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\title{NMR Line Shape in Anisotropic Superconductors \\
in Inclined Magnetic Fields.}
\author{{\it \ Efremova S.A., Proshin Yu.N., Tsarevskii S.L.} \\
Kazan State University, Kremlevskaya, 18, Kazan 420008, Russia \\
{\em E-mail: Sergey.Tsarevskii@ksu.ru}
}
\date{{\small Received December 5, 1997\\ Revised December 23, 1997\\ Accepted
December 23, 1997}}
\begin{document}
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\markright{{\sc Magnetic Resonance in Solids. Electronic Journal }
{\bf 1}, {\sc 4 (1997)}\hfill}
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\begin{center}
{\bf Abstract}
\end{center}
The nuclear magnetic resonance line shapes within a primitive cell of the
vortex lattice of the type II anisotropic superconductors in inclined
magnetic fields are constructed taking into account a change of the local
magnetic field inhomogeneity and skin - effect near the superconductor
surface. The results of the numerical calculations show that the change of
the direction of an external magnetic field modifies the parameters of the
nuclear magnetic resonance line shapes. The derivative of the power of the
absorption energy with respect to the magnetic field is calculated.
It allows to obtain more detailed information about parameters
of the superconductor such as an anisotropy parameter.
\begin{description}
\item[PACS]: 74.60.-w; 74.60.Ge
\item[Keywords]: high-$T_c$ superconductivity, nuclear magnetic resonance,
vortex lattice
\end{description}
\bigskip
Selected for publication by Programme Committee of youth
scientific school "Actual problems of a magnetic resonance
and its applications: Magnetic resonance
in high $T_c$ materials", Kazan, November 20-22, 1997
\newpage
\section{Introduction.}
The nuclear magnetic resonance ($NMR$) is well known as a
useful tool for the investigation of high-$T_c$ superconductors
properties. To interpretate the $NMR$ line shape the following
three important circumstances are necessary to take into account:
the first, homogeneous width of the line, the second, inhomogenenuity of
a local magnetic field $h({\bf r})$ in a superconductor, the third,
peculiarities of a penetration of a microwave magnetic
field in a superconductor. Because the variable electromagnetic
field penetrates into a superconductor on depth by an order of the
$\lambda $ ( $\lambda $ - the penetration depth of a magnetic
field in a superconductor) \cite{r1} only, it is necessary to
take into account the inhomogenenuity of the magnetic field
$h({\bf r})$ in a narrow area near the
superconductor surface. However, the inhomogenenuity of the magnetic
field in a vortex lattice near the surface of the type II
superconductor considerably differs from the inhomogenenuity
$h({\bf r})$ in a bulk superconductor \cite{r2}. In work
\cite{r3} in the case of the perpendicular orientation of the external
homogeneous magnetic field, the lineshape of the $NMR$ line is constructed
using a real change of the inhomogenenuity of the vortex lattice near
the superconductor surface and was shown that these changes strongly effect
on parameters of the $NMR$ line. Besides, the surface effects
drastically change the conclusions about the of the vortex
lattice and parameters of the superconductor that usually are
taken from the analysis of the $NMR$ lineshape \cite{r4}.
As High temperature superconductors are strongly anisotropic it
is interesting to consider the changes of the $NMR$ linehshapes
parameters in the inclined external magnetic fields to the
surface of the superconductor. In present work the $NMR$
lineshape is considered in view of the surface effects that
depend on angle $\theta $ between normal to a surface of the
superconductor and direction of the external magnetic field. It
is shown that the lineshape essentially is modified for various
$\theta $.
\section{Calculation of a distribution function.}
We consider the anisotropic type II superconductor occupying
the half-space $z<0$ in external magnetic field which is directed
at angle $\theta $ ( $\theta $ - the angle between vector $H$ and
axis $z$) assuming the axis $z$ is parallel to axis $c$ of the
superconductor. If $H_{c1}