Anomalous magnetotransport in the single-crystalline half-Heusler antiferromagnet ErPdSb

This study characterizes the thermodynamic and magnetotransport properties of single-crystalline ErPdSb, revealing its antiferromagnetic ordering at 1.2 K, semimetallic behavior with a resistivity hump near 70 K, a transition from weak antilocalization to negative magnetoresistance in magnetic fields, and a sizable anomalous Hall effect at low temperatures indicative of Fermi surface reconstruction.

The Gist

Here is an explanation of the paper on ErPdSb, translated into everyday language with some creative analogies.

The Big Picture: A Crystal with a Split Personality

Imagine you have a tiny, perfect crystal cube made of three elements: Erbium (a rare earth metal), Palladium, and Antimony. Scientists call this ErPdSb.

For a long time, scientists thought this material was a boring, simple semiconductor (like a dim lightbulb that barely conducts electricity). But when the researchers in this paper grew perfect, single-crystal versions of it (instead of the messy, grainy chunks used before), they discovered it has a much more complex and "moody" personality.

It behaves like a semimetal (a material that's half conductor, half insulator) and acts like a magnet that only wakes up when it gets very, very cold.

Here is the story of what they found, broken down into four acts.

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Act 1: The "Sleepy" Magnet

The Discovery:
When the crystal is warm, the magnetic atoms inside are like a crowd of people at a loud party, all spinning and moving randomly. This is called the "paramagnetic" state.

But, as the temperature drops to near absolute zero (about -272°C or 1.2 Kelvin), the party suddenly quiets down. The atoms line up in a strict, alternating pattern (North-South-North-South). This is called Antiferromagnetism.

The Analogy:
Think of a classroom of students. When the teacher leaves (high temperature), everyone is chatting and spinning in their chairs. But when the teacher walks in (low temperature), everyone suddenly snaps into a perfect, alternating line: "Look left, look right, look left, look right." They aren't all facing the same way (which would be a normal magnet); they are facing opposite ways to cancel each other out.

Act 2: The "Traffic Jam" and the "Highway"

The Discovery:
The researchers measured how easily electricity flows through the crystal.

• At room temperature: It's a bit like a highway with a few cars.
• Around 70°C: Something weird happens. The electricity gets "stuck" for a moment, creating a bump in the data. It's like a traffic jam that appears out of nowhere.
• Below 10K: The traffic starts flowing smoothly again, but the cars are moving in a very specific way.

The Analogy:
Imagine driving on a road. Usually, cars (electrons) flow smoothly. But at a specific temperature, the road seems to develop a "speed bump" that slows everyone down. The researchers realized this wasn't a defect in the road; it was a fundamental property of the material's electronic structure.

Act 3: The "Magnetic Switch"

The Discovery:
When they applied a magnetic field, the material did something surprising.

• Weak Magnetic Field: The material resisted the electricity more. This is called Weak Antilocalization.
• Strong Magnetic Field: The material suddenly started letting electricity flow easier. This is called Negative Magnetoresistance.

The Analogy:
Think of the electrons as dancers on a floor.

• In a weak magnetic field: The dancers are confused. They keep bumping into each other and spinning in circles, making it hard to get across the room. The magnetic field makes them more confused (resistance goes up).
• In a strong magnetic field: The magnetic field acts like a strict dance instructor. It forces the dancers to line up and march in a straight line. Suddenly, they can zip across the room without bumping into anyone. The resistance drops, and the current flows better.

The paper suggests this happens because the magnetic field aligns the "spins" of the atoms, removing the chaos that was scattering the electrons.

Act 4: The "Shape-Shifting" Map

The Discovery:
The most exciting part is what happens when they rotate the crystal while applying a magnetic field. They found that the electrical resistance changes depending on the angle, almost like the crystal is changing its shape.

The Analogy:
Imagine the electrons are swimming in a pool.

• Normally, the pool is a perfect circle. It doesn't matter which way you swim; the resistance is the same.
• In this crystal, when you turn on the magnetic field, the pool suddenly stretches into an oval.
• If you swim along the long side of the oval, it's easy. If you swim across the short side, it's hard.
• Even weirder: At a specific magnetic strength (0.6 Tesla), the oval flips! The "easy" direction becomes the "hard" direction.

This "flipping" suggests that the magnetic field is actually rewriting the map of the material's internal landscape (the Fermi surface). It's as if the magnetic field is a magic wand that physically reshapes the terrain the electrons are traveling on.

The "Why Should We Care?" Conclusion

1. It's a Topological Puzzle:
This material belongs to a family called "Half-Heusler" compounds. These are famous for being "topological," meaning their internal electronic structure is knotted in a way that makes them very special for future electronics.

2. The "Single Crystal" Difference:
The paper highlights that previous studies used "polycrystals" (like a brick made of many small stones glued together). Those studies missed the cool stuff because the "glue" (grain boundaries) blocked the interesting effects. By growing a single, perfect crystal (like a flawless diamond), the researchers could finally see the true, exotic behavior of the material.

3. Future Tech:
Understanding how these materials switch between "resisting" and "conducting" based on magnetic fields is crucial for spintronics. This is the next generation of electronics that uses the "spin" of electrons (like a tiny magnet) instead of just their charge. This could lead to computers that are faster, use less energy, and don't lose data when turned off.

Summary

The researchers took a material that everyone thought was boring, grew it perfectly, and discovered it is actually a shape-shifting, magnetic, semi-conducting chameleon. It changes how it conducts electricity based on temperature and magnetic fields, offering a glimpse into a new world of quantum physics that could power the computers of the future.

Technical Summary

Here is a detailed technical summary of the paper "Anomalous magnetotransport in single-crystalline half-Heusler antiferromagnet ErPdSb."

1. Problem Statement and Motivation

Rare-earth (RE) based half-Heusler (HH) compounds, particularly the bismuthide series (RETBi), have garnered significant attention for their non-trivial electronic structures, topological properties, and interplay between magnetism and superconductivity. However, their antimony-containing counterparts (RETSb) have been largely overlooked.

• The Gap: It was hypothesized that replacing Bi (Z=83) with Sb (Z=51) would significantly reduce spin-orbit coupling (SOC), potentially preventing the band inversion necessary for topological non-triviality. Consequently, most existing data on RETSb compounds (including ErPdSb) were derived from polycrystalline samples, which often suffer from grain boundary scattering and compositional inhomogeneities, leading to conflicting reports on their electronic nature (e.g., whether they are semiconductors or semimetals).
• The Objective: This study aims to reinvestigate ErPdSb using high-quality single crystals to resolve discrepancies in previous literature, specifically focusing on:
  • Determining the true ground state magnetic order.
  • Characterizing the electronic structure and transport mechanisms.
  • Investigating anomalous magnetotransport phenomena (Hall effect, magnetoresistance, and angular dependence) to understand the role of topology and multiband effects.

2. Methodology

The research combined experimental synthesis/characterization with first-principles theoretical calculations.

• Sample Synthesis: Single crystals of ErPdSb were grown using the Bi flux method. High-purity Er, Pd, Sb, and Bi were heated to 1050°C and slowly cooled. The resulting silver-shiny cubic crystals (approx. 1 mm³) were confirmed via Energy-Dispersive X-ray Spectroscopy (EDS) to have equiatomic stoichiometry.
• Structural Characterization: Single-crystal X-ray diffraction confirmed a non-centrosymmetric cubic structure (space group $F\bar{4}3m$) with lattice parameter $a = 6.472$ Å.
• Experimental Measurements:
  • Magnetic & Thermal: Magnetic susceptibility ($\chi$) and magnetization ($M$) were measured from 0.5 K to 300 K (up to 7 T). Specific heat ($C_p$) was measured down to 0.4 K.
  • Transport: Electrical resistivity ($\rho$), magnetoresistance (MR), and Hall effect ($\rho_{xy}$) were measured from 2 K to 300 K (up to 9 T).
  • Angular Dependence: Angle-dependent magnetoresistance (AMR) was measured by rotating the magnetic field in the (010) and (001) planes.
• Theoretical Calculations: Electronic structure was calculated using the VASP package with the MBJGGA (modified Becke-Johnson) approach to accurately describe band gaps and include spin-orbit coupling (SOC).

3. Key Results

A. Electronic Structure and Thermodynamics

• Magnetic Ordering: Contrary to some previous reports suggesting paramagnetism down to 1.9 K, the single crystals exhibit antiferromagnetic (AFM) ordering at a Néel temperature $T_N = 1.2$ K. This is evidenced by a peak in magnetic susceptibility and a $\lambda$-type peak in specific heat.
• Magnetization: At 0.5 K, the magnetization shows a faint metamagnetic transition at 0.15 T. The saturation moment is reduced ($6.44 \mu_B$) compared to the free Er$^{3+}$ion ($9 \mu_B$) due to Crystal Electric Field (CEF) effects.
• Band Structure:
  • Calculations indicate an indirect band gap of ~0.15 eV (along the $\Gamma$-X direction).
  • Unlike the GGA prediction (trivial insulator), MBJGGA calculations reveal a band inversion where $s$-type $\Gamma_6$ states reside above the valence band dominated by Sb $5p$ states. This suggests a complex electronic structure similar to the topological insulator TmPdSb.
  • The valence band shows significant splitting (0.3 eV) between heavy and light holes due to strong SOC.

B. Magnetotransport Properties

• Resistivity ($\rho$): The material exhibits semimetallic behavior with a broad hump in resistivity around 70 K. This differs from polycrystalline data, highlighting the sensitivity of transport to sample quality and carrier concentration.
• Magnetoresistance (MR):
  • Low Fields (< 0.5 T): MR is positive, attributed to the Weak Antilocalization (WAL) effect. Fitting to the Hikami-Larkin-Nagaoka (HLN) model yielded a phase coherence length $L_\phi \approx 64$ nm.
  • High Fields (> 0.6 T): MR becomes negative (reaching ~-15% at 6 T). This is not due to the Chiral Magnetic Anomaly (CMA) because the effect is isotropic (present in both longitudinal and transverse configurations). Instead, it is well-described by the de Gennes-Friedel (dGF) formalism, where negative MR arises from the suppression of spin-disorder scattering as magnetic moments align with the field.
• Hall Effect:
  • Holes are the dominant charge carriers ($n_h \sim 10^{19}$ cm$^{-3}$).
  • A distinct low-field anomaly (a dip in $\rho_{xy}$ below 1 T) is observed, persisting up to 200 K. This is attributed to multiband transport rather than a simple single-band model.
  • Two-band model fitting at 150 K and 200 K confirmed the coexistence of holes and electrons with distinct mobilities.

C. Angular Magnetoresistance (AMR)

• The AMR exhibits unusual evolution with magnetic field. At low fields, the angular dependence is complex.
• A critical transition occurs at $B \approx 0.6$ T, where the peaks and valleys of the AMR invert (a "peak-valley inversion").
• This inversion coincides with the crossover from positive to negative MR. The authors suggest this may indicate a field-induced reconstruction of the Fermi surface, potentially involving a Lifshitz transition where the Fermi level intersects different bands (hole-type at $\Gamma$, electron-type at $X$) as the field increases.

4. Key Contributions

1. Resolution of Magnetic Ground State: Definitively established the AFM ordering of ErPdSb at 1.2 K using single crystals, correcting previous assumptions based on polycrystalline data.
2. Identification of Transport Mechanisms: Decoupled the contributions of WAL (low field) and spin-disorder scattering (high field) to magnetoresistance, providing a clear physical picture of the transport regime.
3. Evidence of Multiband Topology: Demonstrated that despite the bulk band gap, the transport is governed by multiband effects and potential Fermi surface reconstruction, evidenced by the low-field Hall anomaly and AMR symmetry breaking.
4. Structural Confirmation: Validated the non-centrosymmetric MgAgAs structure and provided precise lattice parameters for future theoretical comparisons.

5. Significance

This work highlights the critical importance of using single-crystalline samples to uncover the intrinsic properties of half-Heusler compounds, as polycrystalline data can mask subtle quantum phenomena like WAL and band inversion.

• Topological Relevance: The observation of band inversion in ErPdSb (an Sb-based compound) challenges the notion that only heavy-element (Bi-based) HH compounds exhibit topological features.
• Spintronics Potential: The coexistence of AFM order, strong SOC, and anomalous magnetotransport (large Hall effect, negative MR) makes ErPdSb a promising candidate for exploring the interplay between magnetism and non-trivial topology, relevant for next-generation spintronic devices.
• Model System: The clear observation of field-induced Fermi surface reconstruction and AMR symmetry inversion provides a testbed for understanding how magnetic fields manipulate electronic band structures in correlated electron systems.