Observation of anomalous thermal Hall effect in altermagnets

This paper reports the systematic observation of a pronounced anomalous phonon thermal Hall effect in the altermagnet candidates MnTe and CrSb, establishing this phenomenon as an intrinsic feature of altermagnets and providing a sensitive probe for identifying this new class of quantum magnets.

The Gist

Imagine you are trying to understand how different types of "magnetic teams" behave. For a long time, scientists only knew about two types of teams:

1. The Ferromagnets (The Unifiers): Think of a marching band where everyone faces the same direction. They are loud, they have a strong net magnetic pull, and they create a "traffic jam" for electrons, causing them to curve sideways (this is the famous Anomalous Hall Effect).
2. The Antiferromagnets (The Perfect Opposites): Imagine two rows of dancers facing each other perfectly. One row faces North, the other South. They cancel each other out completely. To the outside world, they look like they have no magnetism at all. Because they are so balanced, they usually don't cause electrons to curve sideways.

Enter the New Kid: The Altermagnet
Recently, scientists discovered a third type of team called the Altermagnet. These are tricky! Like the Antiferromagnets, they have zero net magnetism (the North and South rows cancel out). But, like the Ferromagnets, they have a secret internal structure that splits their energy levels.

The big mystery was: If they look like the balanced Antiferromagnets, do they act like the Unifiers? Specifically, do they create that "sideways curve" in electricity?

The Problem with the Old Test
Scientists tried to test this by sending electricity through these materials (MnTe and CrSb). But the results were confusing. Sometimes the "sideways curve" was there, sometimes it wasn't, and sometimes it was so weak it was hard to measure. It was like trying to hear a whisper in a noisy room; the electrical signal was getting lost.

The New Idea: Listen to the Heat
The authors of this paper decided to stop listening to the electricity and start listening to the heat.

Imagine the material is a busy highway.

• Electrons are the fast sports cars.
• Phonons (vibrations of the atoms) are the heavy trucks carrying the heat.

In most materials, heat travels straight. But in a magnetic field, these "heat trucks" might get pushed to the side. This is the Thermal Hall Effect.

The Discovery
The researchers took two altermagnet candidates, MnTe (a semiconductor) and CrSb (a metal), and heated one end while cooling the other. They applied a magnetic field and watched where the heat went.

Here is what they found, using a simple analogy:

• The "Normal" Heat: In most materials, if you push the heat trucks with a magnet, they drift sideways in a straight line. The harder you push, the more they drift. This is the "conventional" effect.
• The "Anomalous" Heat: In these altermagnets, the heat trucks didn't just drift; they did a U-turn. As the magnetic field got stronger, the heat didn't just go further sideways; it actually switched directions!

This "U-turn" behavior is the smoking gun. It's the thermal version of the "sideways curve" that ferromagnets are famous for.

Why is this a Big Deal?

1. It's the Real Deal: The researchers proved that this weird heat behavior comes from the unique "Altermagnet" structure itself, not from a tiny bit of leftover magnetism (which would be like a tiny leak in the perfect dance).
2. It's Better than Electricity: The electrical tests were messy and unreliable. But the heat test was loud and clear. It's like trying to find a specific person in a crowd: looking for them by their voice (electricity) was hard because the crowd was noisy, but looking for their shadow (heat) was easy and distinct.
3. The Mechanism: It seems the magnetic structure of these materials is so special that it twists the "heat trucks" (phonons) directly, even though the material has no net magnetism. It's as if the road itself is curved by the magnetic rules of the altermagnet.

The Bottom Line
This paper says: "Stop trying to find altermagnets by looking for electrical currents; they are too quiet. Instead, look for the Anomalous Thermal Hall Effect."

If you heat a material and the heat suddenly curves sideways in a weird, non-linear way, you've likely found a new, exotic type of magnet that could be the key to future super-fast, low-energy computers. They found this "heat signature" in both MnTe and CrSb, proving that this new class of magnets is real and ready to be explored.

Technical Summary

1. Problem Statement

Altermagnets (AMs) are a recently proposed third category of collinear magnets, distinct from ferromagnets (FMs) and antiferromagnets (AFMs). They possess zero net magnetization (like AFMs) but exhibit spin-splitting in momentum space (like FMs) due to specific crystal symmetries (rotation or mirror operations connecting magnetic sublattices).

• The Challenge: While spectroscopic evidence for altermagnetism exists, experimental observation of the Anomalous Hall Effect (AHE)—a hallmark of broken time-reversal symmetry (TRS)—has been elusive or inconsistent in candidate materials like MnTe and CrSb. In MnTe, AHE signals are weak and sample-dependent; in CrSb, nonlinear Hall signals are attributed to multi-band effects rather than intrinsic altermagnetism.
• The Gap: There is a need for a robust, sensitive probe to identify genuine altermagnetic order and confirm TRS breaking in these materials, particularly where electrical transport measurements fail to provide clear signatures.

2. Methodology

The authors conducted systematic transport measurements on two representative altermagnet candidates:

• Materials:
  • $\alpha$-MnTe: A semiconducting altermagnet with a NiAs-type structure ($P6_3/mmc$). Mn spins are aligned parallel in the $ab$-plane and antiparallel along the $c$-axis.
  • CrSb: A metallic altermagnet with a similar magnetic structure but spins aligned along the $c$-axis.
• Sample Preparation:
  • MnTe single crystals were grown via an Sb-flux method.
  • CrSb single crystals were grown via chemical vapor transport using iodine.
• Experimental Techniques:
  • Magnetization: Measured using a Vibrating Sample Magnetometer (VSM) to characterize magnetic anisotropy and transition temperatures ($T_{N} \approx 307$ K for MnTe, $>700$ K for CrSb).
  • Electrical Transport: Resistivity ($\rho_{xx}$) and Hall conductivity ($\sigma_{xy}$) were measured to determine carrier type and contribution.
  • Thermal Transport: Longitudinal thermal conductivity ($\kappa_{xx}$) and Thermal Hall conductivity ($\kappa_{xy}$) were measured using a three-thermometer method in a Physical Property Measurement System (PPMS) under magnetic fields up to 9 T.
• Data Analysis:
  • Separation of Contributions: The total thermal Hall signal was decomposed into electronic and phonon contributions. The electronic part was estimated using the Wiedemann-Franz (WF) law ($\kappa_{el} = L_0 T \sigma$).
  • Modeling: The phonon thermal Hall conductivity ($\kappa^{ph}_{xy}$) was fitted to separate conventional (linear-in-field) and anomalous (nonlinear/saturating) components using the function: $\kappa^{ph}_{xy} = kB + \kappa_A \tanh(B/B_0)$.

3. Key Results

• MnTe (Semiconductor):
  • Heat transport is dominated by phonons.
  • The total thermal Hall conductivity ($\kappa_{xy}$) shows a distinct hump around 1 T followed by a sign reversal (positive to negative).
  • After subtracting the negligible electronic contribution, the phonon thermal Hall conductivity ($\kappa^{ph}_{xy}$) exhibits a strong anomalous component that saturates at high fields, mimicking the behavior of ferromagnets.
• CrSb (Metal):
  • Heat transport has a significant electronic contribution, but the phonon contribution is substantial.
  • The total $\kappa_{xy}$ mirrors the nonlinear electrical Hall behavior.
  • After subtracting the electronic contribution, the remaining phonon thermal Hall signal is robust and displays a similar anomalous, saturating behavior to MnTe.
• Comparison with Ferromagnetism:
  • The anomalous signal in both materials saturates at fields $\ge 1$ T.
  • However, the weak ferromagnetic components (canted spins) in these materials saturate at much lower fields ($\sim 0.1$ T).
  • This discrepancy rules out weak net magnetization as the primary cause of the anomalous thermal Hall effect.

4. Key Contributions

• Discovery of Anomalous Phonon Thermal Hall Effect (pTHE): The paper reports the first observation of a pronounced, intrinsic anomalous pTHE in altermagnets. This effect persists even when the net magnetization is zero.
• Superior Probe for Altermagnets: The study demonstrates that thermal Hall measurements are more sensitive to altermagnetic order than electrical Hall measurements. While AHE is weak or absent in MnTe and CrSb, the anomalous pTHE is robust and clear.
• Mechanism Identification: The authors propose that the effect arises from Néel-vector-driven symmetry breaking rather than net magnetization. Two potential mechanisms are discussed:
  1. Intrinsic Crystal Thermal Hall Effect: Berry curvature in the phonon sector driven by the specific arrangement of nonmagnetic ligands and Néel vector orientation.
  2. Magnon-Phonon Hybridization: Coupling between magnons and phonons transfers magnetic Berry curvature to the phonon sector, creating chiral phonon modes that carry heat transversely.

5. Significance

• Validation of Altermagnetism: The observation of anomalous pTHE provides strong experimental evidence for the existence of altermagnetic order and the breaking of combined time-reversal and spatial-translation symmetries in MnTe and CrSb.
• New Paradigm for Detection: It establishes phonon-mediated thermal transport as a superior diagnostic tool for identifying new altermagnetic materials, overcoming the limitations of electrical probes which are often obscured by multi-band effects or weak signals.
• Fundamental Physics: The findings bridge the gap between magnetic order and lattice dynamics, suggesting that phonons in altermagnets can carry topological information (Berry curvature) previously thought to be exclusive to electronic or magnonic systems. This opens new avenues for studying topological phononics and spin-phonon coupling in quantum magnets.