Signs of exchange interactions in TB2J

[Iram Bel]

Dear HeXu,

Thank you very much for your guidance and for all the help you provide to the group.  

I am wondering about the signs of the exchange interactions obtained from TB2J. Are these signs definitive, such that one can directly interpret a negative value as an antiferromagnetic interaction and a positive value as a ferromagnetic one? Or should the signs be inverted before interpreting the results?

I ask because I obtained the opposite trend compared to the usual Néel–Slater curve, and I am concerned that this might be related to a sign convention issue.

Thank you for your clarification.

Best regards,
Iram

[Gavin Abo]

For the Néel–Slater curve (likely more commonly known as the Bethe–Slater curve [1-2]), could you elaborate on what you used for and/or how you computed the exchange axis (i.e., y-axis)?

An exchange energies (Eex) relation to the exchange values (Jex) [3]:

For the y-axis, did you plot Eex similar to [4]

or similar to [5]

Or did you plot Jex of individual or total interactions similar to [6] 

Or exchange integral similar to [7]:

Where the exchange integral might be for example similar to or different from that in [8]:

Or something other than those?

According to the TB2J webpage at [9], it uses the Hamiltonian where positive exchange values favor ferromagnetic alignment.  If you plotted Jex, was it just for example for the isotropic term Jiso (= 2*Jex)?  At [8], it looks like the Hamiltonian uses the isotropic term Eex = -Jiso*Si dot Sj (of note, the section "2.1. Heisnberg model" in [10] mentions both Jij and Jji are both accounted for in the Hamiltonian which should correspond with the prefactor 2 in that reference [3] equation: Eex = -2*Jex*Si dot Sj [Or Jex = Jij: Eex = -2*Jij*Si dot Sj such that 2*Jij = Jiso: Eex = -Jiso*Si dot Sj].  Or did you include other terms such as Jani and Dij if you plotted the y-axis with Eex?

[1] https://en.wikipedia.org/wiki/Bethe%E2%80%93Slater_curve

[2] https://www.physicsforums.com/threads/fields-in-ferromagnetism-and-proper-range-of-atom-size.100173/

[3] Slide 19: https://spintronics.cmshom.co.kr/up/file/blog/admin/ISM%20Chapter4_2.ppt

[4] https://www.researchgate.net/figure/Neel-Slater-curve-and-the-distances-between-iron-atoms-situated-in-sites-located-around_fig2_267424844

[5] https://www.researchgate.net/figure/Bethe-Slater-Curve-like-behavior-and-interlayer-FM-AFM-transition-of-bilayer-CrX2_fig1_333773155

[6] https://doi.org/10.1038/s41598-017-04427-9

[7] https://www.researchgate.net/figure/The-Bethe-Slater-curve-showing-the-variation-of-the-exchange-integral-with-3d-orbital_fig19_237246024

[8] https://doi.org/10.3762/bjnano.16.110

[9] https://tb2j.readthedocs.io/en/latest/src/convention.html

[10] https://arxiv.org/pdf/2009.01910v2

Kind Regards,

Gavin

TB2J user

[celine belhabib]

Dear Gavin,

Thank you very much for your valuable response.

Here is the procedure I followed: I first performed a collinear spin VASP calculation without activating any wannier90 parameters. Then, I ran a second VASP calculation with wannier90 parameters enabled, still in the collinear spin configuration along the z-axis, and without including spin–orbit coupling.

For reference, it is known experimentally that the easy magnetization axis in my compound is the z-axis.

After that, I executed TB2J, which provided the Jiso values (I did not compute Janiso or DMI interactions, since I read that they are not yet reliable for production use). From the exchange.out file, I took the raw Jiso values for each pair as they are, converted them into Kelvin, and plotted Jiso(Co–Co) as a function of interatomic distance.

However, the resulting curve decreases with distance the opposite trend of the typical Néel–Slater curve.
Could you please let me know if I might have made a mistake in one of these steps?

Thank you very much for your time and help.

Best regards,
Iram

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[Gavin Abo]

Unfortunately, I'm not a VASP user as I don't have a license for it at this time.  If one of the VASP users that posted to the group before have experienced the same thing, perhaps they will have some advice.

Kind Regards,

Gavin

TB2J user