Complex Temperature-dependent Thermal Conductivity in a Sawtooth Chain Magnet Fe$_\mathrm{2}$SiSe$_\mathrm{4}$

Abstract: Geometrically frustrated magnets provide an ideal platform for exploring the interplay between lattice geometry and spin degrees of freedom. Here, we investigate the interactions between lattice and spin via thermal-transport measurements on the triangular sawtooth-lattice olivine magnet Fe$\mathrm{2}$SiSe$\mathrm{4}$, which exhibits successive magnetic transitions at $T_1 = 110$ K (antiferromagnetic) and $T_2 = 50$ K (ferrimagnetic). Although phonons dominate the thermal conductivity, its temperature dependence displays a pronounced double-peak structure arising from spin-phonon coupling. In the intermediate temperature range between $T_1$ and $T_2$ , resonant scattering of phonons by magnetic excitations around 5 meV produces a broad maximum around 60 K. Below $T_2$, the resonant spin-phonon scattering is strongly suppressed, leading to a rapid increase in thermal conductivity upon cooling and a pronounced low-temperature peak near 11 K, characteristic of heat transport governed by conventional phonon scattering mechanisms. Notably, this low-temperature peak is enhanced by a factor of $\sim 5$ compared to the broad maximum at higher temperatures. These results demonstrate the strong sensitivity of thermal transport to spin-lattice interactions and highlight spin-phonon scattering as an effective mechanism for tailoring thermal conductivity in geometrically frustrated magnets.

• The paper demonstrates that spin-phonon coupling induces a distinct double-peak thermal conductivity in Fe₂SiSe₄ across multiple magnetic phases.
• The methodology integrates high-precision measurements of thermal expansion, specific heat, and conductivity, modeled via the Debye–Callaway framework.
• Results indicate that tunable magnetic transitions modulate phonon scattering, offering insights for thermoelectric applications and advanced phase-probing techniques.

Complex Thermal Conductivity and Spin-Phonon Coupling in the Sawtooth Chain Magnet Fe$_2$SiSe$_4$

Introduction

The study investigates the intricate thermal transport behavior in single crystals of the sawtooth-chain olivine magnet Fe$_2$SiSe$_4$, which features pronounced geometrical frustration, strong spin-orbit interactions, and multiple magnetic transitions. Unlike traditional $A_2BX_4$ olivine systems (with $A$ = Mn, Fe, Co, Ni; $B$ = Si, Ge; $X$ = O, S, Se, Te), Fe$_2$SiSe$_4$ supports successive antiferromagnetic ($_4$0 K) and ferrimagnetic ($_4$1 K) transitions, in addition to a weaker transition at $_4$2 K. This system explicitly couples spin, lattice, and orbital degrees of freedom, yielding a thermal conductivity $_4$3 with a nontrivial double-peak structure, which is highly sensitive to the underlying spin-lattice interactions.

Figure 1: Crystal and magnetic structures of Fe$_4$4SiSe$_4$5 showing the sawtooth chain arrangement and the distinct single-$_4$6 and double-$_4$7 magnetic orders below $_4$8 and $_4$9, respectively.

Experimental Approach

High-quality Fe$_2$0SiSe$_2$1 single crystals were synthesized using chemical vapor transport and characterized via magnetization, specific heat, thermal expansion, and longitudinal thermal conductivity (along the chain $_2$2 axis). Thermal expansion measurements employed a high-resolution capacitive dilatometer; specific heat was measured via the relaxation method. $_2$3 was acquired in steady-state geometry with field-calibrated thermometry, ensuring less than 4% systematic uncertainty below 150 K.

Magnetic and Structural Phase Behavior

Fe$_2$4SiSe$_2$5 exhibits pronounced magnetic anisotropy in $_2$6, dominated by easy-plane alignment and a strong $_2$7-factor anisotropy due to low-symmetry crystal fields. The system transitions from a paramagnetic phase to a single-$_2$8 antiferromagnetic state at 110 K, characterized by Fe2 moments ($_2$9/Fe) aligned along $_4$0, with feeble canting on Fe1. Below $_4$1 K, a double-$_4$2 structure is realized, introducing $_4$3-axis ferrimagnetism and additional moment components. While $_4$4 yields only minor thermodynamic anomalies, an associated first-order lattice transition is captured in the thermal-expansion coefficient.

Figure 2: Specific heat and linear thermal expansion as a function of temperature, revealing sharp lambda anomalies at $_4$5, first-order jumps at $_4$6 and $_4$7, and highly anisotropic uniaxial responses.

Thermal expansion ($_4$8, $_4$9) constrains the nature of each transition: second-order at $A_2BX_4$0, weakly first-order at $A_2BX_4$1 (no detectable hysteresis), and strongly first-order at $A_2BX_4$2 (hysteresis $A_2BX_4$34.5 K in $A_2BX_4$4). These results, combined with Clausius–Clapeyron/Ehrenfest analyses, show $A_2BX_4$5 and $A_2BX_4$6 display strong uniaxial pressure dependences, suggesting underlying magnetoelastic coupling is both robust and directionally selective.

Double-Peak Thermal Conductivity and Resonant Scattering

$A_2BX_4$7 is dominated by phonons, with negligible electronic or purely magnetic heat transport, validated by resistivity and Wiedemann–Franz analysis. The most salient feature is its double-peak form: a broad maximum near $A_2BX_4$8 K and a sharper, more intense peak near $A_2BX_4$9 K. This is inconsistent with typical phonon thermal transport in insulators, implicating additional scattering channels.

Figure 3: Temperature dependence of the in-plane thermal conductivity $A$0 displays a pronounced double-peak structure. Fits reveal resonant spin-phonon scattering dominates between $A$1 and $A$2.

Quantitative fits using the Debye–Callaway model isolate three regimes:

• Region I ($A$3): Paramagnetic; $A$4 well-modeled by boundary, point-defect, and Umklapp scattering. High point-defect scattering reflects short-range spin fluctuations acting as dynamic scatterers.
• Region II ($A$5): Single-$A$6 phase; phonon thermal transport is dominated by resonant scattering with a gap $A$7 meV. This is attributed to phonons interacting with discrete magnetic excitations associated with spin-orbit-split levels on Fe$A$8, analogous to neutron-scattering-observed modes in Fe$A$9SiO$B$0 at 5.4–5.9 meV. The broad maximum at 60 K appears precisely where this resonance occurs.
• Region III ($B$1): Double-$B$2 ground state; resonant contribution is quenched, and $B$3 recovers a strong peak near 11 K, corresponding to the crossover between boundary and Umklapp scattering. The low-temperature peak amplitude ($B$423 W m$B$5 K$B$6) is %%%%67$A$68%%%% that of the resonant maximum.

Below $B$9, abrupt lattice and magnetic reordering shifts the spin excitation spectrum out of resonance with the dominant phonon modes, effectively restoring conventional phonon-limited heat transport. The phonon mean free path $X$0, evaluated from the kinetic formula and measured/fitted parameters, displays a sharp increase on cooling below $X$1, corroborating the suppression of spin-phonon scattering.

Broader Implications and Outlook

The work establishes Fe$X$2SiSe$X$3 as a canonical frustrated magnet where thermal conductivity can be intricately tuned by manipulating spin-orbit and spin-lattice interactions. The strong sensitivity to local crystal field environments demonstrates the utility of thermal transport as a probe of subtle magnetic and electronic microstructures, extending the understanding of heat flow beyond simple phonon paradigms.

The data imply several theoretical and application consequences:

• Thermoelectric Strategies: Controlled spin-phonon scattering in frustrated magnets provides a mechanism to modulate $X$4 independently of charge carrier behavior. Materials with switchable or tunable spin excitation spectra are promising for the design of thermal management or thermoelectric devices in which decoupled control of thermal and electrical conductivity is crucial.
• Excitation Engineering: Since the observed resonance is attributed to spin-orbit-induced crystal field excitations, modifying the ligand (e.g., S or Te substitution for Se), or applying pressure/strain along specific axes, may permit further manipulation of the magnetic excitation spectrum and the resulting resonance conditions.
• Phase-Competition Probes: The double-peak structure in thermal conductivity serves as a highly sensitive measure for transitions or incipient ordering tendencies, suggesting that analogous measurements in other frustrated or low-dimensional compounds could elucidate hidden quantum phase behaviors.

Conclusion

This study demonstrates that the thermal conductivity of Fe$X$5SiSe$X$6 is a direct and sensitive probe of spin-lattice coupling, manifested in an unusual double-peak structure driven by resonant spin-phonon scattering at the single-$X$7 antiferromagnetic phase and its abrupt suppression in the double-$X$8 ground state. Fe$X$9SiSe$_2$0 establishes a new platform for exploring the interplay of geometric frustration, spin-orbit interactions, and lattice dynamics, and highlights the potential of frustrated quantum magnets in thermoelectric and thermal management applications (2606.06858).