Anisotropic magnetic exchange in the non-collinear system without SOC.

[Bohr Cong]

We have a system with a magnetic ground state being non-collinear. We would like to determine the exchange constant in case of no SOC. The non-collinear magnetic order requires a DFT calculation with a supercell three times larger than the primitive cell. I have a general question concerning such a non-collinear magnetic system without SOC. For magnetic systems with SOC, we know that there exist anisotropic and DMI terms no matter whether the magnetic order is collinear or non-collinear. However, it is not clear to me if, theoretically, the anisotropic and DMI terms will also exist if there is no SOC. My understanding is that, in non-collinear systems, there also exists the single-particle coupling between spin-up and spin-down components. As a consequence, the anisotropic and DMI terms are also allowed from the TB2J formulas.

If they are allowed to exist in non-collinear systems without SOC in principle, how can they be determined in TB2J? In the spin-rotation and structure-average methods, which one is more reliable in this case?

[Xu He]

Hi, 

This is a very interesting question. There are some research on whether the DMI can exist just because of the non-collinear spin. Perhaps you'll find this paper interesting https://www.nature.com/articles/s41598-020-77219-3. What they propose is like what you said, the DMI is allowed by the formulas. 

But I am not sure I fully understand the conclusion. It seems in that paper nothing like the structure-average method or the spin-rotation average method is applied. In my opinion, this procedure is necessary. The average method for non-collinear spin is not yet available in TB2J. 

Best regards,

HeXu

[Bohr Cong]

Thanks for the prompt reply and the reference. It indeed confirms our suspect. The magnetic force theorem does not depend on the specific magnetic configuration but only the matrix elements do. Some elements vanish in the case of collinear magnetism such that the anisotropy and DM terms vanish, too. I also agree with you that the rotation scheme is still required. If the quantization axis is along z, the z-related component will not appear in the second-order perturbation expansion of the total energy and the Hamiltonian regardless of the magnetic configuration. It would be great that you can work this out and provide the corresponding script.


I have another question: how reliable are the results if I perform collinear calculations for such non-collinear ground state?