Extracting DMI and J_ani for highly canted non colinear magnetic state

[Siddharth Pandya]

Dear HeXu and the TB2J development team,

I am working on a material with a strongly noncollinear magnetic ground state, where some magnetic moments within the unit cell are canted by 70–90° from the ferromagnetic axis. I am using the standard TB2J workflow , rotating structures with TB2J_rotate, running seven VASP+Wannier90 calculations, and merging with TB2J_merge ,to extract the full exchange tensor including DMI and symmetric anisotropic exchange J_ani.

I am finding that the merged DMI magnitudes are unphysically large, with |D|/|J_iso| ratios exceeding 1.0 for a 3d transition metal system where I would expect values in the range 0.05–0.2. TB2J itself emits a warning that the reconstruction matrix is close to singular. Shell-by-shell validation shows large leave-one-out errors and poor consistency between the six rotated calculations after back-rotation to a common frame, particularly for DMI and J_ani. The J_iso extracted from the noncollinear reference state is also significantly underestimated compared to a collinear FM reference calculation, which I attribute to the LKAG projection problem for strongly noncollinear spin configurations.

My specific questions are:

1. Is the standard TB2J_rotate and TB2J_merge workflow valid for strongly noncollinear reference states, or does the LKAG formalism break down when the local spin quantization axes differ by 70–90° between sites?
2. What is the recommended procedure for extracting reliable DMI and J_ani parameters in this regime? Is a spin spiral approach more appropriate, and if so, does TB2J support noncollinear spin spiral Hamiltonians as input?
3. Is there a way to assess whether the near-singular reconstruction matrix is a fundamental limitation of the reference state or a numerical issue that can be resolved with a different set of rotation axes?

Any guidance would be greatly appreciated.

Best regards, Siddharth   

[Xu He]

Hello, 

1. For strongly non-collinear state, use the TB2J_rotate.py --noncollinear option to generate six configurations, instead of 3, which is to avoid the near singularity issue. 

2. Indeed if your system is in a spin spiral state, using spin spiral method in DFT can likely give better description of the ground state. If this is done with the generalized Bloch Theorem, the type of Hamiltonian is not supported in TB2J. If you use a supercell approach, then yes you can use TB2J. 

3. See answer to 1. Sometimes even 6 configuration is not enough, then you can generate more rotated structures. 

Best regards, 

HeXu

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[Siddharth Pandya]

I have tried 6 rotations and indeed they do not seem to be enough, matrices are near singular !

How do I generate more rotations and is there any criteria in which i can know how many and what king of rotations are necessary?