Proximity-Induced Magnetization (PIM)

• Proximity-Induced Magnetization (PIM) is a phenomenon where nonmagnetic materials acquire interfacial magnetic moments via exchange coupling with adjacent magnetic systems, critical for spintronic applications.
• PIM’s magnitude and spatial decay are quantified using techniques like XRMR and polarized neutron reflectometry, with induced moments reaching up to 0.6 μB in heavy metals such as Pt and Pd.
• Interface engineering, precise material selection, and structural tuning enable control of PIM, thereby modulating spin–orbit torques, magnetoresistance, and chiral spin textures in advanced devices.

Proximity-Induced Magnetization (PIM) refers to the phenomenon in which a nominally nonmagnetic material—such as a heavy metal or two-dimensional conductor—acquires a finite, interfacially confined magnetic moment due to direct electronic coupling with an adjacent ferromagnetic, antiferromagnetic, or otherwise magnetically ordered system. The spatial extent, magnitude, and physical effects of this induced magnetization are determined by quantum hybridization, band alignment, Stoner enhancement, and spin-orbit coupling at the interface. PIM is central to spintronics, exerting pronounced influence on transport, magnetic anisotropy, magnetoresistance, spin–orbit torques, Dzyaloshinskii–Moriya interactions (DMI), and advanced quantum devices.

1. Microscopic Mechanism of Proximity-Induced Magnetization

At the interface between a ferromagnet (FM) and a paramagnet or heavy metal (HM) with high Stoner susceptibility (e.g., Pt, Pd, Ir), hybridization between the FM's spin-split 3d bands and the HM's 5d (or 4d) bands produces an exchange splitting in the HM electronic states. This effect is short-ranged, typically confined to 0.5–2 nm or a few atomic layers adjacent to the interface (Moskaltsova et al., 2020, Klewe et al., 2015).

The induced magnetic moment $\mu_{\text{HM}}$ per HM atom at the interface scales with the FM magnetization, decays nearly exponentially with distance into the HM, and is strongly contingent on the local density of states at the Fermi level. The magnitude is maximal in HMs like Pt or Pd, which are close to the Stoner instability, but is negligible in HMs like W, reflecting their low spin susceptibility (Belmeguenai et al., 2017).

The PIM mechanism is universal: it occurs in metallic multilayers (Pt/Co, Pd/Fe, Ir/Co), in 2D heterostructures (graphene/YIG, graphene/Co), in topological insulators and Rashba 2DEG/ferromagnet hybrids (Bosnar et al., 2020, Hosseinzadeh et al., 2018, Shen et al., 2020, Phong et al., 2017), and in S/F or S/A (superconductor/ferromagnet or superconductor/altermagnet) proximity devices (Heras et al., 4 Dec 2025, Hikino, 2017). In all cases, the transfer of spin polarization is governed by interfacial exchange, local hybridization, and symmetry-allowed coupling terms.

2. Quantitative Characterization: Spatial Profile, Magnitude, and Threshold Effects

Depth Profile and Amplitude

Element-specific, depth-resolved probes such as X-ray resonant magnetic reflectivity (XRMR) and polarized neutron reflectometry have established that PIM is sharply localized at the interface. In Pt/FM and Pd/FM systems, the spin-polarized region's full width at half maximum (FWHM) is typically 0.8–1.2 nm, corresponding to 3–5 atomic layers (Moskaltsova et al., 2020, Klewe et al., 2015, Mayr et al., 2019).

The interfacial moment can reach $0.3\text{–}0.6\ \mu_B$/Pt (Pd) atom for strong FM contacts (Fe or Co-rich alloys), while substantially weaker for Ni (Klewe et al., 2015, Mayr et al., 2019). The spatial decay can be modeled as a Gaussian (to include roughness) or exponential:

$M(z) = M_0\,e^{-|z|/\xi}$

with $M_0$ the interfacial moment, $\xi$ the decay length ($0.3$–$0.5$ nm typical for Pt, Pd).

Threshold and Nonlinearity

Depth-resolved magnetometry has uncovered a threshold effect: PIM will not appear until the FM interfacial magnetization exceeds a finite threshold $M_{\text{thr}}$, modifying the scaling law to (Inyang et al., 2019):

$$\mathrm{PIM}(T) = \chi_{\text{eff}} [M_{\mathrm{int}}(T) - M_{\text{thr}}]\,\Theta\left(M_{\mathrm{int}}(T) - M_{\text{thr}}\right)$$

Here $\chi_{\text{eff}}$ is the effective interface susceptibility (including Stoner and exchange enhancement), and $\Theta$ is the Heaviside step function. This implies that under conditions of weak FM or close to $T_C$ of the FM, PIM vanishes abruptly even as a finite FM interface moment persists.

Interface Dependence and Asymmetry

PIM is exquisitely sensitive to atomic-scale interface structure. Crystallographic orientation (e.g., Pt(111) vs Pt(011) in Pt/Co), atomic ordering, roughness, degree of intermixing, and choice of buffer vs capping layer have dramatic effects on the amplitude and extent of PIM (Mukhopadhyay et al., 2019, Belmeguenai et al., 2017). For example, the Pt(111)/Co interface yields $\mu_{\text{Pt}}\approx 0.14\,\mu_B$, whereas Pt(011)/Co gives $\approx 0.05\,\mu_B$ (Mukhopadhyay et al., 2019); similarly, Pt as buffer produces higher PIM than Pt as cap (Belmeguenai et al., 2017).

3. Techniques for PIM Detection and Depth Profiling

Technique	Depth Resolution / Specificity	Quantitative Output
XRMR	∼0.5 nm, element-specific (e.g., Pt L₃ edge)	Magnetic moment profile $M(z)$ in HM
PNR	∼0.2 nm, sensitive to overall $S_z$ in multilayers	Total and local $M(z)$, differentiation of FM and HM moments
VSM, SQUID	Average magnetization, no depth specificity	Effective saturation $M_s$, total PIM fraction
XMCD	Element/species-specific, surface sensitive	Local magnetic moment per atom [see comparison with XRMR]

XRMR exploits field (or helicity)-dependent magneto-optic corrections at absorption edges (Pt, Ir, Pd L₃), with both magnitude and phase dependence of the reflectivity asymmetry ratio providing $M(z)$. PNR provides high depth resolution but less elemental specificity.

Quantitative analysis involves modeling $M(z)$ using Gaussian or exponential forms convolved with interface roughness, fitting both non-magnetic and magnetic reflectivity data (Moskaltsova et al., 2020, Klewe et al., 2015, Mayr et al., 2019). Absolute calibration can be derived from ab initio magneto-optic data.

4. Material and Structural Dependence: Competing Interactions and Engineering

Material Selection

PIM strength is dictated by the Stoner factor and density of states. Pt and Pd are optimal for strong PIM ($\mu_{\rm HM}\sim 0.4\text{–}0.6\,\mu_B$), Ir yields moderate, and W is essentially inert due to weak susceptibility (Belmeguenai et al., 2017).

Structural Control

Epitaxial orientation, buffer/capping asymmetry, interface chemical composition, and post-growth annealing all modulate PIM (Mukhopadhyay et al., 2019, Belmeguenai et al., 2017). For instance, annealing sharpens the interface and increases PIM by reducing the dead layer and enhancing chemical order (Belmeguenai et al., 2017). The nature of the buffer (e.g., Ta insertion) can switch Pt from (111) to (011) and thus reduce PIM threefold (Mukhopadhyay et al., 2019).

Composition of the FM controls PIM amplitude, scaling linearly with the FM magnetization for strong FMs (Fe, Fe-rich alloys), but vanishingly small for weak FMs (Ni) (Klewe et al., 2015).

Decoupling from Long-Range Exchange and Indirect Coupling

PIM decays monotonically with the loss of direct contact or through the introduction of non-magnetic spacers (e.g., Au, Ir) of sub-nanometer thickness. The critical thickness for PIM quenching is ∼0.4–0.7 nm (Ir), ∼1.1 nm (Au), and is extremely sensitive to monolayer coverage due to roughness (Rowan-Robinson et al., 2017).

Notably, while PIM and interfacial DMI co-vary for sub-monolayer insertions, DMI persists and continues to evolve with further thickness, revealing a fundamentally longer-range, indirect (e.g., RKKY-mediated) mechanism for DMI compared with the local, hybridization-driven nature of PIM (Rowan-Robinson et al., 2017, Mayr et al., 2019).

5. PIM in Nonmetallic and 2D Hybrid Systems

PIM is not confined to metallic multilayers; it is robust in nonmetallic and low-dimensional heterostructures:

• Graphene/Ferromagnet or MI: PIM in single-layer and bilayer graphene generated by contact with either classic ferromagnets (Co, Fe) or magnetic insulators (YIG, EuO, EuS). Exchange splitting $\Delta_{\mathrm{ex}}$ in the Dirac point up to 1 meV is gate-tunable via Au/Pt passivation layers (Bosnar et al., 2020, Solis et al., 2019, Pan et al., 2021, Phong et al., 2017). For YIG/MNP–decorated graphene, the PIM decay length matches the contact region, and composite devices show marked enhancement of magnetoimpedance (Hosseinzadeh et al., 2018).
• Rashba 2DEGs/Surface States: PIM in proximity to ferromagnetic insulators introduces a sizable exchange splitting ($10$–$30$ meV), shifting spin textures and leading—when combined with Rashba SOC—to pronounced tunneling anisotropic magnetoresistance up to tens of percent, unattainable by Rashba SOC alone (Shen et al., 2020).
• S/F/N/F/S Junctions and S/Altermagnet Hybrids: Theoretical treatments show that PIM can occur in normal metals and altermagnets sandwiched between superconductors and F (or altermagnet) layers, with the amplitude and spatial profile governed by the pairing symmetries and order-parameter gradients (Heras et al., 4 Dec 2025, Hikino, 2017).

6. Consequences and Applications in Spintronics and Hybrid Devices

PIM alters both static and dynamic spintronic observables:

• Saturation Magnetization ($M_s$): PIM can raise the total $M_s$ of thin films by 5–10%; neglecting PIM results in systematic errors in quantifications of spin–orbit torque efficiency ($\theta_{\text{SH}}$), suggesting up to 10% misestimation in extracted spin Hall angles or torque ratios (Moskaltsova et al., 2020).
• Spin-Orbit Torque and Spin-Charge Conversion: Since spin-orbit torque efficiencies are $(M_s)^{-1}$-weighted, accurate incorporation of the PIM contribution is essential for both torque magnitude and for distinguishing field-like from damping-like torques (Moskaltsova et al., 2020, Belmeguenai et al., 2017).
• Magnetoresistance and Hall Effects: PIM directly produces anomalous Hall and Nernst signals in nominally nonmagnetic HMs in contact with FMs. This is particularly important for the correct interpretation of ISHE, SMR, or spin-pumping data (Klewe et al., 2015, Yang et al., 2013).
• Engineering DMI, Domain Wall Dynamics, and Chiral Spin Textures: Interface-localized PIM is correlated with regions of strong DMI, essential for stabilizing and controlling chiral domain walls, skyrmions, and related phenomena (Rowan-Robinson et al., 2017, Mayr et al., 2019).
• Controllable Interfacial Magnetism: Structural tuning (texturing, buffer/insertion, annealing) offers avenues for tailoring interface PIM and thus manipulating device response (e.g., using Ta buffer to control Pt crystallography/PIM asymmetry (Mukhopadhyay et al., 2019)).
• 2D Quantum and Topological Effects: In graphene and topological insulators, proximity exchange opens masses/gaps and yields phases from half-metallic to Chern and spin-Chern insulators, with consequences for anomalous/spin Hall responses (Phong et al., 2017).

7. Theoretical and Experimental Generalizations

PIM is universal to systems with suitable interface coupling and large spin susceptibility. In hybrid S/AM (superconductor/altermagnet) systems, it emerges from the coupling of spatial gradients in the order parameter to the spin sector of the Green's function, leading to magnetization profiles whose symmetry and sign mirror the underlying order (Heras et al., 4 Dec 2025). In S/F/N/F/S Josephson junctions, induced magnetization can be modulated by phase gradients and manifests signatures of spin-triplet superconducting correlations, enabling $0$–$\pi$ transitions and phase-controlled spin currents (Hikino, 2017).

PIM is thus a key handle in modern spin–orbitronic, hybrid quantum, and low-dimensional physics, enabling both fundamental studies and device-level engineering through atomic-scale interface control, spectral selectivity in detection, and integration in multilayered and 2D materials platforms.