Quantum Order-by-Disorder in Strongly Correlated Metals

Abstract

Entropic forces in classical many-body systems, e.g. colloidal suspensions, can lead to the formation of new phases. Quantum fluctuations can have similar effects: spin fluctuations drive the superfluidity of Helium-3 and a similar mechanism operating in metals can give rise to superconductivity. It is conventional to discuss the latter in terms of the forces induced by the quantum fluctuations. However, focusing directly upon the free energy provides a useful alternative perspective in the classical case and can also be applied to study quantum fluctuations. Villain first developed this approach for insulating magnets and coined the term order-by-disorder to describe the observed effect. We discuss the application of this idea to metallic systems, recent progress made in doing so, and the broader prospects for the future. CONTENTS

Mechanism for transitions between ferromagnetic and antiferromagnetic orders in d-electron metallic magnets

“…Nevertheless, experimental discrimination between large ( Q ~ π ) or small ( Q ~ 0) ordering vector of the AFM state in LaCrGe 3 is highly desirable. Large vector would be consistent with two-channel Stoner physics whereas small one with the mechanism based on the quantum fluctuation arguments 11,13,14 .…”

“…In turn, the generic microscopic mechanisms triggering such transitions, except material specific ones 8,9 , are mostly unidentified. The effective action approach incorporating corrections due to quantum fluctuations 10,11 constitutes a notable exception. Namely, it has been shown that in the vicinity of the ferromagnetic quantum critical point quantum fluctuations favor reconstruction of the phase diagram and the first-order transition at zero temperature or emergence of the spatially modulated magnetic phase is predicted 10–14 .…”

Fermionic order by disorder in a van der Waals antiferromagnet

“…We propose the possible mechanism leading to emergent hard axis ordering in terms of fermionic order by disorder in itinerant systems 36 , 37 . Our observation is that the change in chemical pressure enhanced the magnetic quantum fluctuation and altered the direction of Néel vector to the apparent “hard axis”.…”

Emergence of a real-space symmetry axis in the magnetoresistance of the one-dimensional conductor Li 0.9 Mo 6 O 17

“…The interband exciton has a spin triplet configuration that strongly suppresses the electron-hole recombination probability through photon emission and gives the resulting dark exciton a long lifetime (and allows for spin exchange scattering with the d xy fermions). At high temperatures, excitons behave as free particles (with a hopping energy of the order 1 to 2 meV), while at low temperatures, the physics of these emergent particles is governed by a quantum order-by-disorder transition ( 35 ), which leads to a Wigner-like periodic arrangement of the excitons. The d xy fermions that remained mobile in the presence of the (slightly incommensurate) Umklapp processes associated with quarter-filling now localize on this additional potential, leading to an upturn in the resistivity below T min .…”