Fully compensated and uncompensated ferrimagnetic ferrovalley semiconductors

Abstract: Altermagnets (AMs) and fully compensated ferrimagnets (FC-FIMs) are emerging classes of magnetic materials that combine the advantages of antiferromagnets and ferromagnets. Here, we elucidate the mechanism behind the uniaxial strain-driven transformation from AM to FC-FIM and find that the accompanying non-relativistic valley polarization is positively correlated with the net magnetic moment between magnetic atoms in opposite spin sublattices. We then propose an uncompensated ferrimagnetic monolayer VCrSeTeO to achieve large intrinsic valley polarization. Spin-orbit coupling (SOC) is shown to further increase the valley polarization to over 400 meV under uniaxial strains and the reason is explained in terms of SOC perturbation theorem. Furthermore, we reveal a distinctive anomalous valley Hall effect in which the valley Hall voltage is reversed within the same valley in ferrimagnet VCrSeTeO. This work proposes a strategy for realizing giant valley polarization and provides theoretical guidance for the application of ferrimagnetic ferrovalley semiconductors derived from altermagnets in valleytronics.

• The paper demonstrates that strain-induced sublattice inequivalence triggers an AM-to-FC-FIM transition, leading to significant valley polarization.
• The paper employs VASP-based DFT and heterovalent substitution (V to Cr) to achieve giant intrinsic valley splitting, with values up to 414 meV observed.
• The paper shows that spin-orbit coupling amplifies valley polarization and induces an anomalous valley Hall effect with reversible valley voltage upon magnetization reversal.

Fully Compensated and Uncompensated Ferrimagnetic Ferrovalley Semiconductors: Mechanisms and Applications

Background and Motivation

The dichotomy between ferromagnetism and antiferromagnetism has long structured 2D magnetism research, but emergent classes such as altermagnets (AMs) and fully compensated ferrimagnets (FC-FIMs) occupy an intermediate regime with unique electronic and magnetic properties. These systems lack net magnetization, analogously to AFMs, while maintaining momentum-space spin splitting, akin to FMs and FIMs. FC-FIMs and AMs thus exhibit intrinsic advantages including high-density spintronics applications and minimized stray fields. Of particular interest is the control and exploitation of the valley degree of freedom in low-dimensional systems, which is foundational in valleytronic device paradigms.

In this context, the present study elucidates the intrinsic relationship between strain-modulated magnetic sublattice inequivalence and valley polarization in AM-to-FC-FIM transitions, and leverages sublattice engineering (via heterovalent TM atom substitution) to propose and theoretically validate materials with giant intrinsic valley polarization. The work proceeds to further analyze the interplay of SOC and symmetry, culminating in the prediction of anomalous valley Hall effects in these ferrimagnetic ferrovalley semiconductors.

Strain-Driven AM to FC-FIM Transition and Valley Polarization

The authors deploy VASP-based DFT (PBE+U) calculations, analyzing prototypical monolayer V$_2$Se$_2$O and its Janus derivative V$_2$SeTeO as representatives of the AM class. Upon application of uniaxial strain, a quasi-linear emergence of net magnetic moment difference between the V atoms in opposite spin sublattices is observed, while the net magnetization remains zero. This is a definitive indicator of the AM-to-FC-FIM transition: strain breaks underlying symmetry and locally differentiates V sublattice site physics.

Critically, induced valley polarization—the difference in energy between high-symmetry points (e.g., X and Y) in the Brillouin zone—is shown to scale with this emergent sublattice magnetization. For instance, at $-5\%$ compressive strain, a maximum valley polarization of approximately $-167$ meV is reached in V$_2$SeTeO, co-occurring with the onset of a semimetallic state at the Y valley (i.e., realization of a half-semimetallic FC-FIM).

The underlying origin is traced to strain-modulated hopping interactions: in the octahedral local environment, the V($d_{x^2-y^2}$)-Se($p_{x/y}$) hybridization exhibits unequal strain sensitivity between sublattices, producing an imbalance in local moments and, consequentially, momentum-resolved spin splitting.

Engineering Giant Valley Polarization via Sublattice Substitution

To surpass the symmetry/strain limitations of AMs and FC-FIMs with zero net moment, the study proposes a direct sublattice engineering strategy: substitution of one transition metal sublattice by an element with a different valence, thus intentionally constructing a ferrimagnetic order with finite net moment and intrinsically broken diagonal mirror symmetry.

The VCrSe$_2$O and VCrSeTeO monolayers (V replaced by Cr in one sublattice) are confirmed as stable uncompensated FIM (UFIM) systems. The results show pronounced valley splitting ($\sim162$ meV for VCrSe$_2$0O, $_2$1 meV for VCrSeTeO, intrinsic, i.e., without SOC or external fields). The physical origin is the large difference between V and Cr local moments, maximizing the inequivalence in the magnetic environment at each valley.

Notably, in UFIM VCrSeTeO, the valley polarization can exceed $_2$2 meV under moderate uniaxial strain and with SOC included. This is a significant enhancement over both conventional ferrovalley materials and strain-induced FC-FIMs.

Spin-Orbit Coupling and Anomalous Valley Hall Effect

Contrary to typical ferrovalley systems in which SOC is a prerequisite for valley polarization, these UFIM systems exhibit large intrinsic valley splitting even in the absence of SOC. However, SOC acts as an amplifier, especially when the magnetization is oriented along [010], enhancing valley polarization by up to $_2$3 (from $_2$4 meV to $_2$5 meV in VCrSeTeO).

The authors quantitatively interpret this SOC-dependence using SOC perturbation theory, considering symmetry-allowed orbital coupling channels in the presence of different magnetization orientations. The directionality of the effect is traced to the matrix elements of the SOC Hamiltonian acting between Se/Te $_2$6-orbitals in the vicinity of the X and Y valleys.

Moreover, Berry curvature calculations confirm the appearance of an anomalous valley Hall (AVH) effect in VCrSeTeO under out-of-plane magnetization, with the notable property that the valley Hall voltage is reversed at the same valley upon magnetization reversal—distinct from conventional ferrovalley materials, where reversal usually pertains to switching between valleys.

Numerical Highlights

• Valley polarization up to $_2$7 meV is obtained in VCrSeTeO with $_2$8 strain and SOC ([010] magnetization), the largest reported in this material class.
• SOC amplifies valley polarization by up to $_2$9 for [010] orientation, while suppressing it for others, as dictated by orbital symmetry.
• AVH effect is evidenced by calculations of Berry curvature and valley Hall conductivity, with a sign reversal under magnetization reversal at fixed valley.

Implications and Outlook

The results constitute a prescription for combining materials symmetry, sublattice engineering, and moderate external stimuli (strain, SOC) to design 2D valleytronic materials with large, tunable valley splitting absent field or strong SOC requirements. The demonstrated AVH phenomena extend the functional space of FIM-based valleytronics, introducing a qualitatively new mode of control: fixed-valley sign switching via magnetization.

Practically, such systems could drive advances in ultra-dense nonvolatile memory, topological spintronics, or quantum information devices where control of valley, spin, and charge is essential and stray-field-free operation is required. The explicit mechanistic understanding of the strain and SOC tuning offers a clear route for experimental confirmation via monolayer assembly and heterostructuring.

Theoretically, these findings prompt further investigation into the interplay of reduced symmetry, correlation effects, and valley topology in complex FIM and AM systems, and highlight the importance of sublattice-specific engineering strategies.

Conclusion

The paper rigorously demonstrates, via first-principles calculations and analytic modeling, that valley polarization in AM/FC-FIM systems is directly controlled by sublattice magnetic moment imbalance. Further, sublattice engineering (here, V/Cr substitution) provides a route to UFIM phases with giant, tunable valley splitting. The inclusion of SOC and suitably chosen magnetization orientation allows further enhancement and directional control, including a unique fixed-valley AVH effect. These results undergird new proposals for 2D valleytronic materials and devices, motivating continued exploration at the intersection of symmetry, magnetism, and topological transport in low-dimensional materials (2604.15640).