Ferro-Valley Polarization: Mechanisms & Materials

• Ferro-Valley Polarization is the spontaneous, nonvolatile energy splitting of inequivalent valleys in momentum space driven by factors like exchange, SOC, and ferroelectricity.
• It encompasses multiple mechanisms including magnetic, ferroelectric, altermagnetic, and correlated electron effects that yield switchable valley order.
• Diverse materials from hexagonal monolayers to 2D organometallic lattices demonstrate valley splitting with promising applications in optics, transport, and memory devices.

Ferro-Valley Polarization denotes a spontaneous, nonvolatile lifting of valley degeneracy, such that inequivalent valleys in momentum space acquire different energies in equilibrium and can function as a ferroic degree of freedom. The concept was introduced for magnetic hexagonal monolayers, where intrinsic exchange and spin-orbit coupling (SOC) split the $K_+$ and $K_-$ valleys without any external field, and it has since expanded to ferroelectric orthorhombic semiconductors, 2D organometallic lattices, sliding ferroelectric antiferromagnets, altermagnets, compensated ferrimagnets, and correlated graphene systems (Tong et al., 2016, Shen et al., 2017, Peng et al., 2021, Han et al., 2023, Jiang et al., 28 Jul 2025). In current usage, closely related labels—ferrovalley materials, ferro-valleytricity, FE-valley coupling, and spontaneous spin-valley polarization—refer to a common physical theme: valley order becomes intrinsic, switchable, and in many cases memory-like because it is tied to magnetic, ferroelectric, structural, or correlated electronic order.

1. Terminological development and scope

The original ferrovalley concept was formulated as a new ferroic class characterized by spontaneous valley polarization, in explicit analogy with spontaneous charge polarization in ferroelectrics and spontaneous spin polarization in ferromagnets. In that formulation, a ferrovalley material is a 2D system in which the inequivalent $K_+$ and $K_-$ valleys are intrinsically nondegenerate because SOC coexists with intrinsic exchange interaction; monolayer 2H-VSe$_2$ was proposed as the prototype realization (Tong et al., 2016).

The scope widened when monolayer group-IV monochalcogenides were shown to realize ferrovalley order without ferromagnetism. In monolayer GeSe, the paraelectric state was described as a paravalley state with degenerate $V_x$ and $V_y$ valleys, whereas the ferroelectric states $P_x$ and $P_y$ produce an energetically nondegenerate valley pair and thereby an electrically switchable ferrovalley order (Shen et al., 2017). This established that spontaneous valley polarization can be generated by ferroelectric symmetry breaking rather than exchange alone.

Later work further diversified the terminology. In pentalayer rhombohedral graphene, the order parameter was described as ferro-valleytricity, with hysteretic switching, a valley variable $V=\pm1$, and a conjugate composite field $K_-$0; the same system also exhibited a valley-magnetic quartet of four metastable states (Han et al., 2023). In layered antiferromagnets, the language shifted toward FE-valley coupling and spontaneous spin-valley polarization, especially when the valley state became locked to a ferroelectric stacking state or to $K_-$1-breaking in a compensated magnetic phase (Jiang et al., 28 Jul 2025, Feng et al., 4 Jul 2025).

Taken together, these usages show that ferro-valley polarization is now a family concept rather than a single microscopic mechanism. What remains common is the spontaneous inequivalence of valleys and the existence of a bistable or at least symmetry-protected route for reversing that inequivalence.

2. Symmetry foundations and microscopic mechanisms

In the canonical magnetic mechanism, spontaneous valley polarization requires broken inversion symmetry, broken time-reversal symmetry, and SOC. In the two-band description of 2H-VSe$K_-$2, SOC produces valley-dependent spin splitting, intrinsic exchange acts as an internal magnetic field, and the coexistence of the two lifts the $K_-$3/$K_-$4 degeneracy. The resulting chirality-dependent optical gaps differ by $K_-$5, and the Berry-curvature asymmetry supports an anomalous valley Hall effect (Tong et al., 2016).

A more explicit generalized mechanism was given for 2D organometallic lattices. For heterometal $K_-$6-OM frameworks, a gapped Dirac or Kagome-like band structure, broken inversion symmetry, exchange, and SOC together yield valley splitting, with conduction- and valence-band polarizations

$K_-$7

For homometal AFM systems, the splitting appears in a spin-valley-coupled form,

$K_-$8

so the valleys remain inequivalent even though the physics is tied to the product of spin and valley indices rather than to a simple spin-independent valley Zeeman term (Peng et al., 2021). This work also made a practical point that recurs across the literature: robust out-of-plane magnetization is often a defining requirement for ideal ferrovalley behavior.

Ferroelectric mechanisms break the standard magnetic paradigm. In orthorhombic GeSe, ferroelectric distortion lowers the equivalence between the $K_-$9 and $K_+$0 valleys, so $K_+$1 selects $K_+$2 and $K_+$3 selects $K_+$4; the resulting optical selectivity is linear rather than circular, because the relevant valley states are tied to $K_+$5 orbital symmetry rather than to hexagonal $K_+$6 chirality (Shen et al., 2017). In Gd-substituted EuCl$K_+$7, the proposed FE-FV coupling was written directly as

$K_+$8

which reduces for in-plane dipole and out-of-plane spin to

$K_+$9

Here the ferroelectric dipole itself induces inversion breaking, and reversing the dipole reverses the valley splitting (Bhardwaj et al., 23 May 2025).

Antiferromagnetic and compensated-magnet routes further extend the mechanism set. In $K_-$0-broken ferroelectric AFMs, inequivalent layers make the two antiferromagnetic sublattices nonequivalent, so global spin splitting and valley splitting can coexist even at zero net magnetization (Feng et al., 4 Jul 2025). In the fully compensated ferrimagnet Mn$K_-$1BrI, spontaneous spin splitting appears already without SOC because of the built-in layer-dependent electrostatic potential, and SOC then yields valley polarization for an out-of-plane Néel vector (Lv et al., 24 Jun 2026). In non-Janus Fe$K_-$2WS$K_-$3Se$K_-$4, the authors proposed a type III valley polarization in which intrinsic mirror-symmetry breaking of $K_-$5 produces spontaneous $K_-$6 valley splitting even without SOC (She et al., 11 Jun 2025).

A final important development is the demonstration that out-of-plane collinear magnetism is not the only symmetry route. In triangular-lattice single-layer W$K_-$7Cl$K_-$8, non-collinear in-plane magnetism breaks the joint time-reversal–mirror symmetry $K_-$9 while retaining a mirror that enhances the splitting, allowing sizeable in-plane ferro-valleytricity (Liu et al., 2024). In Dirac-like Janus Nb$_2$0SeTeO, the SOC-induced valley polarization was shown to scale as

$_2$1

thereby linking the effect to strong SOC and small band gap even for in-plane magnetization in an altermagnetic setting (Xie et al., 2024).

3. Materials classes and design principles

The literature now spans several distinct materials families.

Family	Representative systems	Distinctive result
Magnetic hexagonal monolayers	2H-VSe$_2$2, 2H-OsBr$_2$3, Janus 2H-Gd$_2$4, Janus GdClF, VSi$_2$5P$_2$6	$_2$7 ferrovalley splitting from exchange + SOC
Organometallic lattices	$_2$8 frameworks	Dirac/Kagome-like valleys and robust perpendicular anisotropy
Ferroelectric nonmagnetic semiconductors	GeSe and related GIVMs	Valley polarization tied to $_2$9
Sliding FE or AFM bilayers	MnPTe$V_x$0, Nb$V_x$1, VX$V_x$2, VSi$V_x$3	Ferroelectric-state or sliding-controlled valley reversal
Altermagnetic and compensated magnets	Fe$V_x$4WS$V_x$5Se$V_x$6, Fe$V_x$7MX$V_x$8, Nb$V_x$9Se$V_y$0O, Nb$V_y$1SeTeO, Mn$V_y$2BrI	Valley polarization without conventional ferromagnetism
Correlated graphene	Pentalayer rhombohedral graphene	Ferro-valleytricity and a valley-magnetic quartet

Among magnetic monolayers, several systems stand out by energy scale. Monolayer 2H-OsBr$V_y$3 was reported to exhibit valley polarization up to 175.49 meV in the 2H phase, while the same material’s 1T bilayer realizes tri-state valley polarization by structural symmetry breaking (Wu et al., 25 Feb 2025). Janus 2H-Gd$V_y$4 monolayers were predicted to combine Curie temperatures above 260 K with spontaneous valley-Zeeman splittings of about 60–120 meV, and 2H-GdIBr reaches 116.9 meV at zero strain (Li et al., 2022). Janus GdClF is notable for small equilibrium splitting but strong strain sensitivity, reaching $V_y$5 meV at $V_y$6 and 29.4 meV at $V_y$7, both above room-temperature thermal energy (Guo et al., 2021).

The organometallic route is distinguished by a systematic design principle: combine (quasi-)planar organic molecules with transition-metal atoms in a hexagonal or Kagome-like lattice, preserve gapped valley states at $V_y$8, break inversion symmetry either by heterometal composition or AFM order, and ensure intrinsic out-of-plane magnetization. High-throughput DFT over 96 frameworks identified twelve promising ferrovalley materials, and NbTa-benzene showed a valley splitting of 278.42 meV together with MAE 17.23 meV (Peng et al., 2021). This is one of the largest reported spontaneous splittings in the supplied literature.

Bilayer and sliding systems introduce a different design logic. In bilayer MnPTe$V_y$9, AB and BA stackings have opposite out-of-plane polarization of 0.33 pC/m, are separated by an energy barrier of 71.5 meV, and invert the valley order at the conduction edge: in AB the $P_x$0-valley CBM is 20.0 meV lower than $P_x$1, while switching to BA reverses that order (Jiang et al., 28 Jul 2025). In stacked bilayer altermagnets Fe$P_x$2MX$P_x$3, sliding along $P_x$4 or $P_x$5 generates large $P_x$6 valley polarization, with $P_x$7 eV reported for Fe$P_x$8WTe$P_x$9 (Li et al., 2024).

Altermagnetic and compensated-magnet platforms are especially important for broadening the field beyond net ferromagnets. Nb$P_y$0Se$P_y$1O and Janus Nb$P_y$2SeTeO were proposed as room-temperature altermagnetic ferrovalley candidates with $P_y$3 K and $P_y$4 K, respectively, and Nb$P_y$5Se$P_y$6O reaches $P_y$7 meV under $P_y$8 uniaxial strain (Xie et al., 2024). The fully compensated ferrimagnet Mn$P_y$9BrI adds a different virtue: zero net magnetization but spontaneous spin splitting up to 0.54 eV and valley polarization 37.8 meV, together with $V=\pm1$0 K in the pristine state (Lv et al., 24 Jun 2026).

4. Switching modalities and ferroic control

Magnetization reversal is the most direct control route in canonical magnetic ferrovalley systems. In 2H-VSe$V=\pm1$1, reversing the magnetic moment reverses which valley has the smaller direct gap, and both the chirality-dependent optical gap and anomalous valley Hall sign invert accordingly (Tong et al., 2016). The same logic governs strain-switchable Janus GdClF, where compressive strain favors $V=\pm1$2 and tensile strain favors $V=\pm1$3, and also governs systems such as 2H-OsBr$V=\pm1$4, whose 2H phase realizes a magnetic/SOC ferrovalley state (Guo et al., 2021, Wu et al., 25 Feb 2025).

Electric-field control can be indirect or direct. In VSi$V=\pm1$5P$V=\pm1$6, an out-of-plane electric field does not directly split valleys; instead it drives the magnetic anisotropy energy from negative to positive, rotates the easy axis from in-plane to out-of-plane near $V=\pm1$7, and thereby switches on spontaneous valley polarization. The semiconducting ferrovalley window was reported as

$V=\pm1$8

with $V=\pm1$9 meV at $K_-$00 (Guo et al., 2022). In GeSe, the coupling is more direct: in-plane electric fields stabilize $K_-$01 or $K_-$02, and the valley order follows the ferroelectric polarization (Shen et al., 2017). In Eu$K_-$03GdCl$K_-$04, reversing the in-plane ferroelectric dipole reverses the preferred Y-$K_-$05 versus Y$K_-$06-$K_-$07 valence valley under $K_-$08 biaxial tensile strain (Bhardwaj et al., 23 May 2025).

Interlayer sliding has emerged as a particularly versatile control knob. In bilayer MnPTe$K_-$09, interlayer sliding between AB and BA reverses the spontaneous out-of-plane polarization and simultaneously inverts the layer-resolved valley polarization and altermagnetic spin splitting (Jiang et al., 28 Jul 2025). In OsBr$K_-$10, sliding distinguishes symmetry-preserving stackings from polar stackings and allows switching between nonmagnetic tri-state valley polarization in the 1T bilayer and triferroic valley states in 2H AA bilayers; the corresponding sliding barriers are low, ranging from 11.39 meV to 28.22 meV for the stackings explicitly reported (Wu et al., 25 Feb 2025). In stacked bilayer altermagnets Fe$K_-$11MX$K_-$12, AC1 and AC2 are symmetry-related slid states with opposite $K_-$13 valley order (Li et al., 2024).

Correlated ferroic control takes a different form in pentalayer rhombohedral graphene. There, valley polarization $K_-$14 is hysteretic under electric-field sweeps, the relevant conjugate field is the composite $K_-$15, and the free-energy coupling is

$K_-$16

The system supports four metastable states $K_-$17 and $K_-$18, allowing independent or joint switching of valley and orbital magnetization (Han et al., 2023). This is a distinct control regime: the valley degree of freedom behaves as a correlated ferroic order parameter rather than as a single-particle band-edge property.

5. Optical, transport, and device signatures

The most direct signature of ferro-valley polarization is unequal valley-resolved band edges. The corresponding experimental observables, however, are often optical or transport-based. In the original magnetic hexagonal picture, opposite circular polarizations couple to opposite valleys, and spontaneous valley splitting therefore appears as a chirality-dependent optical gap. In 2H-VSe$K_-$19, the left- and right-circularly polarized absorption edges differ because the valley energies are intrinsically unequal (Tong et al., 2016). Janus 2H-Gd$K_-$20 monolayers likewise exhibit valley-selective circular dichroism at $K_-$21 and $K_-$22 with nearly perfect $K_-$23 at the valleys (Li et al., 2022).

Other symmetry classes replace circular with linear selectivity. In orthorhombic GeSe, $K_-$24 couples to $K_-$25-polarized light and $K_-$26 to $K_-$27-polarized light, so the ferrovalley state directly controls the polarization of the optical edge (Shen et al., 2017). Sliding-induced ferrovalley states in Fe$K_-$28MX$K_-$29 show a similar but SOC-independent linear dichroism: the $K_-$30 valley absorbs $K_-$31-polarized light and the $K_-$32 valley absorbs $K_-$33-polarized light, and sliding reverses which polarization sees the lower-energy edge (Li et al., 2024).

Berry curvature underlies the transport signatures. A commonly used expression is

$K_-$34

from which anomalous transverse motion follows through $K_-$35 (Peng et al., 2021). In ferromagnetic or ferrimagnetic ferrovalley systems, unequal Berry curvature at nondegenerate valleys yields an anomalous valley Hall effect; in AFM organometallic candidates, ordinary doping can instead produce a spin Hall effect unless circularly polarized light selects a definite spin-valley channel (Peng et al., 2021). In FE-AFMs, the same Berry-curvature formalism leads to sign-reversible valley Hall and valley Nernst conductivities under sliding or ferroelectric reversal (Feng et al., 4 Jul 2025).

Transport studies in correlated graphene provide the strongest direct evidence for ferroic valley order rather than merely valley splitting. In pentalayer rhombohedral graphene, anomalous Hall measurements showed a Hall angle $K_-$36, magnetic hysteresis in $K_-$37, and a butterfly-shaped hysteresis of $K_-$38 under electric-field sweeps that collapsed when plotted against $K_-$39 (Han et al., 2023). This behavior indicates a true ferro-valleytronic order parameter rather than a purely band-structure asymmetry.

Device proposals have begun to exploit contact physics and circuit integration. In RuCl$K_-$40/graphene, a ferrovalley semiconductor/graphene interface was predicted to realize a half-valley Ohmic contact, and the injected current polarization was defined by

$K_-$41

The proposed valleytronic barristor reached valley polarization efficiency greater than 90% with ON/OFF ratios exceeding $K_-$42 under feasible electrostatic gating (Feng et al., 2023). At the circuit level, the PRG-based selector-less cryogenic memory proposal mapped $K_-$43 and $K_-$44 onto logic states and estimated about 6 nW per write operation and 2.3 nW per read operation per cell (Islam et al., 2024).

6. Conceptual boundaries, misconceptions, and open problems

A persistent misconception is that ferro-valley polarization is synonymous with out-of-plane ferromagnetism in a hexagonal $K_-$45 semiconductor. That description remains accurate for the original and many practically robust cases, and several papers stress that intrinsic perpendicular anisotropy is decisive because in-plane magnetization can forbid or strongly weaken valley splitting (Peng et al., 2021, Guo et al., 2022). Yet the later literature shows that this is not a universal requirement: nonmagnetic ferroelectric GeSe, in-plane non-collinear W$K_-$46Cl$K_-$47, mirror-broken altermagnets, $K_-$48-broken FE-AFMs, and fully compensated ferrimagnets all realize spontaneous valley-polarized states by different symmetry routes (Shen et al., 2017, Liu et al., 2024, She et al., 11 Jun 2025, Feng et al., 4 Jul 2025, Lv et al., 24 Jun 2026).

A second misconception is that valleys must be the hexagonal $K_-$49 pair. The supplied literature includes orthorhombic $K_-$50 valleys in GeSe, $K_-$51 valleys in altermagnets and mirror-broken AFMs, three non-high-symmetry valleys $K_-$52 in 1T-bilayer OsBr$K_-$53, and correlated $K_-$54 valley order in rhombohedral graphene (Shen et al., 2017, She et al., 11 Jun 2025, Wu et al., 25 Feb 2025, Han et al., 2023). The unifying criterion is not valley location but spontaneous inequivalence of symmetry-related extrema.

Several practical constraints recur across the field. In Eu$K_-$55GdCl$K_-$56, the FE state is metastable, useful valley splitting appears only after 5% biaxial tensile strain, and the SOC mechanism requires an out-of-plane spin component even though the easy axis is in-plane (Bhardwaj et al., 23 May 2025). In VSi$K_-$57P$K_-$58, the true ferrovalley semiconducting window is narrow, and the gap can be only 26.4 meV (Guo et al., 2022). In sliding bilayers such as MnPTe$K_-$59, the papers explicitly identify sliding control, Fermi-level placement, domain formation, and the need to maintain the relevant AFM order as experimental conditions (Jiang et al., 28 Jul 2025). In PRG, the device concepts are presently cryogenic and derive from measurements at about 100 mK, so their relevance is immediate for cryogenic electronics rather than room-temperature valleytronics (Islam et al., 2024).

At the same time, several results point to genuinely robust regimes. Organometallic frameworks provide splittings up to 278.42 meV with sizable perpendicular MAE (Peng et al., 2021). Altermagnetic Nb$K_-$60Se$K_-$61O and Nb$K_-$62SeTeO were reported with $K_-$63 K and $K_-$64 K (Xie et al., 2024). Fully compensated ferrimagnetic Mn$K_-$65BrI combines zero net magnetization with $K_-$66 K, strain-enhanced PMA, and valley polarization of 37.8 meV in the pristine system (Lv et al., 24 Jun 2026). These results suggest that ferro-valley polarization is evolving from a narrowly defined magnetic monolayer effect into a broader symmetry-engineering framework spanning magnetic, ferroelectric, altermagnetic, and correlated electronic matter.