Gallery of soft modes: Theory and experiment at a ferromagnetic quantum phase transition

Stamp, P. C. E.; Silevitch, D. M.; Libersky, M.; McKenzie, Ryan; Geim, A. A.; Rosenbaum, T. F.

doi:10.1103/PhysRevB.110.134420

Gallery of soft modes: Theory and experiment at a ferromagnetic quantum phase transition

Journal Article · Fri Oct 11 00:00:00 EDT 2024 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.110.134420· OSTI ID:3013564

Stamp, P. C. E. ^[1]; ^[2]; ^[2]; ^[3]; ^[4]; ^[2]

University of British Columbia, Vancouver, BC (Canada)
California Institute of Technology, Pasadena, CA (United States)
Ames National Laboratory, Ames, IA (United States); Iowa State University, IA (United States)
Harvard University, Cambridge, MA (United States)

We examine the low-energy excitations in the vicinity of the quantum critical point in LiHoF4, a physical realization of the Transverse Field Ising Model, focusing on the long-range fluctuations which soften to zero energy at the ferromagnetic quantum phase transition. Microwave spectroscopy in tunable loop-gap resonator structures identifies and characterizes the electronuclear soft mode and higher-energy electronuclear states as a function of frequency and magnetic fields applied transverse and parallel to the Ising axis. These are understood in the context of a theoretical model of a soft electronuclear mode that interacts with soft photons as well as soft phonons. We identify competing infrared divergences at the quantum critical point, coming from the photons and the electronuclear soft mode. It is an incomplete cancellation of these divergences that leads to the muted but distinct signatures observed in the experiments. The application of a longitudinal magnetic field gaps the soft mode. As a result, measurements well away from the quantum critical point reveal a set of "Walker'' modes associated with ferromagnetic domain dynamics.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology, Pasadena, CA (United States)

Sponsoring Organization:: National Sciences and Engineering Research Council of Canada; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-07CH11358; SC0014866

OSTI ID:: 3013564

Alternate ID(s):: OSTI ID: 2474108

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 13 Vol. 110; ISSN 2469-9969; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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