Figure 2
(Color online) (a)–(e) Diffraction data represented as a sum over rocking curves at 5 K and various fields from 2–11 T applied parallel to the crystal
axis. The orientation of the twinned crystal
and
axes for all these data are shown in (f). In (a) and (b), the sum is over rocking curves in both
and
. The rocks at higher field were carried out with
, thus rocking directly through the weak peaks seen in the corners of the diffraction pattern. These and the weak peaks in the wings of the vertical and horizontal strong peaks are made clearer by the use of a logarithmic intensity scale. The intensity near the horizontal and vertical directions is visible by virtue of the relaxed resolution of our SANS setup and the form of the SANS resolution function (Refs.
46,
47); for instance, during a rock through the “top-right” region, the resolution will also encompass the peaks at the top and at the right of the diffraction pattern. Backgrounds taken at
have been subtracted. These data result from four VL domains (two in each crystal domain, each pinned to a different twin-plane orientation). In (f) we illustrate how the VL patterns, seen most clearly in (a) and (b), are formed from the two orientations of crystal anisotropy and two orientations of twin planes present in our sample. The reciprocal-lattice vectors for each VL domain lie on an ellipse which has axial ratio given by the mass anisotropy
(Refs.
45,
48,
49) in the low-field region. The orientation of one of the vectors is known, since one of the VL planes is pinned to a set of twin planes. The magnitude of this reciprocal-lattice vector and the magnitude and direction of the others are then fixed by the shape of the ellipse and flux quantization. Defined in (f) are two angles,
and
, which characterize the configuration of the VL and its diffraction pattern. Due to the two dimensionality of the VL, the shape and distortion of the real-space VL is exactly the same as that of the reciprocal lattice, but rotated by
about the direction of the field; hence the patterns for each domain may also be viewed as real-space pictures of the vortex arrangement—after addition of a spot at the center of the pattern, corresponding to the position of the masked incident beam.
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