In order to include the higher order interactions, the number of columns in the input file mcphas.j has to be increased. The additional columns then contain the higher order exchange constants.
Using the module so1ion, the input file mcphas.j may look as given for the
example GdRuSi
in examples/gdru2si2:
# GdRu2Si2 anisotropic bilinear and biquadratic exchange #<!--mcphase.mcphas.j--> #*************************************************************** # Lattice and Exchange Parameter file for # mcphas version 3.0 # - program to calculate static magnetic properties # reference: M. Rotter JMMM 272-276 (2004) 481 # mcdisp version 3.0 # - program to calculate the dispersion of magnetic excitations # reference: M. Rotter et al. J. Appl. Phys. A74 (2002) 5751 #*************************************************************** # # Lattice Constants (A) #! a=4.165 b=4.165 c=9.654 alpha= 90 beta= 90 gamma= 90 #! r1a= 0.5 r2a= 0 r3a= 0 #! r1b= 0.5 r2b= 1 r3b= 0 primitive lattice vectors [a][b][c] #! r1c= 0.5 r2c= 0 r3c= 1 #! nofatoms=1 nofcomponents=8 number of atoms in primitive unit cell/number of components of each spin #****************************************************************************} #! da= 0 [a] db= 0 [b] dc= 0 [c] nofneighbours=38 diagonalexchange=1 gJ= 2 sipffilename=Gd3p.sipf # da[a] db[b] dc[c] J11[meV] J22[meV] J33[meV] J44[meV] J55[meV] J66[meV] J77[meV] Jbc[meV] %%@ J88[meV]} -1.0 0.0 0.0 0.08390 0.08390 0.21890 -0.0024 -0.0096 -0.0008 -0.0096 -0.0024 1.0 0.0 0.0 0.08390 0.08390 0.21890 -0.0024 -0.0096 -0.0008 -0.0096 -0.0024 0.0 -1.0 0.0 0.08390 0.08390 0.21890 -0.0024 -0.0096 -0.0008 -0.0096 -0.0024 0.0 1.0 0.0 0.08390 0.08390 0.21890 -0.0024 -0.0096 -0.0008 -0.0096 -0.0024 -0.5 -0.5 -0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 -0.5 -0.5 0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 -0.5 0.5 -0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 -0.5 0.5 0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 0.5 -0.5 -0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 0.5 -0.5 0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 0.5 0.5 -0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.5 0.00380 0.00380 0.01000 0.0 0.0 0.0 0.0 0.0 -1.0 -1.0 0.0 -0.03630 -0.03630 -0.09445 0.0 0.0 0.0 0.0 0.0 -1.0 1.0 0.0 -0.03630 -0.03630 -0.09445 0.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 -0.03630 -0.03630 -0.09445 0.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0 -0.03630 -0.03630 -0.09445 0.0 0.0 0.0 0.0 0.0 1.5 -0.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -1.5 -0.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 1.5 -0.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 0.5 -1.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 0.5 1.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 0.5 1.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -0.5 1.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -1.5 -0.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 1.5 0.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -1.5 0.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -0.5 -1.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -0.5 -1.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 1.5 0.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -0.5 1.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -1.5 0.5 0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 0.5 -1.5 -0.5 -0.00072 -0.00072 -0.00188 0.0 0.0 0.0 0.0 0.0 -2.0 0.0 0.0 -0.01754 -0.01754 -0.04567 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 -0.01754 -0.01754 -0.04567 0.0 0.0 0.0 0.0 0.0 0.0 -2.0 0.0 -0.01754 -0.01754 -0.04567 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 -0.01754 -0.01754 -0.04567 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.24850 0.24850 0.13560 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.24850 0.24850 0.13560 0.0 0.0 0.0 0.0 0.0here the meaning of the J11, J22, J33, J44, J55 ...is the exchange constant
By default in module so1ion the operator sequence is
,
,
,
,
,
,
,
,
, ...,
,
,
,
,
,
,
.
according to equation (67) and table 2.
The exchange constants for the
products of these Stevens operators have to be
given according to the following scheme:
11 22 33 12 21 13 31 23 32 (3x3 matrix) 11 22 33 44 12 21 13 31 14 41 23 32 24 42 34 43 (4x4 matrix) 11 22 33 44 55 12 21 13 31 14 41 15 51 23 32 24 42 25 52 34 43 35 53 45 54 (5x5 matrix) etc ...
The other input and output files have the same format as usual, but with the modification, that
there are now components of the 'spins' in mcphas.sps instead of 3 (
,
,
).
The expectation values of the operators
,
,
,
,
, etc. correspond to the
interaction operator sequence of the single ion module, which for so1ion is
by default
,
,
,
,
,
,
,
,
, ...
respectively.
Table 2 contains a list of first and second order Stevens parameters.
For a full list please refer to appendix G.
Note that the
may be completely redefined
by perl parsing the single ion property file - see section 13 for details.
This may be useful to shorten notation, if by symmetry the coupling (67)
may be rewritten in products of linear combinations of operators such as needed
for pseudo spin models of multipolar order [31],
e.g
Stevens Operator | Notation used in module so1ion | cfield |
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