Altermagnetic Inverse Spin-Splitter Effect

• Altermagnetic inverse spin-splitter effect is a phenomenon where momentum-dependent spin splitting in antiferromagnets enables reciprocal conversion between spin and charge currents.
• It arises from symmetry-enforced odd-in-k splitting in band structures and is activated in confined geometries or via external electric fields to restore spin polarization at surfaces.
• This effect underpins innovative spintronic device designs featuring tunable, all-electrical spin–charge interconversion without net magnetization or strong spin–orbit coupling.

Altermagnetic inverse spin-splitter effect refers to the phenomenon where the unique, nonrelativistic, momentum-dependent spin splitting present in certain antiferromagnets—termed altermagnets—enables a reciprocal conversion between spin and charge currents without the necessity for net magnetization or strong spin–orbit coupling. This effect arises directly from the symmetry-enforced spin splitting in the band structure and manifests most robustly in confined geometries, such as thin films or particular surface orientations, or in the presence of external electric fields or strain. The inverse spin-splitter effect extends to both electronic and magnonic channels, contributing multifunctional capabilities to spintronic platforms.

1. Theoretical Basis: Symmetry, Band Structure, and Surface Projections

The defining property of an altermagnet is an antiferromagnetic ground state with a momentum-dependent, odd-in-$\mathbf{k}$ spin splitting, commonly captured in Hamiltonians of the form

$$H_{\rm spin}(\mathbf{k}) = \Delta_{\rm AM}(\mathbf{k})\,\sigma_z$$

with

$$\Delta_{\rm AM}(-\mathbf{k}) = -\Delta_{\rm AM}(\mathbf{k}).$$

A representative functional form is $$\Delta_{\rm AM}(\mathbf{k}) = \Delta_{0} [\sin(k_x a) - \sin(k_y a)]$$, which produces sign-reversal of the spin splitting between symmetry-related momenta. Crucially, in the bulk, the compensation enforced by the crystal’s magnetic space group “hides” the net spin splitting; however, at surfaces or interfaces, the 3D Brillouin zone is projected onto a 2D surface BZ. If high-symmetry momenta ($\mathbf{k}$ and $-\mathbf{k}$) retaining opposite spin splitting project to separate points, the surface state retains nonrelativistic spin splitting; if they merge, the effect is annihilated, and the surface becomes “blind” to altermagnetism (Sattigeri et al., 2023).

The preservation or annihilation of spin splitting under projection is dictated by both the surface orientation and the underlying magnetic order. Consequently, the choice of surface is a crucial parameter: cleaving along the appropriate orientation preserves altermagnetic properties; a “blind” orientation may recover splitting when additional symmetry is broken, e.g., by an electric field perpendicular to the film.

2. Mechanisms and Reciprocal Conversion: Inverse Spin-Splitter Physics

The “inverse” spin-splitter effect arises when the process is reversed: rather than generating spin current from charge current (as in the canonical spin-splitter effect), an injected spin current—aligned according to the symmetry and orientation that preserve the intrinsic splitting—drives a transverse charge current via the unique momentum-space spin texture (Sattigeri et al., 2023). The underlying physical processes are governed by the interplay between the bulk and projected surface symmetries, the spatial orientation of the interface, and any externally applied symmetry-breaking fields.

Systems where the symmetry conditions are realized support a general tensorial relation between spin and charge conductivities,

$j_c^{i} = \theta_{\text{ISSE}}^{ij} j_s^{j},$

where $\theta_{\text{ISSE}}$ captures the conversion efficiency, which is strongly anisotropic and direction-dependent.

3. Predicted Phenomenology and Experimental Protocols

Surface Physics and ARPES

The most direct experimental probe is spin-resolved angle-resolved photoemission spectroscopy (ARPES) on thin films, where the persistence of momentum-dependent spin splitting in the surface BZ is diagnostic of altermagnetism. The effect is maximized for surfaces where the projections of “partner” $\mathbf{k}$-points with opposite splitting remain distinct. If the surface is “blind,” an electric field applied normal to the film can “activate” the splitting by breaking residual symmetry, redistributing the electronic structure and allowing for measurable spin-resolved charge currents.

Electric-Field Activation

An external electric field ($E_z$) perpendicular to a surface that is otherwise degenerate can unbalance the projection of $\pm \mathbf{k}$ points, opening a splitting that is symmetry-forbidden in equilibrium. This field-activation principle provides a practical route for dynamic control over spin polarization in devices.

Spin-Polarized Transport

By injecting a spin current or a spin accumulation into such a surface (using, e.g., spin pumping or spin Hall effect in an adjacent heavy metal), the inverse process—conversion of a spin current into a transverse charge current—can be observed. This conversion is maximized in the symmetry orientation that retains splitting and is tunable via applied fields.

Device Concepts

Potential applications include:

• Nonlocal detection geometries where a spin current injected at one edge gives rise to a charge response at another,
• Electric-field-tunable spin–charge converters,
• Surface/interface-based heterostructures where the effect can be dynamically switched or modulated.

Surface Cleavage Table

Surface Orientation	Spin Splitting Survives?	Effect of Electric Field
“Active” Surface	Yes	Maximal ISSE
“Blind” Surface	No	ISSE activated by $E_z$

The position of the “active” surface is material- and order-dependent.

4. Role of Magnetic Order, Collective Modes, and Tunability

The location and magnitude of the key $\mathbf{k}$-points are set by the microscopic magnetic order. Altering the type or orientation of antiferromagnetic order (for example, by tuning strain, temperature, or external fields) shifts which projections host observable altermagnetic properties (Sattigeri et al., 2023). This coupling allows for device concepts where spin–charge conversion is manipulated by reorienting the Néel vector or altering domain structure.

Moreover, the possibility of interfacing altermagnets with other collective modes (such as phonons or magnons) opens avenues for coupling the ISSE to lattice or spin dynamics, potentially yielding hybrid spintronic/phononic or magnonic functionalities.

5. Spintronics Applications and Outlook

The inverse spin-splitter effect offers several advantages for spintronic device engineering:

• All-electrical operational control: No net magnetization or externally applied magnetic field is required.
• Material versatility: The effect is present in a broad class of compensated antiferromagnets with appropriate symmetry, not limited by strong spin–orbit coupling.
• Design flexibility: By selecting appropriate surface orientations and employing external electric fields or strain, devices can be tailored for maximal conversion efficiency.
• Integration with interfaces: The thin-film or interface-confined nature of the effect is amenable to existing layered device architectures.

These features position the ISSE as a platform for low-dissipation, dynamically tunable spin–charge interconversion, with immediate implications for applications in nonvolatile memory, THz emission, and hybrid quantum devices.

6. Experimental Implementation and Research Directions

Key experimental considerations identified include:

• Controlled surface (or interface) preparation along predicted “active” orientations,
• Incorporation of gating or external field control for dynamic modulation,
• Spin-resolved ARPES and nonlocal electronic transport measurements as diagnostics,
• Integration into heterostructure stacks to exploit proximity with topological, superconducting, or ferroelectric materials.

Future research directions involve:

• Engineering bulk and interface symmetry to stabilize large ISSE,
• Exploring the interplay with magnonic and phononic excitations,
• Quantifying scaling behavior with respect to film thickness, interface roughness, and electronic scattering rates,
• Realizing reconfigurable devices leveraging combined electric, strain, or magnetic control (Sattigeri et al., 2023).

7. Summary

The altermagnetic inverse spin-splitter effect is a manifestation of symmetry-protected momentum-dependent spin splitting in a broad class of collinear antiferromagnets. Its experimental realization and tuning rely on careful choice of interface orientation, magnetic order, and external symmetry-breaking fields. The effect enables all-electrical, magnetic-field-free control over nonlinear spin–charge interconversion, pointing to a new domain of functionality in spintronics unconstrained by traditional magnetization or relativistic mechanisms. The underlying symmetry analysis provides concrete design rules for maximizing the effect in thin films and heterostructures, paving the way for device concepts where spin polarization and charge currents are controlled with high fidelity by electric fields, structural engineering, or interface design.