Altermagnetism: Emerging Spin-Splitting Order

• Altermagnetism is a novel magnetic order characterized by zero net magnetization and momentum-dependent spin splitting, distinguishing it from traditional ferro- and antiferromagnetism.
• It enables electric-field control over spin textures in fractional quantum multiferroics, paving the way for high-performance, voltage-controlled spintronic devices with TMR exceeding 300%.
• It is realized in diverse material systems, including bulk compounds like MnTe and engineered 2D bilayers, which display robust room-temperature antiferromagnetic order and impressive spin-splitting metrics.

Altermagnetism (AM) is a recently identified class of collinear magnetic order, distinct from both conventional ferromagnetism and antiferromagnetism. Defined by a compensated (zero net) magnetization and robust momentum-dependent spin-splitting in the electronic structure, altermagnets break time-reversal symmetry but do not exhibit a macroscopic magnetization. This phase permits novel types of magnetoelectric and spintronic phenomena not achievable with traditional magnetic symmetry classes, and can be realized in various material families, including both three-dimensional compounds and engineered low-dimensional systems. Altermagnetism plays a central role in the emerging class of fractional quantum multiferroics (FQMF), where electric-field switching of ferroelectric polarization controls the spin-splitting of altermagnetic states through symmetry-enforced coupling.

1. Conceptual Foundations

Fractional quantum multiferroics (FQMF) leverage the unique interplay between fractional quantum ferroelectricity (FQFE) and altermagnetism (AM). In FQFE, polarization is generated by fractional (rather than integer) atomic displacements between symmetry-equivalent positions in nonpolar crystal environments, resulting in two (or more) nearly degenerate structural states (L₁, L₂). Altermagnetism, characterized by zero net magnetization and broken time-reversal symmetry, manifests as nonrelativistic, symmetry-protected momentum-dependent spin-splitting in the electronic bands.

A defining property of FQMFs is the symmetry-enforced link between the direction of FQFE polarization and the sign of altermagnetic spin splitting. When the polarization is switched (e.g., by electric field), the spin splitting in the band structure is inverted due to combined parity-time ($\mathcal{PT}$) or time-reversal-fractional translation ($\mathcal{T}\tau$) symmetry operations:

$$\begin{align*} \tau\,\mathcal{PT}\,\epsilon_n(\mathbf{k},\mathbf{s}) &= \epsilon_n(\mathbf{k},-\mathbf{s}) \ \tau\,\mathcal{T}\,\epsilon_n(\mathbf{k},\mathbf{s}) &= \epsilon_n(-\mathbf{k},-\mathbf{s}) = \epsilon_n(\mathbf{k},-\mathbf{s}) \end{align*}$$

Thus, reversing the FQFE polarization does not rotate the Néel vector but flips the momentum-dependent spin splitting across the entire Brillouin zone.

2. Symmetry Mechanisms and Coupling

The fundamental mechanism enabling the coupling between ferroelectricity and altermagnetism in FQMFs is rooted in symmetries specific to nonpolar space groups allowing fractional (rather than integer) atomic displacements and in the antiferromagnetic order underlying AM. In FQMFs, the two polarization states L₁ and L₂ are interconverted by either $\mathcal{PT}$ or $\mathcal{T}\tau$ (where $\tau$ is a fractional lattice translation mapping one nonpolar position to another). As a result, the reversal of polarization leads to a corresponding inversion of the altermagnetic spin texture while preserving the orientation of the magnetic order (i.e., the Néel vector remains intact).

This behavior is encoded in the symmetry properties of the band structure, such that the spin-resolved energy for the two FQFE states are related by the above symmetry operations. In practical terms, this allows purely electric-field-driven control over spin textures, enabling an entirely electrical route to modulate spintronic functionalities in FQMFs.

3. Materials Realization

A wide array of candidate materials are predicted for realizing FQMFs:

Material Type	Example Compounds	Notable Features
Bulk (3D) compounds	MnTe, Cr$_2$S$_3$, Mn$_4$Bi$_3$NO$_{15}$	High Néel T$_N$ ($\sim$300 K, MnTe), large band gap
Two-dimensional (2D) and AB$_2$ bilayers	MnX$_2$ (X=Cl, Br, I), CoCl$_2$, CoBr$_2$, FeI$_2$	Electrically tunable, nonpolar symmetry

In bulk MnTe, FQMF order is demonstrated with a room-temperature Néel ordering ($T_N\sim300$ K) and an electrically switchable spin splitting of approximately 0.8 eV—substantially exceeding the performance of conventional multiferroics. The same mechanism enables FQMF phases in a variety of 2D AB$_2$ bilayers and other nonpolar-layered materials, greatly expanding the playground for voltage-driven spintronic effects.

4. Electric-Field Switchable Spin Splitting: Performance and Figures of Merit

The electric-field tunability of the altermagnetic spin splitting constitutes a primary performance metric in FQMFs. In MnTe, for example:

• Antiferromagnetic order is robust up to $\sim$300 K.
• The electrically controlled spin splitting in the valence band reaches $\sim$0.8 eV.
• The band gap is sizable ($\sim$0.9 eV), ensuring a fully insulating state suitable for ferroelectric operation.

The reversal of FQFE polarization (via modest electric fields) flips the sign of the spin splitting throughout the Brillouin zone, while the magnetic sublattice remains unrotated.

5. Device Concepts: FQMF Tunnel Junctions and Voltage-Controlled Spintronics

A representative device application enabled by FQMFs is the electric-field-controlled tunnel junction (FQMFTJ). In this structure, both fixed and free layers are made of FQMF material (e.g., MnTe):

• In the parallel configuration (both layers in the same FQFE state), their altermagnetic band structures align, resulting in a high tunneling conductance.
• When one layer’s FQFE polarization is switched (antiparallel configuration), the spin splitting is inverted, causing a momentum-space mismatch and suppressing tunneling.
• The resulting tunneling magnetoresistance (TMR) exceeds 300%, substantially higher than values generally observed in conventional multiferroic tunnel junctions.

This effect arises not from standard electronic or atomic-structural band mismatches but from symmetry-enforced inversion of the altermagnetic split bands via electric-field control of FQFE.

6. Experimental and Theoretical Implications

The discovery and theoretical groundwork for FQMFs suggest numerous directions for future research:

• Voltage-controlled spintronics: Electric-field modulation of spin splitting without altering the Néel vector paves the way for nonvolatile, low-power, and ultrafast spin-based logic and memory.
• Materials search: The identification of bulk and 2D candidates with high $T_N$ and large, electrically switchable spin splitting points toward possible room-temperature applications.
• Integration: FQMFs could be employed in hybrid devices (such as tunnel junctions and spin filters) and incorporated into complex heterostructures where both ferroelectric and altermagnetic functionalities are present.
• Fundamental inquiry: The interplay between symmetry, fractional polar displacements, and momentum-dependent spin textures remains rich for theoretical exploration, especially in uncovering additional classes of multiferroic coupling mediated by altermagnetism.

7. Summary Table: Key FQMF Features in MnTe

Property	Value / Feature	Significance
Néel temperature ($T_N$)	$\sim$300 K	Room-temperature antiferromagnetic order
Electrically switchable spin splitting	$\sim$0.8 eV	Large, symmetry-protected, in valence band
Band gap	$\sim$0.9 eV	Supports robust ferroelectric switching
Tunneling magnetoresistance (FQMFTJ)	$>$300%	Outperforms traditional multiferroic junctions
Electric field control	Polarization + spin texture	No Néel vector rotation required

These quantitative and qualitative features highlight the disruptive technological potential of electrically controllable altermagnetic spin textures, with FQMFs standing as a new frontier for voltage-controlled spintronic devices and strongly-coupled multiferroic functional materials (Dong et al., 19 Oct 2025).