Magnetic Proximity Effect Overview

• Magnetic proximity effect is the induction of magnetic order at interfaces via exchange interactions, with the induced moment decaying rapidly away from the boundary.
• It manifests through phenomena like spin splitting, band hybridization, and interlayer charge transfer, and its strength depends on atomic registry, layer thickness, and hybridization.
• Advanced probes such as XMCD, polarized neutron reflectometry, and transport measurements differentiate MPE from other spin transport effects, guiding the design of novel heterostructures.

Magnetic proximity effect (MPE) denotes the interfacial transfer, induction, or reconstruction of magnetic order across a boundary between dissimilar materials. In heavy-metal/ferromagnet bilayers it is defined as a phenomenon in which a ferromagnet induces a magnetic moment in an adjacent heavy metal via exchange interaction, with the induced magnetization localized near the interface and decaying rapidly away from it; in two-dimensional heterostructures it commonly appears as spin splitting, spin-dependent charge transfer, or band hybridization in an otherwise nonmagnetic layer; and in superconductor/ferromagnet structures it may manifest as induced magnetization, suppressed magnetic response, or modified superconducting spectra and local density of states (Zhu et al., 2018, Hua et al., 2023, Ovsyannikov et al., 2015). The term therefore covers a family of short-range interfacial phenomena rather than a single universal mechanism.

1. Conceptual scope and microscopic mechanisms

The conventional exchange-proximity picture treats the adjacent nonmagnetic layer as acquiring an effective exchange field from a neighboring magnet. That description is adequate for some metallic bilayers, where the most direct signature is an enhancement of the measured magnetic moment or effective saturation magnetization beyond what would be expected from the ferromagnetic layer alone (Zhu et al., 2018). In this limit, MPE is an interfacial magnetic phenomenon, and the central quantities are the induced moment, its spatial decay, and the extent to which it modifies transport across the interface.

A more microscopic description becomes necessary when interfacial electronic structure is strongly reconstructed. In graphene on monolayer CrI$_3$, the proposed mechanism is not merely a weak rigid spin splitting but a hybridization-driven proximity effect in which spin-dependent interlayer coupling reshapes the conductor bands themselves (Cardoso et al., 2023). The minimal model is

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$

with perturbative splitting away from resonance

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$

When a spin-polarized ferromagnetic band is resonant with the conductor Fermi level, the result is spin-selective band hybridization rather than a small exchange shift.

Topological-insulator/magnetic-insulator interfaces further show that proximity need not be reducible to a postulated exchange term in a surface Dirac Hamiltonian. In Bi$_2$Se$_3$/MnSe(111), density functional theory yields two distinct interfacial states: an ordinary bound state generated by interface symmetry breaking and band bending, and a topological Dirac state displaced into deeper quintuple layers (Eremeev et al., 2013). The calculated band bending is about $0.8$ eV, the ordinary interfacial state appears around $-0.6$ to $-0.8$ eV, and the Dirac cone gap at $\bar\Gamma$ is about $8.5$ meV. The gap is attributed to overlap between the spin-polarized ordinary state and the relocated topological state, with the analytic estimate

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$0

Layered antiferromagnetic van der Waals magnets reveal an additional distinction between proximity channels. In monolayer WSe$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$1 on bilayer or trilayer CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$2, spin-dependent charge transfer is dominated by the interfacial CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$3 layer, whereas the proximity exchange field inferred from the valley splitting depends on the layered magnetic structure as a whole (Zhong et al., 2020). The optical splitting is described through virtual hopping,

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$4

so even in an atomically thin system the interfacial and deeper magnetic layers can play inequivalent roles.

2. Experimental observables and diagnostic strategies

Because MPE is interfacial and often coexists with other spin-transport mechanisms, it is usually established by combining bulk-sensitive, depth-resolved, and transport-sensitive probes. The same nominal signature—an anomalous resistance change, a Hall nonlinearity, or an enhanced magnetic moment—can otherwise admit competing interpretations.

Probe class	Principal observable	Representative systems
Magnetometry	$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$5, $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$6, total moment $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$7	Pt/Co, AuPt/Co; Py/FeMn; YBCO spin valve
Depth- and element-resolved scattering/spectroscopy	PNR spin asymmetry, XMCD, XRMR, RMCD, HAXPES dichroism	Gd/Nb; YBCO/manganites; WSe$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$8/CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$9; Fe/EuO
Transport and dynamics	AMR, SMR, AHE, ZSHE, SOT efficiencies, FMR shifts	Pt/CFO; Ta/YIG; CrBr$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$0/graphene; Pt/Co; Py/FeMn

In heavy-metal/ferromagnet bilayers, harmonic Hall measurements extract damping-like and field-like spin-orbit torque fields from first- and second-harmonic Hall voltages through the standard relation

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$1

and define torque efficiencies as

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$2

This construction is essential when testing whether a proximity-induced moment actually alters spin transmission or merely coexists with it (Zhu et al., 2018).

Polarized neutron reflectometry is the principal depth-profiling tool in multilayers. In [Gd($$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$3)/Nb(25 nm)]$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$4, the spin asymmetry at a superlattice Bragg peak is defined as

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$5

and functions as a direct probe of the Gd magnetization because the Nb magnetic contribution is much smaller (Khaydukov et al., 2019). In oxide superlattices, the combination of XMCD and XRMR resolves not only whether Cu moments exist but also whether they reside inside YBCO rather than in a manganite layer, thereby excluding contamination-based explanations (Satapathy et al., 2011).

In two-dimensional spin-transport platforms, nonlocal measurements are often interpreted through the Zeeman spin Hall effect. For CrBr$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$6/graphene, the nonlocal resistance is

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$7

and the inferred Zeeman splitting is written as

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$8

so the slope of the nonlocal signal with field can be converted into an effective proximity exchange field (Tang et al., 2019). In buried magnetic interfaces such as Fe/EuO and Co/EuO, hard x-ray photoelectron spectroscopy with circular dichroism provides element-specific depth sensitivity through

$$\delta(\vec k)=|V_{\vec k}|^2\left(\frac{1}{\epsilon(\vec k)-E_\uparrow}-\frac{1}{\epsilon(\vec k)-E_\downarrow}\right).$$9

allowing the interfacial extent of the induced order to be extracted from angular dependence (Rosenberger et al., 2024).

3. Metallic, topological, and oxide interfaces

In metallic heavy-metal/ferromagnet bilayers, the central controversy has been whether an interfacial induced moment substantially controls spin transport. In Pt(4)/Co(0.85) and Au$_2$0Pt$_2$1(4)/Co(0.85), thermal annealing monotonically strengthens the inferred proximity magnetism: the illustrative effective magnetized heavy-metal thickness $_2$2 increases from about $_2$3 to $_2$4 nm for Pt/Co and from about $_2$5 to $_2$6 nm for Au$_2$7Pt$_2$8/Co (Zhu et al., 2018). Yet the damping-like and field-like torque efficiencies do not track that monotonic increase. The reported conclusion is that the MPE has no discernable influence on $_2$9 or $_3$0, and that spin memory loss, spin backflow, and interfacial spin-orbit scattering are more important determinants of spin transparency. The control stack Pt/Hf/Co, in which Hf suppresses MPE, reinforces the interpretation that annealing-tuned magnetic moment and annealing-tuned torque variation are distinct interfacial responses.

By contrast, Pt/CoFe$_3$1O$_3$2 bilayers provide a case in which MPE is directly visible in the nominally nonmagnetic metal. Angle-dependent magnetoresistance distinguishes anisotropic magnetoresistance from spin Hall magnetoresistance by using a $_3$3-scan in the $_3$4-$_3$5 plane and a $_3$6-scan in the $_3$7-$_3$8 plane, while anomalous Hall measurements reveal a hysteretic out-of-plane response attributable to the induced Pt ferromagnetic phase (Amamou et al., 2017). The Cu-spacer control is decisive: inserting $_3$9 nm Cu suppresses the AMR and the AHE-like Hall signal while leaving SMR nearly unchanged, which separates direct proximity-induced Pt magnetization from pure spin-current reflection physics. Density functional theory further finds that Pt atoms nearest the interface acquire magnetic moments that decay within roughly $0.8$0–$0.8$1 Pt layers.

Ta/YIG shows why such separation is necessary. At room temperature, the magnetoresistance ratio is of order $0.8$2 and its angular dependence is similar to Pt/YIG, consistent with SMR. At $0.8$3 K, however, the out-of-plane magnetoresistance polarity flips, which the authors interpret as the onset of MPE-induced AMR superposed on SMR (Yang et al., 2013). The reported conclusion is not that one mechanism excludes the other, but that unconventional magnetoresistance in Ta/YIG contains contributions from both.

Topological systems illustrate that proximity can suppress magnetic response as well as induce it. In 15 nm Bi$0.8$4Sb$0.8$5Te$0.8$6/SrRuO$0.8$7 bilayers, the normalized temperature coefficient of resistance is suppressed by about $0.8$8 just below $0.8$9 relative to the SRO reference film, the coercive-field-related resistance peak shifts by about $-0.6$0 relative to a hypothetical noninteracting parallel-resistor bilayer, and the coercive peaks narrow by $-0.6$1–$-0.6$2 (Koren, 2017). In this case, proximity coupling is inferred from a modified ferromagnetic transport response rather than from an enhanced magnetic moment in the topological layer alone.

4. Van der Waals, moiré, and molecular heterostructures

Van der Waals interfaces have made MPE highly tunable because registry, interlayer spacing, twist angle, and electric field can be varied without the chemical intermixing typical of conventional epitaxy. In graphene on monolayer CrI$-0.6$3, work-function mismatch ($-0.6$4 eV and $-0.6$5 eV) drives charge transfer that aligns the CrI$-0.6$6 majority-spin conduction band near the graphene Dirac point, thereby realizing the resonant condition for strong hybridization (Cardoso et al., 2023). The estimated transferred areal charge density is $-0.6$7, while the integrated DFT charge difference gives about $-0.6$8. In the non-resonant regime the effective splitting of the graphene Dirac bands is about $-0.6$9 meV at zero field and about $-0.8$0 meV under an out-of-plane electric field of $-0.8$1. The striking spectral asymmetry is that the spin-minority Dirac cone remains almost pristine whereas the spin-majority cone hybridizes strongly with the CrI$-0.8$2 conduction band. The effect is reported to be robust to lattice mismatch and only moderately sensitive to twist angle.

First-principles calculations on graphene/CrBr$-0.8$3 reach a related conclusion through different numbers. At an optimized interlayer separation of $-0.8$4 Å, the heterostructure exhibits graphene orbital spin polarization up to $-0.8$5, a miniband split-off gap of $-0.8$6 meV, and a total magnetic moment of $-0.8$7cell, compared with $-0.8$8cell for monolayer CrBr$-0.8$9 (Behera et al., 2019). A perpendicular electric field in the range $\bar\Gamma$0 to $\bar\Gamma$1 V/Å tunes the miniband splitting, Fermi level, and transmission spectrum while changing the total moment only by about $\bar\Gamma$2cell around $\bar\Gamma$3cell. The same study interprets the effect as spin-dependent interlayer hybridization of graphene $\bar\Gamma$4 orbitals with Cr $\bar\Gamma$5 orbitals rather than simple charge transfer.

Experimentally, CrBr$\bar\Gamma$6/graphene nonlocal transport demonstrates that this class of proximity exchange can survive in a fully van der Waals device. The nonlocal resistance at the Dirac point rises sharply with field, collapses above the CrBr$\bar\Gamma$7 Curie temperature $\bar\Gamma$8 K, and exceeds the estimated Ohmic background by about four orders of magnitude (Tang et al., 2019). From the Zeeman spin Hall analysis, the effective Zeeman field seen by graphene is larger than the applied field alone; at $\bar\Gamma$9 T the estimated $8.5$0 is about twice the applied field, and below about $8.5$1 T the low-field slope indicates that the proximity contribution dominates the nonlocal response. Near $8.5$2, the anomalous field dependence of $8.5$3 is interpreted as evidence for proximity-modified many-body ground states.

Molecular magnetic overlayers demonstrate that MPE can coexist with strong electrostatic disorder. In epitaxial FePc on graphene/hBN, FePc introduces hole doping and large mobility degradation in monolayer graphene: the hole density shifts by about $8.5$4, the mobility falls from $8.5$5 to $8.5$6, and the charge inhomogeneity rises from $8.5$7 to $8.5$8 (Pan et al., 2021). Even so, the field-dependent local and nonlocal responses are interpreted as a canted antiferromagnetic state in monolayer graphene and a pronounced Zeeman spin-Hall effect in bilayer graphene, with a temperature scale around $8.5$9 K that tracks FePc magnetism rather than purely electrostatic scattering.

Moiré superlattices convert interfacial proximity into a lateral spin texture. In BAs/CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$00, the local valence-band spin splitting depends strongly on registry: $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$01 meV for H stacking, $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$02 meV for B stacking, and negligible splitting for A stacking (Tong et al., 2019). For small lattice mismatch $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$03 and twist $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$04, the moiré period is

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$05

so twist and strain tune the degree to which miniband wavefunctions average over local registries. Long-period moirés approach the local H-stacking limit, while shorter moirés yield smaller averaged spin splitting. Because the interlayer distance itself is moiré modulated, a perpendicular electric field adds a registry-dependent Stark term and shifts the localization center of the band-edge states, reducing the splitting when localization moves toward A-like regions where the proximity field is weak.

A different kind of layer resolution appears in WSe$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$06/CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$07. The photoluminescence circular polarization $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$08 is dominated by the top CrI$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$09 layer that contacts WSe$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$10, but the valley splitting $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$11 can be larger in antiferromagnetic states than in fully spin-polarized ferromagnetic states because virtual hopping depends on the entire layered magnetic configuration (Zhong et al., 2020). This makes monolayer WSe$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$12 a spatially resolved magnetic sensor for layered antiferromagnetic domains that are invisible to a net-magnetization probe such as RMCD in the bilayer antiferromagnetic ground state.

5. Superconducting and superconducting–ferromagnetic heterostructures

In superconductor/ferromagnet systems, MPE includes both direct magnetic induction and less intuitive feedback of superconductivity onto ferromagnetism. In [Gd($${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$13)/Nb(25 nm)]$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$14, spin-polarized neutron reflectometry shows that the first Bragg-peak spin asymmetry $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$15 is reduced below the Nb transition temperature $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$16 K, but only in an intermediate field range between remanence and saturation (Khaydukov et al., 2019). The suppression weakens as $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$17 increases. The interpretation is electromagnetic rather than exchange-driven: the proximity-coupled Nb layers act as a thick superconducting medium that screens the external field, so the interior Gd layers experience a smaller local field. The fitted Meissner profile is

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$18

with best-fit $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$19 nm.

In oxide superlattices, the electronic state of the magnetic layer strongly controls the proximity response. For $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$20 and $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$21, polarized neutron reflectometry, XMCD, and XRMR show that the effect is pronounced for ferromagnetic-metallic LCMO and almost absent for ferromagnetic-insulating LMO (Satapathy et al., 2011). The induced Cu spin moment is $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$22 in YBCO/LCMO but only $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$23 in YBCO/LMO, with Cu and Mn moments antiparallel in both systems. PNR further indicates that YBCO/LCMO has a depleted Mn-magnetization region near the interface, while YBCO/LMO remains magnetically bulk-like up to within about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$24 Å of the interface. XRMR places the Cu moments inside YBCO rather than in the manganite, supporting an intrinsic interfacial reconstruction.

A related but more explicitly spin-valve geometry is Au/LSMO/SRO/YBCO. SQUID magnetometry, FMR, and neutron reflectometry show an induced magnetic moment in YBCO and a simultaneous suppression of magnetization in the ferromagnetic layers when YBCO becomes superconducting (Ovsyannikov et al., 2015). The change in total moment near $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$25 K is of order $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$26 emu. Neutron-reflectometry fits support an induced moment of about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$27 over a depth of about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$28 nm near the SRO interface; distributing the same signal over that thickness gives an effective $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$29. FMR analysis indicates that the SRO magnetization decreases by about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$30. Because the inferred penetration depth of the induced magnetic moment is about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$31–$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$32 nm, far larger than the cuprate coherence length $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$33 nm, the authors favor orbital reconstruction at the YBCO/SRO interface over a purely coherence-length-limited density-of-states mechanism.

Few-layer van der Waals superconductor/ferromagnet heterostructures depart sharply from the classical thick-film picture. For a 2D ferromagnetic monolayer coupled to an $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$34-layer vdW superconductor, the superconducting order parameter does not simply decrease monotonically with exchange field; instead it exhibits multiple dips whose number is set by the number of superconducting monolayers (Ianovskaia et al., 2024). For $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$35, the normal-state superconducting branches are

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$36

so two resonance conditions with the shifted ferromagnetic branch appear. More generally,

$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$37

The spin-resolved LDOS develops multiple peak structures because each superconducting subband acquires its own spin splitting; the result generally cannot be reduced to a single effective Zeeman field. Gating the ferromagnetic chemical potential $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$38 shifts both spin branches together and can therefore generate about twice as many dips in $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$39 as in $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$40.

6. Collective dynamics, magnonic regimes, and design implications

MPE does not only alter static moments and single-particle spectra; it can also reorganize collective dynamics. In Py/FeMn bilayers, ultrathin FeMn near its effective Néel temperature enters a proximity-dominated regime in which the Py layer induces a net moment in FeMn (Polishchuk et al., 2019). For FeMn thicknesses around $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$41–$${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$42 nm, the saturation magnetization normalized to the Py volume increases by about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$43 relative to the reference Py film. The $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$44 nm sample shows a single angle-independent resonance line at room temperature that is shifted strongly from free Py. A conventional anisotropy explanation would require an unrealistically large field of about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$45 kG, so the large FMR frequency enhancement toward the sub-THz range is attributed instead to a coupled FM/AFM dynamical interaction and a proximity-induced effective field.

A closely related collective phenomenon is the magnonic proximity effect in insulating trilayers. In the atomistic spin model for $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$46 stacks with $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$47, both FM-FM-FM and FM-lAFM-FM geometries show enhanced order in the weak central layer near its lower critical temperature (Brehm et al., 2021). For the ferromagnetic middle layer, the interfaces suppress low-frequency magnons and inject high-frequency spectral weight above the isolated bulk band edge, effectively “cooling” the middle layer and increasing its magnetization. For a layered antiferromagnetic middle layer, the equilibrium order-parameter profile is similar because of the classical symmetry mapping, but the magnon spectrum becomes asymmetric and can display an extra peak near the upper band edge. The proximity effect is therefore dynamic as well as static.

Interfacial exchange can also produce synthetic ferrimagnetism. In Fe/EuO and Co/EuO, hard x-ray magnetic depth profiling and atomistic spin dynamics show that the coupling is antiferromagnetic, short-ranged, and localized to a few monolayers near the interface (Rosenberger et al., 2024). EuO has bulk $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$48 K, yet the interfacial EuO layers remain magnetized above that temperature under coupling to the 3d ferromagnet. The practical dependence on EuO thickness is strong: $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$49 nm EuO emphasizes the interfacial contribution, whereas $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$50 nm EuO dilutes it in the thicker bulk-like interior. The simulations yield a compensation temperature $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$51 K and an interface-magnetized region of about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$52 monolayers for Fe/EuO and about $${\cal H}_\sigma(\vec k)= \begin{pmatrix} \epsilon(\vec k) & V_{\vec k}\ V_{\vec k}^* & E_\sigma(\vec k) \end{pmatrix},$$53 monolayers for Co/EuO. In the 2D limit, the fixed spatial range of the proximity interaction therefore occupies a larger fraction of the whole film and can dominate its magnetic response.

Across these systems, MPE is not a synonym for uniform magnetic enhancement. It can enhance order in a weak magnetic layer, suppress the response of an adjacent ferromagnet, induce moments in a nonmagnetic conductor, open topological or moiré miniband gaps, reshape the LDOS of a proximitized superconductor, or leave a transport coefficient essentially unchanged despite a large induced moment (Rosenberger et al., 2024, Khaydukov et al., 2019, Eremeev et al., 2013, Zhu et al., 2018). The common design variables are consistently interfacial: band alignment, wavefunction overlap, atomic registry, interlayer distance, annealing-controlled interface order, spacer insertion, layer number, and electrostatic gating (Cardoso et al., 2023, Tong et al., 2019, Ianovskaia et al., 2024). This body of work establishes MPE as a general interfacial control principle whose phenomenology must be identified case by case, with explicit separation from competing mechanisms such as spin Hall magnetoresistance, spin memory loss, spin backflow, and purely electromagnetic screening.