Investigating the intrinsic anomalous Hall effect in MnPt3 topological semimetal

This study demonstrates that epitaxially grown MnPt$_3$ thin films exhibit a thickness-dependent ferromagnetic transition and a dominant intrinsic anomalous Hall effect driven by Berry curvature, which is enhanced by strain effects, thereby establishing strain as an effective method for tuning the electronic band topology in this topological semimetal family.

The Gist

Imagine you have a tiny, invisible highway inside a piece of metal where electrons (the tiny particles that carry electricity) are driving. Usually, they drive in straight lines. But in certain special "topological" materials, the road has hidden curves and twists. Because of these twists, the electrons get pushed sideways, creating a voltage even without a magnetic field pushing them. This phenomenon is called the Anomalous Hall Effect (AHE). It's like driving down a straight road, but your car mysteriously drifts to the right because the road itself is warped.

This paper is about a specific material called MnPt3 (a mix of Manganese and Platinum) and how the researchers figured out how to make this "drift" stronger and more useful.

Here is the story of their discovery, broken down into simple concepts:

1. The Material: A New Kind of Highway

Scientists knew that a family of materials called XPt3 (where X is Vanadium, Chromium, or Manganese) acts like a topological semimetal. Think of these materials as having a special "traffic map" where the roads cross over each other in a way that creates a lot of "traffic swirls" (called Berry Curvature). These swirls are what cause the electrons to drift sideways.

• The Knowns: They already knew that the "Chromium" version of this family (CrPt3) was a superstar at creating this drift.
• The Mystery: They didn't know much about the "Manganese" version (MnPt3). It was like knowing one car model was a race car, but having no idea if the similar-looking model next to it was a slow sedan or a hidden supercar.

2. The Experiment: Building Better Roads

The team grew very thin films (sheets) of MnPt3 on a special base (MgO). They made these sheets in different thicknesses, ranging from very thin (20 nanometers) to thicker (70 nanometers).

The Analogy: Imagine building a stack of paper.

• Thin stack (20 nm): The paper is squished tight against the table. It's under a lot of "strain" (stress) because the table forces it to stretch or shrink to fit.
• Thick stack (70 nm): The paper has more room to breathe. It relaxes a bit, and the stress changes.

They found that as the films got thicker, the material's internal "magnetic temperature" (the point where it becomes magnetic) got higher, eventually reaching a point where it stays magnetic even at room temperature.

3. The Discovery: The "Drift" Gets Stronger

When they measured how well these films conducted electricity and how much they drifted sideways (the AHE), they found something amazing: The thicker the film, the stronger the drift.

• The Result: The 70-nm film was a much better "drifter" than the 20-nm film.
• The Cause: The researchers realized this wasn't just because the film was bigger. It was because the strain (the stress from being squished or stretched) changed the shape of the "traffic map" inside the metal. By changing the thickness, they effectively "tuned" the road, making the curves sharper and the drift stronger.

4. The Detective Work: Who is Causing the Drift?

In physics, there are two main reasons electrons drift sideways:

1. The Intrinsic Cause (The Road Design): The road is naturally curved. This is the "Berry Curvature." It's a fundamental property of the material's design.
2. The Extrinsic Cause (Road Debris): The electrons hit bumps, potholes, or dirt on the road and get knocked sideways. This is caused by impurities or defects.

The team used a mathematical "detective tool" (called the Tian-Ye-Jin model) to separate these two causes.

• The Verdict: They found that the Intrinsic Cause (the road design) was the main culprit, responsible for about 70-80% of the drift. The "road debris" (extrinsic factors) played a very small role.
• The Twist: The "road design" drift got stronger as the film got thicker, while the "road debris" drift stayed the same. This proved that the strain was the key to unlocking the material's potential.

5. Why Does This Matter?

Think of this like tuning a guitar.

• Before this paper, we knew MnPt3 existed, but we didn't know how to make it sing a loud note.
• This paper shows that by simply changing the thickness of the film, we can change the strain, which retunes the "strings" (the electronic bands) to produce a much louder, stronger signal (the Anomalous Hall Effect).

The Big Picture:
This is a breakthrough for spintronics (a new type of computing that uses electron spin instead of just charge). If we can control these "drifts" using simple strain engineering (changing thickness or stretching the material), we can build faster, more efficient, and smaller electronic devices. It turns out that MnPt3 isn't just a quiet sedan; with the right tuning, it's a high-performance sports car ready for the future of technology.

Technical Summary

1. Problem Statement

The cubic $XPt_3$ family ($X = \text{V, Cr, Mn}$) is a class of topological semimetals characterized by anti-crossing gapped nodal lines near the Fermi level. These features generate significant Berry curvatures, leading to a large Anomalous Hall Effect (AHE).

• Context: While $CrPt_3$ has been experimentally verified to exhibit a large anomalous Hall conductivity (AHC) comparable to theoretical predictions, its counterparts, $MnPt_3$ and $VPt_3$, remain largely unexplored.
• Gap: Although bulk $MnPt_3$ is known to be ferromagnetic with a Curie temperature ($T_C$) of $\sim390$ K, and large magneto-optical Kerr rotations have been reported in thin films, its spin transport properties and the specific mechanisms governing its AHE (intrinsic vs. extrinsic) had not been systematically investigated.
• Objective: To synthesize high-quality epitaxial $MnPt_3$ thin films, characterize their magnetic and transport properties, and determine the dominant mechanism behind their AHE, specifically investigating how film thickness (and associated strain) influences these properties.

2. Methodology

• Sample Preparation:
  • A series of $MnPt_3$ thin films with varying thicknesses (20, 30, 50, and 70 nm) were epitaxially grown on (001)-oriented MgO substrates.
  • Technique: Magnetron co-sputtering of Mn and Pt targets in an ultrahigh vacuum chamber.
  • Process: Substrates were annealed at 600°C. Deposition occurred at 600°C in an Argon atmosphere. Post-deposition annealing at 600°C was performed to improve crystallinity. A 4-nm Pt capping layer was added to prevent oxidation.
• Structural Characterization:
  • High-Resolution X-ray Diffraction (HRXRD) was used to confirm crystal structure, epitaxial nature (cube-on-cube growth), and lattice parameters.
  • X-ray Reflectivity (XRR) determined film thickness and surface roughness.
  • Reciprocal Space Mapping (RSM) and $\phi$-scans confirmed epitaxial alignment and strain states.
• Magnetic and Transport Measurements:
  • Magnetization: Measured using a Quantum Design MPMS (Field-Cooled protocol, $\mu_0H = 0.1$ T).
  • Transport: Longitudinal resistivity ($\rho_{xx}$) and transverse Hall resistivity ($\rho_{yx}$) were measured using a PPMS system on Hall-bar patterned devices.
  • Temperature Range: 10 K to 400 K.
  • Magnetic Field: Up to 3 T.
• Data Analysis:
  • AHE Separation: The anomalous Hall resistivity ($\rho^A_{yx}$) was extracted by subtracting the linear Ordinary Hall Effect (OHE) term.
  • Scaling Analysis: The relationship between AHC ($\sigma^A_{xy}$) and longitudinal conductivity ($\sigma_{xx}$) was analyzed using power-law scaling ($\rho^A_{yx} \propto \rho_{xx}^\alpha$) and the Tian-Ye-Jin (TYJ) model to distinguish between intrinsic (Berry curvature) and extrinsic (skew scattering/side-jump) mechanisms.

3. Key Results

• Structural Properties:
  • Films exhibited high crystalline quality with a chemically ordered $Cu_3Au$-type structure.
  • Strain Engineering: A clear thickness-dependent strain was observed. As thickness increased from 20 nm to 70 nm, the out-of-plane lattice parameter ($c$) increased while the in-plane parameter ($a$) decreased. This resulted in a transition from negative biaxial strain to positive biaxial strain (reaching 0.64% for the 70 nm film).
• Magnetic Properties:
  • All films exhibited a ferromagnetic (FM) transition.
  • Curie Temperature ($T_C$): $T_C$ increased with film thickness, ranging from 309 K (20 nm) to 344 K (70 nm). The 70 nm film's $T_C$ approached the bulk value ($\sim390$ K).
  • Anisotropy: The films displayed in-plane magnetic anisotropy, with in-plane spontaneous magnetization significantly larger than out-of-plane.
• Transport and AHE:
  • Resistivity: Films showed metallic behavior.
  • AHE Observation: A distinct AHE was observed in the FM state. The anomalous Hall resistivity ($\rho^A_{yx}$) peaked at 150 K and decreased at lower temperatures.
  • Conductivity: The anomalous Hall conductivity ($\sigma^A_{xy}$) increased as temperature decreased and as film thickness increased. The maximum $\sigma^A_{xy}$ reached 419 $\Omega^{-1}cm^{-1}$ at 10 K for the 70 nm film.
  • Scaling Analysis:
    • The power-law exponent $\alpha$ (where $\rho^A_{yx} \propto \rho_{xx}^\alpha$) ranged from 1.40 to 1.62, indicating a mix of mechanisms but leaning toward the intrinsic regime.
    • TYJ Model Decomposition:
      • Intrinsic AHC ($\sigma^{A,int}_{xy}$): Increased significantly with film thickness (from 180 to 333 $\Omega^{-1}cm^{-1}$).
      • Extrinsic AHC: Remained largely independent of film thickness.
      • Dominance: The intrinsic contribution dominated the total AHE, accounting for 68% to 80% of the total AHC as thickness increased.
• Mechanism Correlation:
  • The enhancement of intrinsic AHC correlates strongly with the biaxial strain and the evolution of the chemical ordering parameter ($S$) as thickness increases.
  • The shift in Fermi energy ($E_F$) due to strain and chemical ordering is proposed as the cause for the enhanced Berry curvature.

4. Key Contributions

1. First Systematic Study of $MnPt_3$ Films: This work provides the first comprehensive report on the magnetic and spin transport properties of epitaxial $MnPt_3$ thin films, filling a gap in the $XPt_3$ family literature.
2. Demonstration of Strain-Tunable Topology: The study establishes a direct link between film thickness, biaxial strain, and the intrinsic AHE. It demonstrates that strain engineering can effectively tune the electronic band topology and Berry curvature in this topological semimetal.
3. Mechanism Clarification: By applying the TYJ model, the authors definitively identified the intrinsic Berry-curvature mechanism as the dominant source of AHE in $MnPt_3$, distinguishing it from extrinsic scattering effects.
4. Quantitative Benchmarking: The study reports a large intrinsic AHC (up to 333 $\Omega^{-1}cm^{-1}$) and an anomalous Hall angle ($\Theta_A$) of 0.74°, which are competitive with other topological magnetic materials like $CrPt_3$ and significantly larger than non-collinear antiferromagnets like $Mn_3Ir$.

5. Significance

• Fundamental Physics: The results confirm that $MnPt_3$ is a robust topological semimetal where the Berry curvature is the primary driver of the AHE. This validates theoretical predictions regarding the $XPt_3$ family.
• Spintronics Applications: The ability to tune the AHE via film thickness (and consequently strain) offers a practical route for optimizing spintronic devices. The high Curie temperature (approaching room temperature and above) and large anomalous Hall angle make $MnPt_3$ a promising candidate for next-generation magnetic sensors, memory elements, and spin-charge conversion devices.
• Strain Engineering Strategy: The work highlights strain engineering as a powerful tool for manipulating the electronic band structure and topological properties of magnetic semimetals, suggesting that similar strategies could be applied to other members of the topological material family.