Dimensional crossover in quantum critical metallic magnets

TL;DR

This paper investigates the dimensional crossover from 2D to 3D behavior in quantum critical metallic magnets, analyzing thermodynamic properties and crossover regimes using a generalized Landau-Ginzburg-Wilson approach and renormalization group techniques.

Contribution

It introduces a theoretical framework for understanding the 2D-3D crossover in quantum critical metals, including crossover functions and regimes, with relevance to experimental heavy-fermion systems.

Findings

Identification of separate classical and quantum crossover scales.

Discovery of an intermediate regime with unique power-law behavior.

Sensitivity of thermal expansion and compressibility to the crossover phenomena.

Abstract

Nearly magnetic metals often have layered lattice structures, consisting of coupled planes. In such a situation, physical properties will display, upon decreasing temperature or energy, a dimensional crossover from two-dimensional (2d) to three-dimensional (3d) behavior, which is particularly interesting near quantum criticality. Here we study this crossover in thermodynamics using a suitably generalized Landau-Ginzburg-Wilson approach to the critical behavior, combined with renormalization group techniques. We focus on two experimentally relevant cases: the crossover from a 2d to a 3d antiferromagnet, and the crossover from a 2d ferromagnet to a 3d antiferromagnet. We discuss the location of phase boundary and crossover lines and determine the crossover functions for important thermodynamic quantities. As naive scaling does not apply at and above the upper critical dimension, two crossover scales arise which can be associated with separate dimensional crossovers of classical and quantum fluctuations, respectively. In particular, we find an intermediate regime with novel power laws where the quantum fluctuations still have a 2d and the classical fluctuations already have a 3d character. For the ferromagnet-to-antiferromagnet crossover, the mismatch of the dynamical exponents between the 2d and 3d regimes leads to an even richer crossover structure, with an interesting 2d non-critical regime sandwiched between two critical regimes. For all cases, we find that thermal expansion and compressibility are particularly sensitive probes of the dimensional crossover. Finally, we relate our results to experiments on the quantum critical heavy-fermion metals CeCu(6-x)Au(x), YbRh(2)Si(2) and CeCoIn(5).