Phase diagram of the SU(2) Kondo lattice

Miguel Abele,P S Riseborough

doi:10.1063/1.5043080

Abstract

We examine the SU(2) Kondo Lattice Model, for simple cubic lattices with various magnitudes of the localized spins j and numbers of conduction electrons, nc. For j=1/2, the system undergoes transitions from the paramagnetic to magnetically ordered states. The sequence of low-temperature magnetic states found on increasing nc is symmetric about half-filling and exhibits a preference for commensurate phases over incommensurate phases. On increasing nc from small values, the sequence of magnetic orderings consists of: ferromagnetic phases, planes of ferromagnetically spins which are sequentially twisted by nc-dependent angles, ferromagnetic planes of spins that are aligned antiferromagnetically, antiferromagnetic planes of spins in which the Neel order parameters are twisted through incommensurate angles. Neel order is most stable around half-filling. Magnetic ordered phases are found to be more stable than the Kondo phase for j=1/2, but larger j values may stabilize the Kondo phase. For j=3/2 the sequence of magnetic ordering with increasing nc is the same but, depending on the value of the strength of the Kondo interaction, the Kondo phase may be stabilized in a window 4 ≥ nc ≥ 2. In accordance with Nozieres’s arguments, we find that magnetic ordering is dominant for almost filled and almost empty bands.

Highlights

Heavy-fermion materials exhibit a temperature induced cross-over between a high-temperature phase, in which conduction electrons scatter from localized spins, and a low-temperature Fermiliquid characterized by heavy quasi-particle masses
For j=1/2, the phase diagram is symmetrical about nc = 1, which corresponds to the half-filled conduction band
As nc approaches half-filling, we find that the magnetic ordering consists of planes of antiferromagnetically aligned spins in which the direction of the Neel vector is rotated between consecutive planes

Summary

INTRODUCTION

Heavy-fermion materials exhibit a temperature induced cross-over between a high-temperature phase, in which conduction electrons scatter from localized spins, and a low-temperature Fermiliquid characterized by heavy quasi-particle masses. Heavy-fermion systems are often described as exhibiting Kondo physics due to a logarithmic temperature dependence of the resistivity over a limited range of temperatures, despite the fact that the low-temperature Fermi-liquid state shows coherent transport properties.[1] doubts have been expressed whether there are sufficient conduction electrons present to completely compensate the local moment magnetism of the crystalline compounds by forming localized spin singlets.[2] An alternate paradigm has been suggested based on the observation that heavy-fermion materials are often found in the vicinities of quantum critical points.[3] The heaviness of the quasiparticle masses can be attributed to interaction with low-frequency large-amplitude spin fluctuations. Found for SU(N) Anderson Lattice Models.[6,7] we consider the effects of spatial correlations and show that they can significantly enhance the stability of magnetically ordered phases for particular occupations of the conduction band, compared with theories that have only considered restricted types of spatial correlations.[8]

THE MODEL

CALCULATION

RESULTS

CONCLUSION