Anomalies in the thermal conductivity of honeycomb antiferromagnet MnPS$_{3}$

This study reveals that the thermal transport properties of the honeycomb antiferromagnet MnPS$_3$, particularly the sign reversals in thermal Hall conductivity and multiple valleys in longitudinal thermal conductivity below 2 K, are caused by the redistribution of Berry curvature in magnon bands, highlighting the effectiveness of thermal Hall measurements for detecting topological features in magnetic insulators.

The Gist

The Big Picture: A Magnetic Puzzle

Imagine a material called MnPS₃ (Manganese Phosphorus Sulfide). Think of this material as a microscopic, two-dimensional city where tiny magnets (called "spins") live on a honeycomb-shaped grid, like a beehive. At normal temperatures, these magnets are busy and chaotic. But as you cool the material down, they start to line up in an orderly, anti-parallel dance (an antiferromagnetic state).

Scientists have long been trying to understand how "heat" moves through this magnetic city. Usually, heat is carried by vibrating atoms (called phonons), like sound waves traveling through a room. But in magnetic materials, heat can also be carried by the magnetic waves themselves (called magnons).

The goal of this study was to see how these magnetic waves move when you apply a strong magnetic field, especially at extremely cold temperatures (colder than almost anything found in nature).

The Experiment: The Heat Traffic Test

The researchers set up a special experiment to measure how heat flows through this material.

• The Setup: They heated one side of a crystal and measured how the heat traveled.
• The Twist: They applied a magnetic field from the top (like a giant magnet hovering over the city).
• The Measurement: They looked at two things:
  1. Longitudinal Conductivity: How well heat travels straight from the hot side to the cold side (like cars driving down a highway).
  2. Thermal Hall Conductivity: A weird effect where heat gets pushed sideways, perpendicular to the flow, creating a "thermal wind" (like a car drifting sideways on a curved road).

What They Found: The "Sign Reversal" Mystery

The team discovered some very strange behavior when they cooled the material down to near absolute zero (below 2 Kelvin).

1. The "Valleys" in the Highway
When they increased the magnetic field, the amount of heat flowing straight through didn't just go up or down smoothly. Instead, it hit several "valleys" (dips) where heat flow suddenly dropped. This suggests that the magnetic waves were getting blocked or scattered in specific ways at certain magnetic strengths.

2. The "U-Turn" of the Sideways Wind
The most surprising discovery was in the sideways heat flow (the Thermal Hall effect).

• Imagine the sideways heat flow is a river. Usually, a river flows in one direction.
• In this material, as they changed the magnetic field, the river didn't just get stronger or weaker; it actually changed direction.
• At one field strength, the heat drifted to the left. At a slightly stronger field, it suddenly flipped and drifted to the right. Then, at an even stronger field, it might flip again.

The paper calls this a "sign reversal." It's like driving a car and suddenly finding that the steering wheel has been reversed, sending you the opposite way without you touching the wheel.

The Explanation: The "Topological Map"

Why did the heat change direction? The authors suggest it's due to something called Berry Curvature.

• The Analogy: Imagine the energy levels of the magnetic waves are like a complex, hilly landscape. The "Berry curvature" is like a hidden magnetic force embedded in the shape of these hills.
• The Redistribution: As the external magnetic field changes, it reshapes this landscape. The "hills" and "valleys" of energy shift around.
• The Result: When the landscape shifts, the "traffic rules" for the heat-carrying waves change. The waves suddenly find a new path that pushes them in the opposite direction. The researchers believe they are seeing these "topological transitions" happen in real-time.

Why This Matters (According to the Paper)

The paper claims that this experiment proves that thermal Hall measurements are a super-sensitive tool.

• The Magnetometer Blind Spot: If you just measure the magnetism of the material (how strong the magnets are), you might not see anything special. The paper notes that their magnetometers didn't see any "kinks" or changes at the exact moments the heat flow changed direction.
• The Heat Sensor's Superpower: The heat sensors, however, saw everything. They detected these subtle shifts in the "topological map" of the magnetic waves that the magnetometers missed.

Summary

In simple terms, the scientists cooled a honeycomb magnetic crystal to near absolute zero and turned up the magnetic field. They found that the heat flowing through the crystal started doing a "U-turn" and flowing in the opposite direction multiple times. They believe this happens because the magnetic field is reshuffling the invisible "map" of the material's energy, forcing the heat waves to change direction. This proves that measuring heat flow is a powerful way to see the hidden, complex geometry of magnetic materials.

Technical Summary

Technical Summary: Anomalies in the Thermal Conductivity of Honeycomb Antiferromagnet MnPS₃

Problem and Context
Intrinsic two-dimensional (2D) magnets serve as a platform for exploring collective, charge-neutral, and low-energy excitations. Distinguishing the specific roles of these excitations experimentally has remained a challenge. While the thermal Hall effect (THE) is a powerful tool for studying charge-neutral excitations such as magnons, phonons, and spinons in magnetic insulators, the correspondence between experimental observations and theoretical calculations in three-dimensional magnets remains unclear due to complex spin Hamiltonians. The 2D van der Waals magnet MnPS₃, with its honeycomb lattice and Néel temperature ($T_N$) of 78 K, offers an ideal platform to investigate topological magnon transport and low-dimensional magnetism. Previous studies on MnPS₃ above 20 K detected finite thermal Hall conductivity ($\kappa_{xy}$), attributing it to exchange and single-ion magnetostriction, but the behavior at ultra-low temperatures and high magnetic fields remained unexplored.

Methodology
The authors investigated the thermal transport properties of high-quality MnPS₃ single crystals grown via chemical vapor transport. The study extended thermal-transport measurements to ultra-low temperatures ($< 0.01 T_N$, down to 0.5 K) and high magnetic fields (up to 15 T).

• Experimental Setup: Measurements were performed using a standard steady-state method with a one-heater-three-thermometer configuration. Heat current ($J_Q$) was applied parallel to the $a$-axis, while the magnetic field ($B$) was applied along the $c^*$-axis.
• Measurements: Both longitudinal thermal conductivity ($\kappa_{xx}$) and transverse thermal Hall conductivity ($\kappa_{xy}$) were measured simultaneously. Magnetization ($M$) was measured using a commercial MPMS-XL5 above 2 K and a home-built Faraday-force magnetometer below 2 K.
• Data Analysis: To isolate magnetic contributions, the linear phonon thermal Hall background (observed at high fields) was subtracted from the total $\kappa_{xy}$ to estimate the magnetic component ($\Delta\kappa_{xy}$). Two samples with different thicknesses were measured to ensure reproducibility and assess sample dependence.

Key Contributions and Results

1. Longitudinal Thermal Conductivity ($\kappa_{xx}$):

   • At high temperatures, $\kappa_{xx}$ exhibits a peak around 20 K, characteristic of phonon transport.
   • Below 50 K, the field dependence of $\kappa_{xx}$ shows a sharp dip at the spin-flop (SF) transition field ($B_{sf} \approx 4.5$ T) and a significant suppression within the SF phase.
   • Below 1 K, $\kappa_{xx}$ follows a $T^{2.8}$ dependence, indicating ballistic phonon conduction with a mean free path comparable to the sample thickness.
   • The suppression of $\kappa_{xx}$ above 6 T is attributed to a decrease in the magnon contribution ($\kappa_{xx}^{mag}$) due to the field-induced increase of the magnon gap in the SF phase, rather than magnon-phonon resonance scattering.

2. Thermal Hall Conductivity ($\kappa_{xy}$) Anomalies:

   • Above 30 K, $\kappa_{xy}$ shows a linear field dependence attributed to the phonon thermal Hall effect.
   • Below 20 K, distinct peaks and valleys emerge in the SF phase ($B > B_{sf}$).
   • Sign Reversals: Most notably, below 2 K, the field dependence of the subtracted magnetic thermal Hall conductivity ($\Delta\kappa_{xy}$) exhibits multiple sign reversals within the SF phase. Specifically, positive and negative peaks appear at specific fields ($B_1, B_2, B_3$), with the signs of the peaks at $B_1$ and $B_2$ reversing as the temperature drops from 5 K to 2 K.
   • Correlation with $\kappa_{xx}$: The fields corresponding to the sign reversals in $\Delta\kappa_{xy}$ coincide with multiple valleys (minima) in the field dependence of $\kappa_{xx}$.
   • Magnetization: Crucially, these anomalies in thermal transport occur without corresponding anomalies in the magnetization ($M$) curve, which only shows the kink at $B_{sf}$. This indicates that thermal transport is highly sensitive to subtle changes in the magnon band structure that are averaged out in bulk magnetization measurements.

Significance and Interpretation
The paper suggests that the observed anomalies—specifically the multiple sign reversals in $\kappa_{xy}$ and the multiple valleys in $\kappa_{xx}$ within the SF phase—are caused by a redistribution of Berry curvature in the magnon bands.

• The sign of magnon $\kappa_{xy}$ reflects the sign of the dominant Berry curvature. The observed sign reversals imply multiple topological phase transitions within the SF phase, potentially driven by magnon band inversions or magnon-phonon hybridizations.
• While previous theoretical calculations predicted topological transitions in the SF phase, the specific critical fields and temperatures observed in this study differ from those predictions, likely due to the omission of further-neighbor spin interactions in the models.
• The study demonstrates the superior sensitivity of thermal Hall measurements compared to magnetization for detecting Berry curvature distributions and topological transitions in magnetic insulators. The results highlight that thermal transport can reveal topological features of the magnon spectrum that are invisible to standard magnetic probes.

The authors conclude that these findings underscore the capability of thermal Hall measurements to probe the complex topological nature of magnon bands in 2D antiferromagnets, providing a critical experimental benchmark for future theoretical refinements involving further-neighbor interactions and magnon-phonon couplings.