Quantum Griffiths singularities in ferromagnetic metals

TL;DR

This paper develops a theory for quantum Griffiths phases in disordered ferromagnetic metals, revealing stronger singularities than in antiferromagnets and comparing predictions with experimental data.

Contribution

It introduces a novel theoretical framework for quantum Griffiths singularities in ferromagnetic metals, highlighting the impact of order parameter conservation on rare region dynamics.

Findings

Rare region dynamics are slower than in usual quantum Griffiths cases.

Quantum Griffiths singularities are stronger than power laws, with specific exponential forms.

Comparison with experimental data on NiV alloys supports the theory.

Abstract

We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $\rho(\epsilon)$ takes the asymptotic form $\exp[\{-\tilde{\lambda}\log (\epsilon_0/\epsilon)\}^{3/5}]/\epsilon$ with $\tilde{\lambda}$ being non-universal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\rm{Ni}}_{x}{\rm{V}}_{1-x}$.