Complex electronic topography and magnetotransport in an in-plane ferromagnetic kagome metal

This study characterizes the ferromagnetic kagome metal ScMn6(Sn0.78Ga0.22)6, revealing an in-plane easy magnetization axis that preserves a gapless Dirac cone and flat bands, thereby demonstrating how magnetic orientation modulates the material's topological electronic structure and anomalous Hall effect.

The Gist

Imagine a microscopic city built on a very specific, repeating pattern called a kagome lattice. If you were to draw this pattern, it would look like a honeycomb made of triangles that share corners. In the material described in this paper, this city is built out of atoms of Manganese (Mn), Scandium (Sc), Tin (Sn), and a little bit of Gallium (Ga).

Here is what the researchers discovered about this "city," explained through simple analogies:

1. The Traffic Jam and the Highway (Flat Bands vs. Dirac Cones)

In this atomic city, electrons (the tiny particles that carry electricity) usually zoom around like cars on a highway. However, the unique triangular shape of the kagome lattice creates a special traffic situation.

• The Flat Band (The Traffic Jam): The researchers found a "flat band." Imagine a section of the highway where the cars are completely stuck in a massive traffic jam. They can't move forward or backward; they are just sitting there. In physics, this means the electrons have very little energy to move. This happens because the waves of the electrons cancel each other out perfectly in this triangular pattern, creating a "dead zone" where electrons are trapped.
• The Dirac Cone (The Superhighway): Right next to this traffic jam, there is a "Dirac cone." Think of this as a perfectly smooth, frictionless slide or a superhighway where electrons can zip around at incredible speeds without any resistance. The researchers found this superhighway located just below the "ground level" (Fermi level) of the material's energy.

2. The Magnetic Switch (Turning the Gap On and Off)

One of the most exciting findings is how the material behaves when you change the direction of its magnetism. Think of the electrons on the superhighway as needing a specific gate to pass through.

• The Gatekeeper: The researchers discovered that the direction the magnetic "compass" points acts like a gatekeeper.
• Pointing Up (Out-of-Plane): If the magnetic compass points straight up (perpendicular to the layers), the gatekeeper slams the gate shut, creating a small gap (about 15 meV). The electrons on the superhighway are blocked.
• Pointing Sideways (In-Plane): If the magnetic compass points sideways (parallel to the layers), the gate swings wide open. The gap disappears, and the electrons can flow freely again.
• The Experiment: The team confirmed that in their specific material, the magnetic compass naturally points sideways. This means the "gate" is open, and the electrons are flowing freely on that superhighway.

3. The "Ga" Ingredient (Stabilizing the Magnet)

The original version of this material (without Gallium) is a bit of a mood swing artist. It changes its magnetic personality depending on the temperature and magnetic fields, sometimes acting like a chaotic crowd (antiferromagnetic).

The researchers added a small amount of Gallium (about 22% of the Tin atoms were swapped for Gallium). Think of Gallium as a stabilizer or a glue. This addition calmed the material down, forcing it to stay in a single, happy, organized state called ferromagnetism (where all the tiny magnetic compasses point in the same direction) below a temperature of 375 K. It also forced the compasses to point sideways, which is crucial for keeping that "gate" open on the superhighway.

4. The Anomalous Hall Effect (The Curved Path)

When the researchers sent an electric current through this material and applied a magnetic field, the electrons didn't just go straight; they curved. This is called the Anomalous Hall Effect.

Imagine driving a car on a straight road, but suddenly the road curves sharply to the side without you turning the steering wheel. This happens because the "geometry" of the atomic city (the kagome lattice) and the magnetic fields create a hidden force that pushes the electrons sideways. This effect is very strong in this material, suggesting the electrons are moving through a very complex, twisted landscape.

Summary

In short, the researchers took a complex, triangular atomic material, added a little Gallium to make it magnetically stable, and discovered that it hosts two very different worlds for electrons: a "traffic jam" (flat band) and a "superhighway" (Dirac cone). They also found that the direction of the material's magnetism acts like a switch that can open or close the gate to that superhighway. This helps scientists understand how to control electricity and magnetism in these unique, geometric materials.

Technical Summary

Technical Summary: Complex Electronic Topography and Magnetotransport in an In-Plane Ferromagnetic Kagome Metal

Problem and Context
Kagome materials have attracted significant attention due to their unique lattice geometry, which hosts Dirac cones, Van Hove singularities, and flat bands. These features, when combined with spin-orbit coupling (SOC) and magnetism, can lead to intrinsic Chern quantum phases and significant anomalous Hall effects (AHE). The $RMn_6Sn_6$ family ($R$ = rare-earth, Sc, Y) is a focal point of research in this domain. While pristine $ScMn_6Sn_6$ exhibits antiferromagnetic (AFM) ordering below a Néel temperature ($T_N$) of 390 K with complex magnetic phase transitions under external fields, the specific electronic and topological properties of its ferromagnetic (FM) counterparts remain less explored. The challenge lies in stabilizing the FM phase in this system to study the interplay between flat bands, Dirac fermions, and magnetic ordering without the complications of multiple magnetic transitions.

Methodology
This study investigates the Ga-doped kagome magnet $ScMn_6(Sn_{0.78}Ga_{0.22})_6$. High-quality single crystals were synthesized using the self-flux method. The research employs a multi-faceted approach:

• Experimental: Magnetization and transport measurements were conducted using a vibrating sample magnetometer (VSM) and a four-probe method. Angle-resolved photoemission spectroscopy (ARPES) was performed at the Advanced Light Source (ALS) beamline 4.0.3 on cleaved (001) surfaces at 11 K (within the FM phase) using linear horizontal (LH) and linear vertical (LV) polarizations.
• Theoretical: Density Functional Theory (DFT) calculations were performed using the Vienna Ab Initio Simulation Package (VASP) with Projector Augmented Wave (PAW) pseudopotentials. The study utilized the Virtual Crystal Approximation (VCA) to model the 22% Ga doping and included spin-orbit coupling (SOC). A tight-binding model incorporating a Kane-Mele SOC term was also employed to theoretically analyze the dependence of the Dirac gap on magnetization orientation.

Key Results

1. Magnetic Properties: The Ga-doped compound exhibits a paramagnetic-to-ferromagnetic transition at $T_c \approx 375$ K. The system displays strong magnetic anisotropy with an in-plane easy magnetization axis; the in-plane magnetization is approximately five times greater than the out-of-plane susceptibility. Isothermal magnetization curves show saturation at lower fields for the in-plane direction compared to the out-of-plane direction.
2. Transport and Hall Effect: Longitudinal resistivity measurements indicate metallic behavior. Magnetoresistance (MR) measurements reveal nonlinearity and a sign change from negative to positive at low temperatures depending on the current and field orientation. Hall resistivity measurements demonstrate a substantial contribution from the anomalous Hall effect (AHE), with the behavior closely mirroring the magnetization data.
3. Electronic Structure (ARPES and DFT):
   • Dirac Cone: ARPES measurements and DFT calculations confirm the presence of a Dirac cone at the K point of the Brillouin zone, with the Dirac point located approximately 100 meV below the Fermi level ($E_F$).
   • Flat Band: A flat band, attributed to the destructive interference of wave functions within the Mn kagome lattice, was observed spanning a significant portion of the Brillouin zone at a binding energy of $\sim -0.4$ eV.
   • Polarization Dependence: Polarization-dependent ARPES reveals distinct orbital characters: the flat band is enhanced under LV polarization (associated with $Mn$ $d_{x^2-y^2}$, $d_{z^2}$, and $d_{yz}$ orbitals), while the Dirac cone is prominent under LH polarization (associated with $Mn$ $d_{xy}$ and $d_{xz}$ orbitals).
4. Magnetization-Dependent Gap Modulation: Theoretical calculations and tight-binding modeling reveal that the gap in the Dirac cone is tunable via the orientation of the magnetic moment. An out-of-plane magnetization orientation opens a gap of approximately 15 meV, whereas an in-plane alignment results in a gapless state. This theoretical prediction is corroborated by the ARPES observation of a gapless Dirac cone, consistent with the material's in-plane FM ground state.

Significance and Claims
The authors claim that this work provides a comprehensive analysis of the electronic structure of a magnetic kagome material where multiple characteristics—strong correlations (implied by flat bands), non-trivial band topology (Dirac cones), magnetic ordering, and geometric frustration—coexist. By successfully stabilizing the FM phase in $ScMn_6(Sn_{0.78}Ga_{0.22})_6$ through Ga doping, the study isolates a system free from the complex magnetic transitions of the parent compound. The observation of a gapless Dirac cone in the in-plane FM state, contrasted with the theoretical prediction of a gapped state in the out-of-plane orientation, offers valuable insights into the interplay between magnetization direction and topological band structures. The paper posits that these findings pave the way for exploring novel topological phases within the $RMn_6Sn_6$ family, particularly those driven by the tunability of the Dirac gap through magnetic anisotropy.