Magnetocrystalline Anisotropy

The magnetocrystalline anisotropy is an inherent property of the material, which defines the spin orientation in respect with the crystal lattice, at the microscopic level. The experimental value of this magnetocrystalline anisotropy corresponds to approximately 0.1 meV, due to the 8 T requirement of external magnetic field at the spin-flop transition (spins flopping from the c-axis to the ab-plane).

In our results shown in the figure above, we use the Magnetocrystalline Anisotropy Energy (MAE), which is the required energy to switch the spin orientation from parallel to the ab-plane to parallel to c-axis. A series of calculations were performed with different sets of U and J values, where U_eff = U - J corresponds to the on-site Coulomb correction, and for both in-plane and out-of-plane spin orientations. The continuous lines presented in Figure 3 correspond to constant U_eff = U - J values, with simultaneous increase of both U and J along the x-axis of the graph. Within the LDA+U approach, we find that the best results that reproduce the 8 T spin-flop transition observed by the experiment were achieved for U_eff = U - J = 5 eV, with U = 6.5 eV and J = 1.5 eV.

We also performed the same series of calculations with structural relaxation at each (U, J) sets of values, because it will be crucial for the following step of our DFT parametrization. The MAE values seem to be suppressed by the relaxation, possibly due to the underestimation of bond lengths and lattice constants within the LDA approximation. However, the optimal values of (U, J) = (6.5, 1.5) still manage to result in high enough values for the MAE.