Dipolar anisotropy in quasi-2D honeycomb antiferromagnet MnPS 3

The nature of the anisotropy in magnetic systems which show isotropic Heisenberg exchange is crucial in determining their magnetic properties. This is particularly true in low-dimensional systems in which the very existence of long-range order depends on the anisotropy. The honeycomb lattice MnPS3 system has been studied as an example of a magnetically quasi-two-dimensional system of unusual symmetry. In this paper the effect of the dipole-dipole interaction in MnPS3 on the magnetic ordering is explored through modelling. It is found that the dipolar anisotropy can explain the spin directions both in zero field and above the spin flop phase transition, but it is important that real rather than idealised atomic coordinates are used; this latter consideration is significant because in performing theoretical calculations, it may sometimes be assumed that small deviations away from the ideal can be ignored, but in truth they determine key aspects of the behaviour

Direct Computation of Shape Cues Using Scale-Adapted Spatial Derivative Operators

This paper addresses the problem of computing cues to the three-dimensional structure of surfaces in the world directly from the local structure of the brightness pattern of either a single monocular image or a binocular image pair. It is shown that starting from Gaussian derivatives of order up to two at a range of scales in scale-space, local estimates of (i) surface orientation from monocular texture foreshortening, (ii) surface orientation from monocular texture gradients, and (iii) surface orientation from the binocular disparity gradient can be computed without iteration or search, and by using essentially the same basic mechanism. The methodology is based on a multi-scale descriptor of image structure called the windowed second moment matrix, which is computed with adaptive selection of both scale levels and spatial positions. Notably, this descriptor comprises two scale parameters; a local scale parameter describing the amount of smoothing used in derivative computations, and a..