Phonon Thermal Hall Effect in Strontium Titanate

Xiaokang Li, Benoît Fauqué, Zengwei Zhu, and Kamran Behnia

Phys. Rev. Lett. 124, 105901 – Published 9 March 2020

Abstract

It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in the presence of a magnetic field. Recent studies of thermal Hall conductivity, $κ_{x y}$ , in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of $κ_{x y}$ in quantum paraelectric ${SrTiO}_{3}$ , which is a nonmagnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as “giant.” Remarkably, $κ_{x y} (T)$ and $κ (T)$ peak at the same temperature and the former decreases faster than the latter at both sides of the peak. Interestingly, in the case of ${La}_{2} {CuO}_{4}$ and $α − {RuCl}_{3}$ , $κ_{x y} (T)$ and $κ (T)$ peak also at the same temperature. We also studied ${KTaO}_{3}$ and found a small signal, indicating that a sizable $κ_{x y} (T)$ is not a generic feature of quantum paraelectrics. Combined to other observations, this points to a crucial role played by antiferrodistortive domains in generating $κ_{x y}$ of this solid.

Received 16 September 2019
Accepted 20 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.105901

Physics Subject Headings (PhySH)

Ferroelasticity Thermal Hall effect

Ferroelectrics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaokang Li^1,2, Benoît Fauqué³, Zengwei Zhu², and Kamran Behnia ^1,4

¹Laboratoire de Physique et d’Etude des Matériaux (CNRS) ESPCI Paris, PSL Research University, 75005 Paris, France
²Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
³JEIP, USR 3573 CNRS, Collège de France, PSL University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
⁴II. Physikalisches Institut, Universität zu Köln, 50937 Köln, Germany

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Vol. 124, Iss. 10 — 13 March 2020

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Images

Figure 1
Quantifying the thermal Hall effect in ${SrTiO}_{3}$ . (a) Setup for measuring longitudinal and transverse thermal differences ( $Δ T_{x} = T_{1} - T_{2}$ , $Δ T_{y} = T_{3} - T_{2}$ ) generated by a longitudinal thermal current. (b) A photograph of the sample and the setup. The heater and the heat sink were connected to two sides of the sample and at the same level. Three thermometers were mounted near the middle of the sample. (c) Field dependence of $Δ T_{y}$ and $Δ T_{x}$ at $T_{2} = 24 K$ (labeled as sample temperature $T$ below), $Δ T_{y}$ has been shifted vertically to cancel an unavoidable misalignment offset. Note that $Δ T_{x}$ is even dominant and $Δ T_{y}$ is odd dominant in magnetic field. (d) Extracted thermal Hall conductivity $κ_{x y}$ and field-induced change in thermal conductivity $Δ κ = κ (μ_{0} H) - κ (0)$ as function of field. The latter signal is noisier, because the measurement of $Δ T_{x}$ has not been done in differential mode.
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Figure 2
Thermal Hall conductivity and its correlation with longitudinal thermal conductivity. (a) The temperature dependence of $κ_{x y}$ in presence of a magnetic field of 12 T in ${SrTiO}_{3}$ . (b) A comparison of the temperature dependence of longitudinal and transverse thermal conductivity, $κ_{x y}$ has been multiplied by a factor $α$ equal to $- 450$ . Both peak at the same temperature, but $κ_{x y}$ falls faster at both sides of the peak. (c) Schematic sketch of the temperature dependence of specific heat, mean-free-path and velocity generating a peak in $κ$ . Off-diagonal response may be caused by the skew scattering [transverse mean-free-path $ℓ_{x y}$ (d) or the off-diagonal velocity $v_{x y}$ (e)].
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Figure 3
$κ_{x y}$ and $κ$ in other insulators. (a) Longitudinal thermal conductivity $κ$ in ${SrTiO}_{3}$ and ${KTaO}_{3}$ , the inset shows a logarithmic plot. (b) Transverse thermal conductivity $κ_{x y}$ in ${SrTiO}_{3}$ and ${KTaO}_{3}$ . The inset shows an enlargement of the magnitude of the resolved signal. (c) A comparison of the temperature dependence of $κ_{x y}$ at 15 T (multiplied by $- 400$ ) with $κ$ [46] in ${La}_{2} {CuO}_{4}$ . (d) The same comparison in the case of $α − {RuCl}_{3}$ . Here, $κ_{x y}$ at 16 T is multiplied by 2280. In all these cases, $κ_{x y}$ and $κ$ peak at the same temperature and the transverse signal decreases more rapidly below and above the peak.
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Figure 4
Variability of $κ_{x y}$ in ${SrTiO}_{3}$ . (a) $κ (T)$ in two different samples, the data is almost same. (b) Temperature dependence of $κ_{x y}$ in three ${SrTiO}_{3}$ samples. (c),(d) Two samples with the same field-induced change in $κ$ display a threefold difference in their $κ_{x y}$ , data extracted from the field-sweeping curves. (e) Even in the same sample, the magnitude of $κ_{x y}$ changes after warming it above $T_{AFD}$ . The two curves show the data measured before (measurement 1) and after (measurement 2) being warmed to room temperature and staying in air for days. (f) $κ_{x y}$ of the same sample at 24 K as a function of measuring sequence, separated by the warming history of being warmed to room temperature and staying in air for days, data extracted from the field-sweeping curves.
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