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 KCuF_{3} . 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 *J _{H}* = 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: *J _{0}* ,

*J*, and

_{1}*J*. One may see that the largest is

_{2}*J*= 35.7 meV (AFM). Studying

_{0}*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:

*J*= −0.5 meV, while corresponding distance is on slightly larger (4.14 Å). Thus, as it was explained above, KCuF

_{1}_{3}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 (2*J*Σ* _{i>j} S_{i} S_{j} *[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

*J*= 17.85 meV or 207 K. This is very close to

_{0}*J*= 187 − 190 K obtained experimentally [4, 5].

_{0}

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)