Sixteen-State Energy Mapping for First-Principles Four-Spin Ring Exchange: Validation on $La_2CuO_4$ and $SrFeO_2$

Four-spin ring (cyclic) exchange $J_{ring}$ is an essential ingredient of the Heisenberg spin Hamiltonian of cuprates and other square-lattice magnets, yet it has lacked the kind of direct, local first-principles extraction that the four…

Four-spin ring (cyclic) exchange $J_{ring}$ is an essential ingredient of the Heisenberg spin Hamiltonian of cuprates and other square-lattice magnets, yet it has lacked the kind of direct, local first-principles extraction that the four-state method provides for bilinear…