🔬 mesoscale physics

Engineering nonrelativistic spin splitting in semiconductors by altermagnetic proximity

This paper proposes and theoretically validates a proximity engineering strategy where coupling conventional semiconductors to gapped $d$ -wave altermagnets induces robust nonrelativistic spin splitting while allowing electrostatic tuning to suppress competing relativistic Rashba effects, thereby enabling the creation of pure nonrelativistic spin-split states in established semiconductor platforms.

Original authors: Sing Lam Wong, Marcel Franz

Published 2026-10-19

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CC BY 4.0

Original authors: Sing Lam Wong, Marcel Franz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of modern electronics, the way we store and process information is shifting from using electric charge to using a property called spin. Think of spin as a tiny, intrinsic magnetic arrow attached to every electron, pointing either up or down. For decades, scientists have tried to harness this arrow to build faster, more efficient devices. A major hurdle in this effort has been the need for strong magnetic fields to control these arrows, which often interfere with delicate electronic components. Recently, a new class of materials called altermagnets has emerged as a promising solution. These materials possess a unique internal order where the magnetic arrows of their atoms cancel each other out perfectly, resulting in no net magnetic field, yet they still manage to split electrons based on their spin direction. This splitting depends on the electron's momentum, or the direction and speed at which it moves, rather than on external magnets. While this sounds ideal for creating advanced quantum devices and spin-based electronics, a significant problem remains: no single material known today combines the necessary magnetic properties with the ability to conduct electricity like a semiconductor, while also keeping unwanted relativistic effects under control.

Researchers at the University of British Columbia have proposed a clever workaround to this material shortage. Instead of searching for a perfect, one-of-a-kind substance, they suggest building a sandwich-like structure. Imagine placing a thin film of a standard, non-magnetic semiconductor directly on top of an insulating altermagnet. In this setup, the two materials do not need to be chemically bonded into a single compound; they simply need to be close enough for their electrons to interact. The scientists developed a theoretical model to show that when these two layers are brought together, the unique magnetic properties of the altermagnet can be transferred to the semiconductor through a process of virtual tunneling. Electrons in the semiconductor briefly and invisibly jump into the altermagnet layer and return, picking up a signature of the altermagnet's momentum-dependent spin splitting along the way. This effectively turns the ordinary semiconductor into a material that behaves like a d-wave altermagnet, possessing the desired spin-splitting properties without needing to be magnetic itself.

A critical discovery in this work is the ability to fine-tune the system to eliminate a common nuisance known as Rashba coupling. In most interfaces between different materials, the breaking of symmetry creates a relativistic effect that twists the electron spins in a way that complicates the desired magnetic behavior. The researchers found that by carefully adjusting the energy alignment between the two layers—a process that can be controlled with an electric gate—they could make this unwanted twisting effect vanish completely. At a specific tuning point, which they call a "sweet spot," the relativistic interference disappears, leaving behind a clean, strong spin splitting driven purely by the altermagnetic proximity. This means the semiconductor layer retains its high-quality electronic properties while gaining the powerful, non-relativistic spin control needed for next-generation devices.

The study confirms through detailed calculations that this mechanism is robust. The induced spin splitting can reach energy scales of tens of millielectronvolts, which is significant enough to be observed in experiments, particularly at low temperatures. The researchers also noted that the strength of this effect grows with the density of electrons in the semiconductor, suggesting that devices with higher carrier concentrations would exhibit even more pronounced behavior. By separating the difficult requirements of magnetic ordering and semiconducting behavior into two different materials, this approach offers a general strategy for engineering quantum states that were previously thought to be impossible to create in a single compound. It opens a path toward building field-free spin qubits and advanced spintronic circuits that can be controlled entirely by electricity, without the need for bulky magnets or complex magnetic fields.

Technical Summary: Engineering Nonrelativistic Spin Splitting in Semiconductors by Altermagnetic Proximity

Problem Statement
Altermagnets represent a promising class of materials for spintronics and quantum devices due to their combination of vanishing net magnetization and momentum-dependent, nonrelativistic spin splitting (often with $d$ -wave symmetry). However, their practical application is currently hindered by a scarcity of materials that simultaneously possess the required altermagnetic symmetry, a semiconducting electronic structure, and weak spin-orbit coupling (SOC). Specifically, known semiconducting altermagnets (e.g., MnTe) often exhibit $g$ -wave symmetry, which forbids key functionalities like the spin-splitter effect, while $d$ -wave altermagnets are typically metallic or insulating but not semiconducting. Furthermore, intrinsic altermagnetic hosts must satisfy stringent conditions: being gapped, single-valley, low in nuclear-spin isotopes, and amenable to electrostatic gating. No single known material satisfies all these criteria.

Methodology
The authors propose a proximity engineering strategy to decouple these conflicting material requirements. They model a heterostructure consisting of a thin-film, non-magnetic, single-valley semiconductor (the "host") interfaced with an insulating, $d$ -wave altermagnet (the "donor").

Theoretical Framework: The system is described by a minimal continuum model Hamiltonian comprising the semiconductor ( $H_s$ ), the altermagnet ( $H_{ALM}$ ), and an interlayer tunneling term ( $H_g$ ). The semiconductor is modeled as a parabolic band with no intrinsic SOC. The altermagnet is a two-band model with $d$ -wave spin splitting ( $\eta_n \propto k_y^2 - k_x^2$ ) and an insulating gap.
Derivation: The authors employ a Schrieffer-Wolff transformation to integrate out the gapped altermagnetic degrees of freedom, deriving an effective Hamiltonian for the proximitized semiconductor. This approach captures virtual tunneling processes where electrons tunnel from the host to the donor bands and back.
Validation: The analytical results are cross-validated against the exact diagonalization of the full 6 $\times$ 6 Bloch Hamiltonian of the heterostructure. The spectral function projected onto the semiconductor block is computed to simulate spectroscopic probes (e.g., ARPES).

Key Contributions and Results

Induced Nonrelativistic Splitting: The study demonstrates that virtual tunneling transfers the $d$ -wave altermagnetic spin splitting to the semiconductor host. The induced splitting, $\eta^{\text{ind}}_0$ , scales with the square of the tunneling amplitude and can reach tens of meV for realistic parameters, even though the host itself is non-magnetic.
Differential Band Alignment Dependence: A central finding is the distinct dependence of induced nonrelativistic splitting and relativistic Rashba SOC on the band alignment parameter $x$ $x$ (defined by the relative position of the host band edge within the donor gap).
- The induced altermagnetic splitting ( $\eta^{\text{ind}}_0$ ) receives contributions from both the donor valence and conduction bands that reinforce each other (assuming same-sign splitting parameters).
- The induced Rashba SOC ( $\lambda^{\text{ind}}_R$ ) arises from virtual processes involving the valence and conduction bands that contribute with opposite signs.
The "SOC Sweet Spot": Due to the opposing signs in the Rashba contribution, there exists a specific band alignment ( $x^*$ ) where the induced Rashba coupling vanishes exactly, while a substantial $d$ -wave altermagnetic splitting persists. This allows for the creation of a "pure" nonrelativistic altermagnetic semiconductor.
Tunability: The relative band alignment $x$ can be controlled experimentally via electrostatic gating or transverse electric fields. This provides a tunable control knob to access the SOC-free regime.
Density Dependence: The magnitude of the observable spin splitting near the Fermi surface depends on the carrier density ( $k_F$ ). Since the altermagnetic splitting scales as $k_F^2$ while Rashba splitting scales as $k_F$ , higher carrier densities favor the dominance of the nonrelativistic altermagnetic effect.
Robustness: Exact diagonalization confirms that the mechanism holds beyond the perturbative regime. While the "sweet spot" generally acquires a weak momentum dependence in generic systems, it can be made exact and momentum-independent in a symmetric limit.

Significance and Claims
The paper claims that altermagnetic proximity engineering offers a general strategy to disentangle magnetic and relativistic spin interactions in quantum heterostructures. By separating the requirements for the magnetic source (large $d$ -wave splitting, insulating gap) and the electronic host (clean, gate-tunable semiconductor), the authors provide a route to realize functional altermagnetic semiconductors without relying on a single, currently non-existent material.

The proposed heterostructures are presented as a versatile platform for:

Spintronics: Enabling spin-splitter effects and spin filters that require $d$ -wave symmetry and electrostatic control.
Spin Qubits: Facilitating the design of field-free, electrically tunable spin qubits. The zero net magnetization of the altermagnet eliminates stray fields, preserving high-fidelity readout with superconducting resonators, while the momentum-dependent splitting allows for individual qubit addressability via orbital confinement.

The authors conclude that this approach circumvents the scarcity of intrinsic altermagnetic semiconductors and establishes a foundation for engineering nonrelativistic spin-split electronic states in established semiconductor platforms.

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