Observation of anomalous thermal Hall effect in altermagnets

Abstract: Altermagnets, recently proposed as a third category of collinear magnets, combine the features of zero net magnetization in antiferromagnets and the spin splitting in ferromagnets. While abundant spectroscopic evidence for altermagnetism has been reported, experimental observation of the anomalous Hall effect, a hallmark of ferromagnetism, remains scarce. Here, we present systematic measurements of the thermal Hall effect in two representative altermagnet candidates, MnTe and CrSb. In both materials, we observe a pronounced anomalous phonon thermal Hall signal, with no electrical counterpart observed, attributed to the coupling of this distinctive magnetic structure with phonons. Our findings establish the anomalous phonon thermal Hall effect as an intrinsic feature of altermagnets, and provide a sensitive probe to identify this new kind of quantum magnets.

• The paper identifies a robust anomalous phonon thermal Hall effect in α-MnTe and CrSb as a definitive signal of altermagnetism.
• It employs precise thermal transport measurements to isolate phonon contributions from negligible electrical Hall signals.
• The study correlates field-dependent sign reversals and saturation behaviors to lattice symmetry and resonant magnon-phonon hybridization.

Observation of Anomalous Thermal Hall Effect in Altermagnets

Introduction and Motivation

Altermagnets constitute an emergent class of collinear magnetic materials, defined by alternating spin orientations in both real and reciprocal space. This symmetry paradigm, distinct from conventional ferromagnets (FMs) and antiferromagnets (AFMs), enables momentum-space spin splitting without recourse to spin-orbit coupling and absent net magnetization. Experimental identification of altermagnetic order has primarily relied on spectroscopic signatures and band splitting; however, direct transport evidence, notably of the anomalous Hall effect (AHE), remains scarce and inconclusive. This work presents a comprehensive investigation into the thermal Hall effect (THE) in two prototypical altermagnets, α-MnTe and CrSb, not only targeting novel heat transport phenomena but also establishing thermal Hall measurements as a sensitive probe for altermagnetism.

Experimental Approach and Material Systems

Single crystals of α-MnTe (semiconducting) and CrSb (metallic) were synthesized via Sb-flux-assisted growth and chemical vapor transport, respectively. Both materials exhibit collinear compensated spin configurations, confirmed by magnetometric analysis. For transport characterization, resistivity, Hall conductivity, and thermal conductivity were measured in both longitudinal and transverse geometries using a three-thermometer technique under high-vacuum conditions and variable magnetic fields.

Principal Findings

Absence of Electrical Anomalous Hall Effect

In α-MnTe, electrical Hall measurements disclosed linear field dependence across all temperatures with the absence of obvious anomalies, paralleling the behavior reported in previous literature for some MnTe samples. In CrSb, nonlinear Hall signals were observed but attributed to multiband effects rather than intrinsic AHE. This reinforces the ongoing challenge in using electrical Hall transport to definitively identify altermagnetic phases.

Robust Anomalous Thermal Hall Response

Both materials display a pronounced anomalous phonon thermal Hall conductivity, exceeding any electronic thermal Hall contributions estimated from the Wiedemann-Franz law. The total thermal Hall conductivity in α-MnTe follows the characteristic phonon peak and exhibits a nontrivial field dependence—including a sign reversal—distinct from conventional linear-in-field behavior. By decomposing the thermal Hall signal into conventional (linear) and anomalous (nonlinear, saturating) components, a strong anomalous phonon THE is extracted in both systems. For CrSb, after rigorously subtracting electronic contributions, a robust and qualitatively analogous anomalous phonon THE emerges, with saturation fields and magnitude increasing as a function of temperature.

Field Dependence and Magnetization Disparity

The saturation fields for the anomalous phonon THE (~1 T) substantially exceed the fields associated with any weak ferromagnetic component (~0.1 T), observed in magnetization curves. Such mismatch indicates that the anomalous thermal Hall effect is decoupled from net magnetization and thus cannot be ascribed to weak ferromagnetic ordering.

Mechanistic Interpretation

The anomalous phonon THE in these altermagnets is interpreted as stemming from intrinsic time-reversal symmetry breaking and lattice symmetry effects, governed by the Néel vector rather than net magnetization. Resonant magnon-phonon hybridization is a plausible further mechanism, facilitating chiral phonon modes and transferring magnetic Berry curvature into the phonon sector. These hybrid modes have been experimentally observed in related altermagnetic systems, supporting their relevance for driving strong thermal Hall responses. Importantly, the presence and magnitude of the anomalous phonon THE do not necessarily correlate with anomalous electrical Hall signals, resolving prior contradictions regarding Hall response detection in altermagnets.

Implications and Future Directions

Practical Implications

The identification of a robust anomalous phonon thermal Hall effect in altermagnets suggests that phonon-mediated heat transport constitutes a more sensitive and definitive probe of altermagnetic order than conventional electrical Hall measurements. This has implications for device applications in spin-caloritronics and for the development of thermal sensors and control elements exploiting altermagnetic materials.

Theoretical Implications

These findings promote a re-examination of the microscopic mechanisms underlying Hall effects in quantum magnets, emphasizing the roles of lattice symmetry, Berry curvature, and magnon-phonon coupling. The results support theoretical predictions of intrinsic crystal Hall effects and highlight the Néel vector as a dominant order parameter.

Future Developments

Several avenues for further study are indicated:

• Controlled manipulation of the Néel vector (via external magnetic fields or strain) to elucidate symmetry-driven sign and magnitude changes in thermal Hall conductivity.
• High-resolution neutron, Raman, or THz spectroscopy to resolve magnon-phonon anticrossing and test hybridization models.
• Extension to additional altermagnetic materials and exploration of device-level heat transport phenomena.

Conclusion

This work establishes the anomalous phonon thermal Hall effect as an intrinsic and substantial transport signature of altermagnets, observed in α-MnTe and CrSb—materials where electrical Hall effects fail to provide conclusive evidence of altermagnetic order. The anomalous thermal Hall signal is unambiguously attributed to Néel vector and lattice symmetry effects, potentially magnified by magnon-phonon hybridization. These results advance the experimental toolkit for identifying quantum magnetic phases and deepen the understanding of phonon-driven transverse transport in symmetry-broken materials (2604.03183).