Atomically thin CrI3 sandwiched between graphite contacts acts as a spin-filter magnetic tunnel junction: magnetoresistances of 95%, 300% and 550% for two-, three- and four-layer barriers arise from antiferromagnetic interlayer coupling, and inelastic electron tunneling spectroscopy (IETS) reveals collective magnetic excitations (magnons) at approximately 3, 7 and 17 meV. The 2018 discovery paper left the microscopic physics of these junctions unexplained in several respects that remain only partially resolved: (i) how the CrI3/graphite band alignment — density functional theory places majority-spin Cr 3d bands at or very near the graphite Fermi level — nevertheless produces the experimentally observed finite effective tunneling barrier heights and the per-layer spin transmission ratio T_P/T_AP of roughly 3.5; (ii) the detailed nature of the electron–magnon coupling responsible for the inelastic tunneling spectra and its role in bias-dependent spin transport; (iii) a quantitative account of the anomalously large magnetic-field dispersion of the 7 meV inelastic peak, whose slope corresponds to about 8 Bohr magnetons instead of the 2 μB (0.12 meV/T) expected for single-magnon Zeeman shifts, for which the original thermal-magnon-renormalization picture remains qualitative; and (iv) the device-level exploration (switching dynamics, spin-orbit-torque detection, integration with topological insulators, superconductors and low-symmetry crystals) that these tunnel barriers enable. This problem asks for a quantitative microscopic theory of elastic spin-dependent and inelastic magnon-assisted tunneling in CrI3 van der Waals junctions, together with the temperature- and field-dependent measurements needed to test it.

Background

A magnetic tunnel junction (MTJ) is a two-terminal device in which electrons quantum-mechanically tunnel between two conductors through a thin insulating barrier; when the barrier is a ferromagnetic insulator, electrons of opposite spin see different barrier heights, so the tunneling current becomes spin-polarized (the spin-filter effect). Chromium triiodide (CrI3) is a layered van der Waals (vdW) crystal — one whose layers are held together by weak interlayer forces, so atomically thin sheets can be stacked into heterostructures — that is a ferromagnetic insulator in each monolayer with adjacent layers antiferromagnetically coupled in few-layer form. Stacking two to four CrI3 layers between graphite contacts therefore realizes a 'double spin filter': in zero field the alternating magnetizations suppress tunneling, while a field-induced metamagnetic transition aligns the layers and strongly increases the conductance. Klein, MacNeill, Lado, Soriano, Navarro-Moratalla, Watanabe, Taniguchi, Manni, Canfield, Fernández-Rossier and Jarillo-Herrero (Science 360, 1218 (2018)) measured magnetoresistances of 95%, 300% and 550% for bilayer, trilayer and tetralayer CrI3 barriers, deduced a per-layer transmission ratio T_P/T_AP of about 3.5 between parallel (P) and antiparallel (AP) layer magnetizations (corresponding to spin polarizations of roughly 85–99%), and observed that the junction resistance decays exponentially with barrier thickness — proof that transport is tunneling-dominated with a finite effective barrier. A puzzle they identified is that their density functional theory (DFT) shows the majority-spin (spin-up) Cr 3d bands of CrI3 lying very close to, or crossing, the graphite Fermi energy, while spin-down bands lie more than 1 eV higher; how that band alignment coexists with a finite measured barrier was left to future transport calculations. In the same issue, Song et al. (Science 360, 1214 (2018), DOI 10.1126/science.aar4851) and Wang et al. (Nat. Commun. 9, 2516 (2018), DOI 10.1038/s41467-018-04953-8) reported similarly giant tunneling magnetoresistance in graphite- and graphene-contacted CrI3 junctions, establishing the phenomenology. Beyond the elastic (zero-bias) conductance, Klein et al. measured the differential conductance dI/dV versus bias and its numerical second derivative, i.e. inelastic electron tunneling spectroscopy (IETS), in which a step or peak appears when the bias energy eV suffices to excite a collective mode of the barrier or electrodes. Their junctions showed symmetric inelastic features at approximately 3, 7 and 17 meV, present in every device, with onset tracking the appearance of magnetic order — evidence for magnons, the quantized spin-wave excitations of an ordered magnet, in which a single magnon is a delocalized spin flip carrying a magnetic moment of about 2 μB (μB is the Bohr magneton). By the Zeeman effect, magnon energies should then blueshift with field at 0.12 meV/T: this roughly fits the 3 meV peak, but the 7 meV peak disperses with a slope corresponding to about 8 Bohr magnetons, an anomaly the authors could only address qualitatively, through the idea that a magnetic field depletes thermally excited magnons, increases the spin stiffness and thereby renormalizes the magnon spectrum on top of the Zeeman shift. Later work has clarified part of the elastic side: Paudel and Tsymbal (ACS Appl. Mater. Interfaces 11, 15781 (2019), DOI 10.1021/acsami.9b01942) computed spin-dependent transport for Cu/CrI3/Cu junctions from first principles, attributing spin filtering to spin- and wave-vector-dependent evanescent (decaying) states in the barrier plus Cu-to-CrI3 charge transfer; Heath, Costa, Buongiorno-Nardelli and Kuroda (Phys. Rev. B 101, 195439 (2020), DOI 10.1103/PhysRevB.101.195439) combined first-principles electronic structure with ballistic transport for graphene/CrI3 junctions, finding that tunneling dominates, that quantum confinement and layer-layer interactions are essential, and that the short barrier width invalidates the usual bulk complex-band description, in which tunnel decay constants are read off the complex band structure (Bloch wave vectors with an imaginary component) of the infinite bulk crystal, while reproducing magnetoresistance values close to experiment. On the inelastic side, Ghazaryan et al. (Nat. Electron. 1, 344 (2018), DOI 10.1038/s41928-018-0087-z) showed in graphene/CrBr3/graphene devices that magnon emission is the dominant inelastic tunneling channel at low temperature, and theoretical frameworks for tunneling spectroscopy of magnons in two-dimensional magnets have been developed (Carrega, Vera-Marun and Principi, Phys. Rev. B 102, 085412 (2020), DOI 10.1103/PhysRevB.102.085412; Mitra, Corticelli, Ribeiro and McClarty, Phys. Rev. Lett. 130, 066701 (2023), DOI 10.1103/PhysRevLett.130.066701), but no microscopic calculation of the electron–magnon coupling in the graphite/CrI3/graphite junctions themselves — its matrix elements, selection rules and IETS line shapes for the 3, 7 and 17 meV peaks — nor a quantitative explanation of the 8 μB field dispersion has been published. Independent probes of the CrI3 magnon spectrum (inelastic neutron scattering of Dirac-point magnons — spin-wave branches with linear, Dirac-cone-like crossings — by Chen et al., Phys. Rev. X 8, 041028 (2018); Raman spin-wave branches by Jin et al., Nat. Commun. 9, 5122 (2018); magneto-Raman magnons in atomically thin CrI3 by Cenker et al., Nat. Phys. 17, 20 (2021)) constrain the magnon energies and exchange/anisotropy parameters but do not address the tunneling spectroscopy anomaly. The remaining questions are scientifically linked: together they ask for the microscopic theory that makes vertical tunneling a quantitative probe, not just a detector, of magnetism in atomically thin insulators, and that supplies the design rules for CrI3-based spin-filter devices.

Problem Statement

Provide a quantitative microscopic account of electron tunneling through atomically thin CrI3 barriers in graphite/CrI3/graphite (and closely related graphene-contacted) van der Waals tunnel junctions, covering the four linked issues raised by the 2018 discovery paper: (1) the tunneling pathways and finite effective barrier heights — explain, by transport calculation from the CrI3/graphite electronic structure, how the majority-spin Cr 3d bands lying at or very near the graphite Fermi level coexist with the experimentally observed finite tunneling barrier (evidenced by the exponential thickness dependence of the junction resistance) and quantitatively reproduce the per-layer spin transmission ratio T_P/T_AP ≈ 3.5 that yields the measured 95%, 300% and 550% magnetoresistances and 85–99% spin polarizations for two-, three- and four-layer barriers; (2) the electron–magnon coupling — determine its microscopic form (matrix elements, momentum and spin selection rules) and show how it generates the observed inelastic tunneling spectra, with steps and d²I/dV² peaks near 3, 7 and 17 meV, and how it enters bias-dependent spin transport; (3) the anomalous magnetic-field dispersion — give a quantitative explanation of why the 7 meV inelastic peak blueshifts with a slope corresponding to about 8 Bohr magnetons rather than the ≈2 μB (0.12 meV/T) single-magnon Zeeman shift that roughly fits the 3 meV peak, going beyond the qualitative thermal-renormalization picture, and test it against temperature- and field-dependent tunneling spectroscopy; and (4) the device physics these barriers enable — as a brief, secondary outlook rather than a research program, note how device operation and switching dynamics in these vdW magnetic tunnel barriers follow from the spin-filter transport, and which single one of the further directions (spin-orbit-torque detection (torques on a magnetization exerted by spin currents generated by spin–orbit coupling), integration with topological insulators (materials with an insulating bulk and spin–momentum-locked conducting surfaces), superconductors and low-symmetry crystals, or probing bosonic topological phenomena in honeycomb ferromagnets) is most immediately testable. The account is to be confronted with the measured transport and spectroscopic data on the same devices and is to include the temperature- and field-dependent measurements that would test it; no new experiments are to be performed.

References

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