Thermal Hall Effect: New Insights from Quantum Materials

Recent research on the thermal Hall effect in quantum materials is revealing unexpected behaviors that challenge conventional theories. Unlike its extensively studied electrical counterpart, the thermal Hall effect involves heat transport influenced by magnetic fields, offering insights into exotic excitations and interactions within materials.

Understanding this phenomenon could lead to advancements in quantum technology and novel material applications. Researchers are now clarifying how phonons, magnons, and other quasiparticles contribute to thermal transport.

Distinguishing Thermal Hall and Electrical Hall

The Hall effect describes how particles experience a transverse force when subjected to a perpendicular magnetic field. In the electrical Hall effect, this force acts on charge carriers, typically electrons, causing them to accumulate on one side of a material, leading to a measurable voltage difference. First observed by Edwin Hall in 1879, this phenomenon underpins technologies such as Hall sensors and quantum Hall systems.

The thermal Hall effect, by contrast, involves the deflection of energy carriers rather than charge carriers, making its mechanisms more complex. Unlike electrons, which respond directly to the Lorentz force, the energy carriers responsible for the thermal Hall effect—such as phonons, magnons, or other quasiparticles—lack charge. Their deflection in a magnetic field cannot be explained by conventional electromagnetic interactions alone but is influenced by mechanisms like spin-lattice coupling, Berry curvature effects, and topological properties. These factors depend on the specific nature of the excitations in a given system.

A key difference between the two effects is their dependence on material properties. The electrical Hall effect is dictated by the density and mobility of charge carriers, which can be tuned through doping or external fields. In contrast, the thermal Hall effect is highly sensitive to interactions between quasiparticles and the lattice structure. For instance, in magnetic insulators, magnons—collective spin excitations—can exhibit a thermal Hall response even in the absence of free electrons. Similarly, in certain nonmagnetic materials, phonons—quantized lattice vibrations—can contribute to a transverse heat current despite their neutral charge. These distinctions highlight the broader range of phenomena governing thermal transport compared to electrical conduction.

Phonon and Magnon Contributions

The thermal Hall effect in quantum materials is closely tied to phonons and magnons, which serve as primary heat carriers in insulating systems. Unlike electrons, these neutral excitations exhibit transverse transport through more intricate mechanisms. Understanding their contributions requires examining how they couple to external fields, the role of intrinsic material symmetries, and the topological effects influencing their motion.

Phonons, the quantized vibrations of a crystal lattice, typically follow diffusive or ballistic transport in the absence of magnetic effects. However, in certain materials, they acquire an effective transverse velocity due to interactions with spin textures or lattice asymmetries. In magnetic insulators, spin-phonon coupling can induce asymmetric phonon scattering, as observed in materials like Tb\(_3\)Ge\(_5\)O\(_{12}\). Recent studies suggest that phonons can acquire a Berry curvature in systems with broken time-reversal symmetry, leading to a topological thermal Hall effect even without magnons.

Magnons, the collective excitations of spin systems, provide another pathway for transverse heat transport. In magnetically ordered materials, magnons propagate by carrying spin angular momentum. In systems with nontrivial magnetic textures, such as ferromagnets with Dzyaloshinskii-Moriya interactions or frustrated magnets with chiral spin states, magnons experience an effective Lorentz-like force. This results in a magnonic Hall effect, where heat carried by magnons is deflected perpendicular to the thermal gradient. Experimental data from materials like Lu\(_2\)V\(_2\)O\(_7\) support this phenomenon, showing significant thermal Hall conductivity linked to magnon transport.

The interplay between phonons and magnons can enhance or suppress the thermal Hall effect depending on the material’s structure and temperature. In some cases, phonons carry the dominant heat current, but their scattering off magnons leads to an indirect magnon-mediated thermal Hall response. Conversely, in systems with weak phonon-magnon coupling, their contributions remain largely independent, allowing researchers to disentangle their roles through careful experimentation. Studies on YIG (yttrium iron garnet) reveal a temperature-dependent crossover between phonon- and magnon-dominated transport, shedding light on their relative importance.

Experimental Approaches

Measuring the thermal Hall effect in quantum materials is challenging due to the need for precise heat flow control and detecting transverse temperature gradients at extremely small scales. Unlike electrical measurements, which use well-established voltage probes, thermal transport experiments require highly sensitive thermometry techniques. Researchers employ microfabricated thermal sensors, such as nanometer-scale resistance thermometers or scanning thermal microscopy, to achieve the necessary resolution.

To isolate the thermal Hall signal, experiments are conducted in cryogenic environments where quantum materials exhibit pronounced thermal transport properties. Cooling to millikelvin temperatures reduces phonon scattering and enhances the contribution of collective excitations like magnons or spinons. Applying an external magnetic field perpendicular to the heat current allows researchers to probe field-dependent behavior. Measurements of thermal Hall conductivity often use a differential method, comparing temperature gradients under positive and negative field orientations to eliminate background noise.

Material preparation is critical for reliable data. Single-crystal samples with well-defined lattice structures are preferred, as polycrystalline materials introduce grain boundary effects that can obscure intrinsic thermal transport. High-purity synthesis techniques, such as floating-zone crystal growth or molecular beam epitaxy, minimize defects that could disrupt quasiparticle motion. Sample geometry is also optimized to maintain uniform heat distribution, with elongated bar-shaped specimens commonly used to enhance measurement accuracy.

Observations in Quantum Materials

Recent investigations into the thermal Hall effect in quantum materials have revealed unexpected behaviors that challenge conventional theories. In magnetic insulators such as Tb\(_3\)Ge\(_5\)O\(_{12}\) and Lu\(_2\)V\(_2\)O\(_7\), significant thermal Hall signals have been attributed to magnon and phonon interactions with spin textures. These materials exhibit a pronounced transverse heat flow even without mobile charge carriers, reinforcing the idea that collective excitations play a dominant role. The magnitude of the thermal Hall conductivity in these systems often defies simple models based on conventional scattering mechanisms, suggesting deeper quantum mechanical effects.

In frustrated magnets like the pyrochlore compounds Pr\(_2\)Zr\(_2\)O\(_7\) and Tb\(_2\)Ti\(_2\)O\(_7\), a thermal Hall response emerges despite the absence of long-range magnetic order. This suggests that exotic excitations like spinons—fractionalized quasiparticles predicted in quantum spin liquids—may contribute to heat transport in ways not yet fully understood. The presence of a sizeable thermal Hall conductivity in these systems has spurred theoretical efforts to explore how topological features of the spin liquid state generate a transverse thermal current. Experimental studies using neutron scattering and specific heat measurements provide complementary evidence supporting these unconventional quasiparticles.

Theoretical Models

Developing a theoretical framework for the thermal Hall effect in quantum materials requires accounting for the diverse ways in which neutral quasiparticles interact with external fields and lattice structures. Unlike the electrical Hall effect, which can often be described using classical Lorentz force arguments or simple band topology, thermal transport involves more intricate quantum interactions. Researchers have turned to models incorporating Berry curvature effects, spin-lattice coupling, and topological excitations to explain the observed phenomena.

One approach involves extending topological band theory, which has successfully described electronic systems, to phonons and magnons. In materials with broken time-reversal symmetry, phononic modes can acquire a nontrivial Berry curvature, leading to a transverse thermal response even without magnetic order. Similarly, in magnetic insulators, magnon bands can develop topological gaps, resulting in robust thermal Hall conductivity. Numerical simulations using the Boltzmann transport equation and Green’s function methods provide predictions that align with experimental data.

Beyond band-theoretic descriptions, researchers explore field-theoretic models to capture the role of fractionalized excitations in quantum spin liquids. In these systems, emergent gauge fields and spinon dynamics introduce additional contributions to the thermal Hall effect. Theoretical studies suggest that a chiral spin liquid phase can give rise to a quantized thermal Hall response, analogous to the quantized electrical Hall conductivity observed in topological insulators. These predictions motivate further experimental efforts to identify materials exhibiting such exotic transport signatures, potentially leading to the discovery of novel quantum phases.