Altermagnetic Band Splitting in CrSb Films

• Altermagnetic band splitting is a phenomenon where symmetry in collinear antiferromagnets creates a momentum-dependent, nonrelativistic spin splitting with g-wave characteristics.
• CrSb thin films grown via molecular beam epitaxy demonstrate robust, up to 1 eV, g-wave band splitting as confirmed by ARPES and complementary structural analyses.
• This strategy enables high spin polarization without net magnetization, offering a promising route for scalable, room-temperature spintronic devices.

Altermagnetic band splitting refers to the momentum-dependent, symmetry-protected, nonrelativistic spin splitting observed in the electronic band structure of altermagnets—a class of collinear antiferromagnets wherein the spin sublattices possess zero net magnetization yet yield notable electronic spin polarization. In 10 nm epitaxial CrSb thin films, this phenomenon is robustly established via molecular beam epitaxy growth, comprehensive structural verification, and angle-resolved photoemission spectroscopy (ARPES), demonstrating that the prototypical “g-wave” altermagnetic band structure persists down to nanometer thicknesses at room temperature (Santhosh et al., 1 May 2025).

1. Altermagnetic Symmetry and Band Splitting Mechanism

Altermagnetism arises from the unique intertwining of magnetic order and crystal symmetry. In CrSb’s NiAs-type structure, two magnetic sublattices host antiparallel spin orientations, yet global symmetry operations (including six-fold rotations combined with half-unit-cell translations and time reversal, e.g., $[\mathrm{C}_{6z}t_{1/2}]T$) map real-space spin configurations into momentum space in a way that imparts a momentum-dependent, sign-reversing band splitting. Unlike conventional antiferromagnets—which remain spin-degenerate by virtue of Kramers theorem and net-zero exchange field—altermagnets display a finite, nonrelativistic spin splitting that reaches a maximum away from symmetry-protected nodal planes, with the splitting $\Delta(\mathbf{k})$ exhibiting $g$-wave symmetry:

$$E(\mathbf{k}) = E_0(\mathbf{k}) \pm \Delta(\mathbf{k}),$$

where $\Delta(\mathbf{k})$ reverses sign according to the direction in $k$-space.

2. Thin Film Synthesis and Structural Characterization

The NiAs-phase CrSb thin films are synthesized by co-evaporation of Cr and Sb (typical flux ratio $\sim$1:5.8) onto SrTiO$_3$(111) substrates precoated with a 2 nm Sb$_2$Te$_3$ buffer, promoting epitaxy despite the lack of van der Waals layers. Film growth temperatures near 240 °C and low rates (as slow as 0.04 nm/min for 10 nm films) yield high crystallinity. Key characterization includes:

• Reflection High Energy Electron Diffraction (RHEED): Streaky patterns indicative of flat, smooth surfaces;
• X-ray Diffraction (XRD): Peaks consistent with NiAs $c$-axis, six-fold symmetry from $\varphi$ scans;
• HAADF-STEM: Atomically sharp film–substrate interfaces and correct 1:1 Cr:Sb stoichiometry;
• Polarized Neutron Reflectometry (PNR): Absence of net magnetization, confirming the antiferromagnetic ground state.

These techniques collectively establish that epitaxial CrSb films preserve the essential crystallographic and magnetic framework underpinning altermagnetic band splitting.

3. ARPES Measurements and Electronic Structure

In situ vacuum ARPES is employed to resolve detailed band structures in CrSb films (10–100 nm). By varying photon energy (20–100 eV, including He lamp at 21.2 eV), full three-dimensional momentum space ($k_x$, $k_y$, $k_z$) is accessed. The salient observations include:

• Three-dimensional momentum-dependent band splitting consistent with theoretical predictions, reaching up to nearly 0.7–1.0 eV depending on $k$-space location.
• Anisotropy and g-wave symmetry: The magnitude of $\Delta(\mathbf{k})$ varies strongly with momentum direction; maximal splitting occurs away from high-symmetry planes (e.g., along M–$\Gamma$–M), while nodes appear where symmetry-protected degeneracies persist.
• Thickness robustness: The splitting remains prominent for films as thin as 10 nm, with no loss of bulk-like features.
• Room-temperature survival: The ARPES signatures of altermagnetic band splitting are observed at $T \approx 300$ K, substantially below the CrSb Néel point ($T_N \sim 700$ K).

These data provide compelling experimental validation that the predicted g-wave altermagnetic band splitting is fully realized even in highly confined epitaxial geometries.

4. Symmetry Analysis and Theoretical Representation

The momentum-dependent band splitting follows from spin-group symmetry operations inherent to the crystal. For CrSb, combined operations (e.g., rotation $C_{6z}$, translation $t_{1/2}$, time-reversal $T$) mandate that $\Delta(\mathbf{k})$ switches sign under transformation between certain regions of the Brillouin zone. This results in a characteristic six-lobed (star-of-David) pattern in the angular map of splitting magnitude—defining the $g$-wave nature of altermagnetism in momentum space.

Mathematically, one can summarize: $$E(\mathbf{k}) = E_0(\mathbf{k}) \pm \Delta(\mathbf{k}),\qquad \Delta(\mathbf{k}) \propto f(k_x, k_y, k_z)$$ where $f(k)$ encodes both the angular dependence (arising from crystal symmetry) and the suppressed splitting along symmetry-protected planes.

5. Spin Transport and Device Implications

The distinctive features of altermagnetic band splitting in CrSb confer several key advantages:

• Large spin splitting at $E_F$ (up to $\sim$1 eV): Favors efficient spin polarization of conducting electrons, essential for high-performance spintronic devices.
• Absence of net magnetization: Altermagnets exhibit antiferromagnetic order so that stray magnetic fields—problematic for device scaling and cross-talk—are avoided.
• High $T_N$ and thin-film resilience: Functional band splitting is preserved at room temperature and down to 10 nm, supporting integration into nanoscale logic or memory architectures.
• Momentum-dependent control: The $g$-wave symmetry offers potential avenues for $k$-selective device responses and nontrivial manipulation of electronic and spin textures.

Such properties position CrSb and similar altermagnets as front-runners in the development of next-generation, high-speed, and field-robust spin-transport and spintronic platforms.

6. Outlook and Fundamental Significance

The experimental confirmation of altermagnetic band splitting in ultrathin CrSb epitaxial films highlights the critical role of spin-group symmetry in controlling electronic structure beyond the usual paradigms of spin–orbit driven splitting. This work provides a template for exploring quantum confinement, interfacial effects, and further symmetry engineering in antiferromagnetic spintronic materials. Future efforts might include sub-10 nm regimes, interface functionalization, or heterostructure assembly for emergent band-splitting phenomena and tailored spin responses.

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In summary, the “band-splitting strategy” in 10 nm CrSb thin films consists of leveraging the non-relativistic, spin-group symmetry-protected nature of altermagnetism to achieve robust, momentum-dependent spin splitting that combines the essential benefits of high-$T_N$ antiferromagnetism with exceptionally large electronic spin polarization—all confirmed through precise synthesis, crystallographic verification, and full-momentum ARPES mapping (Santhosh et al., 1 May 2025).