Metamagnetism and Fermi Surface in the Anderson Lattice Model

TL;DR

This paper studies how magnetic fields affect the Fermi surface in the Anderson lattice model, revealing a metamagnetic transition characterized by a kink in magnetization and a change from large to small Fermi surfaces, consistent with experimental observations.

Contribution

It provides a theoretical analysis of metamagnetism and Fermi surface evolution in the Anderson lattice model using the $1/N$-expansion, highlighting the transition from large to small Fermi surfaces.

Findings

Magnetization exhibits a kink at a critical field $H_M$.

Differential susceptibility peaks around $H_M$ at finite temperature.

Fermi surface changes from large to small across $H_M$.

Abstract

We investigate magnetization as functions of external magnetic field $H$ in the $U$-infinite Anderson lattice model within the leading order approximation in the $1/N$-expansion. At $T=0$, at $H=H_M$ where the Zeeman energy is equal to a certain characteristic energy in the system, the magnetization curve has a kink and the differential susceptibility $dM/dH$ shows a jump. At finite temperature, $dM/dH$ shows a peak around $H_M$. Its maximum value increases with decreasing $T$ and saturates to a finite value at $T\to 0$. When $H<H_M$, the $f$ and the conduction electrons form the renormalized bands with a large Fermi surface determined by the Luttinger sum rule. On the other hand, when $H>H_M$, the bands reform themselves significantly free from the Luttinger sum rule, eventually leading to a small Fermi surface at $H \gg H_M$. The results are consistent with the metamagnetic properties observed in the heavy fermion CeRu$_2$Si$_2$.