spinw.intmatrix method

generates interaction matrix

Syntax

[SS, SI, RR] = intmatrix(obj,Name,Value)

Description

[SS, SI, RR] = intmatrix(obj,Name,Value) lists the bonds and generates the corresponding exchange matrices by applying the bond symmetry operators on the stored matrices. Also applies symmetry on the single ion anisotropies and can generate the representation of bonds, anistropies and atomic positions in an arbitrary supercell. The output argument SS contains the different types of exchange interactions separated into different fields, such as SS.DM for the Dzyaloshinskii-Moriya interaction, SS.iso for Heisenberg exchange, SS.all for general exchange etc.

Input Arguments

obj: spinw object.

Name-Value Pair Arguments

'fitmode'

Can be used to speed up calculation, modes:

true No speedup (default).
false For the interactions stored in SS, only the SS.all field is calculated.

'plotmode'

If true, additional rows are added to SS.all, to identify the couplings for plotting. Default is false.

'sortDM'

If true each coupling is sorted for consistent plotting of the DM interaction. Sorting is based on the dR bond vector that points from atom1 to atom2, for details see spinw.coupling. After sorting dR vector components fulfill the following rules in hierarchical order:

dR(x) > 0
dR(y) > 0
dR(z) > 0.

Default is false.

'zeroC'

Whether to output bonds with assigned matrices that have only zero values. Default is false.

'extend'

If true, all bonds in the magnetic supercell will be generated, if false, only the bonds in the crystallographic unit cell is calculated. Default is true.

'conjugate'

Introduce the conjugate of the couplings (by exchanging the interacting atom1 and atom2). Default is false.

Output Arguments

SS

structure with fields iso, ani, dm, gen, bq, dip and all. It describes the bonds between spins. Every field is a matrix, where every column is a coupling between two spins. The first 3 rows contain the unit cell translation vector between the interacting spins, the 4th and 5th rows contain the indices of the two interacting spins in the spinw.matom list. The following rows contains the strength of the interaction. For isotropic exchange it is a single number, for DM interaction it is a column vector [DMx; DMy; DMz], for anisotropic interaction

[Jxx; Jyy;
            Jzz]

and for general interaction

[Jxx; Jxy; Jxz; Jyx; Jyy;
            Jyz; Jzx; Jzy; Jzz]

and for biquadratic exchange it is also a single number. For example:

SS.iso = [dl_a; dl_b; dl_c; matom1; matom2; Jval]

If plotmode is true, two additional rows are added to SS.all, that contains the idx indices of the obj.matrix(:,:,idx) corresponding matrix for each coupling and the idx values of the couplings (stored in spinw.coupling.idx). The dip field contains the dipolar interactions that are not added to the SS.all field.

SI

single ion properties stored in a structure with fields:

aniso Matrix with dimensions of , where the classical energy of the -th spin is expressed as E_aniso = spin(:)*A(:,:,i)*spin(:)'
- g g-tensor, with dimensions of $[3\times 3\times n_{magAtom}]$ . It determines the energy of the magnetic moment in external field: E_field = B(:)*g(:,:,i)*spin(:)'
- field External magnetic field in a row vector with three elements $(B_x, B_y, B_z)$ .

RR

Positions of the atoms in lattice units in a matrix with dimensions of $[3\times n_{magExt}]$ .