The Heisenberg model used in the **JaSS** is written in the form

H = Σ_{i>j}J_{ij}**S**_{i}**S*** _{j}*. (1)

If exchange constants are to be compared with models, where the summation runs twice over each pair of indexes (i.e. Σ_{i>j}J'_{ij}**S**_{i}**S*** _{j}* ), then 2

*J'*=

_{ij}*J*.

_{ij}In order to obtain exchange interaction parameters one can focus on single coupling *J _{mn}* between spins on

*m*and

*n*sites. Following Ref. [1] one can rewrite (1) in the following form:

H = *J _{mn}*

**S**

_{m}**S**

*+*

_{n}**S**

_{m}**K**

*+*

_{m}**S**

_{n}**K**

*+*

_{n}*E*,

_{other}where

**K*** _{m}* = Σ

_{i≠m,n}J_{mi}**S**

_{i}*,*

**K*** _{n}* = Σ

_{i≠m,n}J_{ni}**S**

_{i}*,*

*E _{other}* = Σ

_{i,j≠m,n}J_{ij}**S**

_{i}**S**

_{j}.It should be noted that **K*** _{m}*,

**K**

*and*

_{n}*E*do not depend on the spin directions on sites

_{other}*m*and

*n*. Let’s consider four collinear spin configurations (with the spins along

*z*quantization axis), where ↑

*or ↓*

_{m}*denote spin direction on site*

_{m}*m*:

1) . . . ↑* _{m}* . . . ↑

_{n}2) . . . ↑

*. . . ↓*

_{m}_{n}

3) . . . ↓

*. . . ↑*

_{m}_{n}

4) . . . ↓

*. . . ↓*

_{m}_{n}

In these four spin states, the spin orientations on sites other than *m* and* n* are the same. These four states have the following energy:

*E1 = E _{other} + J_{mn}S^{2} + K_{m}S + K_{n}S,*

*E2 =*

*E*−_{other}

*J*+_{mn}S^{2}

*K*−_{m}S

*K*,_{n}S*E3 =*

*E*−_{other}

*J*−_{mn}S^{2}

*K*+_{m}S

*K*,_{n}S*E4 =*

*E*+_{other}

*J*−_{mn}S^{2}

*K*−_{m}S

*K*._{n}SThen one can obtain the expression for * J_{mn}* as

* J_{mn}* = (E 1 − E 2 − E 3 + E 4)/(4

*S*

^{2}).Computationally, this approach is rather inefficient since the calculation of *N* exchange interactions requires the energies of *4N* spin configurations. But in complex magnets it turns out to be very useful for analysis of multiple, heavily intertwined exchanges.

[1] H. Xiang, E. Kan, S.-H. Wei, M.-H. Whangbo, X. Gong, Phys. Rev. B 84, 224429 (2011).