Hidden Fully-Compensated Ferrimagnetism

• Hidden fully-compensated ferrimagnetism is defined by zero net magnetization arising from antiparallel, non-symmetry-related sublattices that produce ferromagnet-like spin splitting.
• Experimental identification relies on band structure, transport, and optical techniques rather than conventional magnetometry, uncovering its concealed magnetic order.
• Multiple strategies—such as electric-field modulation, built-in Janus asymmetry, and spin-order engineering—enable controlled realization of this unique zero-moment phase.

Hidden fully-compensated ferrimagnetism denotes a class of zero-net-magnetization magnetic states in which antiparallel magnetic sublattices are not related by the symmetries that characterize conventional collinear antiferromagnets, yet the electronic structure retains ferromagnet-like spin splitting or sector-resolved spin polarization. In current usage, the term covers both zero-moment ferrimagnets whose magnetic character is hidden from net-moment probes but revealed by band, transport, or optical responses, and $PT$-symmetric “hidden” constructions in which two inversion-partner sectors each host fully-compensated ferrimagnetism while the total band structure remains spin-degenerate (Li et al., 16 Mar 2026, Guo, 15 Jul 2025).

1. Definition and taxonomic position

Fully compensated ferrimagnetism is defined by three simultaneous conditions. First, the system contains localized magnetic sublattices with antiparallel moments. Second, the total magnetization vanishes,

$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$

Third, the magnetic sublattices are not related by the symmetry operations that enforce spin degeneracy in conventional $PT$-symmetric antiferromagnets; correspondingly, the bands can remain spin split in a ferromagnet-like, nearly isotropic manner across the Brillouin zone (Li et al., 16 Mar 2026).

This distinguishes the state from four neighboring categories. In a ferromagnet, parallel spins produce finite $M$ and exchange-split bands. In a conventional collinear antiferromagnet, antiparallel sublattices are symmetry related, $M=0$, and combined operations such as $PT$ enforce spin-degenerate bands. In an altermagnet, $M=0$ coexists with spin splitting, but that splitting is strongly anisotropic in momentum space and changes sign under crystal symmetries. In an ordinary ferrimagnet, inequivalent antiparallel sublattices generate spin splitting but compensation is incomplete, so $M\neq 0$ (Li et al., 16 Mar 2026).

A central recent refinement is that exact compensation in fully compensated ferrimagnets is described as filling-enforced rather than symmetry-enforced. The sublattice exchange fields can be large, yet equal total spin-up and spin-down occupations keep the total moment zero. This makes the magnetic order easy to miss in bulk magnetometry while preserving ferromagnet-like band and response properties (Li et al., 16 Mar 2026).

A related sector-resolved notion appears in $PT$-symmetric bilayers. There, the total system can be globally spin degenerate, but each inversion-partner sector separately realizes fully-compensated ferrimagnetism with nonzero local spin polarization in real space; this is the sense in which hidden fully-compensated ferrimagnetism is introduced for bilayer $\mathrm{CrMoC_2S_6}$ (Guo, 15 Jul 2025).

2. Symmetry logic and the hidden character

The basic symmetry distinction is between zero moment enforced by symmetry and zero moment retained after symmetry breaking. In monolayer CoS and CoSe, the zero-field ground state is a collinear Néel antiferromagnet in a centrosymmetric $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$0 structure. In this phase, $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$1 interchanges the two Co sublattices, $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$2 flips spins, and the combined antiunitary symmetry $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$3 is preserved. Because $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$4 for spin-$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$5 electrons, the bands are doubly degenerate at each $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$6 (Li et al., 16 Mar 2026).

Once an out-of-plane electric field $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$7 is applied, inversion symmetry is broken by a layer-dependent electrostatic potential. Since time reversal is already broken by antiferromagnetic order, $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$8 is immediately lost. The Kramers-like degeneracy is lifted, but the local Co moments remain equal and opposite, so the total magnetization stays zero while the bands become spin split. This is the prototypical “hidden” fully compensated ferrimagnetic transition: the net moment remains invisible to standard magnetometry, whereas the band structure and response tensors become ferromagnet-like (Li et al., 16 Mar 2026).

A complementary symmetry formulation is given for collinear zero-net-moment magnets by the relation

$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$9

with $PT$0 a spatial symmetry such as inversion, rotation, or mirror. In $PT$1-antiferromagnets and altermagnets, this enforces equality of global spin-resolved densities of states, $PT$2, so conventional half-metallicity is forbidden at the global level (Guo et al., 12 Jan 2026). Hidden sector constructions evade this by decomposing the Hilbert space into symmetry-related sectors—typically layers—each of which is individually half-metallic or fully-compensated ferrimagnetic, while the global spectrum remains balanced (Guo et al., 12 Jan 2026, Guo, 15 Jul 2025).

Spin-order engineering makes the same point in a different way. In bilayer $PT$3, one spin arrangement preserves $PT$4 and yields a $PT$5 antiferromagnet with spin-degenerate bands, whereas flipping the Néel vector of one layer breaks $PT$6 without changing the lattice. If $PT$7 and $PT$8 are also absent, the result is a fully-compensated ferrimagnet with global, $PT$9-wave-like spin splitting and zero net moment (Guo et al., 14 Jul 2025).

3. Microscopic routes to realization

Several distinct microscopic routes to hidden fully-compensated ferrimagnetism now exist.

Electric-field-induced $M$0 breaking in two-dimensional antiferromagnets: Monolayer CoS and CoSe have collinear Néel antiferromagnetic ground states with out-of-plane Néel vectors, local Co moments $M$1, indirect gaps of $M$2 eV and $M$3 eV, and estimated $M$4 K and $M$5 K, respectively. An out-of-plane electric field breaks $M$6, lifts $M$7 degeneracy, and drives an AFM $M$8 fully-compensated ferrimagnet transition. Clear spin splitting appears already at $M$9 V/Å, and around $M=0$0 V/Å the systems become fully spin-polarized metals, with only spin-down bands crossing $M=0$1 for $M=0$2 V/Å and only spin-up bands crossing $M=0$3 for $M=0$4 V/Å (Li et al., 16 Mar 2026).

Built-in electrostatic asymmetry in Janus magnets: Janus Mn$M=0$5BrI breaks inversion symmetry structurally, so its AFM1 order is no longer $M=0$6-symmetric. The built-in layer-dependent electrostatic potential yields spontaneous spin splitting without SOC, with an indirect band gap of about $M=0$7 eV and spin splitting up to about $M=0$8 eV at $M=0$9. With SOC and an out-of-plane Néel vector, valley polarization $PT$0 meV emerges; atomistic simulations give $PT$1 K for the pristine monolayer (Lv et al., 24 Jun 2026).

Vertical heterojunction design: Stacking two different but equally magnetized ferromagnetic monolayers and stabilizing A-type antiferromagnetic interlayer order generates zero total moment without any symmetry relating the two layers. The proposal is verified for $PT$2, where each monolayer carries $PT$3 per cell and the bilayer becomes fully compensated once AFM1 interlayer order is stabilized; tensile strain is more favorable for achieving this state (Guo et al., 13 Sep 2025).

Spin-ordering engineering without lattice modification: Bilayer $PT$4 realizes fully-compensated ferrimagnetism by changing only the spin ordering. In the B-stacked bilayer, the $PT$5-symmetric magnetic ordering is only $PT$6 meV lower in energy than the non-$PT$7 one. Each Cr carries $PT$8, the total magnetic moment remains $PT$9, and the non-$M=0$0 configuration exhibits global spin splitting (Guo et al., 14 Jul 2025).

Sector-hidden constructions: In $M=0$1-bilayer $M=0$2, each inversion-partner sector separately hosts fully-compensated ferrimagnetism with nonzero local spin polarization, while the total bilayer remains spin degenerate. An out-of-plane electric field separates the hidden sector polarizations and reveals the underlying spin splitting (Guo, 15 Jul 2025).

Disorder-mediated realization: Cr$M=0$3Al provides an extreme case where complete A2 disorder does not destroy the desired state but stabilizes it. Single-crystal XRD, synchrotron powder XRD, and neutron diffraction show complete Cr/Al site mixing; nevertheless, NPD, XMCD, magnetometry, and SQS calculations establish a fully compensated ferrimagnetic state with ordered moment $M=0$4f.u. experimentally and $M=0$5f.u. theoretically, together with spin-gapless-semiconducting transport (Philip et al., 11 Dec 2025).

Platform	Route	Reported outcome
CoS, CoSe monolayers	External $M=0$6 breaks $M=0$7 and $M=0$8	Electric-field-induced fully compensated ferrimagnetism (Li et al., 16 Mar 2026)
Janus Mn$M=0$9BrI	Built-in layer-dependent electrostatic potential	Spontaneous spin splitting and compensated ferrimagnetism (Lv et al., 24 Jun 2026)
$M\neq 0$0	AFM-coupled vertical heterojunction of equally magnetized ferromagnets	Fully-compensated ferrimagnet with pronounced spin splitting (Guo et al., 13 Sep 2025)
Bilayer $M\neq 0$1	$M\neq 0$2-symmetric sector construction	Hidden fully-compensated ferrimagnetism (Guo, 15 Jul 2025)
Cr$M\neq 0$3Al	Complete A2 disorder	Disorder-mediated FCF + SGS behavior (Philip et al., 11 Dec 2025)

4. Electronic, transport, optical, and topological signatures

The defining observable is the decoupling of net magnetization from spin-resolved electronic response. In CoS and CoSe, the electric-field-induced fully-compensated ferrimagnetic metallic regime supports fully spin-polarized longitudinal currents: without SOC, $M\neq 0$4 and $M\neq 0$5 near $M\neq 0$6 for one field orientation, with the opposite assignment after reversing $M\neq 0$7. The current polarization is essentially $M\neq 0$8 near $M\neq 0$9, so the electric field functions as an electrical spin valve in a zero-moment material (Li et al., 16 Mar 2026).

The same field-induced state has nonzero Berry curvature and anomalous Hall conductivity. At $PT$0, $PT$1 enforces $PT$2. At finite $PT$3, strong valley-contrasting Berry-curvature peaks appear at $PT$4 and $PT$5, producing intrinsic anomalous Hall response despite $PT$6. The magneto-optical response is equally ferromagnet-like: the calculated Kerr rotation is stated to be comparable to monolayer CrI$PT$7, even though the net moment remains zero (Li et al., 16 Mar 2026).

Janus Mn$PT$8BrI extends the same logic into valleytronics. With SOC and an out-of-plane Néel vector, the valleys at $PT$9 and $\mathrm{CrMoC_2S_6}$0 become inequivalent, with $\mathrm{CrMoC_2S_6}$1 meV in the unstrained monolayer and $\mathrm{CrMoC_2S_6}$2 meV at $\mathrm{CrMoC_2S_6}$3 tensile strain. The Berry curvature develops valley-contrasting hotspots, and the magnetic space group $\mathrm{CrMoC_2S_6}$4 is compatible with anomalous Hall conductivity, enabling anomalous valley Hall response in a zero-net-moment fully compensated ferrimagnet (Lv et al., 24 Jun 2026).

A related sector-resolved phenomenon is hidden half-metallicity. In $\mathrm{CrMoC_2S_6}$5-symmetric bilayer $\mathrm{CrMoC_2S_6}$6, the total bands are spin degenerate, but each layer separately is half-metallic: one layer is metallic only in spin-up, the other only in spin-down. An out-of-plane electric field breaks inversion symmetry, drives the bilayer into a fully compensated ferrimagnetic metal, and preserves layer-resolved spin selectivity. This establishes a route from a hidden half metal to a zero-moment ferrimagnetic metal (Guo et al., 12 Jan 2026).

The broader electronic versatility of fully compensated ferrimagnets is illustrated by proposals for topological superconductivity. In fFIM-based heterostructures, sublattice-opposite exchange fields supply the effective Zeeman term needed for Majorana modes while the vanishing net magnetization avoids the usual conflict between tunability and superconducting coherence. One-dimensional end modes, two-dimensional chiral Majorana edge states, and higher-order corner Majoranas are all predicted within this framework (Li et al., 28 Apr 2025).

An earlier bulk precursor is CrVTiAl, where theory and experiment identify a fully compensated ferrimagnet with predominantly spin-gapless semiconducting behavior. Magnetization is only $\mathrm{CrMoC_2S_6}$7f.u., the ferrimagnetic transition occurs near $\mathrm{CrMoC_2S_6}$8 K, and the transport lacks activated semiconducting behavior, consistent with a disorder-mixed state combining fully compensated ferrimagnetism and spin-gapless transport (Venkateswara et al., 2017).

5. Representative material families and experimental identification

The most direct experimental challenge is that hidden fully-compensated ferrimagnetism evades net-moment probes. In CoS and CoSe, standard magnetometry would detect nearly zero moment and would not by itself distinguish the field-induced fFIM state from an ordinary antiferromagnet. The proposed discriminants are neutron scattering or XMLD for the Néel order, spin-resolved ARPES for exchange-split bands, transport measurements for spin-polarized currents and anomalous Hall response, and Kerr or Faraday spectroscopy for nonzero off-diagonal optical conductivity (Li et al., 16 Mar 2026).

Cr$\mathrm{CrMoC_2S_6}$9Al shows how this works in a chemically disordered bulk system. Magnetometry gives only $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$00f.u. and a nearly linear $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$01, but neutron diffraction resolves robust ferrimagnetic order up to $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$02 K, while XMCD at the Cr $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$03 edges is nearly zero because oppositely aligned Cr-site contributions cancel element-wise. Transport then identifies the accompanying SGS character through weakly temperature-dependent conductivity, very low Seebeck coefficients, electron-hole compensated transport, and unusual Hall-derived carrier densities (Philip et al., 11 Dec 2025).

A different experimental route is through half-metallic fully compensated ferrimagnets. NiAs-type hexagonal $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$04 is reported as a half-metallic fully compensated ferrimagnet with zero magnetization, $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$05 spin-polarized Fermi surfaces, compensation temperature around $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$06 K, and coercive field $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$07 kOe at $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$08 K. Below the compensation temperature, $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$09 is linear, a characteristic signature of full compensation (Semboshi et al., 2021).

Historically related notions of hidden ferrimagnetism predate the modern fFIM vocabulary. In Fe$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$10Mo$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$11O$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$12, each Fe–O layer is ferrimagnetic, but interlayer stacking cancels the bulk moment in zero field; a modest field unveils the ferrimagnetism and produces giant magnetoelectric effects, including polarization jumps of $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$13 and differential magnetoelectric coefficients on the order of $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$14 ps/m (Wang et al., 2015). In CaFe$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$15O$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$16, resonant x-ray measurements distinguish an antiferromagnetic phase from a ferrimagnetic phase whose minute net moment arises solely from crystallographic inequivalence of Fe$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$17 sites with equal multiplicity (Ueda et al., 2022).

These examples establish a practical experimental rule: net magnetization close to zero is not evidence against ferrimagnetism. Site-sensitive, layer-sensitive, or momentum-resolved probes are required whenever magnetic compensation and spin splitting are expected to coexist.

6. Distinctions, controversies, and outlook

The most important conceptual distinction remains that between altermagnetism and fully compensated ferrimagnetism. In altermagnets, zero moment and spin splitting coexist because spin-opposite sublattices are related by crystal symmetry, which enforces $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$18 globally. In fully compensated ferrimagnets, no such symmetry exists; the compensation is not symmetry protected, and the spin splitting is ferromagnet-like rather than sign-changing in momentum space (Li et al., 16 Mar 2026, Guo et al., 5 Dec 2025).

This difference has operational consequences. For monolayer $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$19, the altermagnetic parent metal cannot develop a net magnetic moment under carrier doping as long as the altermagnetic symmetry remains intact. Breaking the $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$20 symmetry by electric field or uniaxial strain converts the system into a fully compensated ferrimagnetic metal, and only then can subsequent carrier doping induce a net magnetization. On that basis, strain-driven “piezomagnetism” is reinterpreted as a strain-induced switch from altermagnetism to fully compensated ferrimagnetism, and the electric-field analogue is termed “electromagnetism” (Guo et al., 5 Dec 2025).

Another emerging distinction is between bulk-hidden and sector-hidden forms. Bulk-hidden fFIM refers to zero-moment ferrimagnetism concealed from net-moment probes but revealed by band, transport, and optical responses, as in CoS, CoSe, Mn$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$21BrI, CrVTiAl, or Cr$\mathbf{M}=\sum_i \mathbf{m}_i = 0.$22Al. Sector-hidden fFIM refers to $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$23-symmetric bilayers such as $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$24, where the total spin polarization vanishes but each inversion-partner sector separately carries fully-compensated ferrimagnetism and local spin polarization (Guo, 15 Jul 2025). This suggests a broader family of hidden spin-polarized materials in which local or sector-resolved order survives under global compensation.

A further development is the extended Néel-diagram framework for ferrimagnets. Mean-field analysis identifies a critical point where full magnetic compensation is maintained below the Curie temperature and extends past the nominal compensation point. Ferrimagnets tuned near this point show altermagnetic-like features and enhanced coercive fields, suggesting a bridge between compensated ferrimagnetism and altermagnetic phenomenology at the level of macroscopic observables and exchange-split bands (Ali et al., 30 Jan 2026).

The current materials landscape indicates that hidden fully-compensated ferrimagnetism is not tied to a single mechanism. It can be induced by external electric fields, built-in Janus asymmetry, vertical heterojunctions, spin-ordering engineering, or even complete chemical disorder. A plausible implication is that future progress will depend less on one privileged symmetry route than on the controlled separation of three ingredients: exact or near-exact compensation of sublattice moments, removal of the symmetries that enforce spin degeneracy, and preservation of a clean spin-selective low-energy spectrum. That combination is what allows a material to remain magnetically hidden in $\mathbf{M}=\sum_i \mathbf{m}_i = 0.$25 while behaving electronically like a ferromagnet.