[Paper Review] Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl₃

Peter Czajka, Tong Gao+7 more|arXiv (Cornell University)|Feb 22, 2021

Advanced Condensed Matter Physics37 references186 citations

TL;DR

This study reports large-amplitude quantum oscillations in the thermal conductivity of α-RuCl3 within the quantum spin liquid (QSL) phase under magnetic fields (7.3–11 T), despite the material being an insulator with a 1.9 eV gap. The oscillations are periodic in 1/H, exhibit strong field and temperature dependence, and are intrinsic to the QSL state, suggesting a possible spinon Fermi surface, with periodicity governed by the in-plane magnetic field component Ha.

ABSTRACT

In the class of materials called spin liquids a magnetically ordered state cannot be attained even at millikelvin temperatures because of conflicting constraints on each spin; for example, from geometric or exchange frustration. The resulting quantum spin-liquid state is currently of intense interest because it exhibits unusual excitations as well as wave-function entanglement. The layered insulator α-RuCl₃ orders as a zigzag antiferromagnet at low temperature in zero magnetic field. The zigzag order is destroyed when a magnetic field is applied parallel to the zigzag axis. At moderate magnetic field strength, there is growing evidence that a quantum spin-liquid state exists. Here we report the observation of oscillations in its thermal conductivity in that field range. The oscillations, whose amplitude is very large within this field range and strongly suppressed on either side, are periodic. This is analogous to quantum oscillations in metals, even though α-RuCl₃ is an excellent insulator with a large gap. As the temperature is raised above 0.5 K, the oscillation amplitude decreases exponentially, anticorrelating with the emergence of an anomalous planar thermal Hall conductivity above approximately 2 K.

Motivation & Objective

• To investigate the nature of thermal transport in the quantum spin liquid (QSL) state of α-RuCl3 under high magnetic fields.
• To determine whether the observed oscillations in thermal conductivity are intrinsic and related to electronic or topological excitations in the QSL phase.
• To probe the role of magnetic field orientation and temperature on the oscillation behavior and its connection to the QSL phase.
• To rule out extrinsic origins such as strain or lattice defects and confirm the oscillations are a fundamental property of the QSL state.

Proposed method

• Measured thermal conductivity (κxx) and thermal Hall conductivity (κxy) in single-crystalline α-RuCl3 samples at temperatures down to 0.43 K using a dilution refrigerator.
• Employed the stepped-field method to correct for magnetocaloric effects and ensure accurate field-sweeping in κxx measurements.
• Performed field tilting experiments in the a-c plane to isolate the in-plane component (Ha) and test the dependence of oscillation period on Ha.
• Used derivative analysis (dκxx/dB) to identify extrema and confirm periodicity in 1/H, distinguishing from periodicity in H.
• Extracted oscillatory amplitude (∆κamp) by subtracting a smooth background curve (κbg) fitted through midpoints between extrema.
• Correlated oscillation amplitude with lattice disorder via phonon thermal conductivity (κph) in the polarized state, where κxx is dominated by phonons.

Experimental results

Research questions

• RQ1 Are the observed thermal conductivity oscillations in α-RuCl3 intrinsic to the quantum spin liquid state, or artifacts of experimental conditions?
• RQ2 What is the field and temperature dependence of the oscillations, and how do they correlate with the phase diagram of α-RuCl3?
• RQ3 Why do the oscillations exhibit periodicity in 1/H rather than H, despite the absence of free carriers in this insulator?
• RQ4 How does the in-plane magnetic field component (Ha) control the oscillation period, and what does this imply about the underlying Fermi surface?
• RQ5 What is the relationship between the oscillations and the emergence of planar thermal Hall conductivity (κxy) above ~2 K?

Key findings

• Oscillations in κxx reach amplitudes of 30–60% of the total thermal conductivity at 0.43 K, peaking sharply at 9.6 T within the QSL phase (7.3–11 T).
• The oscillation period is strictly periodic in 1/H, with a high-field slope Sf = 41.4 T (H ∥a) and low-field slope Sf = 30.6 T, indicating a non-trivial Fermi surface-like behavior.
• Tilting the magnetic field out of the plane shows that the oscillation period depends only on the in-plane component Ha, confirming the in-plane character of the oscillation mechanism.
• Above 11 T, in the field-polarized state, oscillations vanish abruptly, confirming their absence in the gapped, non-QSL regime.
• The oscillation amplitude anti-correlates with the emergence of anomalous planar thermal Hall conductivity (κxy) above ~2 K, suggesting a competition or interplay between the two phenomena.
• Sample 3 exhibits a 6-fold larger oscillation amplitude than Sample 1, which correlates with higher lattice disorder as inferred from phonon thermal conductivity in the polarized state.