Magnetic Proximity Effect in Quantum Materials

• Magnetic Proximity Effect is a quantum interfacial phenomenon where magnetic order is induced in adjacent nonmagnetic or correlated materials without the need for chemical doping.
• Experimental techniques like PNR, XMCD, and magnetotransport reveal measurable spin polarization, exchange gap formation, and modifications in superconducting correlations at the interface.
• Tunable via material choice, interface configuration, and electric field control, MPE enables promising applications in spintronics, topological quantum devices, and nanoscale reconfigurable electronics.

The magnetic proximity effect (MPE) is a quantum interfacial phenomenon by which magnetic order penetrates from a magnetically ordered material (ferromagnet, ferrimagnet, or antiferromagnet) into an adjacent nonmagnetic, superconducting, semiconducting, topological, or otherwise correlated material. This proximity-induced magnetism redistributes the interfacial spin, orbital, and occasionally charge degrees of freedom without the need for chemical doping or atomic substitution, allowing control of magnetism, transport, and topological properties at the atomic or few-atomic-layer scale.

1. Fundamental Mechanisms and Theoretical Formulation

At the core of the MPE is interfacial exchange coupling, which can be described by an effective Hamiltonian combining the relevant material terms, such as

$$H = H_{\text{host}} + H_{\text{mag}} + H_{\text{ex}},$$

where $H_{\text{host}}$ describes the nonmagnetic substrate (e.g., graphene, superconducting layer, topological insulator), $H_{\text{mag}}$ the magnetic layer, and $H_{\text{ex}}$ is the proximity-induced exchange term, often modeled as

$H_{\text{ex}} = J \mathbf{M} \cdot \mathbf{s}$

with coupling strength $J$, local magnetization vector $\mathbf{M}$ (from the magnetic side), and electron spin operator $\mathbf{s}$ (of the adjacent material).

In proximity, interface hybridization and exchange can induce observable effects:

• formation of spin-polarized states in the otherwise nonmagnetic or topologically trivial host,
• possible band inversion if the exchange splitting $\Delta_\text{ex}$ rivals the fundamental band gap,
• opening of a Dirac mass or exchange gap in topological surface states,
• modification of superconducting correlations.

The range of MPE varies by system, from sub-nanometric in heavy metal/ferromagnet stacks (Moskaltsova et al., 2020, Häuser et al., 2023) to several nanometers in topological insulator/magnetic interfaces (Akiyama et al., 2019).

2. Experimental Methodologies and Direct Probes

A diverse experimental toolkit has enabled quantitative investigation of MPE across materials systems:

• Polarized Neutron Reflectometry (PNR): Depth-profile of magnetic scattering length density, resolving the extension of induced magnetism (Satapathy et al., 2011, Akiyama et al., 2019, Li et al., 2017).
• X-ray Magnetic Circular Dichroism (XMCD) / X-ray Resonant Magnetic Reflectivity (XRMR): Element-specific measurement of interface magnetization and spin polarization, with fitting models for Gaussian-like magnetooptic profiles (Moskaltsova et al., 2020, Li et al., 2017).
• Magnetotransport (AHE, AMR, SMR): Hall effect and angular-dependent magnetoresistance serve as indirect signatures of proximity-induced ferromagnetism; e.g., observation of anomalous Hall effect in nonmagnetic layers with FM proximity (Pt/CoFe$_2$O$_4$, Ta/YIG, Pt/$\alpha$-Fe$_2$O$_3$) (Yang et al., 2013, Amamou et al., 2017, Cheng et al., 2019).
• Quantum Oscillations (SdH/fan diagram): Identification of surface conduction from topological surface states, or Fermi surface modification, triggered by MPE (Fukuoka et al., 12 May 2025).
• Nonlocal and Local Spin Transport: Detection of Zeeman spin Hall effect and induced spin splitting in proximity to 2D magnets or molecular layers (Tang et al., 2019, Pan et al., 2021).

Table 1 summarizes common probe techniques and what they measure:

Method	Direct Observables	Typical Application
PNR/XRMR/XMCD	Magnetic depth/profile, spin polarization	Interfacial/element specificity
AHE/AMR/SMR	Magnetotransport response	Confirmation of induced moment
SdH/Quantum transport	Band structure/topological signatures	Surface state activation
Nonlocal voltage	Spin-dependent transport over macroscopic lengths	MPE in 2D or molecular systems

3. System-Dependent Manifestations and Control Parameters

The MPE exhibits highly nonuniversal and tunable properties, depending critically on materials choices, interface configuration, and external controls:

• Nature of Magnetic Proximizer:
  • Ferromagnetic metals/insulators (e.g., Fe, CoFeB, CrBr$_3$, YIG) induce strong, often short-range MPE with robust exchange fields (Satapathy et al., 2011, Häuser et al., 2023, Tang et al., 2019).
  • Ferrimagnets and antiferromagnets (e.g., YIG, $\alpha$-Fe$_2$O$_3$) can also generate MPE; in antiferromagnets, uncompensated interfacial spins govern the effect (Cheng et al., 2019).
  • Molecular magnets (e.g., Fe-phthalocyanine monolayers) are shown to generate detectable exchange fields in graphene (Pan et al., 2021).
• Host Response:
  • Nonmagnetic metals (Pt, Ta, IrMn) show induced moments at interfaces, modifying transport and damping (Moskaltsova et al., 2020, Häuser et al., 2023, Yang et al., 2013).
  • Superconductors (YBCO): MPE leads to locally suppressed superconductivity and depth-dependent magnetic order (Satapathy et al., 2011).
  • Topological states: MPE in topological insulator/ferromagnet or TCI/Fe opens exchange gaps and creates/splits Dirac cones, supporting chiral surface conduction (Eremeev et al., 2013, Akiyama et al., 2019, Fukuoka et al., 12 May 2025).
• Atomic registry and moiré superstructures: In van der Waals heterostructures, the MPE is highly sensitive to local stacking; moiré patterns yield spatial modulation of spin splitting, controllable by twist angle, strain, or field (Tong et al., 2019). Analytical expressions for miniband splitting (e.g., $E_s(r)$) capture the spatially modulated MPE.
• Gate and Electric Field Control: Dual control of carrier density and orbital overlap enables in situ tuning of MPE in low-dimensional systems, enabling gate-controllable odd-parity magnetoresistance and proximity-induced quantum phase transitions (Takiguchi et al., 2020, Takiguchi et al., 2021, Li et al., 2017).
• Thickness and Proximity length scales: Proximity-induced magnetization decays within nanometers, but substantial hybridization can yield measurable effects up to several nm from the interface (e.g., SnTe/Fe, BPN/YIG) (Akiyama et al., 2019, López-Alcalá et al., 31 Oct 2024).

4. Key Phenomena and Quantitative Models

MPE results in a set of experimentally and theoretically tractable phenomena:

• Induced Exchange Gap / Spin Splitting:
  • In heterostructures with strong SOC or Dirac band structures (topological insulators, Dirac semimetals, graphene), MPE opens a gap

  $$H_{2D,\text{TI}} = \hbar v_F (\sigma_x k_y - \sigma_y k_x) + A(M \cdot \sigma)$$

  yielding $E_{k,s} = s \sqrt{(...)}$ with $s = \pm$ (Fukuoka et al., 12 May 2025). - In 2D semiconductors, the spin splitting due to MPE can be described by $E_s \sim \sum_i (t_i^2/\Delta_i)$, where $t_i$ are interlayer hopping amplitudes, and $\Delta_i$ are energy offsets (Tong et al., 2019). - In biphenylene/YIG, ab initio calculations show spin splittings up to 130 meV, enhanced by proximity and vdW distance (López-Alcalá et al., 31 Oct 2024).

• Proximity-Induced Magnetotransport:

  • Anomalous Hall and anisotropic magnetoresistance signals in nominally nonmagnetic layers reveal proximity-induced order (e.g., Pt/CoFe$_2$O$_4$, Ta/YIG, Pt/$\alpha$-Fe$_2$O$_3$) (Amamou et al., 2017, Yang et al., 2013, Cheng et al., 2019, Zhou et al., 2015).
  • The MPE enters models for magnetoresistance, e.g.,

  $$\rho_{xx} = \rho_0 + \Delta\rho_{AMR} m_j^2, \;\; \rho_{xy} = \Delta\rho_{AMR} m_t m_j + \rho_{AHE} m_n$$

  versus spin Hall magnetoresistance (SMR) contributions, which have opposite temperature and angular dependence (Zhou et al., 2015).

• Superconductivity and π-Junctions:

  • MPE-induced exchange fields can trigger 0–π transitions in Josephson junctions. The Usadel formalism describes the exchange-induced oscillatory decay of superconducting order:

  $$\hbar D \partial_x^2 f_{\pm} - 2\hbar|\omega| f_{\pm} \pm 2i H_{eff} f_{\pm} ... = 0$$

  with phase reversals (0→π state) determined by the interplay of exchange field, N thickness, and spin–orbit scattering (Hikino et al., 2014).

• Spin Transport and Damping:

  • In N/F/N trilayers (e.g., CoFeB/Pt), the MPE increases magnetic damping in the adjacent nonmagnetic layer, altering spin diffusion length and effective mixing conductance in spin pumping models (Häuser et al., 2023).
  • Spin transport models must incorporate interfacial exchange, modified spin-mixing conductance, and MPE-induced changes in total magnetic moment (Moskaltsova et al., 2020).
• Quantum Hall and Topological States:
  • MPE can induce or modulate topological surface states (TSS) in materials that are otherwise trivial semiconductors, provided the induced exchange exceeds the band gap,

  $\Delta_{ex} > E_g$

  leading to band inversion and observation of TSS; experimentally evidenced by the emergence of high-mobility, linear-dispersion surface states in magneto-oscillation data (Fukuoka et al., 12 May 2025).

5. Applications and Quantum Materials Engineering

The MPE offers multiple compelling routes for quantum control and device engineering:

• Spintronic Devices: MPE-driven interface magnetization enables all-electrical spin injection, spin filtering, nonlocal logic elements, and low-power memory in 2D vdW and oxide heterostructures (Xu et al., 2018, Tang et al., 2019, Pan et al., 2021). Robustness at room temperature is achieved, e.g., in Fe/SnTe (Akiyama et al., 2019), and spin switchability by gate bias or interface structure is available.
• Topological Quantum Functionality: Creation of chiral edge states, realization of quantum anomalous Hall effect (QAHE), and axion insulator physics are made accessible without chemical doping, preserving material coherence and minimizing disorder (Eremeev et al., 2013, Akiyama et al., 2019, Fukuoka et al., 12 May 2025).
• Programmable Nanoscale Devices: In moiré-patterned vdW stacks, spatial modulation of MPE by stacking registry yields arrays of spin-polarized quantum dots, programmable spin filters, and anisotropic spin waveguides. These architectures exploit both mechanical and electrical degrees of freedom for device reconfigurability (Tong et al., 2019).
• Magnetic Control of Superconductivity: Interfacing superconductors with tunable MPE layers yields phase-controllable Josephson junctions and potential superconducting spin valve elements (Hikino et al., 2014, Satapathy et al., 2011).
• Metrology/Sensing: The large, gate-tunable odd-parity magnetoresistances enabled by MPE are promising for high-sensitivity magnetic field sensors (Takiguchi et al., 2020).

6. Open Challenges and Outlook

Critical considerations and future research directions include:

• Decoupling MPE from spin-orbit torque, spin memory loss, and spin backflow in heavy metal/ferromagnet interfaces—MPE is not always the dominant interfacial effect responsible for spin transport phenomena (Zhu et al., 2018).
• Quantitative characterization of interface chemistry, stacking, and atomistic roughness, which strongly influence the spatial extent and magnitude of MPE (Amamou et al., 2017, Moskaltsova et al., 2020).
• Theoretical progress on the interplay between proximity exchange, spin–orbit coupling, and quantum geometry for engineered band topologies, especially in designer 2D materials or TCI/ferromagnet stacks (López-Alcalá et al., 31 Oct 2024, Fukuoka et al., 12 May 2025).
• Scaling and robustness: Demonstrating room-temperature, high-mobility topological or spintronic response in proximity-engineered materials, as seen in the persistence of MPE up to 297 K in Fe/SnTe (Akiyama et al., 2019).
• Tunability and reversibility: Control over MPE via gate, electric field, mechanical strain, or programmable stacking remains central to maximizing device relevance (Takiguchi et al., 2021).
• Cross-correlations with superconductivity, Kondo effect, and long-range quantum coherence remain largely uncharted, with recent observations of gate-tunable MPE magnetoresistance and odd-parity effects in low-dimensional semiconductors (Takiguchi et al., 2020).

The MPE serves as a principal platform for the intentional and reversible design of magnetic, topological, and quantum phenomena at complex interfaces, now spanning oxide heterostructures, van der Waals stacks, molecular layers, and semiconductor heterojunctions. Its role is central to both the exploration of emergent quantum matter and the practical control of nanoscale spin and topology for next-generation electronics and spin-based information technologies.