Antisymmetric exchange in triangular trimers

[DominikD]

Hello,

I have a question concerning antisymmetric exchange in triangular trimers with three S=1/2 ions. The Hamiltonian for the antisymmetric exchange should be H=G[(S1xS2)+(S2xS3)+(S3xS1)]. Apparently Easyspin calculates the matrix elements and energy levels with the last term (S3xS1) replaced by (S1xS3). I checked this by calculation of the matrix elements and energies for both Hamiltonians with Mathematica and I found that the Easypin calculation corresponds to the (S1xS3) case.

I used the following to describe the isotropic (J) and antisymmetric exchange (G) components of the coupling between the pairs of electrons:

Sys.S = [1/2 1/2 1/2];
ee12 = [Jx Gz -Gy; -Gz Jy Gx; Gy -Gx Jz];
ee13 = [Jx Gz -Gy; -Gz Jy Gx; Gy -Gx Jz];
ee23 = [Jx Gz -Gy; -Gz Jy Gx; Gy -Gx Jz];
Sys.ee = [ee12;ee13;ee23];

Is there really something wrong in the Easyspin calculation or have I missed something?

Dominik

[Stefan Stoll]

Hi,

EasySpin doesn't assume anything about antisymmetric exchange. It's up to you how you define it. What EasySpin does define, however, is the order of the spins in the bilinear product S1.J.S2, where J is the general 3x3 coupling tensor. As you have found, EasySpin always orders the spins according to the order in Sys.S.

For two spins, for example, the electron-electron term is S1.J.S2, and not S2.J.S1. You have to set the matrix elements in J accordingly.

So, if you want to specify G*(S3xS1), you need to flip the signs of Gx, Gy, and Gz in your second matrix, since G*(S3xS1)=-G*(S1xS3).