The goal of this tutorial is to illustrate how one can calculate exchange parameters using the total energy method, see Sec. 2 of the JaSS manual , and pseudopotential VASP code for KCuF3 . This is famous material, which has three-dimensional crystal structure, but due to a specific orbital ordering magnetic subsystem in this compound turns out to be one-dimensional [1]. In order to get correct (insulating) ground state one needs to use GGA+U method, which takes into account strong on-site electronic correlations. We chose U = 7.6 eV and JH = 1 eV following Ref. [2].

As explained in Sec. 3 one needs to prepare 4 input files for VASP calculations (INCAR, KPOINTS, POSCAR, POTCAR). Whole set of these files is accessible via tutorial archive, but one can easily make them by themselves. We chose the crystal structure to allow so called polytype a [3], which contains the unit cell with 4 formula units.

The jass.inp file can be as simple as

[main]
ncore = 24
[DFT]
S = 0.5
magion = Cu

Here we only specified that 24 CPUs should be used by VASP and that magnetic ion is Cu, which spin is S = 1/2.

To calculate exchange parameters just execute JaSS in the command-line and study jass.out. Program finds that with the given unit cell one may calculate only exchange integrals: J0 , J1, and J2 . One may see that the largest is J0 = 35.7 meV (AFM). Studying jass.out we find this exchange corresponds to distance 3.92 Å and it couples two nearest Cu ions along c axis (the translation vectors are [0, 0, 1] and [0, 0, −1]). The exchange between nearest neighbors in the ab plane is much smaller and, moreover, it is ferromagnetic: J1 = −0.5 meV, while corresponding distance is on slightly larger (4.14 Å). Thus, as it was explained above, KCuF3 is one-dimensional AFM.

One may compare calculated exchange parameters with those found experimentally using optical, susceptibility and specific heat measurements [4, 5]. One needs to take into account that in corresponding papers slightly different formulation of the Heisenberg model (2JΣi>j Si Sj [6]) was used, i.e. each pair was counted once (exactly as in JaSS), but the coupling parameter was set to 2J instead of J . Thus, in order to compare with experiment one needs to divide exchange parameter obtained by JaSS by factor of two. Then we get J0 = 17.85 meV or 207 K. This is very close to J0 = 187 − 190 K obtained experimentally [4, 5].

 

1. S. V. Streltsov and D. I. Khomskii, Physics-Uspekhi 60, 1121 (2017)

2. N. Binggeli, M. Altarelli, Phys. Rev. B 70, 085117 (2004)

3. A. Okazaki, J. Phys. Soc. Jpn. 26, 870 (1969)

4. S. Kadota, I. Yamada, S. Yoneyama, and K. Hirakawa, J. Phys. Soc. Jpn. 23, 751 (1967)

5. K. Iio, H. Hyodo, K. Nagata, and I. Yamada, J. Phys. Soc. Jpn. 44, 1392 (1978)

6. J. Bonner and M. Fisher, Phys. Rev 135, A640 (1964)

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