Phase diagram of ferromagnetic and metamagnetic transitions in itinerant electron system

Abstract

We analyze a mean-field model of itinerant electrons with an ferromagnetic interaction on a square lattice and perform a comprehensive study of the phase diagram in the three-dimensional space spanned by the chemical potential, a magnetic field, and temperature. The ferromagnetic phase is stabilized below a dome-shaped transition line T c (µ) with the maximal T c near van Hove filling. The transition is second order at high temperatures and becomes first order at low temperatures. When the interaction strength becomes large, another ferromagnetic dome is realized near the band edge with a quantum critical point at the band edge and a first-order transition on the other edge of the dome. The two ferromagnetic phases merge into one for further larger interaction strength. By applying a magnetic field, wing structures develop from the first-order transition lines at zero field. The wing describes a first-order transition surface, namely a metamagnetic transition. Notably, the metamagnetic transition occurs as a function of not only the field but also the chemical potential. The upper edge of the wing corresponds to a critical end line.When the system is tuned close to the band edge in the field, the wing can shrink and vanish, leading to a quantum critical end point (QCEP) at zero temperature. This QCEP is a Lifshitz point in the sense that the Fermi surface of either spin band vanishes. Close to the QCEP, another wing develops at very low temperatures in a higher field region. For a large interaction strength, however, the QCEP disappears. Furthermore, a metamagnetic transition occurs also inside the ferromagnetic phase without a magnetic field. Consequently another wing also develops from that by applying the field. These rich phase diagrams originate from the breaking of particle-hole symmetry in the presence of a next nearest-neighbor-hopping integral t ′ , which is expected in actual materials. We also find that ferromagnetic and metamagnetic transitions are usually accompanied by a Lifshitz transition at low temperatures, i.e., a change of a Fermi surface topology including the disappearance of a Fermi surface. Our obtained phase diagrams are discussed as a possible connection to itinerant ferromagnetic systems such as UGe 2 , UCoAl, ZrZn 2 , and others including magnetocaloric effect materials.