In experiments to determine ,
single crystals are
much preferred over polycrystalline samples. This is true for several
reasons. Because
is strongly anisotropic,
the orientation of the sample in the applied field is significant. With
single crystals one has control over this feature. By positioning
the single crystal with its *c*-axis parallel to the applied field, one can
readily proceed to determine the magnetic penetration depth in the *ab*-plane
(or Cu-O plane),
(or
).
In an analogous fashion, suitable orientation of the single crystal in the
applied field in principle
allows measurement of
or
(*i.e.* the magnetic penetration depth perpendicular to the Cu-O planes).
This is much more difficult to perform experimentally, however,
since the crystals grow in such a way
that the -dimensions are much greater than in the -direction.

With polycrystalline samples, the principal axis of each grain is randomly
oriented with respect to the applied field. Consequently one must
average over all possible orientations of the *c*-axis to
simulate the field distribution and then try to extract
a value for the magnetic
penetration depths
and
.
This could be difficult, since different
combinations of values of
and
may give similar line shapes.

Further considerations attached to the use of powdered samples include the dissimilarity in shape of the individual grains. Consequently, each grain has a different demagnetization factor and thus a slightly different average field. This leads to an additional broadening of the field distribution, which if not properly taken into account will lead to an underestimate of the magnetic penetration depth.

In general, the magnetic penetration depth in an anisotropic superconductor
is determined by replacing the effective mass *m*^{*}
of the superconducting electrons by an effective-mass tensor
**m**^{*} [67].
Until very recently, the -anisotropy had been considered negligible, so it has always been
assumed that,
for the uniaxial high-temperature
superconductors, **m**^{*} has a degenerate eigenvalue
*m*_{ab}^{*}(*i.e.*
)
associated with
supercurrents flowing in the *ab*-planes that screen magnetic fields
perpendicular to the planes, and a nondegenerate eigenvalue *m*_{c}^{*}associated with supercurrents flowing along the c-axis, which help
screen magnetic fields parallel to the Cu-O planes [68].
Thus for a uniaxial, anisotropic superconductor:

and

One can define an anisotropic ratio for uniaxial superconductors, such that:

For , [69].

2001-09-28