Microscopic origin and quantitative characterization of the magnetic proximity effect at the Bi2Se3/EuS topological-insulator/ferromagnetic-insulator interface

Depositing the ferromagnetic insulator EuS on the topological insulator Bi2Se3 was reported in 2013 (Wei et al., Phys. Rev. Lett. 110, 186807) to induce a magnetic moment at the interface, produce hysteretic magnetoresistance attributed to chiral modes at magnetic domain walls, and generate a small anomalous Hall effect. The authors left open the microscopic coupling mechanism, the magnitude of the exchange gap in the Dirac surface states, the interpretation of the domain-wall magnetoresistance, the role of bulk carriers in shorting the anomalous Hall signal, and the temperature scale of the interfacial magnetic order. A decade of follow-up work has directly imaged chiral currents at domain boundaries in this very heterostructure and has achieved large anomalous Hall responses in lower-carrier topological-insulator/ferromagnetic-insulator systems, but the central questions — whether a genuine magnetic proximity effect exists at the Bi2Se3/EuS interface, what its microscopic mechanism is, how large the induced moment and the exchange Dirac gap are, and at what temperature the interfacial order survives — remain in direct experimental conflict, with positive reports from magnetometry, neutron reflectometry, and second-harmonic generation contradicted by null results from x-ray magnetic circular dichroism, muon spin rotation, surface x-ray diffraction, and first-principles calculations.

Background

Three-dimensional topological insulators (TIs) such as Bi2Se3 host metallic surface states with a Dirac-cone dispersion (linear in momentum, like massless fermions) whose spin-momentum locking — the fixed correlation between an electron's momentum and its spin direction — is protected by time-reversal symmetry (TRS). Breaking TRS at the surface opens an exchange gap in the Dirac spectrum — the prerequisite for the quantum anomalous Hall effect (quantized Hall conductance arising from intrinsic magnetization rather than an applied magnetic field), the topological magnetoelectric (axion) response (the coupling between electric and magnetic response fixed by the topological term of the band structure), and Majorana-based schemes. Because magnetic doping introduces disorder and impurity states in the gap, the cleaner route is the magnetic proximity effect: depositing a ferromagnetic insulator (FMI) whose short-range exchange interaction magnetizes the TI surface without disturbing its structure. EuS is a canonical FMI choice — a Heisenberg ferromagnet with bulk Curie temperature $T_C \approx 16.5$ K and a $7\,\mu_\mathrm{B}$ saturation moment per Eu$^{2+}$ ion — that grows epitaxially on Bi2Se3 by molecular beam epitaxy (MBE) with a sharp interface.

Wei et al. (Phys. Rev. Lett. 110, 186807 (2013)) reported magnetometry with a superconducting quantum interference device (SQUID, an ultra-sensitive magnetometer) and magnetotransport on MBE-grown Bi2Se3 (20 nm)/EuS (1–10 nm) bilayers. They found a saturation moment per Eu$^{2+}$ ion exceeding the $7\,\mu_\mathrm{B}$ EuS limit (up to $11.3\,\mu_\mathrm{B}$/Eu for 1 nm EuS), whose thickness dependence extrapolates to an interfacial induced moment $m_0 = (1.3 \pm 0.5)\times10^2\,\mu_\mathrm{B}/\mathrm{nm}^2$; they attributed the excess moment to the interface, possibly arising from magnetized interfacial atoms, spin polarization of the Bi2Se3 electron gas (aided by its large Landé g factor), or hybridized interface electronic states. In transport they observed hysteretic, v-shaped magnetoresistance minima at the coercive field below about 4 K — attributed, though not proven, to chiral conduction modes predicted to propagate along perpendicular domain walls of the canted interfacial magnetization — and a small anomalous Hall effect (AHE), the nonlinear part of the Hall voltage of ferromagnetic origin, partially shorted by the $n \approx 4\times10^{19}\,\mathrm{cm}^{-3}$ bulk carriers of the 20 nm Bi2Se3 film. The paper explicitly deferred the interfacial characterization needed to identify the coupling mechanism, noted that the exchange gap of the Dirac surface states was not measured, and anticipated that the interfacial ordering temperature is lower than the EuS film $T_C$ while better interfaces could raise the remnant perpendicular magnetization.

Subsequent literature on this interface and its close relatives is sharply split. In favor of a strong proximity effect: spin-polarized neutron reflectometry found interfacial ferromagnetism in EuS/Bi2Se3 persisting to room temperature and extending about 2 nm into the Bi2Se3 (Katmis et al., Nature 2016); magnetic second-harmonic generation — a nonlinear-optical probe in which light emitted at the doubled frequency reports the magnetization of buried interfaces — directly measured both in-plane and out-of-plane magnetization induced at the buried interface (Lee et al., Nat. Commun. 2016); and transport anomalies appeared well above EuS $T_C$ in (Bi,Sb)2Te3/EuS (Yang and Kapitulnik, PRB 2018). Against it: x-ray magnetic circular dichroism (XMCD), an element-selective probe of magnetic moments, found no induced moment in the TI above roughly $10^{-3}\,\mu_\mathrm{B}$ per atom and no Eu-moment enhancement (Figueroa et al., PRL 2020); low-energy muon spin rotation (LE-muSR) found similar stray fields adjacent to EuS whether the neighbor was Bi2Se3 or topologically trivial titanium (Krieger et al., PRB 2019); surface x-ray diffraction with ab initio calculations found no magnetization within the first Bi2Se3 quintuple layer (the five-atom Se-Bi-Se-Bi-Se repeating stacking unit of its layered crystal structure) and a maximum Néel temperature — the antiferromagnetic ordering temperature — of 226 K (Meyerheim et al. 2021); first-principles work found charge transfer without induced magnetization (Tristant et al., PRB 2021); and Raman spectroscopy likewise indicated charge transfer (Osterhoudt et al., PRB 2018). Meanwhile the one direct spectroscopic measurement of a topological-surface-state gap in this material family, on Pb1-xSnxSe/EuSe, attributed the observed gap mainly to quantum confinement and concluded the proximity coupling is weak (Wang et al., Commun. Phys. 2023).

Problem Statement

Establish whether a magnetic proximity effect operates at the epitaxial Bi2Se3/EuS interface and, if so, characterize it quantitatively. The common objective is a single self-consistent microscopic account of the exchange-coupling-induced interfacial magnetism reported in 2013 and of its action on the topological surface states, comprising three linked questions: (1) Mechanism and structure — determine the microscopic origin of the induced interfacial moment (magnetized interfacial atoms, spin polarization of the TI electron gas, hybridized interface states, charge transfer, or a combination), identifying the actual interface structure and growth conditions that produce it, since the moment inferred in 2013 from the excess saturation magnetization ($m_0 \approx 1.3\times10^2\,\mu_\mathrm{B}/\mathrm{nm}^2$) must be reconciled with the element- and depth-selective nulls (XMCD bounds near $10^{-3}\,\mu_\mathrm{B}$/atom; muon-spin-rotation stray-field measurements; first-principles charge-transfer results) and with the positive neutron-reflectometry and second-harmonic-generation reports; (2) Consequence for the Dirac spectrum — determine the magnitude and spatial extent of the exchange-induced gap in the Bi2Se3 Dirac surface-state spectrum (distinguishing an exchange gap from hybridization or quantum-confinement gaps), which requires dealing with the bulk carriers of Bi2Se3 that short surface-sensitive signals; and (3) Temperature scale — determine the strength and ordering temperature of the interfacial ferromagnetism relative to the bulk EuS $T_C \approx 17$ K and the mechanism (e.g. TI-surface-mediated exchange, canted interfacial spins, quantum fluctuations) that sets it, adjudicating between claimed room-temperature interfacial order and inferred Néel-type ordering below 226 K. Auxiliary 2013 questions — whether domain-wall chiral modes cause the hysteretic magnetoresistance (directly imaged by scanning SQUID in the same heterostructure in 2015, with gate tuning) and whether reducing the bulk carrier density unmasks a clean anomalous Hall effect (achieved in other low-carrier TI/ferromagnetic-insulator systems) — are largely settled by the later literature and delimit, rather than belong to, the surviving core above.

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