Direct probe of magnetic field effects on phonons by ultrasound propagation in a quasi-two-dimensional honeycomb magnet Na$_2$Co$_2$TeO$_6$

TL;DR

The paper investigates how out-of-plane magnetic fields influence phonons in the quasi-two-dimensional honeycomb magnet Na2Co2TeO6 using ultrasound to probe spin–lattice coupling. Through temperature- and field-dependent measurements of sound velocity and attenuation, the authors identify a ferrimagnetic order below $T_N=27$ K and provide evidence supporting a triple‑Q ground state, complemented by a discussion of hysteresis and cooling-history effects. A detailed comparison with literature on thermal conductivity suggests phonons play a dominant role in low-temperature transport, with possible phonon–magnon hybridization explaining discrepancies in intermediate regimes. Overall, the work demonstrates ultrasound as a powerful probe of magnetic transitions in frustrated magnets and highlights the need to disentangle phonon contributions when interpreting transport data in these systems.

Abstract

We study the phonon behavior of a Co-based honeycomb frustrated magnet Na$_2$Co$_2$TeO$_6$ under magnetic field applied perpendicular to the honeycomb plane. The temperature and field dependence of the sound velocity and sound attenuation unveil prominent spin-lattice coupling in this material, promoting ultrasound as a sensitive probe for magnetic properties. An out-of-plane ferrimagnetic order is determined below the Néel temperature $T_N=27$~K. A comprehensive analysis of our data further supports a triple-Q ground state of Na$_2$Co$_2$TeO$_6$. Furthermore, the ultrasound data were systematically compared to the thermal transport results from literature, to unveil the importance of phononic contribution to the observed transport behaviors.

Figures (5)

• Figure 1: (a) Representative temperature dependence of $\Delta v/v_0$, collected in the LA mode at the ultrasound frequency $f\approx141$ MHz. (b) The low temperature data at different ultrasound frequencies. Three anomalies $T_N=27$ K, $T'=16$ K, and $T"=4$ K can be addressed. The cartoons illustrate the experimental geometry.
• Figure 2: (a) Field dependence of $\Delta v/v_0$ at different temperatures. The curves are shifted vertically for clarity. Note the different rescale factors for each curve. The black arrows indicate the dips in some curves. (b) The gray circles and squares are phase boundaries of NCTO inferred from its magnetic susceptibility data Zhang2024b. The red stars are the positions of anomalies from Fig. 2(a). We follow the notation for the critical fields $H_1$ and $H_2$ from Ref. Zhang2024b. The dashed gray lines are guide-to-the eyes of the boundaries of the contour plot of $dM/dH$ data in Ref. Zhang2024b. Although there is a clear line below $H_1$ observable, it was not labeled as a critical field in Ref. Zhang2024b. Nevertheless, an electron spin resonance (ESR) work identified it also as a phase transition Bera2023. Thus we use $H_0$ to name this line. The dashed black lines indicate the parameter space reached in Fig. 2(a).
• Figure 3: Field dependence of (a) $\Delta v/v_0$ and (b) $\Delta \alpha$ at 1.8 K, measured after cooled in opposite field directions. The first field-sweep run was done after the sample was cooled in zero, or in small ($<14$ mT) remanent field of our magnet. The second and third measurements were done after cooling in a finite field applied along opposite directions.
• Figure 4: (a) $\Delta v/v_0(H)$ isotherms measured in NCTO in opposite field directions. The curves are shifted vertically for clarity. (b) The temperature dependence of the integrated hysteretic region of $\Delta v/v_0(H)$ isotherms normalized to the maximum change of $\Delta v/v_0$ at each temperature. The integration of $\Delta v/v_0(H)$ hysteresis for data collected under different experimental settings (see text) are rescaled to show a common temperature behavior. The yellow stripe is a guild to the eye.
• Figure 5: Field dependence of $\Delta v/v_0$ and $\Delta \alpha$ at selected temperatures: (a) 300 mK, (c) 625 mK, (e) 3 K, (g) 5 K, and (i) 15 K. The corresponding estimates of the change of phonon conductivity (see text) are plotted in red in (b), (d), (f), (h) and (j), respectively. Field dependence of the thermal conductivity $\Delta\kappa/\kappa_{0T}$ at similar temperatures reported in the literature is also shown Yang2022Hong2024Li2023. For $T=$5 K, the ultrasound data of two frequencies were presented. (k) Field dependence of $\Delta\kappa/\kappa_{0T}$ and $\Delta v/v_0$ of $\alpha-$RuCl$_3$ at comparable temperatures, with the field applied along the same in-plane crystallographic direction. Data are from Refs. Hauspurg2024Czajka2021.