Anomalous magnetotransport in a non-collinear correlated kagome ferromagnet MgMn6Sn6

This study characterizes the room-temperature non-collinear kagome ferromagnet MgMn6Sn6 through neutron diffraction and transport measurements, revealing its complex magnetic structure, large intrinsic and anisotropic extrinsic anomalous Hall effects, and strong electron correlations, thereby establishing it as a promising platform for investigating the interplay between topology, magnetism, and correlations.

The Gist

Imagine a microscopic city built on a unique architectural blueprint called a kagome lattice. Instead of squares or circles, the streets are arranged in a pattern of corner-sharing triangles, much like a woven basket or a pattern of stars. In this city, electrons (the tiny particles that carry electricity) don't just move in straight lines; they dance to the rhythm of this complex geometry.

The paper focuses on a specific "building" in this city made of MgMn6Sn6 (a compound of Magnesium, Manganese, and Tin). Here is what the researchers discovered about this material, explained simply:

1. The Magnetic Dance Floor

In most magnets, the tiny internal magnets (called "spins") all point in the exact same direction, like a crowd of soldiers marching in lockstep. However, in MgMn6Sn6, the researchers found something unusual. Using a powerful "camera" called neutron diffraction, they saw that the manganese atoms' magnetic spins are non-collinear.

The Analogy: Imagine a group of dancers on a stage. Instead of all facing North, they are arranged in a circle, each facing slightly different directions, but they are all staying on the same flat floor (the "basal plane"). They aren't marching in a straight line; they are swirling in a coordinated, non-straight pattern. This "swirl" happens at room temperature, which is rare and exciting.

2. The Electronic Traffic Jam (Correlations)

The paper notes that the electrons in this material are "correlated." In a normal metal, electrons zip around like cars on an empty highway. In this material, the electrons are so sensitive to each other that they move like a crowded dance floor where everyone is constantly bumping into and reacting to their neighbors.

The Evidence: The researchers measured how much heat the material holds (specific heat). They found a value that is surprisingly high for a material without heavy "f-electrons" (which usually cause this behavior). This suggests the electrons are "heavy" or sluggish because they are so deeply connected to one another, a sign of strong electronic correlation.

3. The One-Way Street (Anomalous Hall Effect)

When you push electricity through a normal wire, it goes straight. But in this magnetic kagome material, the electricity gets pushed sideways, creating a voltage at a right angle. This is called the Anomalous Hall Effect (AHE).

The Analogy: Think of a river flowing through a magnetic field. Usually, the water flows straight. But in this material, the magnetic "current" acts like a giant, invisible hand that constantly pushes the water sideways.

• The Intrinsic Part: The researchers found a huge, built-in "sideways push" (about 0.29 units of a fundamental constant) that comes from the shape of the electronic bands themselves. It's like the riverbed is naturally curved to force the water sideways, regardless of how fast the water is flowing.
• The Extrinsic Part: At very low temperatures, the "sideways push" changes depending on which way the external magnet is pointing. This is like the riverbed having different bumps and potholes that only affect the water when it's moving very slowly. The researchers found that "skew scattering" (electrons bouncing off impurities at an angle) is responsible for this change.

4. The Directional Sensitivity

One of the most interesting findings is that the material behaves differently depending on which way you apply the magnetic field.

• Easy Mode: If you push the magnetic field along the "easy" plane (flat), the material responds strongly and easily.
• Hard Mode: If you push the field from the top (the "hard" axis), it takes much more effort to align the magnetic spins, and the electrical resistance changes differently.

The researchers also noted that the "sideways push" (Hall effect) actually flips its sign (goes from left to right) at a specific low temperature when the field is applied from the top. This is like a switch flipping, indicating that the way electrons scatter off impurities changes dramatically based on the direction of the magnetic field.

5. The Blueprint (Theory)

To understand why this happens, the researchers used computer simulations (First-Principles Calculations). They mapped out the "energy landscape" of the electrons.

• They found "flat bands" (like a flat plateau in a mountain range) where electrons can get stuck or move very slowly, which explains the strong correlations.
• They found "Weyl nodes" (like mountain peaks or valleys in the energy landscape) that act as sources of the "sideways push."
• The computer model confirmed that the material's unique geometry creates a "Berry curvature"—a fancy term for a magnetic-like force in momentum space that forces the electrons to curve as they move.

Summary

In short, the paper describes MgMn6Sn6 as a room-temperature magnetic material where:

1. The internal magnets swirl in a non-straight pattern.
2. The electrons are highly interactive and "heavy."
3. The material naturally pushes electricity sideways (Anomalous Hall Effect) due to its unique geometric shape.
4. This sideways push is a mix of a built-in geometric effect and a temperature-dependent scattering effect that changes direction based on how you apply the magnetic field.

The researchers conclude that this material is a perfect playground for studying how electron interactions and magnetic geometry combine to create exotic electrical behaviors.

Technical Summary

Technical Summary: Anomalous Magnetotransport in a Non-Collinear Correlated Kagome Ferromagnet MgMn6Sn6

Problem and Context
Magnetic kagome metals represent a critical platform for investigating the interplay between electronic topology, electron correlations, and magnetic order. While the $RMn_6Sn_6$ family (where $R$ is a rare-earth element) is well-studied for its diverse magnetic ground states and topological Hall effects, most members exhibit antiferromagnetic or ferrimagnetic ordering at low temperatures. Replacing the rare-earth ion with alkali or alkaline-earth metals (e.g., Mg, Li) induces room-temperature ferromagnetism, a feature notably absent in most rare-earth-based variants. However, the microscopic magnetic structure of the room-temperature ferromagnet $MgMn_6Sn_6$ has remained elusive, with previous studies relying on bulk magnetization that suggested soft, easy-plane ferromagnetism without resolving the specific spin arrangement. Furthermore, the extent of electron correlation in this Mn-based system and its specific contribution to anomalous magnetotransport properties require further clarification.

Methodology
This study employs a comprehensive multi-technique approach combining experimental characterization and theoretical modeling:

• Single-Crystal Neutron Diffraction (SCND): Performed at the ISIS Neutron and Muon Source to determine the microscopic magnetic structure and symmetry of $MgMn_6Sn_6$ across a temperature range of 5–380 K.
• Magnetotransport Measurements: Systematic measurements of resistivity, magnetoresistance (MR), and Hall effect were conducted on high-quality single crystals. Configurations included in-plane ($B \parallel y$) and out-of-plane ($B \parallel z$) magnetic fields relative to the current direction ($I \parallel x$).
• Heat Capacity Measurements: Low-temperature specific heat data were analyzed to extract the Sommerfeld coefficient and assess electron correlation strength.
• First-Principles Calculations: Density Functional Theory (DFT) calculations within the $PBE+U+SOC$ framework were used to compute electronic band structures, Berry curvature distributions, and intrinsic anomalous Hall conductivity (AHC).

Key Contributions and Results

1. Non-Collinear Magnetic Structure:
   SCND measurements reveal that $MgMn_6Sn_6$ possesses a non-collinear but coplanar magnetic structure within the basal plane of the kagome bilayer. The Mn magnetic moments are confined to the $ab$-plane, with a canting angle of approximately $5.5^\circ$ at 5 K, which increases with temperature. Two symmetry-allowed magnetic space groups ($Cm'mm'$ and $Cmm'm'$) were found to be consistent with the diffraction data, both indicating a non-collinear arrangement driven by competing exchange interactions. The Curie temperature ($T_C$) is confirmed at $\approx 300$ K.

2. Anomalous Hall Effect (AHE) and Transport Anisotropy:
   The material exhibits a substantial intrinsic AHC of approximately $0.29 e^2/h$ per kagome layer, which is nearly isotropic with respect to the magnetic field orientation. This value is comparable to other rare-earth based $RMn_6Sn_6$ compounds.

   • Field Orientation Dependence: A pronounced anisotropy is observed in the temperature evolution of the AHE. For in-plane fields ($B \parallel y$), the AHC shows a monotonic increase with temperature. Conversely, for out-of-plane fields ($B \parallel z$), the AHC undergoes a sign reversal just above 10 K.
   • Scaling Analysis: A detailed scaling analysis ($\rho^A_{ji}M_s(2K)/M_s(T)$ vs. $\rho^2_{ii}$) separates intrinsic and extrinsic contributions. The intrinsic component is temperature-independent, while the low-temperature behavior is dominated by extrinsic skew scattering. The sign reversal in the out-of-plane configuration suggests that skew scattering contributes with opposite polarity along different crystallographic directions, highlighting the anisotropic nature of extrinsic scattering in this kagome system.

3. Enhanced Electron Correlations:
   Heat capacity measurements yield a large Sommerfeld coefficient of $\gamma \approx 72.9 \pm 0.3$ mJ mol$^{-1}$ K$^{-2}$. This value is significantly higher than that of many other $d$-electron based $RT_6X_6$ compounds and even exceeds values for some $d+f$ systems. This enhancement, occurring in the absence of $f$-electrons, points to strong electron correlations and an increased quasiparticle effective mass, likely driven by the presence of nearly flat bands near the Fermi energy ($E_F$).

4. Electronic Structure and Berry Curvature:
   DFT calculations confirm the presence of Weyl points and symmetry-protected linear band crossings slightly below $E_F$. The calculated Berry curvature distribution exhibits distinct "hot spots" with three-fold rotational symmetry. To match the experimental AHC magnitude, the Fermi level was shifted downward by $\sim 20$ meV, consistent with hole-dominated transport observed in Hall measurements.

Significance
The paper establishes $MgMn_6Sn_6$ as a robust candidate for studying the effects of electron correlation on magneto-transport in kagome ferromagnets. The key findings are:

• It resolves the long-standing ambiguity regarding the magnetic structure of this room-temperature ferromagnet, confirming a non-collinear, in-plane spin arrangement.
• It demonstrates that while the intrinsic AHE is driven by Berry curvature and is largely isotropic, the extrinsic contributions (specifically skew scattering) exhibit strong directional sensitivity and can even reverse sign depending on the field orientation.
• It highlights the presence of strong electron correlations in a Mn-based system without $f$-electrons, evidenced by the large Sommerfeld coefficient, linking these correlations to the kagome-driven flat bands near the Fermi level.

The authors conclude that $MgMn_6Sn_6$ exhibits characteristic features of a correlated topological metal, where the interplay of non-collinear magnetism, topological band features, and electron correlations governs its anomalous transport properties.