Hybrid/combined supercell and incommensurate calculations

[mducle]

SpinW currently allows calculations which mix both a supercell and an incommensurate k-vector. However, it is not clear whether this is valid in all (or even most) cases, and this should be investigated.

(Single-k) incommensurate calculations in SpinW are done using a rotating coordinate frame in which all spins are rotate by the same phase factor (determined by the propagation k-vector) between unit cells. When users specify a supercell using nExt (such that prod(nExt)>1) the phase factor applies between spins in neighbouring supercells, which might not generate the same magnetic structure as the user intended. In addition, the propagation vector specified to SpinW k and the true propagation vector of the magnetic structure of the combined/hybrid supercell plus incommensurate would not be the same. E.g. if nExt=[2 1 1] and k=[0.5 0 0], then the combined structure should have a propagation vector of [0.25 0 0], but SpinW will treat it as a doubling of the supercell rather than a quadrupling of the structural cell. This might invalidate the equations for the -k and +k spin wave branches.

Similarly to #107 which tests consistency between supercell and incommensurate spin wave calculations, a consistency test should be done to check between fully supercell and hybrid calculations.

[RichardWaiteSTFC]

MWE of a hybrid incommensurate modulation in a supercell

cycloid = spinw;
cycloid.genlattice('lat_const',[3 8 10], 'sym',0);
cycloid.addatom('r',[0 0 0],'S',1,'label','Cu1');
cycloid.gencoupling('maxDistance',7);
cycloid.addmatrix('label','J2','value', 1);
cycloid.addcoupling('mat','J2','bond',2);
% modulation of [1/4 0 0] gets transfromed in gemagstr to
% [0.5 0 0] for nExt = [2 1 1]
cycloid.genmagstr('mode', 'helical', ...
                  'S', [1 0; 0 1; 0 0], 'n', [0 0 1], ...
                   'nExt', [2 1 1], 'k', [0.25, 0, 0]);

Note this was used in a unit test to assert warning thrown in spinwave in this instance (dce6838 - part of PR #115) - once this has been validated the warning and test should be removed.