🔬 materials science

Thermodynamic and electrical transport properties of the half-Heusler plumbide TbAuPb

This study investigates the structural, thermodynamic, and electrical transport properties of the half-Heusler compound TbAuPb, revealing its antiferromagnetic ordering, multiband hole-dominated transport with strong magnetoresistance coupling to magnetic phases, and a field-induced transition from a band-inverted semimetal to a topologically trivial state.

Original authors: Abhinav Agarwal, Snehashish Chatterjee, Maciej J. Winiarski, Orest Pavlosiuk, Dorota A. Kowalska, Piotr Wisniewski, Dariusz Kaczorowski

Published 2026-07-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Abhinav Agarwal, Snehashish Chatterjee, Maciej J. Winiarski, Orest Pavlosiuk, Dorota A. Kowalska, Piotr Wisniewski, Dariusz Kaczorowski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of materials science as a giant, bustling city where atoms are the citizens. Some cities are boring, with everyone standing in neat, predictable rows. But other cities are wild, chaotic, and full of secret tunnels and hidden shortcuts. In the world of physics, these "wild cities" are called quantum materials. They are special because the electrons (the tiny particles that carry electricity) inside them don't just flow like water in a pipe; they dance to a different rhythm, sometimes behaving like waves or even acting as if they have no mass at all. Scientists are obsessed with finding these materials because they might hold the keys to super-fast computers, ultra-efficient energy devices, and technologies we haven't even dreamed of yet.

To understand the story in this paper, you need to know about two main characters. First, there are "half-Heusler" materials. Think of these as a specific type of architectural blueprint where three different types of atoms arrange themselves in a perfect, cubic dance. For a long time, scientists thought these blueprints could create "topological insulators"—materials that are insulators (blocking electricity) on the inside but conductors (letting electricity flow) on the surface, like a chocolate bar with a conductive silver coating. Second, there is the concept of "band inversion." Imagine a stack of books where the heavy ones are supposed to be at the bottom and the light ones at the top. In normal materials, this is how it works. But in these special quantum materials, the heavy and light books swap places. This swap creates a strange, twisted electronic landscape that can lead to magical properties. The big question scientists are asking is: What happens when you add magnetism to this mix? Does the magnetic pull of the atoms straighten out the twisted books, or does it make the dance even more complex?

This paper dives into a brand-new member of the half-Heusler family called TbAuPb (pronounced "Tb-Au-Pb," made of Terbium, Gold, and Lead). The researchers grew perfect, triangular crystals of this material and put them through a rigorous workout. They cooled them down to near absolute zero, zapped them with strong magnetic fields, and measured how electricity flowed through them. They found that TbAuPb is a bit of a shape-shifter. At low temperatures, experimental data indicates it orders its magnetic atoms in an "antiferromagnetic" pattern, which is like a crowd of people standing in a line where everyone faces the opposite direction of their neighbor. This happens at a chilly 5 Kelvin (about -268°C). When they applied a magnetic field stronger than 5 Tesla (which is about 100,000 times stronger than a fridge magnet), the material appears to flip into a different magnetic state. However, the exact arrangement of these magnetic atoms is still a mystery; the researchers note that a neutron diffraction experiment is required to verify the specific magnetic structure.

The most exciting part of the story is how the electricity behaved. The material acts like a "semimetal," meaning it has a tiny bit of both metal and insulator in it. The researchers discovered that the main carriers of electricity are "holes" (which act like positive charges, or missing electrons). But here is the twist: the way electricity moves changes dramatically depending on the angle of the magnetic field. When they rotated the magnetic field, the resistance to electricity didn't just go up or down; it formed a weird, butterfly-shaped pattern. This suggests that the electrons are getting tangled up with the magnetic order in a very specific way.

The scientists also ran computer simulations to see what the atoms were doing inside. They found that in its normal, non-magnetic state, TbAuPb has that "band inversion" we talked about earlier—the heavy and light books have swapped places, suggesting it might be a topologically interesting material. However, when they simulated what happens when a strong magnetic field forces the material into a ferromagnetic state (where all the magnetic atoms line up in the same direction), the magic disappears. The books swap back to their normal positions, and the material becomes "topologically trivial," meaning it loses those special quantum shortcuts.

So, what did they find? They observed that TbAuPb is a real, physical material that shows signs of magnetic ordering at 5 K and undergoes a transition at 5 Tesla. They measured its resistance, heat, and Hall effect (a way to see if positive or negative charges are moving) and confirmed it has multiple types of charge carriers. They suggested, through their computer models, that the material is likely a band-inverted semimetal that loses its topological "coolness" when magnetized. They did not prove that it is a Weyl semimetal (a specific type of topological material) or that it has a "chiral anomaly" (a specific quantum effect), because their data showed the negative magnetoresistance was too small and isotropic (the same in all directions) to support that claim. Instead, they suggest that the strange transport properties come from the interplay between the magnetic order and the electronic bands, specifically noting that the "avoided band-crossings" (where electron paths get close but don't touch) might be responsible for the weird electrical behavior.

In short, TbAuPb is a new, heavy-metal playground for electrons. It starts as a potentially topological material, but the moment you turn on a strong magnetic field, it changes its personality, becoming a more ordinary, though still interesting, magnetic metal. The researchers are now calling for more experiments, specifically using neutron diffraction (a way to see the magnetic atoms directly), to map out exactly how the magnetic atoms are arranged. Until then, TbAuPb remains a fascinating puzzle piece in the quest to understand how magnetism and topology dance together in the quantum world.

Technical Summary: Thermodynamic and Electrical Transport Properties of the Half-Heusler Plumbide TbAuPb

Problem and Motivation
The search for quantum materials with non-trivial electronic band structures is a central focus in condensed matter physics, driven by both fundamental interest and potential technological applications. Rare-earth-based half-Heusler (HH) phases ($RTX$) have been extensively investigated as candidates for topological insulators and semimetals. While bismuthides like $RPtBi$ and stannides like $RAuSn$ have shown intriguing phenomena such as Weyl semimetal behavior and field-induced topological transitions, experimental data on the plumbide series $RAuPb$ remains scarce. Specifically, the magnetic and transport properties of the novel compound $TbAuPb$ had not been previously investigated. This study aims to fill that gap, motivated by the fact that $TbAuPb$ contains heavy constituent elements (suggesting strong band inversion similar to established systems like $GdAuPb$) and possesses partially filled 4 $f$ orbitals that introduce intrinsic magnetism and strong crystal electric field (CEF) interactions, distinct from the zero-orbital-momentum $Gd$ systems.

Methodology
The study employed a combination of experimental characterization on single crystals and first-principles theoretical calculations:

Synthesis and Characterization: Single crystals of $TbAuPb$ were grown using the self-flux method. Structural verification was performed via single-crystal X-ray diffraction, confirming a non-centrosymmetric cubic $MgAgAs$-type structure (space group $F\bar{4}3m$ ).
Experimental Measurements: Thermodynamic properties (magnetic susceptibility, specific heat) were measured in the 2–300 K range under fields up to 7 T. Electrical transport properties, including electrical resistivity, magnetoresistance (transverse and longitudinal), angular magnetoresistance (AMR), and Hall resistivity, were studied up to 9 T.
Theoretical Calculations: Electronic band structure calculations were performed using Density Functional Theory (DFT) within the VASP package. The study utilized the Generalized Gradient Approximation (GGA) and the modified Becke-Johnson (MBJGGA) exchange-correlation functionals, including spin-orbit coupling (SOC). Calculations were conducted for both the non-magnetic state and a field-induced ferromagnetic (FM) state (with a Hubbard $U_{eff}$ of 7 eV for Tb 4 $f$ states).

Key Results

Structural and Thermodynamic Properties: $TbAuPb$ crystallizes in the cubic HH structure with a lattice parameter of $a = 6.745$ Å. Magnetic susceptibility measurements reveal antiferromagnetic (AFM) ordering below a Néel temperature $T_N = 5$ K, with a paramagnetic Curie temperature $\theta_p = -38$ K indicating strong AFM exchange interactions. Specific heat data shows a sharp lambda-like anomaly at $T_N$ , confirming a second-order phase transition.
Magnetic Field Response: Magnetization isotherms indicate a field-induced transition at a critical field $B_c$ (approx. 5 T at 2 K), suggesting a change in the AFM magnetic structure.
Electrical Transport: The compound exhibits semimetallic behavior with a residual resistivity ratio (RRR) of ~5.3.
- Magnetoresistance (MR): In the ordered state, MR is positive at low fields but develops a negative contribution at high fields, forming a broad maximum near $B_c$ . In the paramagnetic state, MR is predominantly negative.
- Angular Dependence: Angular magnetoresistance measurements reveal a systematic evolution with the magnetic field. Below $T_N$ , the MR symmetry changes near the spin-reorientation transition ( $B_c$ ), exhibiting a complex "butterfly-shaped" pattern with higher-order symmetry terms above 5 T. In contrast, the paramagnetic state shows conventional two-fold symmetry.
- Hall Effect: Hall resistivity is positive, indicating hole-like majority carriers. A distinct feature near 1.5 T and a slope change near $B_c$ suggest the presence of an anomalous Hall effect (AHE) and Fermi surface reconstruction, though multiband contributions complicate the separation of the AHE signal. Two-band model analysis at high temperatures ( $T \ge 100$ K) quantified carrier concentrations and mobilities.
Electronic Structure:
- Non-Magnetic State: Calculations predict $TbAuPb$ to be a band-inverted semimetal with small Fermi pockets at $\Gamma$ and $X$ points. The band inversion involves $\Gamma_6$ and $\Gamma_8$ states, driven by strong SOC and heavy elements.
- Ferromagnetic State: In the field-induced FM state, the band inversion is lifted, resulting in a topologically trivial semimetal. The Fermi level lies in a pseudogap in both magnetic phases.
- Pressure Effects: Theoretical analysis suggests the system is close to a topological critical point, where hydrostatic pressure could potentially drive a transition from a non-trivial to a trivial semimetal.

Significance and Claims
The paper establishes $TbAuPb$ as a new half-Heusler compound that serves as a potential platform for studying the interplay between magnetism and band topology. The authors claim that the material exhibits a rich set of phenomena, including metamagnetic transitions, anomalous Hall effects, multiband transport, and a field-tunable topological character (transitioning from a band-inverted semimetal in the non-magnetic state to a trivial semimetal in the ferromagnetic state).

The study highlights that while the non-magnetic state possesses the characteristics of a topologically non-trivial material, the magnetic ordering (specifically the AFM ground state and the field-induced FM state) significantly modifies the electronic structure. The authors note that a complete theoretical understanding of the AFM phase requires knowledge of the specific magnetic structure, which necessitates future neutron diffraction experiments. Similarly, extracting the precise origin of the anomalous Hall effect requires higher magnetic field measurements and more detailed theoretical calculations of the Berry curvature. The work underscores the importance of studying unexplored $RTX$ compounds to deepen the understanding of how magnetism influences band topology in heavy-element systems.

More like this