Calculated magnetic exchange interactions in the quantum spin chain materials K2CuSO4Cl2 and K2CuSO4Br2

Using density functional calculations, we present a comprehensive study of the electronic and magnetic properties of the quantum spin chain materials ${\mathrm{K}}₂{\mathrm{CuSO}}₄{\mathrm{Cl}}₂$ and ${\mathrm{K}}₂{\mathrm{CuSO}}₄{\mathrm{Br}}₂$. With the first-principles linear response method, we calculate the magnetic exchange parameters, and the theoretical values are in a quantitatively good agreement with experiments. Depending on the signs and magnitudes of the interchain magnetic exchange interactions, we find that the magnetic order of ${\mathrm{K}}₂{\mathrm{CuSO}}₄{\mathrm{Br}}₂$ along the $b$ axis is antiferromagnetic, while ${\mathrm{K}}₂{\mathrm{CuSO}}₄{\mathrm{Cl}}₂$ has strong frustration along the $b$ axis. Based on the obtained magnetic exchange parameters, we successfully reproduce the experimental spin-wave dispersion. We also calculate Dzyaloshinskii-Moriya interactions, which are found to dominate in these compounds compared to the interchain magnetic exchange interactions. Finally, we obtain the phase diagram for these two materials using Monte Carlo simulations. Our results are consistent with previous experiments, giving a complete explanation of the magnetic structure.