Calculate DMI of different direction

[Sukhito Teh]

Dear all,

I have a question regarding choosing the appropriate direction of magnetization(for DFT part) to calculate a specific component of DMI. According to the manual of TB2J, DMI at z direction can only be reliably obtained with magnetization at x or y.
excerpt from "TB2J: a python package for computing magnetic interaction parameters":

We note that when all spins are oriented along one direction (e.g. z), the components with u = z or v = z in the J tensor are non-zero if the variation with respect to the rotation is only kept to first order. The xz, yz, zx, zy, and zz components of the anisotropic exchange, and the Dz in the DMI cannot be obtained from a single calculation with magnetization along the z direction.

 But since DMIz is calculated from J tensor of xy component, shouldn't the DMIz be the only reliable value in this case ?(magnetization at z direction). I had found similar argument on the paper "Relativistic exchange interactions in CrX3 (X = Cl, Br, I) monolayers" , which the text mentioned:

Thus, for M||Z, only the Dz component [Eq. (2)] can be computed, while Dx and Dy are extracted from two additional calculations with the magnetization pointing along X and Y ,respectively.

I had also calculated DMI on a Perovskite with heavy metal, the results agrees with DFT results better, when the above principle is used, i.e. Dz calculated with M || z, etc.

Best regards,

Sukhito

[Xu He]

Dear Sukhito,

There are two ways (probably more) of calculating the DMI. The way the DMI is calculated in TB2J is in equation 17 in the TB2J paper:

Another way is D_{ij}^z = Im (A_{ij}^{xy}- A_{ij}^{yx}). The definition of the A can be found in the TB2J paper. If that way is used, you're right that the Dz will be correct.  In fact by combining this two ways the Dx, Dy, and Dz can be calculated without doing the xyz average. Due to different numerical error, the symmetry from this combination is limited and sometimes confusing. We made the choice to just output the one using eqn. 17, which seems better in our test cases, and is claimed to be more accurate in the following reference .

Mankovsky, S. and Ebert, H., Phys. Rev. B 96 (2017) 104416

where the different ways are discussed in detail.

Best regards,

HeXu

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[Sukhito Teh]

Thanks for the clarification!

[Dongzhe Li]

Dear,

If we use equations 15-17 as presented in the TB2J paper.

Should we also correct the J_{ij}^{so}? As far as I can see, there are also "un-correct" A_{ij}^{zz} (when the spin direction along z) enters.

Thanks,

Best regards,

Dongzhe Li