[Paper Review] Glass-like thermal conductivity and narrow insulating gap of EuTiO$_3$

Alexandre Jaoui, Shan Jiang+9 more|arXiv (Cornell University)|Jul 5, 2023

Magnetic and transport properties of perovskites and related materials4 citations

TL;DR

This study reveals that EuTiO₃ exhibits glass-like thermal conductivity due to strong spin-phonon coupling from Eu²⁺ 4f electrons, even above its Néel temperature of 5.5 K. Despite being a simple G-type antiferromagnet without magnetic frustration, the random orientation of large magnetic moments at Eu sites drastically suppresses thermal conductivity, reducing it to levels comparable to amorphous silica over a broad temperature range, with a narrow intrinsic band gap of ~0.22 eV.

ABSTRACT

Crystals and glasses differ by the amplitude and the temperature dependence of their thermal conductivity. However, there are crystals known to display glass-like thermal conductivity. Here, we show that EuTiO$_3$, a quantum paraelectric known to order antiferromagnetically at 5.5 K, is one such system. The temperature dependence of resistivity and Seebeck coefficient yield an insulating band gap of $\sim 0.22$ eV. Thermal conductivity is drastically reduced. Its amplitude and temperature dependence are akin to what is seen in amorphous silica. Comparison with non-magnetic perovskite solids, SrTiO$_3$, KTaO$_3$, and EuCoO$_3$, shows that what impedes heat transport are $4f$ spins at Eu$^{2+}$ sites, which couple to phonons well above the ordering temperature. Thus, in this case, superexchange and valence fluctuations, not magnetic frustration, are the drivers of the glass-like thermal conductivity.

Motivation & Objective

• To investigate the origin of anomalously low thermal conductivity in EuTiO₃, a quantum paraelectric with antiferromagnetic order at 5.5 K.
• To determine whether magnetic degrees of freedom, particularly Eu²⁺ 4f spins, are responsible for the glass-like thermal transport behavior.
• To clarify whether spin-phonon coupling, rather than magnetic frustration or spin liquid behavior, drives the suppression of lattice thermal conductivity.
• To measure the intrinsic electronic band gap of EuTiO₃ using electrical transport and thermopower data.
• To compare thermal and electronic transport in EuTiO₃ with non-magnetic perovskites (SrTiO₃, KTaO₃, EuCoO₃) to isolate the role of 4f electrons.

Proposed method

• Measured electrical resistivity and Seebeck coefficient in single-crystal EuTiO₃ to extract the activation energy and band gap via Arrhenius analysis.
• Used temperature-dependent thermal conductivity measurements to compare the behavior of EuTiO₃ with SrTiO₃, KTaO₃, and EuCoO₃.
• Applied the linearized Boltzmann transport equation to model phonon transport and infer phonon mean free path from thermal conductivity data.
• Estimated phonon mean free path using sound velocity (6.8 km/s) and compared it to the thermal wavevector q_s = k_B T / (ħ v_s) to assess localization effects.
• Evaluated spin-phonon coupling via theoretical modeling of off-diagonal coupling between vibrational modes, extending Eq. (1) to include spin-lattice hybridization.
• Analyzed crystal structure and superexchange pathways (via Ti and O) to assess how spin orientation modulates interatomic force constants and phonon dispersion.

Experimental results

Research questions

• RQ1 What causes the glass-like thermal conductivity in EuTiO₃, given its lack of magnetic frustration or spin liquid character?
• RQ2 How does the presence of Eu²⁺ 4f electrons influence phonon transport above the Néel temperature?
• RQ3 What is the intrinsic electronic band gap of EuTiO₃, and how does it compare to optical and ab initio estimates?
• RQ4 To what extent do random magnetic moments at Eu sites disrupt phonon coherence and reduce thermal conductivity?
• RQ5 Can the observed thermal transport behavior be explained by off-diagonal coupling between phonons and paramagnons, rather than conventional phonon scattering?

Key findings

• EuTiO₃ exhibits a narrow intrinsic band gap of ~0.22 eV, derived from Arrhenius analysis of resistivity and thermopower, consistent with ab initio predictions.
• Thermal conductivity in EuTiO₃ is drastically reduced and shows a monotonic temperature dependence akin to amorphous silica, indicating glass-like behavior.
• The suppression of thermal conductivity occurs well above the Néel temperature (5.5 K), even when magnetic entropy is saturated, indicating that paramagnetic 4f spins are sufficient to scatter phonons.
• The primary source of phonon scattering is the random orientation of large magnetic moments (6.9–7 μB) on Eu²⁺ sites, which disrupt phonon coherence through spin-lattice coupling.
• The phonon mean free path drops below 10 nm at temperatures below 20 K, where q_s ℓ_ph ≈ 1, suggesting the onset of Anderson-like localization due to spin disorder.
• The observed thermal conductivity suppression is attributed to off-diagonal coupling between phonons and paramagnons, not magnetic frustration, and is distinct from spin-liquid systems.