Revealing three-dimensional quantum criticality by Sr substitution in Han purple

Stephan Allenspach,Pascal Puphal,Steffen Krämer,Frédéric Mila,Yoshimitsu Kohama,Antonietta Mira,Jakob Lass,Gregory S Tucker,Joosep Link,Ivo Heinmaa,Christian Rüegg,Franziska Weickert,Shusaku Imajo,Koichi Kindo,Raivo Stern,Nicolas Laflorencie,Ch Niedermayer ,A Madsen ,E Pomjakushina ,B Normand ,M Jaime ,M Horvatić ,C Krellner

doi:10.1103/physrevresearch.3.023177

Abstract

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple.

Highlights

At a continuous classical or quantum phase transition (QPT), characteristic energy scales vanish, characteristic (“correlation”) lengths diverge, and the properties of the system are dictated only by global and scale-invariant quantities [1]
With a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr substitution in Han purple
The experimental confirmation of the absence of frustration was accompanied by detailed quantum Monte Carlo (QMC) simulations of the quantum critical regime, from which it was possible to conclude that the true behavior of the system includes an intermediate field-temperature regime of nonuniversal scaling governed by an anomalous exponent whose value turned out to be φ 0.72 over much of the effective scaling range [54]

Summary

Introduction

At a continuous classical or quantum phase transition (QPT), characteristic energy scales vanish, characteristic (“correlation”) lengths diverge, and the properties of the system are dictated only by global and scale-invariant quantities [1]. Depend only on factors such as the dimensionality of the system, the symmetry group of the order parameter, and in some cases on topological criteria. These fundamental factors are not all independent, but are all discrete, and as a result phase transitions can be categorized by their “universality class.”. An instructive example of the effects of dimensionality is found for systems where the U(1) symmetry of the order parameter is broken [2]. The symmetry-broken phase is the Bose-Einstein condensate (BEC) [3,4] and, while most familiar in three dimensions, this transition can be found in systems whose effective dimension is any real number d > 2. Strictly in two dimensions the physics is quite different, dependent on the binding of point vortices, 2643-1564/2021/3(2)/023177(18)

Methods

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Discussion

Conclusion