A First-Principles Route to Complex Spin Models Beyond Heisenberg

In solids, electrons carry both charge and spin. The arrangement of these spins in a material largely determines its magnetic properties, such as whether it is ferromagnetic, antiferromagnetic, or something more exotic. Because the full many-electron problem is extremely complex, physicists often use spin models that focus only on the spin degrees-of-freedom. A representative example is the Heisenberg model, which contains only bilinear spin-spin interactions. However, recently discovered magnetic phenomena cannot be explained solely by the bilinear interaction. Specifically, higher-order interactions, such as the biquadratic interaction, play a crucial role in stabilizing complex magnetic structures.