Orbital-selective band evolution and out-of-plane correlation in the FeGe-family kagome antiferromagnet ScFe$_6$Ge$_6$

By investigating the kagome antiferromagnet ScFe$_6$Ge$_6$, which lacks charge density wave (CDW) order, the study reveals that orbital-selective band evolution and out-of-plane correlations are critical factors governing the emergence of spin-correlated CDW order in magnetic kagome metals.

The Gist

Imagine a bustling city built on a unique, honeycomb-like grid called a Kagome lattice. In this city, the residents are electrons, and they usually get along in a predictable way. But in a special neighborhood called FeGe, something strange happens: the electrons suddenly organize themselves into a rigid, repeating pattern (like a traffic jam that freezes the whole city), known as a Charge Density Wave (CDW). This happens right at the same time the city's magnetic "compasses" (spins) start pointing in specific directions. Scientists have been trying to figure out: Does the traffic jam cause the compasses to move, or do the compasses cause the traffic jam?

To solve this mystery, the researchers in this paper decided to build a "sister city" called ScFe6Ge6. This new city looks almost exactly like FeGe, but with one crucial difference: the "traffic jam" (CDW) never happens here. By comparing the two cities, the scientists hoped to see what was missing in the sister city that allowed the traffic jam to form in the original one.

Here is what they found, explained simply:

1. The Two Cities: FeGe vs. ScFe6Ge6

• FeGe (The Original): When it gets cold, the electrons freeze into a pattern (CDW), and the magnetic compasses align. It's a chaotic mix of electricity, magnetism, and the physical structure of the city all changing at once.
• ScFe6Ge6 (The Sister City): This city has the same layout, but the electrons never freeze into a traffic jam. Instead, when it gets cold, only the magnetic compasses shift slightly. The physical streets (the crystal lattice) stay perfectly straight, and the electricity flows smoothly.

2. The "Orbital" Secret

In these cities, electrons don't just move; they also have a specific "shape" or "posture" (called an orbital). Some electrons stand up tall (out-of-plane), while others lie flat.

The researchers discovered that in the sister city (ScFe6Ge6), something very specific happened to the standing-up electrons. As the temperature dropped, these specific electrons changed their behavior dramatically, shifting their energy levels, while the "lying-flat" electrons stayed exactly the same.

• The Analogy: Imagine a dance floor where most dancers keep dancing the same way, but suddenly, only the dancers wearing red shirts (the "out-of-plane" electrons) decide to change their dance moves. The scientists call this orbital-selective behavior. It suggests that the magnetic compasses are only talking to the "standing-up" electrons, not the others.

3. The "Spring" Connection (Lattice Vibrations)

The city streets aren't static; they vibrate like springs. The researchers found that in the sister city, there is a specific vibration mode (a "spring" that moves up and down) that gets weird exactly when the magnetic compasses shift.

• The Analogy: Think of the magnetic compasses and the street springs as two people holding hands. When the compasses shift, they tug on the springs, causing a visible "kink" or change in how the springs vibrate. This proves that magnetism and the physical structure of the city are tightly linked, even without a traffic jam.

4. Why No Traffic Jam?

So, why didn't the sister city get a traffic jam (CDW)?

• In the original city (FeGe), the "standing-up" atoms (Germanium) are close enough to hold hands and form pairs (dimers), which triggers the traffic jam.
• In the sister city (ScFe6Ge6), the researchers found that these atoms are pushed slightly further apart by the new layout. They are too far apart to hold hands. Without this "hand-holding," the traffic jam never forms.
• The Takeaway: The traffic jam in the original city relies heavily on these atoms holding hands (dimerization). When you break that connection, the jam disappears, leaving only the magnetic shift.

The Big Conclusion

The paper concludes that orbital physics (which electrons are "standing up") and out-of-plane correlations (how things interact vertically) are the hidden keys to understanding these materials.

Even though the sister city didn't have a traffic jam, it showed that the magnetic compasses are still deeply connected to the specific "standing-up" electrons and the vertical vibrations of the city. This suggests that in the original city (FeGe), the traffic jam isn't just a random accident; it's a complex dance where the magnetic compasses, the specific electron shapes, and the vertical vibrations all work together.

In short: By removing the traffic jam, the scientists saw that the magnetic compasses still have a special, secret conversation with the "standing-up" electrons and the vertical springs of the city. This conversation is likely the same force that causes the traffic jam in the original city, but now we know it's driven by these specific vertical and orbital interactions.

Technical Summary

Technical Summary: Orbital-Selective Band Evolution and Out-of-Plane Correlation in the FeGe-family Kagome Antiferromagnet ScFe6Ge6

Problem Statement
The interplay between charge density wave (CDW) order and magnetism in strongly correlated materials remains a significant unresolved problem. The kagome metal FeGe is a unique system where CDW order emerges deep within an antiferromagnetic (AFM) state, accompanied by unconventional lattice symmetry evolution. However, the microscopic origin of this spin-correlated CDW order, particularly the role of the incommensurate spin phase and the specific mechanism driving the Ge dimerization, is not fully understood. While FeGe exhibits both magnetic and charge ordering, it is unclear which degrees of freedom (spin, charge, orbital, or lattice) are the primary drivers. To isolate the governing conditions for such spin-correlated CDW order, the authors investigate ScFe6Ge6, a derivative compound that retains the structural and magnetic framework of FeGe but lacks the CDW order, thereby reducing the involvement of charge degrees of freedom.

Methodology
The study employs a multi-faceted experimental approach on high-quality single crystals of ScFe6Ge6, grown via the Sn-flux method. The characterization includes:

• Structural Analysis: Single-crystal X-ray diffraction (SXRD) to confirm the HfFe6Ge6-type structure ($P6/mmm$ symmetry) and lattice parameters.
• Transport and Magnetism: Temperature-dependent longitudinal resistivity and magnetic susceptibility measurements (both zero-field cooled and field-cooled) to identify phase transitions.
• Electronic Structure: Angle-resolved photoemission spectroscopy (ARPES) using 102 eV photons at 9 K and varying temperatures to map the electronic band structure, Fermi surfaces, and band evolution across magnetic transitions. Momentum distribution curve (MDC) fitting was used to quantify band shifts and effective masses.
• Lattice Dynamics: Raman spectroscopy using circularly polarized light to identify phonon modes and their temperature dependence, specifically looking for anomalies associated with magnetic transitions.
• Theoretical Support: Density Functional Theory (DFT) calculations were performed to assist in orbital assignments and phonon mode identification.

Key Results

1. Absence of CDW and Structural Distortion: Unlike FeGe, ScFe6Ge6 shows no evidence of CDW order or structural phase transitions. Resistivity data indicates metallic behavior without anomalies, and Raman spectra reveal no emergence of new phonon modes or significant structural distortions across the temperature range.
2. Magnetic Phase Transitions: While ScFe6Ge6 exhibits A-type AFM ordering below $T_N \approx 487$ K, a distinct magnetic transition occurs at $T^* = 195$ K. This transition is observed only in the in-plane magnetic susceptibility, manifesting as a kink, and is absent in the out-of-plane data. This suggests a weak ferromagnetic component arising from Fe spin canting away from the c-axis, replacing the CDW transition seen in FeGe.
3. Orbital-Selective Band Evolution: ARPES measurements reveal that across $T^*$, the electronic band structure undergoes a selective evolution confined to a single kagome Dirac band (DB3).
   • DB3, which originates from out-of-plane Fe $d$-orbitals (specifically $d_{z^2}$ character, confirmed by polarization dependence), shifts in energy and merges with the adjacent DB2 band as temperature increases above $T^*$.
   • This merging is accompanied by a significant renormalization of the effective mass of DB3 (increasing from $0.7m_e$ to $3.2m_e$), indicating strong scattering or coupling mechanisms.
   • Other kagome bands (DB1, DB2, and the flat band) remain relatively rigid, highlighting the orbital-selective nature of the response.
4. Magnetoelastic and Electron-Phonon Coupling:
   • Raman spectroscopy identifies an anomaly in the $A_{1g}$ phonon mode (at $\approx 28$ meV), which corresponds to in-phase out-of-plane vibrations of the Fe kagome plane and Ge atoms. This mode exhibits a frequency kink, linewidth broadening, and intensity dip at $T^*$, signaling a magnetoelastic effect (spin-phonon coupling).
   • ARPES data reveals a "kink" in the electron self-energy at $\approx 28$ meV, matching the energy of the $A_{1g}$ phonon. This indicates a moderate electron-phonon coupling constant ($\lambda \approx 0.3$).
   • The hole band (HB) also shows temperature-dependent shifts correlated with the $A_{1g}$ mode, further supporting electron-phonon coupling.

Significance and Claims
The paper posits that ScFe6Ge6 serves as a critical model for understanding the conditions required for spin-correlated CDW order in FeGe-family materials. The authors claim that:

• Orbital Selectivity is Central: In the absence of charge ordering (CDW), the orbital degree of freedom becomes the dominant factor. The magnetic transition in ScFe6Ge6 is driven by an orbital-selective response where out-of-plane Fe $d$-orbitals couple strongly to spin reorientation (spin canting).
• Out-of-Plane Correlations are Key: The study emphasizes that out-of-plane correlations play an enhanced role in these kagome magnets. The suppression of CDW in ScFe6Ge6 is attributed to the increased distance between kagome planes and the displacement of Ge atoms, which disrupts the Ge dimerization necessary for CDW formation.
• Common Mechanism: Despite the absence of CDW in ScFe6Ge6, the shared importance of out-of-plane fluctuations (spin canting and $A_{1g}$ phonon coupling) with FeGe suggests a common underlying mechanism rooted in out-of-plane correlations. This mechanism governs the rich physics of FeGe-related compounds, where the interplay between spin, electronic, and lattice degrees of freedom determines the presence or absence of novel charge orders.

In conclusion, the work demonstrates that while lattice degrees of freedom are less coupled in ScFe6Ge6 compared to FeGe, the orbital degree of freedom takes a prominent role, mediating the magnetic transition through strong out-of-plane spin-orbital-lattice coupling. This provides a stepping stone toward elucidating how magnetic order can enable or suppress CDW formation in kagome systems.