murren that the Kandahar Ski Club was founded in 1924; it was to lead to the famous Arlberg-Kandahar competition, which is now regarded as the unofficial world championship of the Alpine countries. Attractions and Activities Discover Murren Murren is an ideal place for travelers that wish to enjoy the natural beauties of Switzerland. It is a unique village on a sunny terrace, a hiker's paradise and great for winter sports. We are presenting you just a few of the many activities that are possible on your vacation to Murren, Switzerland and its surroundings.

redpajama_set_name: RedPajamaCommonCrawl


text:
TRACY COOPER-POSEY|Stories Rule
Alpha Listing
By Thumbnail
The Official 100 Books
Ease Yourself Into MMF Romances – Part IV
Where To Find Your MMF Romances
This is Part Four of a Series
Part 1: Ménages Categorized
Part 2: How can MMF be romantic?
Part 3: How To Read Your First MMF Romance
Part 4: Where To Find Your MMF Romances
Part 5: Narrow Down Your List of Potential MMF Novels
Part 6: Keeping Track
You know how to read MMF romance now. You just need to know where to find 'em.
Heading for your nearest bookstore is not the obvious answer. Surprise! The vast majority of MMF romances are published digitally, many of them only in e-book form — or in e-book first, and in print much, much later, or the print version isn't available at your local bookstore, or both, or all three — so if you haven't made the switch to e-book reading yet, this may be the excuse you need to jump over.
One major advantage to reading MMF romances in e-book form is that everyone sitting opposite you on the bus won't be able to tell what you're reading by the lurid cover featuring three scantily clad bodies in suggestive poses that you're holding in your hands. An e-book reader looks so much more innocent by comparison…
There's a three-step process to finding your first MMF romance to read. It's the same process for finding new-to-you authors every time you go looking for fresh voices, new categories, or want to try something new in MMF.
1. Build a list of lots of potential book possibilities
2. Do some easy (and fun) research to narrow down your list and figure out which of these books are for you, and make your choice
3. Keep simple records of your reading, so you can zoom straight back to the source of that great book for more of the same.
It sounds like a pretty simple process, and because it's all done on-line you can sip your favourite beverage while you're doing it. But because we're talking about sex and an industry that is still trying to figure out which way is up, it's not quite as simple as it sounds.
Here's the quickest way to get the most effective results. This way, you stand the best chance of not missing out on any MMF titles that might be hiding on some tiny little publisher's site that is absolutely perfect for you.
Build a list of lots of potential book possibilities
For this step, quantity is the key.
You want as many MMF romance titles on your list that sound intriguing to you as you can find. And for this stage, you cast your net wide. Even if you prefer to only shop on Barnes & Noble.com, you don't only search there. You search everywhere. You can buy your books on B&N later (or even B&N at your local mall), when you've made your final decision. But for now, you're just collecting information, and for that, you look under every virtual rock and leaf.
Even if you can't stand Amazon as a retailing, power-wielding behemoth, start here, because virtually every publisher in the western world has their titles listed here. Remember, you don't have to buy from Amazon. You're just researching. Also, if you want to buy your books in a different format, you can still research here, and buy elsewhere.
And the truly glorious facet about Amazon is categories and tags. Amazon allows authors, publishers and readers to add tags to books, earmarking them for other readers to find. And you can search on those tags.
And yes, there's a tag for MMF romances. How wonderful! If you click here, you can jump straight to a presorted list. You can arrange that list by rankings, popularity, best-sellers and more. Start clicking on titles and covers that intrigue you, and reading the blurbs and excerpts, reader reviews (another advantage that Amazon offers) and building your list of possibilities.
When you have run out of title possibilities at Amazon (and that could take a while), you may want to try:
Members of Goodreads add their favourite books to growing recommendation lists, and there's a collection of various MMF romance ones:
Sandy's Favorite MM/MMF Romance Novels
Paranormal MMF Menage
Best MMF Historical/Regency Romance
Favorite MM/MMF Romance Novels
Favourite MMF romance
You can possibly access the lists without becoming a member of Goodreads (something I can't test for myself, as I'm a member), but consider joining anyway and paying forward for the work that went into these lists by adding your own recommendations when you come across MMF romance novels that you enjoy as well. As you can tell from this article, tracking down good MMF romances isn't always as obvious as it may seem.
3. My own Recommended MMF Romance List.
I started building this list in March 2012, pulling from 4 and 5 star MMF romances from Goodreads, Amazon, and All Romance eBooks — including the lists I quoted above…and I'll always be building it. It is a work in progress. I vet and cross-check titles to eliminate the ones that aren't really MMF romances (they just have a bit of menage fun, but they don't end up MMF forever, say, or they're really MFM, but they crept onto an MMF list somewhere, sometime, and now they're just copied onto everyone's list). There's a bigger and longer explanation for the filtering I do here.
4. Romance Publisher Sites
I won't break down every publisher's site individually, but I will give you one example, because I know it better than others. Be wary of heading directly to publisher sites, because if you've already combed through Amazon, then the titles you find on the publisher site will probably be repeats. There are two minor advantages to heading directly to publisher sites:
Some publishers delay uploading their books to secondary retail sites like Amazon.com and Barnes & Noble by days or weeks, so you will pick up titles that haven't reached the retailers yet.
The classification of the publishers' titles may help you find MMF romance books that readers/authors/reviewers have missed on Amazon.
You can spend a lot of time searching individual publishers' sites, for the odd one or two titles you may have missed on Amazon…that you could eventually catch up with later, via reviews, word-of-mouth, etc.
If you have the time to spare, and a favourite publisher, you may consider the exercise worth it. But digging out MMF Romances, even on a romance-only publisher's site, can prove to be a challenge.
Ellora's Cave, for example, have an entire category devoted to "Menage or more" (which is actually a misnomer, but…). You can sort their entire library of available erotic romance novels on that category link. Which sounds great…until you start combing through the 35 pages of book titles (not books, titles) within that category. And you realize that some of these group romances are MFM, some might be MMF and some (these days) are even MFF. Even more might feature more than three, but it's hard to tell, really, by the descriptions.
There's a sneaky backdoor way to narrow down your search with a bit more certainty. If you search the MM category, which comes just below the menage category, then open up each title, and look for the little three people icon that indicates the book is, in fact, a menage, then you know you've got an MMF menage on your hands.
If you're gun-shy about MM sex, then this isn't going to work for you, first title up. Ellora's Cave only slap the MM category on romances that have very strong MM story lines. As in, that's the dominant thrust of the romance.
I have published seven MMF romances with Ellora's Cave in the past and none of them made it into the MM category and one of them had very nearly more MM romance than MF.
But for later MMF romance titles, if you acquire a taste for it, this will be a great way to hunt down new authors who write strong MM storylines.
For any other publisher, you will have to do similiar detective work on how they sort their romance titles, menages (if at all) and what sort of advanced search functions they offer for you to further filter their titles.
Finally, don't forget that Google Search has an advanced search function that lets you search an individual site, too, so if you're really determined to mine your favourite publisher for gold, Google might cough up nuggets for you if the publisher themselves don't offer tools that do the work. Just add your publisher's name to the line that says "Search within a site or domain".
You'll notice I haven't sent you off to Barnes&Noble.com, Kobo.com, Sony, Apple, and a host of other on-line retailers and book-sellers. Yes, even Smashwords, AllRomanceEbooks, and the new e-tailers who are right there supporting indie authors.
I'm steering you clear of those guys for a reason. Even if they're your favourite, most trustworthy bookstore in the world, their range of information about romance novels, and MMF romance in particular, frankly sucks. They might sell the novels you'll end up wanting to buy, but trying to extract those titles from the morass of "romance" novels lumped together on their sites is a quick lesson in frustration acceleration. These sites are not researcher-friendly. There's also a pretty good chance they don't carry all the titles Amazon does, so you're automatically limiting your range by starting with them.
Narrow Down Your List of Potential MMF Novels
My MMF Romances
Additional Articles:
The MMF Thing…How to Get It
MM and MMF – Let's Try Again. Why Do Women Like Men Who Like Men?
Do Women Like MMF?
The Heroes in MMF Romance Don't Need Classification
Who else would like to know about this?
Tracy Cooper-Posey2016-07-24T09:42:29-06:00Wednesday, October 26, 2011|Categories: Erotic Romances, Ménage à Trois, MMF Romance, Reader Resources, The Romance Industry|Tags: All Romance eBooks, Amazon, Apple, Barnes and Noble, Ellora's Cave, Goodreads, Google, kobo, Ménage à Trois, MMF, MMF Romance, romance publishers, Smashwords, Sony, threesomes|
Round Out Your Scandalous Collection!
24 Unusual Historical Romances. Have you read all these yet?
I Do Not Believe It!
99c For the Entire Paranormal Series!
Kindle Unlimited Romances!
Copyright © 1999 - 2021 Tracy Cooper-Posey | All Rights Reserved |


WHAT TO DO IF A COWORKER IS HARASSING YOU?
Let's talk about bullying. What is a bully?
uses superior strength or influence to intimidate (someone), typically to force him or her to do what one wants.
Lately i have been asked questions about work place harassment and what can qualify as a workers comp claim in that realm.
If someone at your job has been consistently harassing you, belittling you, embarrassing you on purpose in front of co-workers, using intimidation tactics, you might be subject to a claim.
These types of injuries fall under the PSYCHOLOGICAL injury category.


A marketer's data is as good as gold. Certainly, there are number of ways to collect data via internal and external sources.
The most common data sources are first party and third party—first party data is essentially your data. It's the information you collect directly from your customers or your website. In contrast, third party data comes from other sources—it's data aggregated from a variety of sources.
Due to changes that the General Data Protection Regulation (GDPR) requires, the future of third party data is uncertain. Under the GDPR, companies are required to inform consumers about the data they're collecting, such as how they intend to use it and with whom they intend to share it. Given this change, there are concerns that this can lead to the end of third party data as we know it.
With all the shake-up around third party data, now's the time to rethink your marketing strategy and utilize your first party data as much as possible. If your website is already tagged with a remarketing pixel for your various media platforms, then you're off to a good start. Remarketing pixels are considered first party data since they capture the user's behavior and activity while they're on your website.
If you have a customer relationship management (CRM) system to help manage your customer information, then you likely have details about your customer's past purchases and other interactions with your business. When used properly, you can leverage your remarketing audiences and CRM data to create targeted marketing lists to re-engage site visitors and past purchasers.
Most advertisers are already familiar with the basics of remarketing and the importance of segmenting your data to re-engage users with relevant messaging across search and social platforms to increase conversion prospects. But by using your remarketing and CRM data, you can take your strategy to the next level by analyzing customer data and trends to home in on customer retention and repeat purchases, while also using that data to expand your reach to a targeted audience.
Push upsells and cross-sells: Once a visitor converts, leverage CRM data to determine complementary products they may be interested in. For example, if a customer purchases a swimsuit, follow up with ads to sell them a beach towel or swim cover-up.
Re-engage seasonal shoppers: If you have a set of customers who only purchase during a certain time of year (such as holidays or summer), that's okay! Create lists for these purchasers, and ramp up your marketing efforts for them during the time of year they're most likely to convert. Also consider if there are other holidays or promotional events when it might make sense to re-engage these visitors.
Don't forget about video: Video advertising is becoming more and more popular and it's a great way to reach your audience. Consider using a sequential messaging strategy to build a story and keep users interested in your brand.
Expand your reach with lookalikes or similar audiences: Google and Facebook both have the ability to build a new audience based off your first party data. This is a great way to expand your reach and find users who are like your current customers.
While first party data may not offer as much opportunity to scale your marketing efforts as third party data, there's still a lot of potential to leverage first party data to increase revenue and improve ROI. Put your customer data and insights to good use to refine your remarketing, retention, and acquisition strategies.


Hallo i have an new invigation of the piezo cristalls rotation disk. the piezo kristall emitted electrons when this hit and drift. the piezo cristall place on the top of the disk, then you have a heater, bottom of the circle. the Draw have explain.
With the energy it's like the Lottorie ... Anyone who has looked Loto knows runs as the raffle and the lucky one wins the jackpot. This image, the piezoelectric crystal electron spin Erlkärt as a generator.
now flows. This is possible to take advantage of a rotation and electricity by gravity from a piezoelectric crystal.
@sergirafael: have you done any supporting experiments or is it "Gedankenexperiment" only?
How difficult would it be to build such a machine? Could it be done by hand and with materials available on the open market?
must end are deposited on the quartz crystal.
Frequency which is to be supplemented with the ideall resonance frequency of the resonant circuit of the piezoelectric crystal.
To the drawing, the points are points of connection manager, the blue and red plates capacitors as aluminum foil or Aluminiumklebband, the Red Green lines are insulated copper wires.