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Media release: Summer intern appointment at comms agency, Represent
REPRESENT, the Edinburgh-based creative PR, digital marketing and social media management agency, has appointed a new PR and digital intern as the team embark on a packed summer season.
Anna Fresen, a post-graduate student currently studying Arts, Festival and Cultural Management at Queen Margaret University, will be working alongside the team at Represent for a period of ten weeks.
Originally from South Africa, Anna (31) moved to Edinburgh in 2008, and has a strong history in the Scottish food and drink industry.
She also brings with her a passion for great customer service and expertise in communications and online marketing.
Supporting on several client campaigns, Anna will get the opportunity to work with the National Wallace Monument, Green Tourism and the upcoming 177th Royal Highland Show (22 – 25 June 2017).
Speaking of her appointment, Anna said: "I am very excited to be working alongside the dynamic team at Represent, and to be working on campaigns for such a varied array of clients.
"It is clear that the staff here are very experienced, and I am sure that my time spent here will be of great benefit to me."
Judith O'Leary, managing director of Represent, said: "Since our move to Edinburgh, we have been very busy and now with a hectic but exciting summer season ahead of us we are happy to have Anna on board. Her experience and expertise will be a great addition to our team."
Anna will continue the role until 13th July 2017, after which she will return to her studies and running a weekly pub quiz.
For further information about Represent, visit www.representcomms.co.uk
For further information, please contact Katie Goodfellow at katie@representcomms.co.uk or 0131 526 3190.
MEDIA RELEASE issued by Represent. You too can share your stories (aka press or media releases), on this site. Email here for more information.
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Contact: Katie Goodfellow
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By Administrator · May 3, 2017 at 15:00 · Comments Off
Represent · Media - general · Edinburgh and East (postcodes EH, KY and TD)


text:
\section{Introduction}

Low-dimensional magnetic systems have long attracted the attention of
experimental and theoretical physics. In systems with reduced
dimensionality the fluctuations are enhanced and can prevent a system from
long-range ordering. For one- and two-dimensional isotropic
Heisenberg ferro- and antiferromagnets with short-range interaction it has been
proven exactly \cite{Hohen67,Mermin66} that long-range order is absent for
finite temperatures. The existence of long-range order in low-dimensional
systems depends crucially on anisotropies and long-range interactions, as there
are single-ion anisotropy or the dipole-dipole interaction.

In real systems the dipole-dipole interaction is always present in addition to
the short-range exchange interaction. Although the dipole-dipole energy is weak
compared to the exchange energy it plays an important role in low-dimensional
systems due to its anisotropic and long-range character. Maleev \cite{Male76}
showed that in a two-dimensional ferromagnetic system the additional dipolar
interaction leads to a modification of the spin-wave frequency in the long
wavelength limit from a quadratic to a square root wave vector dependence, for
which long-range order is established. For the antiferromagnetic counterpart on
a square and a honeycomb lattice it has also been shown \cite{pich93} that
dipolar interaction stabilizes long-range magnetic order at finite
temperatures. In this cases, however, the dipolar anisotropy leads to a
discrete ground state with spins oriented perpendicular to the plane,
producing an energy gap in the dispersion relation. The finite N\'eel
temperatures in various quasi two-dimensional systems (e.g. K$_2$MnF$_4$) have
been calculated within the dipolar model \cite{pich93}, in good agreement with
the experimental values.

In recent papers \cite{pich95a} we determined the magnetic phase
diagram of the two-dimensional, dipolar Heisenberg antiferromagnet (square and
honeycomb lattice) for fields along the easy-axis, i.e. perpendicular to the
plane. In contrast to models with single-ion anisotropy or an anisotropic
exchange interaction, we found that the dipole-dipole interaction establishes a
new phase, an intermediate phase. With increasing field strength the system
changes by second-order transitions from the N\'eel phase to an intermediate
phase, a spin-flop phase and finally to a paramagnetic phase at high magnetic
fields.

From the results in two dimensions we anticipate that also in quasi
one-dimensional Heisenberg antiferromagnets, the dipolar interaction
will reduce thermal and quantum fluctuations and thus increase
the tendency to order.

In this paper we investigate the influence of the dipolar interaction on the
classical ground states and on quantum fluctuations. It is shown that due to
the competition of the exchange and dipolar interaction we can distinguish two
regions, namely an exchange dominated and a dipolar dominated region.
In the former the dipolar energy leads to a planar anisotropy, whereas
in the latter it leads to an easy-axis anisotropy. We study
the dispersion relations for various relative strengths of the dipolar
interaction. In the exchange dominated region, the dipolar
interaction breaks the continuous symmetry of the ground state partially
and favors states with spins perpendicular to the chain direction. Rotation
symmetry around the chain direction still exists. The dispersion
relation for this phase is modified by the dipolar interaction,
but as in the isotropic counterpart no long-range order can exist even for
$T=0$.

The most famous quasi one-dimensional systems are
the ternary compounds ABX$_3$ (A alkaline, B transition metal and X halogen),
which have been studied intensively experimentally in the context of
Haldane's phase \cite{Haldane} and solitonic excitations \cite{Steiner91}.
Of particular interest are the Mn compounds. Because the angular momentum
$L$ is zero, no crystal field splitting occurs in these systems and the
dipole-dipole interaction should be the most important anisotropy.
Experiments \cite{abanov} show an anisotropy in the magnetization
measurements for fields applied parallel and perpendicular to the spin-chain
axis. We will show that this anisotropy can be understood qualitatively by our
simple one-dimensional dipolar model.
Up to now, only partial aspects of the dipole-dipole
interaction have been considered \cite{Shiba,Santini}.
In Ref[9] the classical ground state has been determined, but no
excitations have been
investigated, whereas in Ref[10] the dipolar interaction is only
considered for nearest neighbors. In this paper the effects of the additional
dipolar interaction will be studied in a systematic way.

In this spin wave theory we disregard kink-like excitations, which even for the
$r^{-3}$ decay of the dipolar interaction destroy one-dimensional long-range
order. However, for wavelengths shorter than the
correlation length magnon excitations become important. This has been shown
experimentally by Steiner for CsNiF$_3$ \cite{Steiner}. The short range
antiferromagnetic order supports spin waves with wave vectors not too close to
the center of the Brillouin zone. Especially for quasi one-dimensional
systems the weak interchain interaction leads to a stabilization of the
magnetic order and spin waves become the relevant excitations.

The outline of this paper is as follows: in section II we introduce the dipolar
model; in III we investigate the ground state, the spin-wave spectrum and the
order parameter for vanishing fields; in IV we study the magnetic phase
diagram for the whole parameter region. In the last section we apply our model
to a quasi one-dimensional system, namely RbMnBr$_3$.

\section{Model}
The Hamiltonian of a dipolar antiferromagnet reads
\begin{equation}
H=-\sum_{l \neq l'} \sum_{\alpha \beta} (J_{ll'} \delta_{\alpha \beta}
+A_{ll'}^{\alpha\beta}) S_l^{\alpha} S_{l'}^{\beta}
- g \mu_B {\bf{H}}_0 \sum_l {\bf{S}}_l \;,
\label{Hamiltonian}
\end{equation}
with spins ${\bf{S}}_l$ at lattice sites ${\bf{x}}_l$.
The first term in brackets is the isotropic exchange interaction $J_{ll'}$
and the second term is the classical dipole-dipole-interaction
\begin{eqnarray}
A_{ll'}^{\alpha\beta}= -\frac{1}{2} {(g \mu_B)^2} &\Biggl(&
\frac{\delta_{\alpha\beta}}{{|{\bf{x}}_l-{\bf{x}}_{l'}|}^3}\nonumber\\
&-& \frac{3 ({{\bf{x}}_l-{\bf{x}}_{l'})}_{\alpha}
{({\bf{x}}_l-{\bf{x}}_{l'})}_{\beta}}{{|{\bf{x}}_l-{\bf{x}}_{l'}|}^5}
\Biggr) \, .
\label{ddw}
\end{eqnarray}
The third term in Eq. (\ref{Hamiltonian}) describes the effect of an
external magnetic field ${\bf{H}}_0$,
where $g$ is the Land\'{e}-factor and $\mu_B$ is the Bohr magneton.
 From this Hamiltonian we calculate the magnon spectrum in the framework of the
Holstein-Primakoff (HP)\cite{HP} transformation.
The Holstein-Primakoff transformation is an
exact transformation which expresses the Hamiltonian of Eq. (\ref{Hamiltonian})
in terms of Bose operators $a_l^{\dagger}, a_l$. For low
temperatures an expansion up to bilinear terms can be used
\begin{eqnarray}
\tilde{S}_{l}^{x} &= &
\sqrt{\frac{S}{2}} (a_l + {a}_{l}^{\dagger}) \; , \quad
\tilde{S}_{l}^{y} = -i \sqrt{\frac{S}{2}} (a_l - {a}_{l}^{\dagger}) \; ,
\nonumber\\
 & & \label{HP}\\
\tilde{S}_{l}^{z} &=& S - {a}_l^{\dagger} a_{l} \quad .\nonumber
\end{eqnarray}
The tilde indicates that we have to use these inner spin coordinates in the
rotated coordinate frame where the $z$-direction lies in the direction of the
classical spins.
For the following discussion we define a dimensionless parameter $\kappa$,
which gives the ratio between the dipolar energy and the exchange energy:
\begin{equation}
\kappa=\frac{{(g \mu_B)}^2}{c^3 J} \ .
\label{kappa}
\end{equation}
Here $J$ denotes the strength of the exchange energy (the negative sign of
the antiferromagnetic exchange interaction $J_{ll'}$ is taken into account
separately) and $c$ denotes the distance between magnetic ions.\\
In the following we consider a spin chain which is directed along the $x$-axis
(see Fig. \ref{fig1}a,b).

\section{Dipolar antiferromagnetic chain without field}

The long-range dipole-dipole interaction and the antiferromagnetic exchange
interaction compete with each other: while the latter favors an
antiferromagnetic spin configuration, the former favors a
ferromagnetic orientation along the chain axis. Thus, we can distinguish an
exchange-dominated region and a dipole-dominated region,
which are separated by the condition (to be shown in Eq. (\ref{bed1}))
\begin{equation}
J_{{\bf{q}}_0}-J_0 +A_{{\bf{q}}_0}^{33} - A_0^{11}\; \lessgtr \; 0
 \; ,
\label{condition}
\end{equation}
where $J_{\bf{q}}$ is the Fourier transform of the
exchange interaction $J_{ll'}$, which equals $J_{\bf{q}}=-2J \cos (q_x c)$
for nearest-neighbor interaction (in the following we set $q_x=q$),
and $A_{\bf{q}}^{\alpha\beta}$
is the Fourier transform of the dipolar tensor Eq. (\ref{ddw})
\begin{equation}
A_{\bf{q}}^{\alpha \beta} = \sum_{l \neq 0} A_{l 0}^{\alpha \beta}
\exp{(i {\bf{q}} {\bf{x}}_l)} \;,
\label{dipft}
\end{equation}
which can be evaluated by Ewald summation \cite{Ewald} (see appendix A). The
wave vector ${\bf{q}}_0=\frac{\pi}{c}(1,0,0)$ describes the antiferromagnetic
order. Eq. (\ref{condition}) leads to a critical value of $\kappa$
\begin{equation}
\kappa_c=\frac{4}{2\zeta(3)-\eta(3)} \approx 2.66 \;,
\label{criticalkappa}
\end{equation}
with $\zeta(n)$ and $\eta(n)$ defined in appendix A.

In the following we investigate the classical ground states and
excitation spectra of the one-dimensional chain as a function of $\kappa$.

\subsection{Exchange dominated region ($\bbox{\kappa < \kappa_c}$)}

For pure exchange energy $J$, the classical ground state is the
configuration where the spins are antiparallel, as described by the
antiferromagnetic wave vector ${\bf{q}}_0$.
This state is continuously degenerate due to the rotational symmetry.
The dipolar interaction breaks the rotational symmetry and favors the
antiferromagnetic ground state, in which the spins lie in a plane perpendicular
to the chain axis, as can be seen by the largest value of the dipole-dipole
tensor ($A_{{\bf{q}}_0}^{33} = A_{{\bf{q}}_0}^{22} > A_{{\bf{q}}_0}^{11}$).
However,
rotation symmetry around the $x$-axis still exists (s.Fig. \ref{fig1}a).

\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure1.eps}}
\hspace{1.5cm}
  \caption{a) Classical ground state of the dipolar, antiferromagnetic chain
in the exchange dominated region ($\kappa < \kappa_c$).
b) Ground state for the dipolar dominated region ($\kappa > \kappa_c$).}
\label{fig1}
\end{figure}

In the following calculations the primitive cell is the chemical cell which is
half the magnetic unit cell.
The antiferromagnetic modulation is taken into account via
\begin{equation}
\sigma_l=e^{i {\bf{q}_0} {\bf{x}}_l} = \left\{
\begin{array}{ll}
+1& l \in {\cal{L}}_1 \\
-1& l \in {\cal{L}}_2
\end{array}
\quad , \quad {\bf{q}}_0=\frac{\pi}{c}(1,0,0)
\label{modulation}
\right.
\end{equation}
where ${\cal{L}}_1 ({\cal{L}}_2)$ denotes the first (second)
sublattice\cite{Ziman}.
If we start from the classical ground state with the spins oriented along the
$\pm z$-axis and perform the Holstein-Primakoff transformation, we get the
following Fourier transformed Hamiltonian
\begin{equation}
H=E_{cl} + \sum_{\bf{q}} A_{\bf{q}}
a_{\bf{q}}^{\dagger} a_{\bf{q}} + \frac{1}{2} B_{\bf{q}}
(a_{\bf{q}} a_{-\bf{q}} + a_{\bf{q}}^{\dagger} a_{-\bf{q}}^{\dagger})
\label{hamvordiag}
\end{equation}
with the classical ground state energy
\begin{equation}
E_{cl} = - NS^2 (J_{{\bf{q}}_0} + A_{{\bf{q}}_0}^{33})
\end{equation}
and the coefficients
\begin{eqnarray}
A_{\bf{q}} & = & S(2J_{{\bf{q}}_0}-J_{{\bf{q}}+{\bf{q}}_0}-J_{\bf{q}})
+S(2 A_{{\bf{q}}_0}^{33} - A_{{\bf{q}}+{\bf{q}}_0}^{22} - A_{\bf{q}}^{11})
\nonumber\\
B_{\bf{q}} & = & S (J_{{\bf{q}}+{\bf{q}}_0}-J_{\bf{q}})
+S (A_{{\bf{q}}+{\bf{q}}_0}^{22}-A_{\bf{q}}^{11}) \;.
\label{bqspectrum}
\end{eqnarray}
The Hamiltonian (\ref{hamvordiag}) is diagonalized by a Bogoliubov
transformation\cite{Akhiezer} and reads in terms of the new Bose creation and
annihilation operators $b_{\bf{q}}^{\dagger}$ and $b_{\bf{q}}$
\begin{equation}
H = E_{cl} + \frac{1}{2} \sum_{\bf{q}} (E_{\bf{q}}-A_{\bf{q}}) + \sum_{\bf{q}}
E_{\bf{q}} \, b_{\bf{q}}^{\dagger} b_{\bf{q}} \; .
\label{hamdiag}
\end{equation}
The second term in Eq. (\ref{hamdiag}) is a correction to the ground state
energy due to quantum fluctuations, while the third term
is the harmonic magnon Hamiltonian.
The ground state energy
\begin{equation}
E(T=0)=E_{cl} + \frac{1}{2} \sum_{\bf{q}} (E_{\bf{q}}-A_{\bf{q}})
\end{equation}
is shown in Fig. \ref{energy} as a function of $\kappa$. The quantum
fluctuations are strongest for pure exchange interaction \cite{Anderson}.
The deviation of the ground state energy from the classical value
\begin{equation}
E(T=0)=E_{cl}(1+0.363/S),
\end{equation}
is most significant in this case
and decreases with increasing dipolar interaction, i.e. the dipolar interaction
tends to stabilize the antiferromagnetic ground state.

\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure2.eps}}
\hspace{1cm}
  \caption{Deviation of the ground state energy from the classical
value due to quantum fluctuations for $\kappa < \kappa_c$. For
$\kappa \geq \kappa_c$ there is no difference between the two energies,
because the Hamiltonian is already diagonal after the HP-transformation
(s. Eq. ({\protect{\ref{2.22}}})).}
\label{energy}
\end{figure}

The magnon dispersion relation reads
\begin{eqnarray}
E_{\bf{q}}&=&\sqrt{A_{\bf{q}}^2-B_{\bf{q}}^2}\nonumber\\
&=&2S\sqrt{(J_{{\bf{q}}_0}
-J_{\bf{q}}+A_{{\bf{q}}_0}^{33}-A_{\bf{q}}^{11})}\nonumber\\
&&\times \sqrt{(J_{{\bf{q}}_0}-J_{{\bf{q}}+{\bf{q}}_0}+A_{{\bf{q}}_0}^{33}
-A_{{\bf{q}}+{\bf{q}}_0}^{22})} \; ,
\label{magspectrum}
\end{eqnarray}
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure3.eps}}
\mbox{}
\hspace{4cm}
  \caption{Dispersion relation for different values of $\kappa$
in the exchange dominated region ($\kappa \leq \kappa_c$).}
\label{gskleink}
\end{figure}
which is shown in Fig. \ref{gskleink} for four values of $\kappa$.
Because of the continuous degeneracy of the ground state
(rotation around the $x$-axis) the Goldstone-mode at ${\bf{q}}=0$
survives in the presence of the dipolar interaction,
but the behavior for small wave vectors is modified.
 If we expand the magnon spectrum around the center of the Brillouin zone,
we get logarithmic corrections
\begin{eqnarray}
E_{\bf{q}}/(4JS) &=& \biggl\{  b_1 {(qc)}^2
-\frac{1}{4} \kappa \Bigl( 1+ \frac{1}{2} \kappa c_5 \Bigr)
{(qc)}^4 \log {(qc)} \nonumber\\
&&{+b_2 {(qc)}^4 +{\cal{O}} \Bigl( {(qc)}^6 \Bigr) \biggr\}}^{1/2}\;,
\label{entw}
\end{eqnarray}
with $q$-independent constants $c_5,b_1,b_2$ (see Eq.
\ref{cvalues}, \ref{bvalue1}, \ref{bvalue2} in Appendix A).

The order parameter, the staggered magnetization, is given by
\begin{equation}
{\text{N}} = g \mu_B \sum_l \sigma_l \langle \tilde{S}_l^z \rangle
\end{equation}
with $\sigma_l$ from Eq. (\ref{modulation}).
Inserting the Holstein-Primakoff transformation (\ref{HP}), we obtain
\begin{equation}
{\text{N}} = g \mu_B N S - {\text{N}}_0 - {\text{N}}_{th}(T)
\end{equation}
with the zero-point contribution
\begin{equation}
{\text{N}}_0
= \frac{1}{2} g \mu_B \sum_{\bf{q}} \left( \frac{A_{\bf{q}}}{E_{\bf{q}}} -1
\right)
\label{2.16}
\end{equation}
and
\begin{equation}
{\text{N}}_{th}(T) =
g \mu_B \sum_{\bf{q}} \frac{A_{\bf{q}}}{E_{\bf{q}}} \, n_{\bf{q}} \;,
\end{equation}
from thermal excitations of spin waves.
$n_{\bf{q}}=\frac{1}{e^{E_{\bf{q}}/kT}-1}$
denotes the Bose-occupation number. Both quantum and thermal
fluctuations reduce the order parameter.
By use of the small wave vector expansion, Eq. ({\ref{entw}}), we see
that the sum ${\text{N}}_0$ diverges for ${\bf{q}} \rightarrow 0$.
Even though the dipolar interaction has the tendency to stabilize
the antiferromagnetic order, it is nevertheless destroyed by quantum
fluctuations even at $T=0$, as found for the isotropic counterpart.
There is yet another stability condition resulting from the requirement that
the spin wave frequencies (Eq. (\ref{magspectrum})) be real which leads to
\begin{eqnarray}
\label{aqbed}
A_{\bf{q}} &>& 0\\
\label{bqbed}
A_{\bf{q}} &>& |B_{\bf{q}}|
\end{eqnarray}
for all wave vectors $\bf{q}$\cite{Cohen}.
We get a lower bound for the strength of the exchange energy from the first
condition (Eq. (\ref{aqbed})) at ${\bf{q}}=0$
\begin{equation}
J_{{\bf{q}}_0}-J_0+A_{{\bf{q}}_0}^{33}-A_0^{11} > 0 \;.
\label{bed1}
\end{equation}
For lower exchange energies the system changes to the dipolar dominated
region.

\subsection{Dipolar dominated region ($\bbox{\kappa > \kappa_c}$)}

For pure dipolar interaction the classical ground state consists of two
states, in which the spins are oriented ferromagnetically along the $\pm
x$-axis (Fig. \ref{fig1}b), because the largest eigenvalue of the dipolar
tensor is $A_{0}^{11}$ (s. Fig. \ref{fig12}), i.e. the dipolar interaction acts
as an easy-axis anisotropy.
If we start with this ground state and perform the HP-transformation we get
\begin{equation}
H=E_{cl} + \sum_{\bf{q}} E_{\bf{q}} a_{\bf{q}}^{\dagger} a_{\bf{q}} \;,
\label{2.22}
\end{equation}
with the classical ground state energy
\begin{equation}
E_{cl} = - NS^2 (J_0 + A_{0}^{11})
\end{equation}
and
\begin{equation}
E_{\bf{q}} = 2S (J_0 - J_{\bf{q}}) + 2S (A_0^{11} - A_{\bf{q}}^{33}) \ .
\label{ferrospectrum}
\end{equation}
Due to the broken rotation symmetry the spectrum has an energy gap at the
zone center
\begin{displaymath}
E_0 = 2S (A_0^{11} - A_0^{33}) \;.
\end{displaymath}
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure4.eps}}
\mbox{}
\hspace{4cm}
  \caption{Spin-wave dispersion relation of the dipolar, antiferromagnetic
chain for $\kappa =\kappa_c=2.66$ (solid) and $\kappa =4$ (dashed).}
   \label{dispgap}
\end{figure}
The minimum of the dispersion relation is found at the zone edge (s. Fig. 4),
which vanishes for $\kappa=\kappa_c$ and increases with increasing dipole
strength.

In linear spin-wave theory the classical ground state and the quantum
mechanical ground state coincide. The Hamiltonian (\ref{2.22}) is diagonalized
by the HP-trans\-formation, and there are no corrections for quantum
fluctuations\cite{pich2000} at $T=0$, i.e. the ground state has long-range
order.  The order parameter is the magnetization in $x$-direction:
\begin{equation}
M^x =  g \mu_B \sum_l \langle S_l^x \rangle =
g \mu_B N S - M_{th}(T)
\label{2.14}
\end{equation}
with
\begin{equation}
M_{th}(T)=g \mu_B \sum_{\bf{q}} \frac{1}{e^{E_{\bf{q}}/k_B T}-1} \ .
\label{mtherm}
\end{equation}
For $\kappa > \kappa_c$ the spin-wave spectrum has gaps at ${\bf{q}}=0$ and
${\bf{q}}={\bf{q}}_0$ (Eq. (\ref{ferrospectrum})). Thus, the sum in
Eq. (\ref{mtherm}) is finite for finite
temperatures and from point of view of the linear spin-wave theory long-range
order should be possible. However, as was shown by
Dyson \cite{Dyson}, kink-like thermal excitations destroy the long-range
order in ferromagnetic Ising systems with interactions decreasing like
$J(r) \propto \frac{1}{r^\alpha}$ for $\alpha > 2$. Thus, we expect that for a
Heisenberg system with dipole-dipole interaction these nonlinear excitations
will ultimately destroy the long-range order as well.

Stability of the ground state requires that the spectrum is positive,
$E_{\bf{q}}>0$. For decreasing dipole energy the instability of the spectrum
sets in at ${\bf{q}}_0$, from which we recover the stability condition
Eq. (\ref{condition})
\begin{equation}
J_{{\bf{q}}_0}-J_0+A_{{\bf{q}}_0}^{33}-A_0^{11} < 0 \;.
\label{bed2}
\end{equation}
The soft mode at ${\bf{q}}_0$ for $\kappa=\kappa_c$
indicates the phase transition to the antiferromagnetic phase
(exchange-dominated region).

Consequently at $T=0$ there is long-range order (LRO) in the dipolar dominated
region, in contrast to the exchange dominated region. However, for finite
temperatures no LRO exists at all due to nonlinear excitations, namely domain
walls.

\section{Magnetic phase diagram}

In this section we determine the magnetic phase diagram of the
dipolar antiferromagnetic chain for both the dipolar dominated and the exchange
dominated region. We study homogeneous magnetic fields along and perpendicular
to the chain axis ($x$-direction). The results are presented in terms of
the parameter $\kappa$ (Eq. (\ref{kappa})) and the dimensionless field
$h=\frac{g \mu_B H_0}{JS}$. The spin orientations are determined from
the classical ground state energy within a two-sublattice model.

\subsection{Field in chain direction}
First we study the case of a magnetic field along the chain axis. In the
dipolar region ($\kappa > \kappa_c$) the field is parallel to the spins, and
thus no reorientation takes place.

In the exchange dominated region ($\kappa < \kappa_c$) the
spins are oriented perpendicular to the $x$-axis and any infinitesimal field
along the axis will lead to a reorientation of the spins in order to gain
energy from the Zeeman term (Eq. (\ref{Hamiltonian})).
In a two-sublattice model (the spins of the sublattice ${\cal{L}}_1
({\cal{L}}_2)$ enclose an angle $\varphi_1 (\varphi_2)$ with the $y$-$z$-plane
(see Fig. \ref{phasex})) we can calculate the classical ground state energy.
For spins lying in the $xz$-plane we get
\begin{eqnarray}
E_{cl}=-\frac{NS^2}{4} &\Bigl[ &
(J_{0}+A_{0}^{11}) {(\sin \varphi_1 + \sin \varphi_2)}^2 \nonumber\\
&+&(J_{{\bf{q}}_0}+A_{{\bf{q}}_0}^{11}) {(\sin \varphi_1 - \sin
\varphi_2)}^2 \nonumber\\
&+&(J_0+A_{0}^{33}) {(\cos \varphi_1 - \cos \varphi_2)}^2 \nonumber\\
&+&(J_{{\bf{q}}_0}+A_{{\bf{q}}_0}^{33}) {(\cos \varphi_1 + \cos \varphi_2)}^2
\Bigr] \nonumber \\
&-&\frac{1}{2}g \mu_B H_0^x N S (\sin \varphi_1+\sin \varphi_2)\;.
\label{eclassicx}
\end{eqnarray}
Minimization with respect to $\varphi_1$ and $\varphi_2$ yields
$\varphi_1=\varphi_2=\varphi$, i.e. a usual spin-flop phase. From the minimum
one determines the relation between the angle $\varphi$ and the magnetic
field:
\begin{equation}
\sin \varphi = \frac{g \mu_B H_0^x}{2S(J_{{\bf{q}}_0}-J_0+A_{{\bf{q}}_0}^{33}
-A_0^{11})} \ . \label{phix}
\end{equation}
Thus the spins become progressively aligned along the field as the field
increases. There is a continuous transition from this spin-flop phase to the
paramagnetic phase for $\varphi=90^\circ$.
The transition occurs at
\begin{equation}
h_{c}^x (\kappa) = 8 + \kappa \bigl( 2 \eta(3) - 4 \zeta(3) \bigr)
\quad {\text{for}} \quad \kappa<\kappa_c \; .
\end{equation}
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure5.eps}}
\mbox{}
\hspace{4.5cm}
  \caption{Magnetic phase diagram of the dipolar, antiferromagnetic chain with
  a field applied in chain direction. The spin arrangements below the $x$-axis
  indicate the phases for vanishing field. In the insert the
  configuration of the spins in a two-sublattice model is shown.}
\label{phasex}
\end{figure}
The complete phase diagram is shown in Fig. \ref{phasex}.
The HP-transformed Hamiltonian in the spin-flop phase has the form of
Eq. (\ref{hamvordiag}) with coefficients
\begin{eqnarray}
A_{\bf{q}}&=& S(2J_{{\bf{q}}_0}-J_{{\bf{q}}+{\bf{q}}_0}-J_{{\bf{q}}}
+ 2 A_{{\bf{q}}_0}^{33} - A_{{\bf{q}}+{\bf{q}}_0}^{22}
- A_{\bf{q}}^{11})\nonumber\\
&&+S \sin^2 \varphi \,
(J_{\bf{q}}-J_{{\bf{q}}+{\bf{q}}_0}+A_{\bf{q}}^{11}-
A_{{\bf{q}}+{\bf{q}}_0}^{33})\nonumber\\
B_{\bf{q}}&=& S(J_{{\bf{q}}+{\bf{q}}_0}-J_{\bf{q}}
+A_{{\bf{q}}+{\bf{q}}_0}^{22}
- A_{\bf{q}}^{11})\nonumber\\
&&+S \sin^2 \varphi \, (J_{\bf{q}}-J_{{\bf{q}}+{\bf{q}}_0}
+A_{\bf{q}}^{11}-A_{{\bf{q}}+{\bf{q}}_0}^{33}) \;,
\label{aqbqx}
\end{eqnarray}
where $\varphi$ is related to the field by Eq. (\ref{phix}).
The dispersion relation is shown in Fig. \ref{dispx} for two values
of the field.

\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure6.eps}}
\mbox{}
\hspace{5cm}
\caption{Dispersion relation for the linear chain in the spin-flop phase for
  two values of $\kappa$; solid lines for vanishing field and
  dashed  lines for $\sin \varphi=0.5$ (Eq. ({\protect{\ref{phix}}})).}
\label{dispx}
\end{figure}

The Goldstone-mode at ${\bf{q}}=0$ remains for finite dipolar energy
because the system is still invariant for rotations around the $x$-axis.

The magnetization in the spin-flop phase can be calculated from the free
energy $F$
\begin{equation}
{\bf{M}} = -\frac{\partial F}{\partial {\bf{H}}_0} \ .
\label{magnet}
\end{equation}
The free energy $F$ is related to the partition function $Z$ by
\[
F=-kT \log Z \quad {\text{with}} \quad Z={\text{Sp}}e^{-\beta H} \quad
{\text{and}} \quad \beta=\frac{1}{k_B T} \; ,
\]
i.e. for the Hamiltonian (\ref{hamdiag})
\begin{equation}
F=E_{cl}+\frac{1}{2} \sum_{\bf{q}} (E_{\bf{q}}-A_{\bf{q}}) + k_B
T \sum_{\bf{q}} \log (1-e^{-\beta E_{\bf{q}}}) \;.
\label{freeenergy}
\end{equation}
Inserting Eq. (\ref{freeenergy}) into (\ref{magnet}) yields for the
magnetization
\begin{equation}
{\bf{M}}={\bf{M}}_{cl}-{\bf{M}}_0-{\bf{M}}_{th}(T) \; ,
\label{magnetisation}
\end{equation}
which consists of a classical part
\begin{equation}
{\bf{M}}_{cl} = -\frac{\partial E_{cl}}{\partial {\bf{H}}_0} \;,
\label{mclass}
\end{equation}
a part arising from quantum fluctuations ($T=0$)
\begin{equation}
{\bf{M}}_0=\frac{1}{2} \sum_{\bf{q}} \left\{
\frac{1}{E_{\bf{q}}} \left(
B_{\bf{q}} \frac{\partial B_{\bf{q}}}{\partial {\bf{H}}_0}
- A_{\bf{q}} \frac{\partial A_{\bf{q}}}{\partial {\bf{H}}_0} \right)
+\frac{\partial A_{\bf{q}}}{\partial {\bf{H}}_0} \right\}
\label{mquant}
\end{equation}
and a part arising from thermal fluctuations
\begin{equation}
{\bf{M}}_{th}(T)=\sum_{\bf{q}} \frac{1}{e^{\beta E_{\bf{q}}}-1}
\frac{1}{E_{\bf{q}}} \left(
B_{\bf{q}} \frac{\partial B_{\bf{q}}}{\partial {\bf{H}}_0}
- A_{\bf{q}} \frac{\partial A_{\bf{q}}}{\partial {\bf{H}}_0} \right) \;.
\label{mthermisch}
\end{equation}
The classical magnetization is reduced by quantum and thermal fluctuations.
For the spin-flop phase the classical magnetization can be obtained by
inserting the expression for the classical ground state energy
(Eq. (\ref{eclassicx})) in Eq. (\ref{mclass}). We get
\begin{equation}
M_{cl}^x = g \mu_B N S \sin \varphi \;,
\label{mclx}
\end{equation}
where $\sin \varphi$ is given by Eq. (\ref{phix}).
The contributions of quantum and thermal fluctuations will be taken into
account numerically when we compare our results with experiments
(s. section IV).

Now we turn to the staggered magnetization in the $z$-direction
\begin{equation}
{\text{N}}_z=g \mu_B \sum_l \sigma_l \langle S_l^z \rangle \;,
\label{nz}
\end{equation}
which leads to
\begin{equation}
{\text{N}}_z=g \mu_B \cos \varphi \left(
NS - \frac{1}{2} \sum_{\bf{q}} \left( \frac{A_{\bf{q}}}{E_{\bf{q}}}
-1 \right) - \sum_{\bf{q}} \frac{A_{\bf{q}}}{E_{\bf{q}}} n_{\bf{q}} \right) \,.
\label{altmag1}
\end{equation}
The second and third term in (\ref{altmag1}) are divergent due to the
Goldstone-mode. Thus, no antiferromagnetic long-range order is possible in this
case, only a finite magnetization.

\subsection{Field perpendicular to the chain direction}

\subsubsection{Exchange-dominated region $(\kappa < \kappa_c)$}

A field perpendicular to the chain leads to a spin-flop-transition; for
infinitesimal fields the spins lie in the $yz$-plane and perpendicular to the
applied field. With increasing field the spins become progressively aligned in
field direction. In the following calculations the field is applied in the
$y$-direction so that for infinitesimal field the spins are oriented in the
$\pm z$-direction.  Again, we study the classical
\begin{figure}[htb]
 \epsfysize=0.9\columnwidth\rotate[r]{
  \epsfbox{figure7.eps}}
\mbox{}  \hspace{4cm}
  \caption{Configuration of the spins for a field applied perpendicular to the
  chain axis; a) for the exchange-dominated region,
  $\kappa < \kappa_c$, b) for $\kappa > \kappa_c$.}
   \label{flopz}
\end{figure}
\noindent
ground state energy of a
general two-sublattice system, for which the usual spin-flop phase turns out to
be stable. The equilibrium condition leads to
\begin{equation}
\sin \varphi = \frac{g \mu_B H_0^y}{2S(J_{{\bf{q}}_0}-J_0
+A_{{\bf{q}}_0}^{33}-A_0^{22})} \; , \label{phiz}
\label{winkelflopz}
\end{equation}
in analogy to Eq. (\ref{phix}) for fields along the chain axis, which
differs only in the dependence on the dipole interaction.
The transition between the
spin-flop phase and the paramagnetic phase occurs at (see Fig. \ref{phasez})
\begin{equation}
h_{c}^y (\kappa) = 8 + \kappa \bigl( 2 \eta(3) +  2 \zeta(3) \bigr)
\quad {\text{for}} \quad \kappa<\kappa_c \; .
\end{equation}
The coefficients of the Hamiltonian, Eq. (\ref{hamvordiag}), in the spin-flop
phase are in linear spin-wave theory
\begin{eqnarray}
A_{\bf{q}}&=& S(2J_{{\bf{q}}_0}-J_{{\bf{q}}+{\bf{q}}_0}-J_{\bf{q}}
+ 2 A_{{\bf{q}}_0}^{33} - A_{{\bf{q}}+{\bf{q}}_0}^{22}
- A_{\bf{q}}^{11})\nonumber\\
&&+S \sin^2 \varphi \,
(J_{{\bf{q}}+{\bf{q}}_0}-J_{\bf{q}}+A_{{\bf{q}}+{\bf{q}}_0}^{22}
-A_{\bf{q}}^{33}) \;, \nonumber\\
B_{\bf{q}}&=& S(J_{{\bf{q}}+{\bf{q}}_0} - J_{\bf{q}} +
A_{{\bf{q}}+{\bf{q}}_0}^{22}
-A_{\bf{q}}^{11})\nonumber\\
&&+S \sin^2 \varphi \, (J_{\bf{q}}-J_{{\bf{q}}+{\bf{q}}_0}
+A_{\bf{q}}^{33}-A_{{\bf{q}}+{\bf{q}}_0}^{22}) \;.
\label{aqbqz}
\end{eqnarray}
For finite $\kappa$ rotational symmetry is lost for the spin configuration
of Fig. \ref{flopz}a and thus no Goldstone-mode is present in the dispersion
relation of Fig. \ref{dispz} showing the spectrum for
two different values of $\kappa$ and $H_0^y$.
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure8.eps}}
\mbox{}
\hspace{5cm}
  \caption{Dispersion relation in the spin-flop phase for
  different magnetic fields applied perpendicular to the chain direction and
  different strengths of the dipolar interaction. The solid lines are without
field and the dashed lines are for $\sin \varphi=0.5$
(Eq. ({\protect{\ref{phix}}})).}
\label{dispz}
\end{figure}
The magnetization in the $y$-direction is obtained from the free energy
(see Eq. (\ref{magnet})) and is of the same form as
Eqn. (\ref{magnetisation})-(\ref{mclx}) with different canting
angle $\sin \varphi$ (Eq. (\ref{phiz})) and different
coefficients $A_{\bf{q}}$ and $B_{\bf{q}}$ (Eq. (\ref{aqbqz})).

Now the staggered magnetization in $z$-direction, which in analogy to
Eqs. (\ref{nz})-(\ref{altmag1}) is given by
\begin{equation}
{\text{N}}_z=g \mu_B \cos \varphi \left(
NS - \frac{1}{2} \sum_{\bf{q}} \left( \frac{A_{\bf{q}}}{E_{\bf{q}}}
-1 \right) - \sum_{\bf{q}} \frac{A_{\bf{q}}}{E_{\bf{q}}} n_{\bf{q}} \right)
\, ,
\end{equation}
is finite, because of the energy gap in $E_{\bf{q}}$
(s. Fig. \ref{dispz}). However, we believe that due
to nonlinear kink-like excitations again no long-range order is possible for
finite temperatures.

If the field is applied in chain direction a Goldstone-mode remains
(s. Fig. \ref{dispx}) and hence the expression for the staggered
magnetization ${\text{N}}_z$ diverges (Eq. (\ref{altmag1})).

\subsubsection{Dipole dominated region ($\kappa > \kappa_c$)}

In this region the spins keep the ferromagnetic orientation but with a canting
angle $\vartheta$ (intermediate phase) with respect to the magnetic field (s.
Fig. 7b). The classical ground state energy is given by
\begin{eqnarray}
E_{cl}&=&- NS^2 \left[ (J_0+A_0^{22}) \sin^2 \vartheta
+ (J_0+A_0^{11}) \cos^2 \vartheta \right] \nonumber\\
&& -g \mu_B H_0^y N S \sin \vartheta \;,
\label{eintermediate}
\end{eqnarray}
the minimization of which gives the following relation between the canting
angle $\vartheta$ and the applied field $H_0^y$:
\begin{equation}
\sin \vartheta = \frac{g \mu_B H_0^y}{2S(A_0^{11}-A_0^{22})} \;.
\label{winkelintermediate}
\end{equation}
Note that this angle depends only on the dipole strength but not on the
exchange energy due to the isotropy of $J_{\bf q}$. The transition
to the paramagnetic phase, in which all spins orient along the magnetic field,
occurs at
\begin{equation}
h_{c}^y (\kappa) = 6 \zeta(3) \kappa \quad {\text{for}} \quad
\kappa>\kappa_c \; .
\end{equation}
The coefficients in the Fourier transformed
Hamiltonian for finite canting angle $\vartheta$ are given by
\begin{eqnarray}
A_{\bf{q}}&=& 2S(J_{0}-J_{\bf{q}})
+ 2S(A_0^{11} - A_{\bf{q}}^{22}) \nonumber \\
&&+ S \sin^2 \vartheta \, (A_{\bf{q}}^{22}-A_{\bf{q}}^{11})\nonumber\\
B_{\bf{q}}&=& S \sin^2 \vartheta \, (A_{\bf{q}}^{22}-A_{\bf{q}}^{11}) \;.
\label{ferro}
\end{eqnarray}
The spectrum is shown for three values of the field in
Fig. \ref{ferrokant.fig}. For decreasing field the energy gap
$E_{{\bf{q}}_0}$ decreases until it vanishes at the transition point.
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure9.eps}}
\mbox{}
\hspace{5cm}
\caption{Dispersion relation for the dipole dominated region with a field
  perpendicular to the chain direction and $\kappa=4$; dashed: $\sin
\vartheta=0$, dot-dashed: $\sin \vartheta=0.5$ and solid: $\sin \vartheta=1$.}
\label{ferrokant.fig}
\end{figure}
Now we investigate the transition from the spin-flop phase to the
intermediate phase as a function of $\kappa$. Comparison of the
classical ground state energy of the two phases shows that the transition line
is independent of the applied field $H_0^y$ (if $H_0^y < H_c^y$), which
explains the vertical line at $\kappa=\kappa_c$
between the spin-flop phase and the
intermediate phase in the phase diagram of Fig. \ref{phasez}.
For $\kappa < \kappa_c$ the spin-flop phase has lower
energy and is thus the stable phase, for $\kappa > \kappa_c$ the intermediate
phase has lower energy. At $\kappa=\kappa_c$ and $h=h_c$ the energies of the
spin-flop phase, the intermediate phase and the paramagnetic phase are the
same.
\begin{figure}[htb]
  \narrowtext
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure10.eps}}
\mbox{}
\hspace{4cm}
  \caption{Magnetic phase diagram of the dipolar, antiferromagnetic chain with
  a field perpendicular to the chain axis. The configurations below
  the $x$-axis correspond to vanishing field.}
   \label{phasez}
\end{figure}

\section{Comparison with experiment}

In this section we compare our theoretical results with measurements on quasi
one-dimensional antiferromagnets in the hexagonal ABX$_3$ structure. Due to
different exchange mechanisms the intrachain interaction is about three orders
of magnitude larger than the interchain interaction, thus that these materials
behave in a quasi one-dimensional manner. The most promising substances are the
manganese compounds, because Mn$^{2+}$ ions have spin $S=5/2$ and vanishing
orbital momentum. Thus, the main contribution to the anisotropy should be the
dipole-dipole interaction. The field-dependent magnetization has been measured
for RbMnBr$_3$ (Fig. \ref{theoexp} dashed lines) \cite{abanov}.  In this
material the spins are forced to orient within the hexagonal plane,
perpendicular to the chain-axis. This planar anisotropy can be fully explained
by the dipole-dipole interaction, which leads in the exchange-dominated region
to just such an orientation (see section II). Magnetization experiments show an
anisotropy: the magnetization for magnetic fields along the spin-chain axis is
about 5 to 10\% larger than for fields perpendicular to it. Part of this
anisotropy can be understood qualitatively even for classical spins by the
dipolar anisotropy, which leads to different dependences of the angle $\varphi$
of the spins on the magnetic field (Eqs. (\ref{phix}) and (\ref{phiz})).  The
classical contribution to the magnetization is larger for parallel than
perpendicular field, since the dipole interaction favors ferromagnetic
orientation in chain direction.  For a quantitative comparison we need the
values of the exchange energy $J$ and the lattice constant $c$ which are given
for RbMnBr$_3$ by \cite{Heller}
$$
J = 9.56 K, \quad c = 3.26 {\rm \AA} \; .
$$
Here the exchange energy was determined by a fit of the spin-wave curves with
the spin-wave spectrum calculated from a Hamiltonian in which the anisotropy is
described by a single-ion term. For this Hamiltonian there exists a
renormalization calculation \cite{Khvesh}, which shows, that the classical
value of the exchange energy has to be renormalized due to magnon-magnon
interactions. The resulting value of $J$ is
$$
J=8.93 K \;.
$$
This corresponds to $\kappa=8.07 \cdot 10^{-3}$, which is deep in the
exchange dominated region of our theory. With this constant we calculate the
classical contributions to the magnetization (see Eq. (\ref{mclx})) in the
spin-flop phase shown in Fig. \ref{theoexp} as the upper and lower thin solid
lines for fields along and perpendicular to the chain-axis. The dashed lines
represent the experimental values. The transition to the paramagnetic phase
takes place at $H_c \approx 130 T$ and cannot be seen here. For perpendicular
fields lower than $H \approx 3.9 T$ the three-dimensional ordering becomes
important: the system changes to a complicated six-sublattice structure
\cite{Chubukov} for which our one-dimensional model is inappropriate.
According to Fig. \ref{theoexp}, the classical magnetization is larger than the
experimental and the splitting for the two directions is almost invisible.
However, in one dimension the quantum fluctuations are strong and must be taken
into account. Numerical evaluation of the magnetization for longitudinal and
perpendicular field direction (Eq. (\ref{magnetisation})), including the
zero-point contributions ($T=0$), yields the thick solid lines in Fig.
\ref{theoexp}. In fact, the quantum fluctuations lead to a pronounced reduction
of the magnetization and increase the splitting, but as to be expected, are
somewhat overestimated in the pure one-dimensional model.  The contribution of
thermal fluctuations to the magnetization (Eq. (\ref{mthermisch})) is
negligible for temperatures as low as in the experiment ($T=1.7 K$). This is in
contrast to the work of Santini et al. \cite{Santini}, who claim that the
classical thermal fluctuations are the relevant contribution and totally
neglect the quantum fluctuations.  Abanov and Petrenko \cite{abanov} also
studied the one-dimensional spin-chain, but with a single-ion anisotropy
favoring orientation perpendicular to the chain instead of the dipolar
interaction. Inserting the fitted value for this anisotropy they get a larger
fluctuation contribution than in our theory. Furthermore, the classical
contribution shows the opposite anisotropy, i.e. the magnetization for a field
along the chain-axis is lower than for a perpendicular field.

In summary, we can explain the anisotropy measured in RbMnBr$_3$
qualitatively by a one-dimensional, dipolar Heisenberg model. We expect that
by taking into account the full three-dimensional structure with interactions
between different chains the quantitative agreement could be improved because
the contribution of quantum fluctuations is reduced in higher dimensions.
\begin{figure}
  \narrowtext
 \epsfxsize=0.8\columnwidth\rotate[r]{
  \epsfbox{figure11.eps}}
\mbox{}
\hspace{4cm}
\caption{Magnetization curves for RbMnBr$_3$
{\protect{\cite{abanov}}}: The dashed lines show the
  experimental measurements at $T=1.7$K.
  The thin lines show the classical results of our
  theory, i.e. without quantum fluctuations. The thick lines show the results
  taking into consideration quantum fluctuations. For each pair of curves the
  upper one refers to field parallel and the lower one to field perpendicular
to the chain.}
\label{theoexp}
\end{figure}
Our prediction for the spin wave dispersion relation of RbMnBr$_3$ (Eq.
(\ref{magspectrum})) is shown in the magnetic Brillouin zone in Fig.
\ref{disprbmn}. Here we set the exchange interaction $J$ to $9.56 \, K$. The
resulting gap of the upper dispersion branch at ${\bf{q}}=0$ equals
$14.16 \, K$.
\begin{figure}[htb]
 \epsfxsize=0.6\columnwidth\rotate[r]{
  \epsfbox{figure12.eps}}
 \hspace{5cm}
\caption{The two branches of the dispersion relation for RbMnBr$_3$ in the
magnetic Brillouin zone with dipolar interaction ($\kappa=8.072 \cdot 10^{-3}$,
$J=9.56$ K).}
\label{disprbmn}
\end{figure}
\section{Summary}
We have considered the one-dimensional, isotropic Heisenberg antiferromagnet
with dipole-dipole interaction in the complete parameter region. We showed that
there exists an exchange dominated phase for $\kappa < \kappa_c$, where the
spins orient antiferromagnetically, perpendicular to the chain axis, i.e. the
dipole-dipole interaction gives rise to a planar anisotropy. For $\kappa >
\kappa_c$, the dipole-dominated phase, the ground state is ferromagnetic along
the chain axis, i.e. the dipole-dipole interaction acts like an easy-axis
anisotropy. Because of the broken rotation symmetry the dipole-dominated region
shows long-range order for $T=0$. In the exchange-dominated region there is
still a Goldstone-mode due to the rotation symmetry around the chain axis.
Although the linear small ${\bf{q}}$ behavior of the acoustic magnon mode is
modified by the dipole energy (Eq. (\ref{entw})), there is no long-range order
neither for finite nor for zero temperature.

The magnetic phase diagram for fields along and perpendicular to the chain in
both the dipole and the exchange dominated regions has been determined and the
predicted magnetization has been compared with experiments on RbMnBr$_3$, a
quasi one-dimensional, planar antiferromagnet. The experimental anisotropy can
be explained qualitatively by the one-dimensional, dipolar model, the
quantitative agreement could be improved by a more elaborate, three-dimensional
calculation.

\acknowledgments
This work has been supported by the BMBF under contract number 03-SC4TUM.
One of us (M.H.) has benefited from a scholarship of the Studienstiftung des
Deutschen Volkes. The work of C.P. has been supported by the Deutsche
Forschungsgemeinschaft (DFG) under the contract no. PI 337/1-1.

redpajama_set_name: RedPajamaArXiv


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text:
Very Cool WW2 Interactive resource from HISTORY.COM
FieldMarshalGames '10 last edited by
Just found this today. Lots of great animations, videos and other resources about the Second World War.
http://www.history.com/shows/wwii-in-hd/interactives/inside-wwii-interactive
Was USA Useless in WW2?
World War II History • • King_Of_Tanks
@king_of_tanks
Definitely. I hate those people.
But yeah, that last sentence works for any country like France, Yugoslavia, Greece, and China.
What would help germany more in ww2?
World War II History • • i rock
@calvinhobbesliker:
How did Poland provoke the Germans into attacking?
they didn't, they just were in between…
WW2 Article: Advanced German Technology
World War II History • • HortenFlyingWing
KurtGodel7, very good post, thank you.
I'm still not convinced however, I'll reply to a few of your points below further:
Germany desperately needed the Russian oil by 1943 (as well as Russian grain which I will discuss further below). That they failed to take the Caucasus during this time was their last realistic chance at victory, IMO. However, had they taken the oil wells, but with the Russians destroying them in the process as was quite likely, would the Germans be able to restore the flow of oil in sufficient time? It might take months, even years to rebuild the necessary infrastructure in the best of circumstances, let alone during a brutal war. The German industry was already hard pressed to supply the necessary armaments and did not have a great deal of experience with oil industry in the first place. I think they would not have been able to do this.
The same idea goes for the chromium, vanadium, etc., though this would be less difficult for the Germans to accomplish (or mitigate as you also suggest) than the oil problem.
While Germany might have been able to supply an equivalent amount of money, material and engineers to work on their atomic program, there simply were much fewer top nuclear physicists in all Europe than existed in the US. Consequently, it would have probably cost more and taken longer than the US program for this reason alone. I have no doubt they could have eventually done it, but I don't see how they develop nuclear weapons before the allies developed a delivery system that could get through their defenses.
The German V-2 was a technological marvel, but other than size, no more advanced than the rockets being built by Dr. Goddard. After the war, when Dr. Goddard was able to examine a captured V-2, he was convinced the Germans had stolen his work. And the Germans might have because most of his designs were on file in the US patent office, available for public viewing (which the Germans did prior to the war). I think had the Americans wanted to (and Dr. Goddard certainly did) they could have built a superior rocket in a couple months and have it mass-produced in six. As the A-bombs designs at that time were quite heavy, it might have taken longer than that to build a nuclear capable rocket…but how much longer?
Alternatively, the Allies could have either copied the German jets to enable a delivery system, or devise other means (boats/submarines? special ops?) to deliver these weapons.
In addition, I consider the German attack on Russia to be about food as well as oil The Ukraine was the breadbasket of Europe, and helped the Germans tremendously in 1943. But food was scarce in 1944 and onward. Partly this was due to Russian recovery of territory. But it was also because the Ukraine was normally not sufficient by itself to feed Germany (the year of the capture of Ukraine by the Germans was one of the best years for Ukrainian agriculture as the weather was nearly perfect). Of course, the poor treatment of the Ukrainians by the Germans did not lend itself to helping this problem either. In order to assure itself of adequate food, I think the Caucasus (the next logical food source) was needed.
Favourite WW2 Tank
World War II History • • Witt
A Jagdpanther of course. Beautiful shape. With sloping frontal armour and the L71/88.
Love the scene when one breaks over the crest in Normandy in Band of Brothers.
Favorite WW2 Torpedo Boat Class
The Italian ones are new to me, only because they were never discussed. However there are plenty of records of the ones in action during the Phillipines and South Pacific Campaigns (JFK, etc.) which gave them plenty of heroic press.
WW2 Generals' November birthdays
@CWO-Marc said in WW2 Generals' November birthdays:
Along similar lines: General Joseph E. Johnston, who had surrendered his forces to General William Tecumseh Sherman in the last days of the Civil War, died just a few weeks after Sherman. He had attended Sherman's funeral and had kept his hat off during the proceedings (despite the cold and rainy weather) as a sign of respect to his former adversary; he caught a cold as a result, and it developed into pneumonia.
True Marc. I also remembered that they, too, were born in the same month. Was February, actually, but 13 years apart. Funny.
MOVED: Greatest Fails in History
World War II History • • Guerrilla Guy
This topic has been moved to General Discussion.
http://www.axisandallies.org/forums/index.php?topic=19552.0
This isn't strictly WW2 history.

redpajama_set_name: RedPajamaCommonCrawl


text:
package com.netflix.spinnaker.orca.clouddriver.tasks.providers.cf;

import static com.netflix.spinnaker.orca.api.pipeline.models.ExecutionType.PIPELINE;
import static org.assertj.core.api.Assertions.assertThat;
import static org.mockito.ArgumentMatchers.matches;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;

import com.netflix.spinnaker.orca.api.pipeline.TaskResult;
import com.netflix.spinnaker.orca.api.pipeline.models.ExecutionStatus;
import com.netflix.spinnaker.orca.clouddriver.OortService;
import com.netflix.spinnaker.orca.clouddriver.tasks.servicebroker.AbstractWaitForServiceTask;
import com.netflix.spinnaker.orca.pipeline.model.PipelineExecutionImpl;
import com.netflix.spinnaker.orca.pipeline.model.StageExecutionImpl;
import java.util.HashMap;
import java.util.Map;
import java.util.function.Function;
import javax.annotation.Nullable;

class AbstractCloudFoundryWaitForServiceOperationTaskTest<T extends AbstractWaitForServiceTask> {
  private final String operationType;
  private final Function<OortService, T> subjectConstructor;

  AbstractCloudFoundryWaitForServiceOperationTaskTest(
      String operationType, Function<OortService, T> subjectConstructor) {
    this.operationType = operationType;
    this.subjectConstructor = subjectConstructor;
  }

  void testOortServiceStatus(
      ExecutionStatus expectedStatus, @Nullable Map<String, Object> serviceInstance) {
    OortService oortService = mock(OortService.class);
    String credentials = "my-account";
    String cloudProvider = "cloud";
    String region = "org > space";
    String serviceInstanceName = "service-instance-name";
    when(oortService.getServiceInstance(
            matches(credentials),
            matches(cloudProvider),
            matches(region),
            matches(serviceInstanceName)))
        .thenReturn(serviceInstance);

    T task = subjectConstructor.apply(oortService);

    Map<String, Object> context = new HashMap<>();
    context.put("cloudProvider", cloudProvider);
    context.put("service.account", credentials);
    context.put("service.region", region);
    context.put("service.instance.name", serviceInstanceName);

    TaskResult result =
        task.execute(
            new StageExecutionImpl(
                new PipelineExecutionImpl(PIPELINE, "orca"), operationType, context));

    assertThat(result.getStatus().toString()).isEqualTo(expectedStatus.toString());
  }
}

redpajama_set_name: RedPajamaGithub


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text:
To be uninformed may pay in employment: TUPE
AuthorPhilip Richardson
The thought of your employment transferring to a new employer can be a daunting experience. However, it can be made ten times worse when you feel like you are being left in the dark. You may feel that you have many questions that are left unanswered such as: How will the transfer affect me? Will I be expected to perform the same duties after the transfer? When will the transfer occur?
In situations where your employment transfers to a new employer you may be protected by what are known as the TUPE regulations.
Under these regulations both your current employer and potential new employer are under a duty to consult either your Trade Union representative or an elected representative in relation to the transfer.
The things employees should be consulted about include:
that a transfer is to take place
the reason for the transfer and when it is expected to take place
the implications for the employees
the measures that the employer expects to take in relation to the employees
the measures that the new employer expects to take in relation to the employees.
If an employee has not been properly consulted with regards to a transfer then they may apply to the Employment Tribunal for compensation of up to thirteen weeks pay. Employees may also have other grounds for complaint depending on the circumstances. Legal advice should be sought so that an employee becomes fully aware of the employment rights during a transfer.
By employment law specialist, Alicia Mulligan
Dealing with discrimination claims relating to face masks
Unsafe and unsupported: Maternity Action reports on work place health and safety for pregnant women during the COVID-19 pandemic
Racial discrimination in the workplace
Can employers enforce a mandatory Covid-19 vaccination programme?
Is being told to 'grow up' by your employer age discrimination?


text:
The Role of Power in Negotiation
20 Negotiation Tactics
By Edward Smith on Fri, 12 Jul 2019
This 70 minute video gives you access to a whole new world of negotiation techniques that you probably have never thought of before. You will learn the psychology of how people make choices, and how you can leverage those choices into your advantage in a negotiation setting. All of these tips were chosen because of how widely they can be applied to all kinds of situations. You will also get 50 real-life examples to use in your own negotiations, so that you can learn to never be taken advantage of. All we need is 70 minutes of your time, and we can have you negotiating like a pro, to be able to have people see your way, no matter what you're proposing. All of these tactics can be applied in many different settings, such as asking for a raise, getting a job, or even winning an argument! All these tactics can change how people view you, and give yourself authority! Read more...
20 Negotiation Tactics Summary
Contents: Video Course
Creator: Martin Collins
Official Website: www.geneva-education.com
My 20 Negotiation Tactics Review
Furthermore, if anyone else has purchased this product or similar products, please let me know about your experience with it.
You have come to the right place to find the information and details about 20 Negotiation Tactics. I invite you to read or go to the Main site for more information now.
Last Updated on Wed, 16 Dec 2015 | Library Congress
But Lincoln's words seemed to have little effect on the tense situation between North and South. Eleven Southern states had already announced their intention to secede from the Union and form a new country that allowed slavery, called the Confederate States of America, by the time Lincoln was inaugurated (sworn in). A few weeks later, the new Confederate government demanded that he remove the Federal troops stationed at Fort Sumter, located in the harbor at Charleston, South Carolina. Confederate president Jefferson Davis (1808-1889 see entry) viewed these troops as a symbol of Northern authority and wanted them to leave. But Lincoln refused to acknowledge the Confederacy as a legitimate country and claimed that the Southern states were engaged in an illegal rebellion against the U.S. government. When negotiations failed, Confederate forces opened fire on the fort on April 12, 1861. This event marked the beginning of the Civil War.
Becomes president of the Confederate States of America
Last Updated on Mon, 04 Sep 2017 | Union Army
For six weeks, Davis tried to negotiate a peaceful settlement with the North. He still wanted to avoid a war if possible. One of the issues he hoped to resolve was the presence of federal troops at Fort Sumter, located in the middle of the harbor at Charleston, South Carolina. He viewed these troops as a symbol of Northern authority and asked Lincoln to remove them. When negotiations failed, Davis ordered Confederate forces to open fire on Fort Sumter on April 12, 1861. The Confederacy gained control of the fort, but the Civil War had begun.
From Appomattox to Liverpool
Last Updated on Wed, 16 Dec 2015 | Federal Corps
Lee's surrender at Appomattox Court House on 9 April 1865 essentially ended the war in the Virginia Theater. Many thousands of men had slipped out of the weary, retreating, Confederate column as the cause became patently hopeless, thus escaping the final surrender. Some of those soldiers attempted to head south into North Carolina to join the Southern army still fighting there under General Joseph E. Johnston. That forlorn hope evaporated when Johnston surrendered to General William T. Sherman near Durham Station on 26 April, after complicated negotiations involving Washington politicians.
The April 1993 Cease Fire
Last Updated on Wed, 16 Dec 2015 | Bosnia Herzegovina
Colonel Tihomir Blaskic, a participant in the meeting, subsequently recorded his own observations on the negotiations, noting that the ABiH delegation seemed preoccupied, cold, and worried about the many Croat civilian casualties caused by their offensive. Blaskic's prophetic assessment of the ABiH was that they are either totally scatter-brained so they have agreed to everything, or they can no longer control their own actions, so now they accept everything in order to create space for a new attack, one they will not give up on. Despite his misgivings, on April 22, Blaskic ordered HVO forces in central Bosnia to implement the chiefs of staff's agreements.4 Subordinate commanders were once again enjoined to halt all combat activities against the ABiH and to not respond to Muslim provocations unless ordered to do so by higher headquarters. Nor were they to restrict the movements of UN and ECMM teams. Colonel Blaskic also ordered the withdrawal of HVO forces from the...
The Road to Appomattox april 29 is65
Last Updated on Wed, 16 Dec 2015 | Federal Army
Pressed the rear of Lee's dwindling army. Surrounded at last by overwhelming force, Lee opened negotiations with Grant which resulted in the surrender of the Army of Northern Virginia at Appomattox Court House on the afternoon of April 9, 1865. This surrender brought the war in Virginia to an end.
Five bishops do not sign
Last Updated on Wed, 16 Dec 2015 | Guerra Civil
The third case, which is very little known, was that of Javier de Irastorza Loinaz, the incumbent Bishop of Orihuela-Alicante. In 1935 the Holy See had appointed an Apostolic Administrator there with full powers and the bishop had been ordered to reside outside his diocese, where he could no longer govern. Why he was removed in this way was not made public, but well informed persons close to the diocesan curia assert that it was owing to a complicated question involving funds. Indeed, once before, when he was a prior to the military orders in Ciudad Real, he had had a problem of the same kind. But when don Juan de Dios Ponce y Pozo, the appointed Apostolic Administrator, was assassinated in 1936, Irastorza considered that he would automatically recover the full government of the diocese, which was still fundamentally his.14 At the end of the Civil War, amidst general surprise, he presented himself at Alicante and assumed his episcopal functions. The Holy See, at that time in the midst...
The Triumph and the Tragedy
Last Updated on Sun, 14 Oct 2018 | Federal Army
But the fall of Fort Fisher did generate another Confederate gesture toward peace negotiations. Jefferson Davis appointed Stephens and two other officials to meet Union representatives with a view to secure peace to the two countries. Lincoln responded with an expression of willingness to receive commis
The consecration of the pronunciamiento
Last Updated on Mon, 15 Jul 2019 | Guerra Civil
The Church had played no role as a conspirator in preparing the Uprising. As we have explained in Chapter 1, the majority of bishops and Right-wing Catholics bore a considerable responsibility for the growing friction that culminated in open warfare. It is safe to say that in the tense atmosphere of the spring of 1936, almost all the bishops wanted an intervention by the Army to put an end to this state of affairs. It is also true that one or two bishops close to the military officers encouraged those who were thinking of a rebellion and that there were even a few who collected funds for the preparation of the coup (there was the case, for example, of someone in the entourage of Irurita, the Bishop of Barcelona), but the only people who could give the coup any likelihood of success were the professional military officers. These, however, conspired together in the utmost secrecy, keeping intimate control over the movement and accepting collaboration only from sectors that were more or...
The Armed Forces of South Russia
Last Updated on Thu, 05 May 2016 | Bullock Collection
Therefore, on 8 January, Krasnov bowed to pragmatism and began negotiations to subordinate his command under Denikin into a new organization known as the Armed Forces of South Russia (AFSR). General A. Bogaevsky, a veteran of the Ice March, replaced Krasnov as Ataman of the Don Cossacks on 15 February, and General
The Confederacy surrenders
Last Updated on Mon, 26 Aug 2019 | Union Troops
Officers of Sherman's and Johnston's armies mingle around the North Carolina home of James Bennett, the site of their generals' surrender negotiations. These talks continued for a few days, because Union authorities did not approve of Sherman's first offer to the surrendering Confederates. They believed the terms were too lenient.
The ABiH Attack on Zepce Zavidovici and Novi Seher June July 1993
Last Updated on Sun, 24 Apr 2016 | Bosnia Herzegovina
On April 18, the ABiH III Corps cleared HVO forces and many Bosnian Croat civilians from the municipality of Zenica and cut the road to Zepce, thereby isolating the HVO forces and Croat civilians in the Tesanj-Maglaj salient. Surrounded by hostile Muslim forces, the Croats in Zepce had only one option for communicating with the outside world through territory held by the Bosnian Serbs. The HVO thus opened negotiations with the Serbs, who for their own reasons were willing to cooperate.13 The Bosnian Croats in Zepce were not eager to deal with the Serbs, but they had no other choice. A cease-fire between the Serbs and Croats in the Zepce area was announced on June 14.
Chinese Civil War Weapons
Last Updated on Thu, 22 Aug 2019 | Chinese Army | 6 comments
An agreement regarding the strength of the PPC was reached between Chiang Kai-shek and Mao Tse-tung in late August 1945. during the period of ostensible peace negotiations. This called for the size of the local PPC to be governed by the population of the province 110 province's PPC should exceed 15.000 men, and their armaments should be limited to pistols, rifles and automatic rifles. This agreement was of course ignored once the Civil War broke out. At the start of the conflict the PPC and other local forces amounted to about 1.5 million men.
Tentative deescalation
Last Updated on Tue, 08 Mar 2016 | Northern Ireland
Once again there were parallels between the end of the civii war and the Anglo-Irish War in that no one could be sure that it was really over. Unlike the Anglo-Irish War, however, there was no truce, no negotiations no settlement the Republicans conceded nothing, not even defeat, and Ireland remained on a war footing. The iRA's guerrillas simply dumped their weapons and went home to await the next time.
The Anglo Irish peace and the Republicans
Last Updated on Sun, 18 Jun 2017 | Northern Ireland | 1 comment
During the London peace negotiations in the autumn and winter of 1921 the British Prime Minister, Lloyd George, continually pressured the Irish negotiators with threats of renewed violence on a scale hitherto unseen. Lloyd George wanted a swift resolution to the peace talks and did not In essence the Treaty confirmed the partition of Ireland enshrined in the 1920 Government of Ireland Act and its provisions applied almost exclusively to the 26 counties of what is now the Irish Republic. As far as Northern Unionists were concerned the 1920 Act was the final settlement to the issue of Home Rule and, much to de Valera's chagrin, they refused to take part in the negotiations despite Lloyd George's efforts. The Treaty also ensured that the new Irish Free State or Saorstat Eireann retained the king as head of state. F.rskine Childers, the Anglo-Irish secretary to the Irish negotiators and ardent Republican, was horrified that 'Irish Ministers would be the King's Ministers' and worse still...
Scotland in 16391640 and the Bishops Wars
Last Updated on Wed, 16 Dec 2015 | Royalist Army
Newcastle upon Tyne was occupied without difficulty by the Scottish army. In their rear, Dumbarton had fallen, Caerlaverock was undergoing vigorous siege, and in September Lord Ettrick was to surrender Edinburgh into covenanting hands. Helpless, Charles summoned a Great Council to York for 24 September, Parliament was summoned to meet on 3 November, and on 2 October negotiations began at Ripon with the Scots which were to lead to the Treaty of Ripon. By this, the Scots occupied Northumberland and Durham with a daily subsidy of 850 to support them until problems were finally hammered out with the sitting of Parliament in London.
Prides Purge and the Kings Execution
Last Updated on Wed, 04 Dec 2019 | Royalist Army | 1 comment
Linked with this step was the purge of Parliament carried out by the army on 6 December, with the connivance of Independent members. The Commons had already concluded that the seizure of the King had been an act of great 'insolency' and on the evening of the 5th had gone so far as to issue a stern rebuke to the army by voting to continue negotiations. On the morning of the 6th therefore, Colonel Pride, commanding the regiment responsible for the security of the House, together with Lord Grey of Groby, stood at the door turning away members unsympathetic to the army's case. Some were actually arrested and locked up temporarily in a nearby public house. Later in the day Cromwell, who had now virtually supplanted his superior, Fairfax, as the prime mover in these affairs, came into London and approved the measures. Amongst those subsequently arrested was the old parliamentary general, Sir William Waller.
Ironclads in the Confederate States Navy
Last Updated on Sat, 10 Aug 2019 | Rear Admiral
In the following weeks Mallory moved to bring his scheme to reality. Lieutenant James H. North was ordered to proceed to London, and with the assistance of Confederate agents already in England, to go to France and open negotiations with the French for the purchase, either directly or indirectly, of one armored frigate of the Gloire class, or failing this, to arrange for a similar ship to be secretly constructed. Another armored ship was to be contracted for in England. Lieutenant North was advised to consult with Captain Cowper Coles, the Royal Navy's ironclad expert, before drawing up specifications. On May 20, 1861, 2 million dollars were allocated for the purchase of 6 armored vessels abroad.
The occupation of New Orleans
Last Updated on Wed, 16 Dec 2015 | Marine Corps
After three further days of unsuccessful surrender negotiations, the remainder of the Marines of Farragut's squadron, augmented by a detachment of sailors with two howitzers, were ordered to land. Commanded by Capt John L.Broome, they made their way along the wide city streets, first to the Customs House, then to the City Hall. Despite being pushed, abused, and spat upon by the angry mob, the Marines maintained their discipline and did not retaliate. At both destinations they raised the national colors and left a Marine Guard. For almost three days Broome's Marines were the sole authority of the US Government in New Orleans, until Gen Benjamin Butler's soldiers arrived and the Army took control of the city. On May 1 the Marines withdrew from New Orleans and returned to die vessels of their squadron.
William Wilbur Edgerton
Last Updated on Thu, 22 Aug 2019 | South Carolina
Several days after the army reached Goldsboro, North Carolina, Edgerton announced to his mother, T am so sick of soldering that my patriotism is below par.' Fortunately, the war did not last much longer, in April, Sherman's army advanced, and just as quickly it halted for negotiations. By the end of the month, the Confederates had surrendered, and the 107th New York began its march for Washington, DC. On 24 May, it proudly participated in the Grand Review along Pennsylvania Avenue, with the
The Third Civil War 164951
Last Updated on Tue, 12 Jun 2018 | Eastern Association
From our soules abominate, and all parties and con-senters thereunto' on 22 February Montrose was appointed the King's Captain-General in Scotland with instructions to raise a loyal army. Rather than accept the severe terms put to him by a Scottish delegation which visited him in Holland in 1649, however, Charles prevaricated in the hopes of success in Ireland. When there was no longer an alternative, he entered into new negotiations with the Scottish Commissioners at Breda. The ruling Scottish Committee of Estates proposed terms which even Argyll considered too strict, but Charles was encouraged by William II to agree, and on 1 May 1650 signed theTrcaty of Breda. By this he undertook to impose Presbyterianism upon England, to outlaw-Roman Catholicism, to acknowledge the Scottish Parliament and renounce the arrangements with Montrose and Ormonde, in return for an invitation to be crowned in Scotland and to have the Engagers' rights restored to them. Probably neither side intended to...
A nineteenthcentury inheritance
Thu, 10 Nov 2016 | Guerra Civil
In 1931 the official doctrine of the Church continued to propagate, almost as a dogma of faith, the principle of a confessional state. In the negotiations for the concordat of 1851, the Holy See had revealed itself to be more inclined to accept disentailment than to renounce the confessional nature of the kingdom. During the Second Vatican Council (1962-65), the Francoist section of the Church showed itself to be an anachronistic defender of the Confessional State and obstinately opposed to the proclamation of religious freedom. In the eyes of these clergy, such a declaration would have appeared tantamount to mere opportunism, for it would have implied, indeed led to, a quid pro quo arrangement by which countries with a Catholic majority would tolerate non-Catholics so that countries where the situation was the reverse would tolerate Catholics. Yet the proposed text was founded theologically on the principle that the act of faith could emanate only from free will and that therefore...
Efforts to prevent the assassinations
Last Updated on Thu, 22 Aug 2019 | Guerra Civil
When later the Republican government, to avoid the charge of favouritism, centralized all prisoner-exchange negotiations under the administration of Jose Giral, there were very few cases that could be resolved satisfactorily. Giral himself has left a detailed account of his labours in that field.84
The Arkansas And The Tennessee
Last Updated on Thu, 22 Aug 2019 | Rear Admiral
In spite of these handicaps, Bullock had a near success. In March, 1862, he contracted for two ironclad turret rams with Laird of Birkenhead, said rams to be 230 feet long with a beam of 42 feet and a 15-foot draft. They were to carry four Armstrong rifles in two turrets. In January, 1863, the British Foreign Secretary, Lord Russell, informed Bullock that unless Her Majesty's government was satisfied that the rams were legally owned by a foreign government ( not the Confederate States of America), they would not be permitted to depart. At that time the rams were only half finished, giving Bullock time to think of some subterfuge. He opened negotiations with the French banking firm of Messrs. Bravay, with the plan of having them act as dummy purchasers of the vessels for the Khedive of Egypt. Adams, the American Minister to Great Britain, got wind of this and bluntly informed Lord Russell that if those rams were allowed to sail, it meant war with the United States. Eventually the ships...
The King the Scots and the Discontented Army
Wed, 20 Sep 2017 | Royalist Army
Evidently the King hoped, when he surrendered to the Scots on 5 May 1646, to place himself in a position to negotiate with them with a view to forming an alliance against Parliament, The Scots were disgruntled both at their treatment from their erstwhile allies, and by Parliament's failure to implement Presbyterianism in England. Nevertheless, the price of Scottish help for the King would involve his acceptance of the Solemn League and Covenant, a price Charles was unwilling to pay, and negotiations failed. The Parliament, itself torn by disagreement between Presbyterians and Independents, secured the King's person from the Scots by paying over to them substantial subsidies in return for their help during the war. The King passed into parliamentary hands on 30 January 1647 and was taken to Holdenby House in Northamptonshire. There, the The Council broke up on 8 November, and on the same day the King, who had been transferred from Newmarket to Hampton Court on 24 August, escaped and...
The North Tightens Its Grip
Thu, 29 Mar 2018 | Abraham Lincoln
As the 1864 U.S. presidential elections drew near, many people believed that war-weary Northerners would vote to replace President Abraham Lincoln (1809-1865) with Democratic candidate George B. McClellan (1826-1885), the former general of the Army of the Potomac. If McClellan won the election, many citizens believed he would enter into peace negotiations to end the war and provide the Confederacy with the independence it wanted. But a late flurry of Union victo-
Military Alliance
Last Updated on Wed, 16 Dec 2015 | Federated Commonwealth | 1 comment
From the moment they had begun negotiations for the Federated-Commonwealth Alliance treaty. Prince Davion and Archon Steiner envisioned a united nation, governed by the progeny of Hanse and Melissa Davion and protected by the most powerful military the Inner Sphere had seen in centuries. Their first actions in support of the military alliance were to sponsor wargames between the two militaries, followed shortly thereafter by the formation of the Federated Commonwealth Corps, an organization of allied troops that eventually encompassed twelve full RCTs, staffed by the finest soldiers that both the Lyran and Federated Suns military academies could produce and equipped with the best military hardware.
The March To London
Last Updated on Wed, 16 Dec 2015 | Dutch Army
Marching from Warwick via Daventry and St Albans, Essex and his army were given a hero's welcome in London on 7 November. Parliament, moved by the King's proximity to London, despatched a petition offering a reconciliation and the King appeared ready to listen, suggesting Windsor casde as a locauon to conduct negotiations.
The Western Delaware
Last Updated on Wed, 24 Oct 2018 | African American
The Delaware Indians lived up to their rhetoric as loyal Unionists. Delaware men served as scouts and home guards, protecting the area from incursions by other Indians and Confederate sympathizers. Enlistment rates for the Delawares were remarkable, with 170 of the eligible 210 men volunteering for service by 1862. The Delaware Indians did more than volunteer. Black Beaver, for example, used his decades of experience as a guide and a scout when the war broke out. Black Beaver helped with diplomatic negotiations with various Indian tribes and helped on the battlefield. He provided advance scouting of Confederate troops and led a dangerous expedition to Kansas, in which several hundred Union troops and their Confederate prisoners traveled 500 miles unscathed through dangerous terrain. Black Beaver received the ire of Confederates who razed his ranch at the Wichita Agency, causing an estimated 5,000 in damage.
Peace is declared
Last Updated on Wed, 16 Dec 2015 | South Carolina
With Davis's reluctant consent, Johnston contacted Sherman to open negotiations for peace. On 17 April, the two generals who had opposed each other in Mississippi, in Georgia, and again in North Carolina, assembled at the home of James and Nancy Bennett, not far from Durham Station. Sherman, forceful in war and soft in peace, offered Johnston mild terms that clearly overstepped his bounds. He permitted
Last Updated on Wed, 24 Oct 2018 | Short Parliament
From queen 142 Oxford Parliament 107-8 pardon of John Goodman 60 parliamentary attacks on revenues 30 peace negotiations with parliament 192, 193, 194, 196 belief in rescue from Ireland 209 exposure of supporters to vengeance 197-8 insincerity of negotiations 200-1 scale of concessions 197, 199-200 treaty of Newport 194-6 preference for personal counsel 5, 114, 117 negotiations with Hyde 79 Hertford, William Seymour, marquess of 5, 122 peace efforts 124-6 support for royalist army 96 Hills, Henry, and printing press 156 Hobbes, Thomas, 131
The Relief Of York
Last Updated on Wed, 04 Dec 2019 | Eastern Association
The situation of Newcastle, locked up in York, was by no means desperate. He had occupied his opponents with treaty negotiations from 8 to 15June. When, on 16June, Major-General Crawford launched part of the Eastern Association army into an ill-coordinated attack presaged by the explosion of a mine under the walls of York, the Parliamentarians were beaten off losing 200 prisoners as well as heavy casualties. Lack of provisions was a more serious threat and Newcastle wrote urgently to Rupert seeking relief. On 28 June the Allied commanders outside York received messengers who told them that Rupert was approaching with 10,000 Horse and 8,000 Foot.
Spanish Vickers
Last Updated on Sun, 28 Jul 2019 | Nationalist Fighter
It was flown by Grupos num 21 and 31 at Madrid, num 22 at Seville, num 23 at Barcelona, num 1 in Africa, and by several training units. Small numbers of other types were pressed into service by whichever side took over their airfields. A relatively large naval air arm also remained largely under government control, including 20 Vickers Vildebeeste recce torpedo-bombers. Finally, three Hawker Spanish-Fury fighters and one Spanish-Osprey - unarmed examples sent in the course of licence-building negotiations - were retained by the government near Madrid and used at first as high-speed recce types.
Kweichow
Last Updated on Mon, 25 Apr 2016 | Chinese Army
February-March General advance by PLA southwards to Yangtze river. KMT government under Sun Fo move to Canton, and attempt negotiations with Mao Tse-tung. Still director general of KMT party. Chiang transfers gold reserves to Formosa, and prepares Nationalist redoubt on that island. April Negotiations break down (19th). PLA cross Yangtze at several points. Fall of Taiyuan and of Nanking (23rd). 27 May Fall of Shanghai.
Last Updated on Thu, 22 Aug 2019 | Northern Ireland
British hopes for the government of Ireland as a solution to the roubles failed to materialize however, during the Treaty negotiations it was obvious that Lloyd George outclassed the Irish plenipotentiaries fed by Collins. By continually threatening to renew hostilities Lloyd George was able to brow beat the Irish representatives into agreeing to a settlement that was to split the Republican movement.
Fort Sumter 186 I
Last Updated on Sun, 14 Oct 2018 | Coastal Fortifications
The fort was not designed to fend off this kind of attack. While the garrison labored to contain the fires and save the powder, smoke filled the casemates, making it almost impossible to breathe. All this time, shot smashed into the casemates. When at last nothing was left of the building but the blackened walls and smoldering embers, it became painfully evident that an immense amount of damage had been done. The interior of the fort and the barrack block on its landward side lay in ruins. Shortly afterwards, negotiations began under a flag of truce and the garrison surrendered. During the two-day bombardment, the fort was subjected to a range of shot from almost every side, but the really damaging rounds came from mortars and the single rifled gun. Both were weapons that the Bernard Board had never imagined would ever be used against one of their coastal fortifications. The rules of fortification were being rewritten.
Vitez Busovaca Area
Even as negotiations to end the Muslim-Croat conflict began, fighting continued in the Vitez area. In early February, the ABiH regrouped and brought in reinforcements from Sarajevo and Zenica in preparation for another major assault to cut the Lasva Valley road at Santici. An ABiH attack toward San-tici on February 8 failed, and the HVO counterattacked to widen the neck of the Vitez Pocket. On February 14, the HVO succeeded in removing the ABiH flag placed in Santici on January 11, and after almost two months of heavy fighting the lines in the Vitez Pocket were back where they had been before the first Muslim offensive in the area. The fighting in the Vitez region tapered off, then resumed briefly as both sides sought a final advantage immediately before the cease-fire pursuant to the peace accords signed in Zagreb on February 23 were to go into effect at noon on February 25.17
Francos victory
Last Updated on Mon, 25 Dec 2017 | Social Revolution
Casado entered into negotiations with Franco's chief of intelligence in Burgos, Colonel Ungria, confident that some terms better than simple unconditional surrender could at this late stage still be achieved. He also began planning a coup against Negrin and his Communist backers. By early March, even General Miaja agreed with Casado's plans, and on 5 March Casado set up a so-called national council in Madrid and informed Negrin of his rebellion. Uncertainty and political confusion were rife, not just in Madrid, but throughout Republican Spain. No one was sure who had what authority, or who would follow any orders. Negrin gave up, and flew out of the country, accompanied by various Communist luminaries. But Communist army commanders in and around Madrid chose to attack Casado, and for one last, desperate time, there was a civil war within the civil war in Republican Spain.
Last Updated on Sun, 11 Nov 2018 | Federal Army
Union cavalry captured the fleeing Jefferson Davis in Georgia on May 10. The United States government discovered evidence of the role of Confederate agents in a plan late in the war to kidnap Lincoln, take him to Richmond and hold him as a bargaining counter in peace negotiations. It was the failure of this plan that had caused Booth and several co-conspirators to assassinate Lincoln, and attempt to assassinate Secretary of State Seward and Vice-President Andrew Johnson. The government thought it also had evidence of the involvement of high Confederate officials, including Jefferson Davis, in the kidnapping and - by implication - the assassination plots. But as it became clear that this evidence would not stand up in court, the government gradually dropped plans to try Davis. The only people tried and convicted were those directly involved in the assassination plots. Four of the conspirators were hanged on July 7, 1865. The other four were imprisoned. One died in prison the other...
A monarchist coup
Sat, 14 Jan 2017 | Guerra Civil
Did the Fascists hope to overthrow the Republic and re-establish the monarchy It is true that some of the conspirators, such as Kindelan and the two Vigon brothers, were monarchists, but Payne is quite right when he observes that 'the majority of the directors of the conspiracy, such as Mola, Goded, Cabanellas and Queipo de Llano felt a veritable antipathy towards monarchy as an institution. Franco himself was obliged to declare that the Moors would act only under the flag of the Republic.'21 Mola, the Director, had been on the point of breaking off negotiations with Fal Conde and the traditionalists because they demanded that the uprising be staged beneath the bi-colour flag of the monarchy. At the last moment and on the express order of Sanjurjo, Fal Conde agreed that the army go out into the streets bearing the Republican flag, provided that the Requetes could carry the monarchist flag. Mola had agreed, in writing, to a Republican dictatorship in which Church and State were...
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