It is shown that the fundamental gauge-symmetry constraints superimposed on the admissible form of the exchange-correlation energy functional lead to the generalized local force theorem for small nonuniform rotations of the spin magnetic moments near equilibrium. The theorem suggests that the magnetic interactions responsible for the low-energy spin-wave excitations near the ground state can be expressed in terms of the effective single-particle potential designed for the ground-state spin-magnetization density. The theorem allows us to obtain an empirical effective potential for MnO by fitting the experimental low-temperature spin-wave dispersion curve. The theorem is further applied to investigate abilities of several different first-principles techniques: local-(spin)-density approximation, LDA plus “Hubbard $U$” $(\mathrm{LDA}+U)$ and optimized effective potential (OEP). None of these approaches treats the magnetic interactions in MnO properly. Limitations of the one-electron band picture underlying the failure are elucidated in each case. As one of the perspective techniques to deal with the electronic structure of narrow-band materials, we propose to combine the $\mathrm{LDA}+U$ form of the single-particle equations with the variational principles of the OEP approach. Several possible approximations along this line are discussed.

• Received 15 May 1998

DOI:https://doi.org/10.1103/PhysRevB.58.15496