Mixed-Valence Ion Model for Incoherent Metallic State in Heavy-Fermion Spinel LiV2O4

For the incoherent metallic state in the heavy-fermion spinel LiV2O4, structural and magnetic properties are explored from the viewpoint of a mixed-valence ion system consisting of localized spin-1 V3+ and spin-1/2 V4+ that may be related to the nondegenerate state of the itinerant electron system. On the basis of precise atomic coordinates including anisotropic displacement parameters, the mixed-valence state for V ion is confirmed definitely. Magnetic susceptibility is almost explained with trigonal field splittings of 103 cm−1 in terms of the mean-field approximation in the pseudospin XXZ model with the single-ion uniaxial anisotropy, where g-factors and exchange coupling constants are renormalized from those of the original LS systems for V3+ and V4+ ions through the spin–orbit coupling. Thus in the incoherent metallic state, all spins of the mixed-valent V ions are suggested to contribute to the temperature-dependent susceptibility, which is anisotropic due to the local trigonal distortion. The localized electron character in the V4+ ion may be due to the nondegenerate effect of the itinerant electron system. In the absence of exchange coupling between V3+ and V4+ for the mixed-valence ion model, spin–lattice relaxation rate of V ions calculated for the completely localized electron state in the high-temperature limit is about 2–3 times the experimental value.