text:
\section{Introduction}
\label{Intro}

The research field of magnonics\cite{Magnon-Spintronics,Neusser,Lenk-2011-1,Magnonics-Krug,Davies-2015-1,TAP-2013} addresses the transport of information in the form of spin waves and the fundamental study of the spin-wave properties in magnetic layer systems. Recently, the spin-wave dynamics in thin magnetic layers sandwiched in an asymmetric layer stack have attracted an increased research interest. This is motivated by the large variety of spin-orbit coupling phenomena which appear in such layer systems with broken structural inversion symmetry\cite{Sampaio-2013-1,Manchon-2014-1,Miron-2010-1, Sklenar-2016-1}. Besides the consequent current-induced effects on the spin-wave dynamics, like the current-induced modulation of the spin-wave damping\cite{Gladii-2016-2, MockelPyPt,Demi-2014-STNO}, this structural inversion asymmetry also influences the spin-wave properties in the absence of a (charge) current. One of these effects is the frequency splitting of the spin-wave dispersion for spin waves traveling in the magnetostatic surface wave configuration, i.e., waves traveling perpendicular to the direction of the static magnetization in an in-plane magnetized ferromagnetic film\cite{DE, Stancil}. In addition to asymmetric interface anisotropies\cite{Burkard-PRL-1990,Gladii-2016} in thin films with thickness of a few tens of nanometers, interfacial Dzyaloshinskii-Moriya interaction (iDMI)\cite{Fert-1990, Di-2015, Moon-2013, Kostylev-2014, Nembach-2015,Stashkevich-2015,Lee-2016} has been recently identified as the origin of such frequency splittings in ultra-thin films (thicknesses of a few nanometers and below). In turn, spin waves have been established as a sensitive probe of the interface characteristics and, next to the study of the domain wall motion\cite{Boulle-2013,Martinez-2013,Brataas-2013,Emori-2013,Ryu-2013,Hrabec-2014-1,Je2013}, they have become an indispensable probe for iDMI.

Recent studies also concerned the effect of the iDMI on the spin-wave spectrum and its potential application. In particular, the realization of a diode-like, uni-directional spin-wave emission was addressed in literature\cite{Lan-2015, Sanchez-2014}, since it promises an efficient control of the spin-wave emission in spin-wave based applications\cite{Magnon-Spintronics}. These previous studies were focused on the utilization of exchange-dominated spin waves, which, due to their large wave-vectors, feature a sizable iDMI-induced splitting of the dispersion. However, these waves generally suffer from a short spin-wave lifetime and they are difficult to access in standard experiments such as Brillouin light scattering spectroscopy or all-electrical propagating spin-wave spectroscopy\cite{BLS1,BLS2,BLS3,Bailleul-2003,Florin-2016,Koji-2012,Koji-2014}. In contrast, the spectrum of dipole-exchange spin waves lies in a wave-vector range compatible with standard detection and excitation schemes\cite{Mockelantenne,Pirro-2011-1}. Here, we provide an analytical and numerical study of the realization of a uni-directional emission of dipole-exchange spin waves in spin-wave waveguides featuring only a weak iDMI. We demonstrate that the wave-vector selectivity provided by a coplanar waveguide (CPW) can suffice to achieve this uni-directionality. By applying the theory for spin waves in thin films to microscopic magnonic waveguides featuring iDMI, we give guidelines for the practical realization of these uni-directional emitters. As model system we choose a layer system incorporating Ni$_{81}$Fe$_{19}$ (Permalloy, Py) and Pt, a system which is commonly used in magnon spintronic applications\cite{Magnon-Spintronics,Neusser,Lenk-2011-1,Magnonics-Krug,Davies-2015-1,TAP-2013, MockelPyPt,Gladii-2016-2,Demi-2014-STNO}. Recently, a weak, yet sizable iDMI was found in this material system\cite{Nembach-2015,Stashkevich-2015}, which is about one order of magnitude lower than the iDMI in Pt/Co/Al$_2$O$_3$\cite{Belmeguenai-PRB-2015} or Pt/Co/MgO\cite{Boulle-2015-RTS}. These systems are known to exhibit a large iDMI, but they feature a significantly larger intrinsic damping.

The structure of the article is as follows: In Section \ref{Anal} we present an overview of the analytical description of spin waves in waveguides made from thin ferromagnetic films and the incorporation of iDMI into this description. Consequently, we present the conducted numerical study of the uni-directional emission in the model system Py/Pt in Section \ref{Num}. Thereafter, we compare the analytical model to the numerical simulations in Section \ref{Res} and we demonstrate the realization of the uni-directional spin-wave emission in Section \ref{Uni}. Ultimately, the paper closes with a discussion of the obtained results in Section \ref{Disc} and a conclusive statement in Section \ref{Conc}.

\section{Analytical model}
\label{Anal}

\begin{figure*}[t!]
	  \begin{center}
    \scalebox{1}{\includegraphics[width=0.9\linewidth, clip]{Fig1.pdf}}
    \end{center}
	  \caption{\label{Fig1}(Color online) a) Schematic layout of the investigated transversely magnetized Ni$_{81}$Fe$_{19}$(Py)/Pt waveguide. The interfacial Dzyaloshinskii-Moriya interaction (iDMI) leads to a frequency splitting of waves running in the $\pm x$-direction with $k_{||,\pm}$. The coplanar waveguide (CPW) is introducing a wave-vector selective excitation. b) Schematic illustration of the concept of the uni-directional emission: The dashed lines show the spin-wave dispersion relation of the fundamental waveguide mode. The iDMI leads to a lifting of the degeneracy of the wave vector for waves running to the left ($-x$) and to the right ($+x$). For a fixed frequency $f_0$ (vertical dashed line), this leads to different excitation efficiencies $\eta$, for waves running in the two opposite direction. These are schematically shown by the solid lines. A proper choice of $f_0$ results in the suppression of one emission direction, which is highlighted by the orange circles.}
\end{figure*}
The standard description of the waveguide modes in transversely magnetized waveguides is based on the dispersion relation for thin films developed in Ref. \cite{Kalinikos-1986-Disp} and has already been successfully applied to describe a large variety of experiments\cite{Pirro-2011-1,Bayer-2006,Vogt-PR}. The waveguide, which is schematically shown in Fig. \ref{Fig1}~(a) features two quantization directions: One across its thickness $d$ ($z$-direction) and one across its width $w$ (short axis, $y$-direction). The quantization across the thickness leads to the formation of perpendicular standing spin-wave (PSSW) modes. Commonly, and in particular for the manifestation of iDMI, the spin-wave waveguides are made from thin magnetic films.
In contrast to the fundamental thickness mode, which corresponds to a homogeneous magnetization across the thickness of the waveguide ($k_z = 0$), the higher PSSW modes feature large exchange energies. Thus, they are separated from the fundamental thickness mode by several tens of GHz. Moreover, these modes feature a negligible dipolar dispersion and, thus, for rather small wave vectors they are essentially not propagating along the waveguide\cite{Kalinikos-1986-Disp,Stancil}. Thus, the fundamental thickness mode is the only mode of interest in terms of magnonic applications. In addition, one should note that for the ultra-thin films, the non-reciprocity induced by asymmetric interface anisotropies can be neglected\cite{Gladii-2016}.

In the following, we discuss exclusively the case of transversely magnetized waveguides, where the transverse magnetization is enforced by an externally applied bias field. In this geometry (also referred to as the Damon-Eshbach geometry), the iDMI causes a non-reciprocity in the wave-vector component $k_{||}$ along the propagation direction along the wire. This results in a wave-vector dependent frequency splitting between the two propagation directions\cite{Moon-2013}.

In the waveguide geometry, the geometric confinement across the short axis leads to the formation of waveguide modes. For a given waveguide mode $n$, this is taken into account by attributing a fixed wave-vector component $k_\perp(n) = n \pi/w_\mathrm{eff} $ across the effective width $w_\mathrm{eff}$ of the waveguide. The effective width is, hereby, determined by the geometrical width of the waveguide as well as the dipolar pinning on the waveguide edges. This results in an inhomogeneous effective field across the waveguide width\cite{Guslienko-eff-width,Mockel-2008-1}. The effective width and the corresponding demagnetization field $\mu_0 H_\mathrm{demag}$ in the waveguide can be approximated following the approach derived in Refs. \cite{Mockel-2008-1,Joseph-1965}, neglecting the small canting of the magnetization at the waveguide edges and assuming that the waveguide is homogeneously magnetized along its short axis ($y$-direction) by the external field. Under this assumption, the effective-field distribution $\mu_0 H_\mathrm{eff}(y) = \mu_0 H_\mathrm{ext} - \mu_0 H_\mathrm{demag}(y)$ in the transversely magnetized waveguide is given by
\begin{widetext}
\begin{align}
\label{Eq:Beff}
\begin{split}
\mu_0H_\mathrm{eff}(y) &= \mu_0H_\mathrm{ext} - \mu_0 M_\mathrm{s} N_{zz,0}(y) = \mu_0H_\mathrm{ext} - \frac{\mu_0 M_\mathrm{s}}{\pi}\left[\mathrm{arctan}\left(\frac{d}{2y + w}\right)-\mathrm{arctan}\left(\frac{d}{2y - w}\right)\right],
\end{split}
\end{align}
\end{widetext}
with $N_{zz,0}$ representing the demagnetization of the homogeneously magnetized waveguide. The effective width $w_\mathrm{eff}$ is taken as the separation between the points where the effective field inside the waveguide drops significantly. In this work we define the effective width as the part of the waveguide cross-section wherein the effective field is at least $85\,\%$ of the value in the waveguide center. The effective field used in the calculations is the average value of the effective field within this width.

Due to the rather large sizes of the considered waveguides\footnote{We consider waveguides of widths and lengths of a few $100\,\mathrm{nm}$, which is large in comparison to the distances relevant for the potential tilt of the magnetization due do iDMI.} and the comparably large ratio between waveguide length and waveguide width, we neglect any influence of the considered comparably weak iDMI on the effective width or the effective field due to a magnetization canting at the waveguide edges\cite{Cubukcu-PRB-2016} in the analytical model. With $w_\mathrm{eff}$ and $\mu_0 H_\mathrm{eff}$, the dispersion is then calculated as a function of the wave-vector component $k_{||}$ and the angle $\theta_k$ between the spin-wave wave vector in the waveguide plane and the magnetization direction. In the transversely magnetized scenario, this angle is given by
\begin{align}
\label{Eq:Thetak}
\theta_k &= \mathrm{atan}(k_{||}/k_\perp(n)).
\end{align}
Consequently, in a ferromagnetic waveguide (in the absence of material-related magnetic anisotropies), the dispersion relation $f(\mathbf{k}$) of the $n$-th waveguide mode for $|\mathbf{k}|d < 1$ can be calculated\cite{Kalinikos-1986-Disp,Di-2015}:
\begin{align}
\begin{split}
\label{Eq:wk}
f_\pm(\mathbf{k}) &= \sqrt{(\omega_0+\omega_\mathrm{M}\lambda_\mathrm{ex}\mathbf{k}^2)(\omega_0+\omega_\mathrm{M}\lambda_\mathrm{ex}\mathbf{k}^2+\omega_\mathrm{M}F_{00})}\\
&\pm\frac{2\gamma}{M_\mathrm{s}}D_\mathrm{int}|\mathbf{k}|\mathrm{sin}(\theta_k),
\end{split}
\end{align}
with the wave vector $\mathbf{k} = (k_{||},k_\perp,0)$, the gyromagnetic ratio $\gamma$ in units of $\mathrm{Hz}\,\mathrm{T}^{-1}$, the vacuum permeability $\mu_0$, $\omega_0 = \gamma \mu_0 H_\mathrm{eff}$, $\omega_\mathrm{M} = \gamma \mu_0 M_\mathrm{s}$, where $M_\mathrm{s}$ is the saturation magnetization, and $\lambda_\mathrm{ex} = 2A_\mathrm{ex}/(\mu_0M_\mathrm{s}^2)$, where $A_\mathrm{ex}$ is the exchange constant. $F_{00}$ is given by
\begin{align}
\label{Eq:F00}
F_{00} = 1 + g(\mathbf{k})(\mathrm{sin}(\theta_k)^2-1)+\frac{\omega_\mathrm{M}g(\mathbf{k})(1-g(\mathbf{k}))\mathrm{sin}(\theta_k)^2}{\omega_0+\omega_\mathrm{M}\lambda_\mathrm{ex}\mathbf{k}^2}
\end{align}
with the function $g(\mathbf{k}) = 1-(1-\mathrm{exp}(|\mathbf{k}|d))/(|\mathbf{k}|d)$. The last part in Eq. \ref{Eq:wk} is the implementation of the iDMI discussed in, for instance, Ref. \cite{Belmeguenai-PRB-2015,Di-2015}, where $D_\mathrm{int}$ is the effective iDMI strength in units of $\mathrm{J}\,\mathrm{m}^{-2}$. The latter is the effective volume strength of the iDMI, which is, for instance, originating from the Py/Pt interface. Thus, it depends on the used material combination, the exact interface and the thickness of the ferromagnetic layer. Moreover, it should be noted that, since the iDMI is a vectorial property, the sign of $D_\mathrm{int}$ depends on the orientation of the DMI-vector $\mathbf{D}$ and, consequently, on the orientation of the interface normal $\mathbf{\hat{n}}$\cite{Moon-2013}. Hence, the sign of $D_\mathrm{int}$ depends, for instance, on the stacking order of the layer system (e.g., it is opposite in Py/Pt and Pt/Py).

In Eq. \ref{Eq:wk}, the $\pm$-sign distinguishes the propagation to the right ($\mathbf{k}\cdot\mathbf{\hat{x}} > 0$) from the propagation to the left ($\mathbf{k}\cdot\mathbf{\hat{x}} < 0$) for a positive applied bias field ($\mathbf{M}$ aligned along the $y$-direction). If the field and, consequently, the magnetization are rotated by $180^\circ$, the two directions change their signs in Eq. \ref{Eq:wk} (i.e. $\mp$ instead of $\pm$). It should be noted that in this geometry, $|\mathbf{k}|\mathrm{sin}(\theta_k) = k_{||}$. Hence, the DMI leads to a splitting of the spin-wave frequency $\Delta f$ given by
\begin{align}
\label{Eq:Df}
\Delta f = f_+ - f_- = \frac{4\gamma}{M_\mathrm{s}}D_\mathrm{int}k_{||}.
\end{align}

From the spin-wave dispersion relation, the spin-wave group velocity $v_\mathrm{g}$ can be obtained straightforward by the differentiation of $f(\mathbf{k})$ with respect to $k_{||}$
\begin{align}
\label{Eq:vg}
v_{\mathrm{g},\pm} = \frac{\partial \omega_\pm(\mathbf{k})}{\partial k_\mathrm{||}} = 2\pi\frac{\partial f_\pm(\mathbf{k})}{\partial k_\mathrm{||}},
\end{align}
which we performed numerically from the calculated spin-wave dispersion relations. It should be noted that the iDMI leads to a constant offset of the group velocity in the two propagation directions $\Delta v_\mathrm{g} = 4\gamma/M_\mathrm{s}\cdot D_\mathrm{int}$, independent of the spin-wave wave vector.

From the phenomenological loss theory\cite{Stancil}, the spin-wave lifetime $\tau_0$ in the absence of iDMI follows to
\begin{widetext}
\begin{align}
\begin{split}
\label{Eq:Tau0}
\tau_0 &= \left(\alpha \omega(\mathbf{k}) \frac{\partial \omega(\mathbf{k})}{\partial \omega_0} \right)^{-1} = \left(2\pi\alpha\left(\omega_0+\omega_\mathrm{M}\lambda_\mathrm{ex}\mathbf{k}^2+\frac{\omega_\mathrm{M}(1+g(\mathbf{k}))(\mathrm{sin}(\theta_k)^2-1)}{2}\right)\right)^{-1},
\end{split}
\end{align}
\end{widetext}
with the Gilbert damping parameter $\alpha$ and $\omega(\mathbf{k}) = 2\pi f(\mathbf{k})$. To incorporate the effect of iDMI on the spin-wave lifetime, we follow the approach presented in Ref. \cite{Di-2015}:
\begin{align}
\label{Eq:Taupm}
\tau_\pm = \frac{\tau_0}{1 \pm \frac{\Delta f}{2 f_0}},
\end{align}
where $f_0$ is the spin-wave frequency in the absence of iDMI, which is calculated from Eq.~\ref{Eq:wk} with $D_\mathrm{int} =0$. With the spin-wave lifetime and group velocity, the exponential spin-wave amplitude decay length $\delta_\pm = v_\mathrm{g,\pm} \cdot \tau_\pm$ can be computed.

Another important parameter of the waveguide modes in the spin-wave waveguides is their ellipticity, which, amongst others, influences the threshold for the parametric instability\cite{LVov,Braecher-2011-1,Schloemann-1960-1,Kostylev-1995-1} and which is given by\cite{Melkov-1996-1}
\begin{widetext}
\begin{align}
\begin{split}
\label{Eq:Ell}
\epsilon &= 1-\frac{|m_z|^2}{|m_x|^2} =\frac{\omega_\mathrm{M} |g(\mathbf{k})\mathrm{sin}(\theta_k)^2-(1-g(\mathbf{k}))|}{\omega_0+\omega_\mathrm{M}\lambda_\mathrm{ex}\mathbf{k}^2+\frac{\omega_\mathrm{M}}{2}(g(\mathbf{k})\mathrm{sin}(\theta_k)+1-g(\mathbf{k}))+\frac{\omega_\mathrm{M}}{2}|g(\mathbf{k})\mathrm{sin}(\theta_k)^2-(1-g(\mathbf{k}))|},
\end{split}
\end{align}
\end{widetext}
with the components $m_x$ and $m_z$ of the dynamic magnetization. Implicitly, the ellipticity becomes different for waves running in the two directions along the waveguide due to the fact that, for a fixed frequency $f$, $k_{||,+} \neq k_{||,-}$.

In addition to the spin-wave frequency and propagation characteristics, we analyze the spin-wave excitation in the presence of iDMI. For this, we follow the approach presented in Refs. \cite{Mockelantenne,Pirro-2011-1} and incorporate the iDMI-dependent changes of the spin-wave dispersion into the calculations. We aim at a description of the excitation efficiency, a relative measure of how efficiently the antenna can exert a net torque on the static magnetization at a given frequency and wave-vector combination. This efficiency is linked to the magnetic susceptibility and the spatial extent of the excitation source\cite{Kostyant}. We assume an excitation source which is homogeneous across the width of the approximately homogeneously magnetized waveguide. Consequently, the excitation efficiency, for an odd waveguide mode $n$ at a given frequency is given by
\begin{widetext}
\begin{align}
\label{Eq:Exeff}
\begin{split}
\eta_\pm(k_{||,\pm}) &= \left|\frac{1}{n} |b_k| \left(\frac{f(k_{||,\pm})}{\gamma}\mp\frac{1}{\mu_0 M_\mathrm{s}}\left(\mu_0 H_\mathrm{eff}^2-\frac{f(k_{||,\pm})^2}{\gamma^2}\right)\right)\right|,
\end{split}
\end{align}
\end{widetext}
and it vanishes for even modes, since they don't exhibit a net magnetic moment integrated across the width of the waveguide. Here, $|b_k|$ represents the wave-vector spectrum of the effective field created by the excitation source, which is assumed to be the Oersted field created by the current flowing through the CPW\cite{Chumakov}. It is obtained via the Fourier transformation of the spatial distribution of the Oersted field $b_\mathrm{CPW}$(see Appendix for further details). The factor $1/n$ results from the decreasing total magnetic moment of the (uneven) waveguide modes. Due to the iDMI-induced wave-vector dependent frequency splitting, the excitation for waves running to the left and waves running to the right features a different periodicity in the spin-wave frequency $f$. This is the basic concept of the uni-directional spin-wave emission discussed in this article, which is schematically illustrated in Fig.~\ref{Fig1}~(b).

With all these ingredients, we are able to present the main equation of this work: The expected spin-wave amplitude, proportional to the dynamic component $m_x$, at a given distance $x$ from the excitation source located at $x_0$:
\begin{align}
\label{Eq:Examp}
m_x(f_\pm)  \propto\sum_n^{n_\mathrm{max}} \eta_\pm(f_\pm,n) \mathrm{exp}\left({\frac{x-x_0}{\delta_\pm(f_\pm,n)}}\right).
\end{align}
Here, the sum is over the various waveguide modes $n$ contributing to the overall amplitude. In the case of an elliptic magnetization trajectory, the out-of-plane component $m_z$ is related to $m_x$ via Eq. \ref{Eq:Ell} and a phase shift of $\pi/2$. The emitted intensity is given by the square of the total amplitude $|m_x|^2=|m_z|^2/(1-\epsilon)$. This equation constitutes the main result of the analytical model in this work, since it allows to predict the relative spin-wave amplitude within the waveguide, including the iDMI-dependent changes of the spin-wave excitation and propagation characteristics. To evaluate the intensity measured by a detector, such as an additional antenna, the intensity has to be multiplied with the detection function of the detector. For a microstrip detector, this is again given by the square of the Fourier transform of its field distribution and another factor $n^{-2}$ accounting for the reduced effective moment of the waveguide modes. Hence, for a homogeneous detector sensitive to the spin-wave intensity, the influence of higher waveguide modes falls off with $n^{-4}$. Thus, in practice, most characteristics are determined by the fundamental waveguide mode $n = 1$.

It should be noted that the presented analytical theory does not account for the presence of edge modes in the waveguides and does not account for a potential dipolar interaction between the waveguide modes, such as avoided crossings\cite{Kalinikos-1986-Disp}. For a precise description of all peculiarities of the spin-wave propagation in a waveguide, these effects should be taken into account. However, they involve a more elaborate derivation of the spin-wave dispersion\cite{Kostylev,Grigoryeva,Micromag} which can generally not be performed analytically anymore. The presented theory has proven to be a very versatile tool for the description of most phenomena observed in spin-wave waveguides in the absence of iDMI unless $k_{||} \rightarrow 0$. As we will show in the following, also in the presence of iDMI, in a wide wave-vector range, the derived analytical theory is in good agreement with the numerical simulations, which take the interaction between the modes as well as the inhomogeneous magnetization distribution into account.

\section{Numerical simulations}
\label{Num}

We compare the aforementioned analytical calculations to micromagnetic simulations using MuMax3\cite{MuMax-2014-1}. The iDMI is implemented in this micromagnetic package by an effective field\cite{MuMax-2014-1,Bogdanov-2001}
\begin{align}
\label{Eq:BDMI}
\mathbf{B}_\mathrm{DMI} = \frac{2D_\mathrm{int}}{M_\mathrm{s}} \left(\frac{\partial m_z}{\partial x}, \frac{\partial m_z}{\partial y}, -\frac{\partial m_x}{\partial x}-\frac{\partial m_y}{\partial y}\right),
\end{align}
with the application of boundary conditions based on Ref. \cite{Rohart-PRB-2013}.

The simulated geometry, which is also used in the analytical calculations, consists of a transversely magnetized waveguide made from Ni$_{81}$Fe$_{19}$(Py)/Pt. We assume a geometrical width of the waveguide of $w = 600\,\mathrm{nm}$ and a Py thickness of $d = 2.5\,\mathrm{nm}$. The Pt is implemented by the creation of an iDMI with the strength $D_\mathrm{int} = 0.175\,\mathrm{mJ}\,\mathrm{m}^{-2}$. This value is in line with recent experimental findings in Py/Pt layer systems of comparable thickness\cite{Nembach-2015,Stashkevich-2015}. Moreover, we account for the spin-pumping induced enhancement of the damping parameter in Py/Pt, which we assume to result in $\alpha = 0.02$. For the simulations, a $30\,\mu\mathrm{m}$ long waveguide is discretized in $8192\times128$ cells in the $x$-$y$-plane (i.e., cell size of about $3.7\times4.7\,\mathrm{nm}^2$). One cell of $2.5\,\mathrm{nm}$ is assumed along the $z$-direction, representing the uniform magnetization across the layer thickness. Reference simulations have been performed in an identical waveguide without iDMI. In all calculations and simulations presented here, a magnetic field of $\mu_0 H_\mathrm{ext} = 25\,\mathrm{mT}$ applied in the $+y$-direction has been assumed. A change of the field-direction interchanges the asymmetry in the antenna excitation as well as the influence of the iDMI with respect to $\pm k_\mathrm{||}$.

Two different types of simulations of the magnetization dynamics in the waveguide have been performed. In the first type, the magnetization is excited by a short Gaussian pulse (width $\Delta t = 20\,\mathrm{ps}$), which is applied locally in a rectangle with dimension $10\times600\,\mathrm{nm}^2$ in the center of the waveguide. This short and highly localized pulse gives access to a wide wave-vector and frequency excitation-span, which is used to determine the spin-wave dispersion and the related parameters in the waveguide. The space-resolved temporal evolution of the magnetization dynamics is simulated for a total of $20\,\mathrm{ns}$, the pulse being applied centered around $1\,\mathrm{ns}$ of simulation time. Snapshots of the space-resolved magnetization in the waveguide are stored every $20\,\mathrm{ps}$. Since, as mentioned above, the excitation and detection of higher modes in practical geometries falls off with $n^{-2}/n^{-4}$ (amplitudes/intensities) and because the higher waveguide modes feature smaller group velocities, we focus our attention on the fundamental waveguide mode $n = 1$, which is the most interesting mode for practical applications due to these facts. To do so, we integrate the obtained $x$-$y$-maps of the dynamic magnetization components across the $y$-direction, thus, reducing the influence of higher modes $n > 1$ to the recorded dynamics significantly. Subsequently, we perform fast Fourier transformations (FFT) of the data in time and space to obtain the magnetization dynamics in the frequency-space- and frequency-wave-vector domain.

From the frequency-wave-vector domain, the spin-wave dispersion relation $f_\pm(k_{||,\pm})$ of the fundamental mode is determined by extracting the frequency  with maximum Fourier amplitude at a given wave-vector $k_{||,\pm}$ in the two propagation directions. The spin-wave group velocity is computed from the derivative of the dispersion relation. The ellipticity is evaluated by determining the Fourier amplitude at a given frequency for the dynamical $m_z$ and $m_x$ components and by evaluating Eq. \ref{Eq:Ell} for both propagation directions. The spin-wave decay length is analyzed in the frequency-space domain by fitting an exponential decay function to the spatial intensity distribution for a given frequency and directly extracting the decay lengths $\delta_\pm$.

In a second set of simulations, we mimic the spin-wave excitation by means of a short-circuited coplanar waveguide (CPW), which is schematically depicted in Fig. \ref{Fig1}. The simulated CPW features a width and a thickness of the conducting wires of $50\,\mathrm{nm}$ each, which are spaced by $300\,\mathrm{nm}$. The Oersted field components $h_x$ and $h_z$ created by the CPW are calculated at the bottom of the CPW (i.e., in direct contact with the Py/Pt) from the (static) Ampere's law, assuming that the outer strips (ground lines) are out of phase with the central wire (signal line) (see Appendix for further detail). The same field distribution is used to calculate the Fourier spectrum $b_k$ and the direction-dependent excitation spectrum according to Eq. \ref{Eq:Exeff}. In the simulation, the magnetization is excited by $10\,\mathrm{ns}$ long pulses with carrier frequencies ranging from $4\,\mathrm{GHz}$ to $20\,\mathrm{GHz}$ in steps of $250\,\mathrm{MHz}$. The pulses are modeled by
\begin{align}
\label{Eq:Pulse}
\begin{split}
\tilde{h}_{x,z} &= 0.5h_{x,z}(x)(\mathrm{tanh}(2f_\mathrm{rise}(t-t_0))\\
&\cdot \mathrm{tanh}(2f_\mathrm{rise}(t_0+\Delta t-t))+1)\cdot\mathrm{sin}(2\pi ft)
\end{split}
\end{align}
with a rising frequency of $f_\mathrm{rise} = 5\,\mathrm{GHz}$, a duration $\Delta t = 10\,\mathrm{ns}$ and $t_0 = 1\,\mathrm{ns}$. The spin-wave dynamics are saved every $20\,\mathrm{ps}$ spatially averaged over regions of $10\times600\,\mathrm{nm}^2$ situated in distances of $\pm j \cdot 250\mathrm{nm}$ from the antenna with $j$ being an integer. The data are analyzed by analyzing the maximum amplitude in the time domain as well as the integrated amplitude of the FFT for each of this regions in space. In this analysis, the first and last nanosecond of the pulse are omitted to eliminate artifacts originating from the rising and falling edges of the pulse. The detector-regions with a length of $10\,\mathrm{nm}$ in the $x$-direction do not falsify the recorded wave-vector spectrum notably since their size is much smaller than the smallest excited wavelength in the presented simulations. Nevertheless, the averaging over the width of the wire in the detector regions leads again to a suppression of the influence of the higher waveguide modes by an additional factor of $n^{-1}$ in amplitude due to the decreased detection efficiency.

\section{Comparison of numerical and analytical results}
\label{Res}

\begin{figure}[t]
	  \begin{center}
    \scalebox{1}{\includegraphics[width=0.5\linewidth, clip]{Fig2.pdf}}
    \end{center}
	  \caption{\label{Fig2}(Color online)Effective field $\mu_0H_\mathrm{ext}$ in the $y$-direction as a function of the position across the $600\,\mathrm{nm}$ wide waveguide according to Eq. \ref{Eq:Beff} (red line) and according to the micromagnetic simulations (black and dashed green lines).  The horizontal magenta line represents the average effective field $\mu_0H_\mathrm{eff} = 21.5\,\mathrm{mT}$ in the central region of the waveguide, which is enclosed by the effective width of the waveguide.}
\end{figure}
In the following Section, we compare the analytically calculated spin-wave properties with the results from our numerical simulations. For the simulations as well as the calculations we use the following material parameters for the Py: Saturation magnetization $M_\mathrm{s} = 800\,\mathrm{kA}\,\mathrm{m}^{-1}$, exchange constant $A_\mathrm{ex} = 13\,\mathrm{pJ}\,\mathrm{m}$ and, as mentioned above, a Gilbert damping parameter $\alpha = 0.02$ as well as an effective iDMI constant of $D_\mathrm{int} = 0.175\,\mathrm{mJ}\,\mathrm{m}^{-2}$. We start by comparing the effective field as a function of the position across the waveguide derived from Eq. \ref{Eq:Beff} with the result of the numerical simulations. The respective effective fields in the $y$-direction are shown in Fig.~\ref{Fig2}. As can be seen from the figure, the field distributions are qualitatively fairly similar. Towards the edges, the profile obtained from the micromagnetic simulations shows a smoother reduction of the effective field which extends slightly further into the center of the waveguide. This is due to the fact that the micromagnetic simulations take into account that the magnetization is changing its orientation at the edges to minimize the dipolar stray fields, an effect which is not taken into account in Eq. \ref{Eq:Beff}. Nevertheless, the two approaches lead to quantitatively the same result in the central region of the waveguide, justifying the use of the analytical formalism to derive the effective magnetic field $\mu_0 H_\mathrm{eff} = \mu_0 H_\mathrm{ext} - \mu_0 H_\mathrm{demag}$ in the waveguide. As mentioned above, the values of the effective field and the effective width of the waveguide used in the analytical model are associated with the waveguide region where the effective field measures $85\,\%$ of its maximum value in the center. The borders of this region give the effective width, which is $w_\mathrm{eff} \approx 450\,\mathrm{nm}$ in the present case. The effective field value of $\mu_0 H_\mathrm{eff} = 21.5\,\mathrm{mT}$ is obtained by the spatial average of the effective field over this central region. Please note that, in agreement with the calculations in Ref.~\cite{Sanchez-2014}, the assumed weak iDMI does not impose significant changes on the magnetization distribution within the waveguide, which reflects in the fact that the effective fields within the waveguide with and without iDMI are basically the same (cf. black solid and green dashed curves in Fig.~\ref{Fig2}).

\begin{figure}[t!]
	  \begin{center}
    \scalebox{1}{\includegraphics[width=0.9\linewidth, clip]{Fig3.pdf}}
    \end{center}
	  \caption{\label{Fig3}(Color online) a) Spin-wave dispersion relations for the two emission directions with iDMI and in the absence of iDMI. Solid lines are the result of the analytical calculations (abbreviation 'A'), dashed lines are simulated values (abbreviation 'S'). The index '$\pm$' refers to calculations/simulations with iDMI for waves propagating in the $\pm x$-direction and '0' to its absence. The inset shows the discrepancy at small wave-vectors which mainly stems from a underestimation of the frequency origin by about $60\,\mathrm{MHz}$ in the analytical calculations. b) Corresponding group velocities.}
\end{figure}
The basic parameters for the analytical calculations being determined this way, we now move on to a comparison of the dispersion relation of the fundamental mode as well as its group velocity. The analytically and numerically derived dispersion relations are shown in Fig.~\ref{Fig3}~(a). As can be seen from the figure, the dispersion relations are in excellent agreement in a wide wave-vector range and only for very small wave vectors, there is a visible deviation. The latter is connected to the approximation of the effective width. This has a notable influence for waves with small wave-vectors $k_{||}$ along the wire ($\theta_k$ close to 0, i.e., $k_{\perp} \gg k_{||}$) and, in particular, for the origin of the spin-wave dispersion relation which is underestimated in the analytical calculations by about $60\,\mathrm{MHz}$ (see inset in Fig.~\ref{Fig3}). In this wave-vector range, the numerical simulations are likely to be closer to reality, since they take the full internal field landscape as well as the non-uniform orientation of the magnetization into account. Nevertheless, for $k_{||} \gtrsim 15\,\mathrm{rad}\,\mu\mathrm{m}^{-1}$ the analytical description is adequate. Due to the small thickness, it also remains adequate for substantially larger $k_{||}$. This is due to the fact that $|\mathbf{k}|\cdot d$ remains significantly smaller than $1$ in the investigated wave-vector range. Consequently, the investigated wave vectors stay far below the limit of the analytical formalism at $|\mathbf{k}|\cdot d\approx 1$\cite{Kalinikos-1986-Disp}. The agreement and discrepancy of the analytically and the numerically computed dispersion relations are reflected in the derived group velocities shown in Fig.~\ref{Fig3}~(b): For small $k_{||}$ there is a small deviation of the analytically calculated group velocities, which vanishes for $k_{||} \gtrsim 15\,\mathrm{rad}\,\mu\mathrm{m}^{-1}$.

Next we address the ellipticity and the spatial decay of the fundamental waveguide mode. In Fig.~\ref{Fig4}~(a), we compare the analytical values of the ellipticity to the numerical values. As can be seen from the figure, the frequency-dependent ellipticity is in almost perfect agreement between the two, indicating that, in this case, the iDMI in the present geometry only results in the wave-vector dependent splitting and does not influence the ellipticity for a given wave vector by itself. The obtained spin-wave amplitude decay lengths are shown in Fig.~\ref{Fig4}~(b). Please note that in the figure, we show both emission directions in the absence of iDMI for completeness, proving that the two emission directions are indeed equal. Once again, we find a small disagreement between the numerical simulations and the analytical calculations for small frequencies. This is mainly caused by the difference in group velocity visible in Fig. \ref{Fig3}~(b). In contrast, for large frequencies, the decay lengths are in very good agreement. This implies that the calculation of the spin-wave lifetime via Eq. \ref{Eq:Taupm} is in good agreement with the spin-wave lifetime obtained in the numerical simulations. Hence, the analytical formalism above is well suited to predict also the spin-wave ellipticity and relaxation frequency, which are important parameters for the spin-wave propagation and the spin-wave amplification by parallel parametric amplification.
\begin{figure}[t!]
	  \begin{center}
    \scalebox{1}{\includegraphics[width=0.9\linewidth, clip]{Fig4.pdf}}
    \end{center}
	  \caption{\label{Fig4}(Color online) a) Ellipticity and b) spin-wave amplitude decay length of the fundamental waveguide mode as a function of frequency. Solid lines are the result of the analytical calculations (abbreviation 'A'), dashed lines are simulated values (abbreviation 'S'). The index '$\pm$' refers to calculations/simulations with iDMI for waves propagating in the $\pm x$-direction and '0' to its absence. The error bars in (b) are given by the uncertainty of the determination of $\delta$ from an exponential fit of the simulated data.}
\end{figure}

\section{Application to the design of uni-directional spin-wave emitters}
\label{Uni}

Ultimately, we want to use the analytical formalism and the numerical simulations to derive the spin-wave excitation by a CPW, highlighting the use of such a wave-vector selective element for the creation of uni-directional spin-wave emission in the presence of iDMI. As mentioned above, the CPW is assumed to have a wire-width of $50\,\mathrm{nm}$ with a center-to-center spacing of $300\,\mathrm{nm}$ between the wires. This leads to a periodic excitation spectrum with minima at $k_{\mathrm{min},l} = l\frac{2 \pi}{s}$ with $l$ being an integer. Due to the frequency-splitting for $k_\mathrm{||,\pm}$, this means that for one emission direction, the minima are situated at different frequencies than for the other direction. This way, an efficient emission in one direction can be achieved while the emission in the other direction is at its minimum. In a two antenna configuration for excitation and detection, this results in a diode-like behavior, where microwave signals can be transmitted in only one direction via spin waves.

The results of the simulated excitation spectra together with the analytical calculated ones are shown in Fig.~\ref{Fig5}. The simulated amplitude has been extracted from the dynamic $m_z$-component at a distance of $4.5\,\mu\mathrm{m}$ from the center of the CPW. The analytical calculations have been performed by evaluating Eq. \ref{Eq:Examp} taking into account the first 9 waveguide modes and with $x - x_0 = 4.5\,\mu\mathrm{m}$ and by accounting for the fact that the ellipticity results in a wave-vector dependent reduction of the $m_z$ component with respect to $m_x$\footnote{For this, the predictions of Eq. \ref{Eq:Examp} are multiplied with ($\sqrt{1-\epsilon} = |m_z|/|m_x|$ to be comparable to $m_z$. We chose a comparison with the dynamic $z$-component for convenience. A comparison with of the simulated $m_x$ component with Eq.~\ref{Eq:Examp} is also in good quantitative agreement.}. Figure \ref{Fig5}~(a) shows the results in the absence of iDMI. As can be seen from the figure, the periodicity of the CPW leads to the expected periodic excitation spectrum. The asymmetry in amplitude between the left and the right emission direction stems from the CPW excitation, namely from the interplay of the excitation by the out-of-plane and the in-plane Oersted field created by the antenna. This is reflected by the $\pm$ term in Eq. \ref{Eq:Exeff}. Nevertheless, in the absence of iDMI (or other effects lifting the frequency degeneracy between $k_{||,+}$ and $k_{||,-})$, the maxima and minima are always at the same wave vectors. The analytical calculations are in good agreement with the numerical simulations. The most pronounced deviation lies in the fact that the minima in the analytic calculations are much sharper than the ones observed in the simulation. This is a consequence of the finite linewidth of the spin waves. While this is not included in the analytic formalism stated above, this is taken into account in the micromagnetic simulation and leads to a broadening of the excitation spectra. Consequently, the minima are not as sharp as predicted analytically.
\begin{figure}[t!]
	  \begin{center}
    \scalebox{1}{\includegraphics[width=0.9\linewidth, clip]{Fig5.pdf}}
    \end{center}
	  \caption{\label{Fig5}(Color online) Spin-wave amplitude spectra at a distance of $4.5\,\mu\mathrm{m}$ from the center of the CPW a) in the absence of iDMI and b) in the presence of iDMI. Solid lines are the result of the analytical calculations (abbreviation 'A'), dashed lines are simulated values (abbreviation 'S'). The index '$\pm$' refers to calculations/simulations for waves propagating in the $\pm x$-direction.}
\end{figure}

In Fig.~\ref{Fig5}~(b), iDMI is included into the calculations/simulations. As expected, this results in a displacement of the minima in one emission direction in frequency with respect to the other, a behavior well visible in the calculated as well as the simulated curve. As a consequence, the minimum of one direction can coincide with a significant emission in the other. This is, for instance, the case around $f \approx 13\,\mathrm{GHz}$, where the emission in the $k_{||,-}$ direction is minimal while the emission in the $k_{||,+}$ direction is maximal. Amplitude ratios exceeding a factor of 10 can easily be achieved, which can be further enhanced by employing a second, identical CPW for detection to obtain the same suppression in the detection efficiency. With this, intensity-asymmetries larger than $10^4$ are easily realized and a very efficient uni-directionality can be achieved. Hereby, the effective emission direction can be interchanged by changing the sign of the externally applied bias field. On the other hand, by changing, for instance, the operation frequency, a basically symmetric emission can be realized, as is the case for $f \approx 7.75\,\mathrm{GHz}$ in Fig.~\ref{Fig5}~(b). By comparing Figs.~\ref{Fig5}~(a) and (b), it is evident that in the presented situation, the iDMI enhances the asymmetry in the amplitude of the emission, independent of the horizontal shift along the frequency axis. Consequently, it leads to an overall enhancement of the unidirectional emission by the CPW in a large wave-vector range. This is due to the fact that the iDMI-induced asymmetry in the propagation characteristics (cf. Fig.~\ref{Fig4}~(b)) and the asymmetric CPW excitation add up. In contrast, if the sign of the iDMI is inverted, for instance by replacing the Py/Pt by a Pt/Py layer, the effects oppose and an overall more symmetric (in terms of maximal amplitude) emission can be achieved\footnote{A rotation of the field changes the efficient direction for both, the excitation asymmetry and the iDMI asymmetry and, hence, simply interchanges the efficient direction. In contrast, if the sign of the iDMI vector changes or the CPW is patterned on the opposite side of the waveguide ($z$-axis), the effects of the nonreciprocity of the antenna excitation and the asymmetric propagation characteristics due to the iDMI are opposing each other. In other words, whether the effects subtract or enhance is determined by the orientation of the iDMI-vector with respect to the placement of the excitation source on top or below the magnetic structure.}. Finally, we would like to remark that, again, the numerical simulation and the analytical calculation are in reasonable agreement, the main differences again originating from the effects of finite linewidth included into the simulations.

\section{Discussion}
\label{Disc}

In this last Section we would like to sum up the results and discuss their significance. As we have demonstrated in the previous Section, the simple analytical formalism presented above is well able to predict most of the features observed in the more realistic micromagnetic simulations. The main discrepancies arise from an imperfect analytical description for very small wave vectors and the influence of finite linewidth. For a real application, the first point does not really impose a major problem, since the miniaturization on the one hand and the wave-vector dependence of the iDMI on the other hand suggest the use of rather large wave vectors. In this wave-vector range, the analytical model is accurate. The effects of finite linewidth hamper the possibility to predict the exact strength of the uni-directionality. However, they do not affect the possibility to optimize the emission characteristics: The parameters of the system (such as thickness of the magnetic material, geometry of the antenna, geometric width of the waveguide, sign and, with some limitations, strength of the iDMI, material parameters of the magnetic material etc.) as well as the parameters of the experiment (applied field and frequency) can be applied to the analytical calculations and the system can be tuned easily to shift the maximum at the desired operation frequency in one emission direction to the minimum of the other.

The presented analytical model allows for such a good prediction of the spin-wave properties because the considered iDMI is rather small. Consequently, its main impacts are the lifting of the frequency-degeneracy and the small changes of the spin-wave lifetime, which can well be described by the first order expansion which is the basis of Eq. \ref{Eq:Taupm}. Any influence of the iDMI on the magnetization configuration in the waveguide or the ellipticity of the magnetization trajectory itself can be neglected in the presented case. It should be noted that other mechanisms which lift the degeneracy of the spin waves in transversely magnetized waveguides, such as the influence of non-uniform surface anisotropy, can easily be implemented into the presented analytical calculations to extend the model to a prediction of their influence as well.

With the used model system of Py/Pt featuring a small iDMI, we have demonstrated that an efficient uni-directional spin-wave emission can be achieved by combining a wave-vector selective excitation with the iDMI-induced non-reciprocity of the spin-wave dispersion. By matching the feature sizes of the excitation source and the material parameters, the uni-directional emission can be tuned to the desired wave-vector range. In particular, it allows for the realization of such emitters even for dipolar-exchange waves and without the need for an involved texture in the spin-wave waveguide. The concept is also applicable to layer systems featuring a frequency non-reciprocity due to a different origin, such as a non-uniform surface anisotropy. We would like to point out that we choose Py/Pt as model system due to its large use in many experiments of spin waves in microstructures. We admit that in a real system of Py/Pt of this thickness, the damping of the waves could even be higher\cite{Ruiz-2015}, depending on the quality and the exact nature of the interface between the materials. Hence, for a real application, this material system is likely not the best choice due to the poor spin-wave propagation characteristics. Other material systems, such as CoFeB/Pt, which are known to exhibit a similar iDMI-strength and a larger spin-wave lifetime\cite{Ruiz-2015,Di-2015-APL, Tacchi-2016, Conca-2014}, and presently unknown or unexplored material combinations of low-damping materials such as the half-metallic Heusler compound CoMnFeSi\cite{Tomseb-2012, Tomseb-2015} with heavy metals could provide more practical systems which allow for a more efficient spin-wave propagation than Py/Pt. Since even with the weak iDMI presented in Py/Pt an efficient uni-directional emission can be achieved, the use of a system with larger iDMI-strength would allow for the use of thicker films, featuring higher group velocities and a lower influence of interfacial damping. The presented analytical formalism can be applied to these systems in a straightforward manner, allowing for the design of the optimum structure for a non-reciprocal, or, if desired, reciprocal spin-wave emission by a periodic excitation source of any kind.

\section{Conclusions}
\label{Conc}

To conclude, we have presented an analytical formalism to predict the spin-wave properties and the spin-wave excitation by periodic excitation sources in micro-structured, transversely magnetized spin-wave waveguides in the presence of iDMI. We have compared the formalism to numerical simulations, demonstrating that the analytical calculations can readily predict the spin-wave system with a high accuracy. This way, the formalism allows for the straightforward design of uni-directional and bi-directional spin-wave emitters on the micro-scale and can be used readily to interpret experiments. We have demonstrated that the iDMI in asymmetric layer systems enables a directed spin-wave emission. This permits a guiding of the excited spin waves in a magnonic network in the desired direction, optimizing the energy flow and avoiding undesired spin-wave beams. The periodic effective field can also be provided by any other excitation source, such as the use of electrical fields for the spin-wave excitation. This allows for a scalable realization of such emitters in any desired wave-vector range compatible with state-of-the art patterning techniques and detection schemes.

\begin{acknowledgements}
Financial support by the spOt project (318144) of the EC under the Seventh Framework Programme, by the DFG (SFB/TRR 173 Spin+X) and by the Nachwuchsring of the TU Kaiserslautern is gratefully acknowledged.
\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


My oldest daughter is no stranger to random acts of kindness. If you don't remember (or haven't read about) her lemonade stand, check it out here.
But she's at it again.
Yesterday she saw something online that prompted her to action. As you can see in the picture, she created one of those flyers that I first saw on the bulletin boards at San Diego State University when I was a student there in the late 80's.
Typically, they were advertisements for used schoolbooks, fitness programs, babysitting, or other goods and services that the students were offering. To respond you would simply rip off one of those little tear-y things and call the number.
But as it turns out, responding to my daughter's flyer is a whole different ballgame.
We then drove around and hung the flyers from light posts and trees and mailboxes in the neighborhood.
We hung them by schools and shopping centers and bus stops.
Her (rather existential) goal was to have people rip off what they felt they needed in their life and, by taking that action, she hoped that it would somehow pour that quality or element into their life on a higher level or greater spiritual plane.
Okay, we didn't officially talk about it. But that's my guess.
But it got me thinking. . .
What if we offered love or kindness or discernment or freedom or wonder or health or adventure to the people in our lives?
What if we could figure out what people needed most and weren't afraid to offer it to them?
What if we were INTENTIONAL about helping people get what they needed WITHOUT them having to rip or tear a single thing?
I'm always proud of my daughters, but I am most proud at moments like this when they instruct me in ways that make me a better person.


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Superb accommodation. Modern fixtures. Cozy kitchen in the room.
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No alcoholic beverages. No bar.


text:
module Riff.SanitizeTest where

import           Riff.Sanitize

prop_removeInvalid1 :: String -> Bool
prop_removeInvalid1 s = length s == length (removeInvalid s)

prop_removeInvalid2 :: String -> Bool
prop_removeInvalid2 s = all (`elem` validChars) (removeInvalid s)

redpajama_set_name: RedPajamaGithub


With our advances in Congress, we need to push harder than ever to actually get action on pro-life legislation like the Life at Conception Act to legislatively overturn Roe v. Wade.
I want to help by joining as a member of the SENTINELS FOR THE VOICELESS.
I do not want any of the special member benefits, I only want to help save the unborn.
I cannot participate in the SENTINELS FOR THE VOICELESS program at this time. However I would like to make a special one time contribution.
Because of NPLA's tax-exempt status under IRC Sec. 501(c)(4) and its state and federal legislative activities, contributions are not tax deductible as charitable contributions (IRC § 170) or as business deductions (IRC § 162(e)(1)). Its web address is http://www.prolifealliance.com.


text:
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Sir Thomas used the motto "Direct from the tea gardens to the teapot" and his business became a booming success in the U.S.
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By 1991, they joined with PepsiCo to market ready-to-drink iced tea in North America.
Today, all Lipton's tea in the U.S. is Rainforest Alliance Certified, ensuring sustainability and supporting smallholder farms. In 2009, Lipton received a Corporate Green Globe Award for their work with the alliance and their own tea estates were among the first to be certified.
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Best tea for migraines: Can tea help a sore head?
Tazo Tea Flavors: Tasty Tazo Teas to Try
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redpajama_set_name: RedPajamaCommonCrawl


text:
O Los Angeles Galaxy, também conhecido como LA Galaxy ou simplesmente de Galaxy, é um clube estadunidense de futebol sediado em Carson, Califórnia. Fundado em 1994, o clube é propriedade da Anschutz Entertainment Group.

O clube é um dos fundadores da Major League Soccer. Seu maior rival é o San José Earthquakes, com quem disputa o California Superclasico. O clube também possui grande rivalidade com o Los Angeles FC, com quem faz o El Trafico. Até 2014 disputava também a Honda SuperClasico contra o Chivas USA.

O Los Angeles Galaxy conquistou a MLS Cup cinco vezes: 2002, 2005, 2011, 2012 e 2014, tornando-se assim o maior campeão da história da MLS até o momento. Em 2005, venceu também a US Open Cup fazendo o chamado Double (dupla, popular "dobradinha" ou 'bi em um ano' no Brasil), que designa a vitória nos dois campeonatos mais importantes do futebol dos Estados Unidos. Venceu também o MLS Supporters' Shield em 1998, 2002, 2010 e 2011. O clube é reconhecido internacionalmente por ter contado com craques como David Beckham, Steven Gerrard, Robbie Keane, Zlatan Ibrahimovic, Landon Donovan e Cobi Jones em seu elenco.

História

Primeiros Anos (1996-2007)

Em 15 de junho de 1994, a Major League Soccer anunciou as sete primeiras franquias da liga. Das 22 cidades que estavam concorrendo, foram escolhidas Boston, Columbus, Los Angeles, Nova Iorque/Nova Jersey, San Jose e Washington, D.C. O time foi nomeado como Galaxy em referência a grande quantidade de estrelas de cinema e celebridades presentes no bairro de Hollywood.

Na temporada inaugural da Major League Soccer, o Galaxy terminou em primeiro da Conferência Oeste, e após eliminar o San Jose Clash e o Kansas City Wizards, o clube foi eliminado para o 	D.C. United na MLS Cup. Em 1999 novamente é derrotado para o D.C. United na MLS Cup, após eliminar o Colorado Rapids e o Dallas Burn nos playoffs.

No ano de 2000, o clube conquista o seu primeiro título internacional do clube, a Copa dos Campeões da CONCACAF de 2000. Após derrotar o Real Club Deportivo España e o D.C. United no mata-mata, o Galaxy derrotou o Club Deportivo Olimpia, de Honduras em Los Angeles, pelo placar de 3 a 2. Foi a primeira e única equipe dos Estados Unidos e da Major League Soccer até agora a conquistar a competição.

Com o título da competição, o Los Angeles Galaxy ganhou o direito de disputar o Mundial de Clubes da FIFA de 2001. Porém, com a falência da ISL, empresa parceira da FIFA, o campeonato foi cancelado e o Galaxy perdeu a oportunidade de ser a primeira equipe norte-americana e da MLS a participar dessa competição.

A temporada de 2002 começou com incertezas sobre a continuidade da MLS. Em crise, a liga havia anunciado a extinção de duas equipes, Miami Fusion FC e Tampa Bay Mutiny. E nesse contexto complicado da liga, o Galaxy consegue conquistar pela segunda vez a Supporters' Shield e pela primeira vez a MLS Cup. Após ficar em primeiro da Conferência Oeste, conquistando assim a MLS Supporters' Shield, e eliminar o Kansas City Wizards e o Colorado Rapids nos playoffs, o clube enfrentou o New England Revolution na decisão, reeditando a final da US Open Cup do ano anterior, na qual o Galaxy saiu vitorioso. No jogo da MLS Cup, o Galaxy venceu o New England Revolution por 1x0 e conquistou o título.

Em 2005 o Galaxy contrata Landon Donovan, atacante que estava no San José Earthquakes. Donovan ficou na equipe entre 2005 e 2014, retornando em 2016 e marcando 141 gols nesse período, se tornando o maior artilheiro da história do clube.

Logo no começo de 2006, o Galaxy foi negativamente surpreendido quando o seu diretor técnico, Doug Hamilton, sofreu um ataque cardíaco aos 43 anos, no avião quando o time viajava para enfrentar o Deportivo Saprissa pela Liga dos Campeões da CONCACAF.

Era David Beckham (2007-2012)

Em 11 de Janeiro de 2007, o Los Angeles Galaxy anunciou a contratação do jogador do Real Madrid David Beckham. Foi a maior contratação de um time da Major League Soccer até então.

Com a assinatura deste contrato e com outros contratos publicitários, David Beckham tornou-se um dos futebolistas mais bem pagos do mundo. O contrato foi de cinco anos e foi acordado um valor de transferência de U$ 250 milhões, salário de U$ 6,5 milhões anuais e o direito de comprar futuramente uma franquia na Major League Soccer, o que se concretizou com a compra da franquia de Miami em 5 de fevereiro de 2014.

A contratação do David Beckham foi tão fora do teto salarial da MLS que a liga teve que criar uma regra de exceção para a contratação ser realizada, a Regra do Jogador Designado, também conhecida como a Regra do Beckham.

Em 14 de maio, o Galaxy também anunciou oficialmente a contratação do defensor português Abel Xavier, que fez sua estréia em 17 de junho na vitória do Galaxy sobre o Real Salt Lake por 3 a 2 com atuação elogiada.

A estreia do Beckham foi no dia 21 de julho em um amistoso contra o Chelsea. Com um público de 35.000 espectadores, maior da história do Home Depot Center até então, o Chelsea venceu por 1x0.

Em 15 de agosto, Beckham marcou seu primeiro gol pelo Galaxy na vitória de 2 a 0 de sua equipe sobre o DC United na disputa da SuperLiga Norte-Americana. Com a vitória, o Los Angeles Galaxy ganhou o direito de decidir, em 29 de agosto, a primeira final da primeira Superliga contra a equipe mexicana Pachuca. Porém perdeu o título na cobrança de penaltis, por 4 a 3, após um empate no tempo normal em 1 a 1.

Em 2008, participou do primeiro Campeonato Pan-Pacífico, em Honolulu, porém foi derrotado pela equipe japonesa do Gamba Osaka e ficou fora da grande final. Mas, ainda assim, obteve o terceiro lugar ao derrotar o Sydney FC.

Na temporada de 2009 surgiu a primeira oportunidade de Beckham conquistar seu primeiro título pelo Galaxy. A equipe se classificou para a MLS Cup, mas foi superado nos pênaltis pela equipe do Real Salt Lake. O primeiro título de Beckham no Los Angeles Galaxy foi a MLS Supporters' Shield, conquistada em 2010 sendo bicampeão em 2011. Nesse mesmo ano conquistou o mais importante título do futebol estadunidense, a MLS Cup.

Em novembro de 2012, Beckham anunciou que deixaria o clube ao final da temporada. Seu último jogo pelo Los Angeles Galaxy foi a MLS Cup de 2012 contra o Houston Dynamo. Com a vitória de 3x1, o Beckham ainda se despediu com o título da competição.

Estádios

Entre 1996 e 2002, o Los Angeles Galaxy jogou seus jogos como mandante no estádio Rose Bowl, em Pasadena. O clube ainda utilizava o Titan Stadium, da Universidade do Estado da Califórnia em Fullerton durante alguns jogos da Lamar Hunt U.S. Open Cup. Inclusive, a final da Lamar Hunt U.S. Open Cup de 2001 foi realizada nesse estádio.

Desde 2003, manda suas partidas no StubHub Center (anteriormente conhecido como Home Depot Center). Com 27.000 lugares, o estádio é localizado dentro da Universidade do Estado da Califórnia, Dominguez Hills. Entre 2005 e 2014, dividiu o estádio com o Club Deportivo Chivas USA.

Desde 2017, o estádio também se tornou a casa provisória do Los Angeles Chargers da NFL.

Entre 2003 e 2013, o naming rights do estádio pertenciam a Home Depot. Desde 2013 pertencem a StubHub.

Rivalidades
O Los Angeles Galaxy tem clássicos contra o Los Angeles FC e o San José Earthquakes. Entre 2005 e 2014 também disputou um clássico contra o Club Deportivo Chivas USA.

El Tráfico

O El Tráfico são os confrontos do Los Angeles Galaxy contra o Los Angeles Football Club. O clássico é realizado desde 2018 e recebeu esse nome por causa do engarrafamento presente em Los Angeles, considerado um dos piores do mundo.

California Clásico

O California Clásico são os confrontos do Los Angeles Galaxy contra o San José Earthquakes. O clássico é realizado desde 1996 e recebeu esse nome por ser considerado por muitos o maior clássico da Califórnia.

SuperClasico

O Honda SuperClasico são os confrontos do Los Angeles Galaxy contra o Club Deportivo Chivas USA. O clássico é realizado desde 1996 e recebeu esse nome em referência ao Súper Clásico mexicano.

Símbolos

Uniformes

Títulos

 Campeão Invicto

Estatísticas

Participações

Elenco atual

Ligações externas

Clubes de futebol fundados em 1994
Clubes campeões da Lamar Hunt U.S. Open Cup
Equipes da MLS

redpajama_set_name: RedPajamaWikipedia


Les Canadiennes are always looking for volunteers! We are 4-time Clarkson Cup Champions and the only Quebec team in the CWHL. We play the highest calibre women's hockey league in the world! The CWHL is a not-for-profit organization, and volunteers help us support our players and grow the game.


The following promotional opportunities are available only to sponsors at the sponsor's cost. Priority will be given based on sponsorship level.
Please contact the Congress Secretariat – Some time slots will be available for commercial sessions.


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As memorials continue for the victims of the January terror attacks, one victim of last year's bloodshed in France has all but been forgotten, a fact made painfully obvious to her family this week.
Last year saw two major terror attacks in Paris - the January atrocities which left 17 dead, and the November carnage where 130 were killed.
While these stories remained at the top of the world news bulletins for weeks, if not months, perhaps few remember the thwarted terror attack in April when a heavily armed gunman was caught, reportedly on the way to carry out shootings in several churches across Paris.
The terrorist killed one person, 32-year-old Aurélie Chatelain, before he was hauled away by police.
The body of the woman, who was a fitness instructor, was found in a car in Villejuif outside of Paris. It is believed she was killed in a botched attempt to steal her car.
The young woman from Caudry, northern France, was a mother to a five-year-old, Juliette. Just hours before her death, she had posted a message on her Facebook page saying how happy she was to be in Paris, where she had come to follow a pilates training course.
And for reasons unknown, Chatelain wasn't among all the other terror victims to be awarded a posthumous Legion of Honour, France's highest honour, in the New Year's ceremony.
On the list, however, were all the victims of the January attacks, as well as the three men who prevented a terror attack on the Thalys train in August.
On Tuesday, Audrie's father went on Europe 1 radio to voice his disappointment that his daughter wasn't among the recipients.
"I am disappointed with the French justice system," Jean-Luc Châtelain, told the station. "And not just because she didn't get the award, but also because it had been asked for by the mayor and many others since April."
The man added that it was "tough to comprehend" that she had been killed by a man with a so-called "fiche S" ("S file"), which includes individuals suspected of links to a terrorist movement or group.
He said he hoped that his daughter's failure to receive the Legion of Honour was an oversight, adding that didn't want to have to end up writing a letter to France's President François Hollande.
"I hope the president will react before it gets to the stage of me writing to him," he said.
The Legion D'Honneur awards are handed out in France on three occasions each year. Over 600 people were decorated with the honour this time around, including several survivors of the January attacks.


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CREB 2022 HOUSING MARKET FORECAST
Posted on Jan 25, 2022 in Market Updates
Calgary housing market expected to remain strong in 2022 after record-breaking 2021 – Housing market activity in 2022 is expected to moderate relative to record levels of activity in 2021, while remaining stronger than historical levels.
"Despite challenges with COVID-19, we are starting to see a turnaround in our job and migration numbers, and while interest rates are expected to rise, they remain relatively low. All these factors are expected to support strong housing demand into 2022," said CREB®Chief Economist Ann-Marie Lurie.
"The biggest question will be whether supply can meet that demand. It will take time for housing to move out of sellers' market conditions, so we do anticipate prices will continue to rise this year."
Rising lending rates are expected to cool some of the demand later this year, but rates are still exceptionally low, supporting strong housing sales, especially from those who experienced increased savings and equity gains throughout the pandemic. Economic improvements are also expected to support both job and population growth, adding new sources of demand for housing.
During the pandemic, supply has been a struggle for many industries, including the housing market. New listings have improved, but it has not been enough to offset high sales levels, keeping inventories relatively low and likely limiting sales growth in the market.
As we move through 2022, new listings in the resale market should remain relatively strong thanks to higher home prices. At the same time, the new-home sector recorded a surge in starts last year, and the completion of those starts should help add to overall supply choice in the market.
Supply levels are expected to improve relative to demand this year. However, conditions are expected to remain relatively tight throughout the spring market, supporting further price gains.
As the market balance gradually improves, upward price pressure in the housing market should ease. Overall, price growth is expected to ease to four per cent in 2022.
"While conditions in the housing market are expected to remain strong, there is a significant amount of uncertainty that could impact housing," said Lurie.
"If supply levels remain low relative to demand, we could see stronger-than-expected price growth. On the other hand, if rates rise much faster and higher than expected, it could cause a more significant pullback in sales."
2022 CREB FORECAST SUMMARY
Housing market sales in 2022 are expected to moderate relative to record levels of activity in 2021, while remaining stronger than historical levels.
Rising lending rates are expected to cool some of the demand later this year, but rates are still exceptionally low, supporting strong housing sales, especially from those who experienced increased savings and equity gains throughout the pandemic. Economic improvements are also expected to support both job and population growth, adding new sources of demand for housing. Overall, all of these factors point toward relatively strong sales in 2022.
Throughout the pandemic, supply has been a struggle for many industries, including the housing market. New listings have improved, but it has not been enough to offset high sales levels, keeping inventories relatively low and likely limiting sales growth in the market. As we move through 2022, new listings in the resale market should remain relatively strong thanks to higher home prices. At the same time, the new-home sector recorded a surge in starts last year. The completion of those starts should help add to the overall supply choice in the market.
Supply levels are expected to improve relative to demand this year. However, conditions are expected to remain relatively tight throughout the spring market, supporting further price gains. As the market balance gradually improves, upward price pressure in the housing market should ease. Overall, annual price growth is expected to slow to four per cent in 2022.
TOP CONSIDERATIONS FOR 2022:
COVID-19 IMPACTS ON ECONOMY AND INFLATION
Supply disruptions caused by COVID-19 are expected to ease in 2022. However, if new variants emerge that delay a full re-opening, this could impact the economic recovery, while prolonging supply challenges and inflationary pressure.
The Bank of Canada is expected to increase interest rates in 2022. While gradual gains are anticipated, rates are expected to remain below pre-pandemic levels – low enough to continue to support housing demand, but not at the pace seen in 2021.
The flow of migration will be an important component of sustaining high levels of demand in housing markets.
HOUSING SUPPLY
New construction and elevated levels of listings in the resale market are expected to help add to the undersupplied housing market. The spring market is expected to remain relatively tight, but if supply levels do not start to improve in the second half of the years, this will have significant implications for home prices.
CALGARY RESALE MARKET ACTIVITY - 2021 REVIEW
Housing market activity in 2021 far exceeded our expectations, as sales in the city surpassed record highs set back in 2006. Both sales and prices were expected to improve, but the annual pace of growth was far stronger than forecasted. Demand was exceptionally strong throughout the spring as expected, but supply levels did not rise enough to meet that demand, causing stronger-than-expected price growth. The pace of sales growth did slow through the latter half of the year, but the growth was still stronger than the gains in new listings, preventing the market from returning to balanced conditions.
The persistent sellers' market conditions in 2021 contributed to an annual price gain of over eight per cent. After significant price declines for the better part of the past five years, the shift toward sellers' market conditions helped support the recovery in home prices. Home prices hit new highs in the detached and semi-detached sectors, but improvements in the row and apartment sectors were not enough to support full price recovery.
WHY WAS DEMAND SO STRONG?
Last year saw some of the lowest mortgage rates on record. Levels did rise from the lows reported earlier in the year, but rates remained far below what was available in the market before the pandemic. This was one of the main drivers of the strong housing demand growth recorded in 2021.
As restrictions prevented many from travelling or spending as much as they typically would on recreational activities, household savings improved across the country. Improved savings among those whose incomes were not impacted by the pandemic, as well as more hybrid work arrangements and our young demographic, led many consumers to purchase homes. Activity showed signs of slowing down moving into the fourth quarter. However, that abruptly changed as concerns over inflation and future rate increases supported another surge in demand from buyers looking to get into the market before any rate changes took effect.
Rising prices and longer construction timelines in the new-home sector caused many buyers to consider their options in the resale market, which saw a larger increase in activity relative to the new-home market in 2021.
HOUSING IN 2022
Rising lending rates and higher home prices are expected to slow demand growth in 2022, bringing sales down from 2021's record levels. However, overall, levels are expected to remain much higher than long-term trends, reflecting a strong demand environment. As we move through the economic recovery and job prospects improve, demand for resale housing will remain relatively strong.
The challenge in 2022 is expected to be related to supply. Starts activity did improve last year, which should help
with overall housing supply in 2022, but resale supply may struggle to remain at adequate levels to support balanced conditions throughout the earlier part of the year.
Higher prices should prevent a significant slide in new listings growth this spring, ensuring conditions are not as tight as in 2021. However, the return of more balanced conditions is not expected until the latter part of 2022. The slow return to balanced conditions is expected to continue to support price gains this year, albeit at a slower pace than in 2021. Overall, citywide annual prices are forecasted to increase by over four per cent.
HOUSING MARKET - DETACHED
The combination of consumers' desire for more space and easing lending rates helped detached home sales in 2021 improve by over 71 per cent compared to the previous year. The total of 17,038 sales was just shy of the record set in 2005. The strongest demand started in the lower price ranges, but supply eased, creating exceptionally tight conditions in the lower end of the market that impacted prices. The price gains in the lower end also provided more opportunity for move-up buyers looking to take advantage of those gains, as conditions were not as tight in the upper price ranges. However, by the end of the year, supply/demand balances tightened across every price range, with less than two months of supply for all detached homes priced under $700,000.
Persistent sellers' market conditions resulted in benchmark home prices rising by nearly 10 per cent in 2021, the highest increase among all property types. This reflected a full recovery and new record-high price for detached homes. Price gains did vary significantly from district to district, ranging from nearly 12 per cent in the South East to a low of six per cent in the City Centre. The City Centre was the only district where prices did not recover to previous highs.
As we move into 2022, we will be starting the year from a place of exceptionally low levels of supply relative to demand. From August 2021 onward, the sales-to-new-listings ratio remained around 80 per cent for the rest of the year, accelerating the decline in inventory levels and pushing the months of supply down to just over one month, something that has not happened in over a decade. The strong sales growth in 2021 far outpaced any gains in new listings, leaving inventory levels over 20 per cent lower than long-term trends.
Rising rates and higher prices should slow demand from the record levels seen in 2021, but demand is expected to remain relatively strong in 2022. At the same time, supply is still expected to struggle to keep pace, especially during the first half of the year. Supply options in the new-home market and higher prices should keep new listings above long-term averages, but it will take some time before the detached sector returns to more balanced conditions. With tight market conditions likely to persist during the early part of the year, detached home prices are expected to continue recording strong price gains, increasing by over five per cent in 2022.
HOUSING MARKET - SEMI-DETACHED
Demand for semi-detached homes remained exceptionally strong in 2021, reaching record levels and leading to sales nearly 50 per cent higher than long-term averages. New listings increased, but it was not enough to offset the sales growth. On average, inventories declined by nearly 20 per cent in 2021 and were nearly 16 per cent lower than long-term trends.
The end result was persistent sellers' market conditions in the semi-detached sector, resulting in an annual benchmark price gain of eight per cent in 2021. Price gains occurred in every district. Overall, prices recovered to previous highs, but prices in the City Centre, North East and South fell short of previous highs for those districts.
In 2022, sales activity is expected to slow but remain well above long-term trends. Like the detached sector, the semi-detached sector will take time to return to more balanced conditions, supporting further price gains in 2022 – albeit at a slower pace.
HOUSING MARKET - ROW
Row sales activity reached record levels in 2021, with 3,936 sales. Thanks to significant improvements in new listings earlier in the year, inventory levels improved throughout the busier spring months and conditions did not get as tight as what was seen in the detached or semi-detached sectors.
By the end of the year, persistent sales growth started to cause inventories to ease and market conditions to tighten to some of the lowest levels seen since 2014. As it did take longer for the market to shift into sellers' conditions, price 800 gains were not as strong for row homes as they 600 were for some home types. On an annual basis, row 400 benchmark prices improved by six per cent. While the 200 recent gains helped erase some of those losses, prices remain nearly nine per cent lower than previous highs.
Unlike detached and semi-detached homes, row home inventory levels remained higher than long-term averages in 2021. As demand slows, this segment of the market will move into balanced conditions sooner, as supply challenges were not as prevalent for this property type. These balanced conditions will slow the pace of price growth in 2022.
HOUSING MARKET - APARTMENT
Prior to the pandemic, the apartment condominium sector was struggling with excess supply and consecutive annual price declines from 2015 to 2020. In 2021, we saw demand improve enough to help shift the market toward balanced conditions and those conditions supported price growth of just over two per cent. The reversal in price trends is welcome news to condo sellers, but this segment never saw conditions shift to favour the seller and prices remain over 14 per cent lower than previous highs.
In 2021, average inventory levels for apartment condominiums were still higher than levels seen in 2020 and well above long-term trends. Unlike other property types, where both demand growth and supply restrictions drove the sellers' market conditions, balanced conditions in the apartment sector were driven by the growth in demand.
In 2022, rate gains and further price increase are expected to keep demand in this sector relatively strong, as more people seek out affordable product. However, given that supply levels are not an issue, we do not expect to see any further tightening in this market. Persistent balanced conditions should continue to support modest price growth for apartment condominiums in 2022.
Source: Creb 2022 Forecast


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The constitution and other laws and policies protect religious freedom and, in practice, the government generally enforced these protections.
The country has an area of 109,483 square miles and a population of 14.8 million. The Roman Catholic Church estimates 85 percent of the population identifies itself as Catholic, with 15 percent of the population actively practicing. Some groups, particularly indigenous persons who live in the highlands, follow a syncretic form of Catholicism that combines indigenous beliefs with orthodox Catholic doctrine. In the Amazon jungle region, Catholic practices often are combined with elements of shamanism.
Estimates of the number of non-Catholic Christians start at one million. Southern Baptists, The Church of Jesus Christ of Latter-day Saints (Mormons), Jehovah's Witnesses, and Pentecostals find converts among persons who practice syncretic religions, particularly among indigenous people in the highland provinces of Chimborazo, Bolivar, Cotopaxi, Imbabura, and Pichincha, and in other groups marginalized by society. Evangelical groups include the Assemblies of God, in urban areas, and the Church of the Word of God, which is growing rapidly in indigenous areas. Rural indigenous areas tend to be either overwhelmingly Catholic or overwhelmingly Protestant. Protestant organizations were usually divided between predominantly indigenous organizations, such as the Council of Evangelical Indigenous People and Organizations, and mestizo organizations. Many mestizos in the Guayaquil area are Protestant. In large cities, Protestant megachurches with more than 10,000 members continued to experience substantial growth. Hundreds of evangelical churches exist, many of which are not affiliated with a particular denomination. Some multidenominational Christian groups, such as the Gospel Missionary Union, now called Avant Ministries, the Christian and Missionary Alliance, and Hoy Cristo Jesús Bendice (Today Jesus Christ Blesses), have been active for decades.
Many registered religious groups, including Anglicans, Bahais, Buddhists, Episcopalians, Jews, Lutherans, Muslims, Eastern Orthodox believers, Presbyterians, Unification Church members, and followers of Inti (the traditional Inca sun god) have few members.
The constitution took effect in 2008. It includes provisions for freedom of religion, as did the prior constitution. The constitution grants all citizens and foreigners the right to practice publicly and freely the religion of their choice and prohibits discrimination based on religion.
The 1937 Law of Worship requires religious groups to register with the Ministry of Interior. To register, a religious organization must possess a charter; have nonprofit status; include in its application all names used by the group to ensure that names of previously registered groups are not used without their permission; and provide signatures of at least 15 members, typically leaders of the organization. In addition, Presidential Decree 982 from 2008 requires all nongovernmental organizations, including churches and other religious groups, to register with the government. All nonprofit organizations, including more than 2,200 registered religious groups, are required to report on the expenditure of any government funding received.
In 1937 the government entered into an official legal agreement with the Holy See called the Modus Vivendi, which grants the Catholic Church privileges such as official passports for clergy and state funding of churches and schools.
The government does not generally permit religious instruction in public schools. Private schools may provide religious instruction, as may parents in the home.
The government observes the following religious holidays as national holidays: Carnival, Good Friday, All Souls' Day, and Christmas.
There were no reports of abuses, including religious prisoners or detainees, in the country.
Muslim leaders reported that members of their community occasionally experienced discrimination when applying for work or housing, or among children at school, but that these acts stemmed more from ignorance than discrimination. The Muslim community combats this prejudice with informational pamphlets explaining their practices and traditions.
The U.S. government discusses religious freedom with the government as part of its overall policy to promote human rights. U.S. embassy officials discussed religious freedom with local and visiting leaders representing a broad spectrum of religious groups.


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Most Americans don't know how much to sock away for the future. Here are some guidelines that will help.
We're told time and time again about the importance of saving for retirement, especially since Social Security alone won't be enough to pay the bills. The problem, though, is nailing down just how much money to accumulate. After all, there's no magic number that guarantees financial security in retirement, and while it stands to reason that you're better off saving $3 million than $300,000, there's clearly a pretty sizable gap in between.
In fact, 60% of Americans say they really have no idea how much to save for retirement, according to data from TD Ameritrade. If you're one of them, here are some general guidelines to follow.
Many people assume that their expenses will magically shrink in retirement, but that generally doesn't end up being the case. When you consider the various things you spend money on at present, there's no reason to think you'll pay less for them 5, 10, or 20 years in the future. (Quite the contrary -- they'll most likely cost more thanks to inflation.) That's why, as a general rule, it's a good idea to plan on needing about 80% of your former income to pay the bills without stress in retirement. This means that if you're earning $60,000 at the end of your career, you'll want about $48,000 a year once you stop working.
Of course, not all of that has to come from savings. Social Security, for example, pays the average beneficiary around $17,000 annually at present, so if you're eligible for something in that ballpark, you're looking at a $31,000 gap to fill each year.
Americans are living longer these days, and while that's a good thing in theory, it also means workers need to ramp up their savings to ensure that they last long enough. While the average U.S. retirement currently lasts 18 years, if your health is strong and you retire in your 60s, there's no saying you won't be looking at a 25- to 30-year retirement at the least. And planning for that eventuality is a smarter bet than selling your own life expectancy short.
So far, we've discussed the fact that your expenses probably won't drop much in retirement and that you could end up living longer than anticipated. So where does that leave you from a savings perspective? It's simple: You should aim to start socking away money at an early age, and allocate as much of your paycheck to your nest egg as you can afford to part with.
If you start saving in your 20s, you can probably get away with consistently setting aside 10% of your earnings. That's really the minimum, though, and if you start a bit later in life, you'll want to aim to set aside 15% to 20% of your income.
So what do these figures mean? As a general rule, you can plan on withdrawing about 4% of your nest egg's value each year in retirement without having to worry about running out of money over a 30-year period. Therefore, if you were to retire with $1.2 million, that would translate into $48,000 a year in income, which would make for a very comfortable retirement based on our example. If you were to wind up with $829,000, you'd have $33,000 a year in income, which also nicely fills the gap in our aforementioned example.
Watch what happens, however, as we work our way down that table. An ending balance of $567,000 looks impressive, but it translates into just $22,700 a year. And if you wind up with $379,000 or $246,000, you'll get just $15,000 or $9,800 a year to work with, respectively.
Therefore, as you accumulate wealth in your nest egg, run that 4% calculation to see how much yearly income it'll actually buy you. This will help you determine whether you're on track for retirement or need to start saving more.
Pinpointing your exact retirement savings target is easier said than done. But if you follow the above guidelines, you'll put yourself in a better position to save appropriately and retire comfortably.