GG-05 Transition metals: Matching microscopic quantum dynamics with macroscopic magnetic order

Metals may show long-range magnetic order if the electron correlations are sufficiently strong. This metallic magnetism does not fit the Pauli or Stoner pictures. Static, weak-coupling theories with no local magnetic moments do not account for the Curie-Weiss behavior of the magnetic susceptibility if the critical temperature lies below the Fermi energy of the degenerate Fermi gas. The first theory that qualitatively correctly reproduces the Curie-Weiss law in weak ferromagnetic metals was proposed by Moriya and collaborators [1]. This theory describes consistently only the critical behavior above the transition temperature. It suffers, as other dynamical approximations, from a serious drawback when continued into the ordered phase. The transition point derived from the vanishing of magnetization is not identical to the critical point of the magnetic susceptibility in the paramagnetic phase. The reason for this mismatch is the discrepancy between the microscopic quantum dynamics and the macroscopic thermodynamic order. A generic feature of all dynamical approximations such as RRPA, FLEX, or parquets is the impossibility of simultaneously conforming the quantum dynamical Schwinger-Dyson equation with the thermodynamic conservation laws [2]. It means that the two-particle vertex from the Schwinger-Dyson equation differs from that in the Ward identity guaranteeing that the long-range order emerges at the critical point of the magnetic susceptibility [3]. We found that to match the vanishing of magnetization with the critical point of the magnetic susceptibility one has to suppress specific non-conserving processes in the ordered phase. We demonstrate the proper continuous extension of the dynamical approximations into the ordered phases suppressing the non-conserving diagrams on the half-filled Hubbard model at intermediate coupling within the dynamical mean-field approximation.References: [1] T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Springer Verlag, Berlin, Heidelberg (1985) [2] V. Janiš, P. Zalom, V. Pokorný and A. Klíč, Phys. Rev. B 100, 195114 (2019) [3] V. Janiš, V. Pokorný, and Š. Kos, Phys. Rev. B 109, 075171 (2024)