Giant orbital Zeeman effects in a magnetic topological van der Waals interphase

TL;DR

The paper addresses how a magnetic topological van der Waals interphase at a graphene/Fe$_3$GeTe$_2$ interface hosts giant orbital Zeeman effects that cannot be explained by spin Zeeman physics alone. Using scanning tunneling spectroscopy through graphene's inelastic gap, complemented by density functional theory and electrostatic modeling, the authors identify two coupled orbital contributions: band orbital moments (BOM) near the topological gap and canting-induced chiral orbital moments (COM). They report effective g-factors up to $g \approx 230$ and show that the interfacial dipole, tunable by electrostatic gating, controls the magnitude of these effects. The findings demonstrate a gate-tunable vdW interphase where topology, magnetism, and interface electric fields coherently shape the electronic response, with potential implications for chiral orbitronics and interfacial spintronics.

Abstract

Van der Waals (vdW) heterostructures allow the engineering of electronic and magnetic properties by the stacking different two-dimensional vdW materials. For example, orbital hybridisation and charge transfer at a vdW interface may result in electric fields across the interface that give rise to Rashba spin-orbit coupling. In magnetic vdW heterostructures, this in turn can drive the Dzyaloshinskii-Moriya interaction which leads to a canting of local magnetic moments at the vdW interface and may thus stabilise novel 2D magnetic phases. While such emergent magnetic "interphases" offer a promising platform for spin-based electronics, direct spectroscopic evidence for them is still lacking. Here, we report Zeeman effects with Landé $g$-factors up to $\approx230$ at the interface of graphene and the vdW ferromagnet Fe$_3$GeTe$_2$. They arise from a magnetic interphase in which local-moment canting and itinerant orbital moments generated by the non-trivial band topology of Fe$_3$GeTe$_2$ conspire to cause a giant asymmetric level splitting when a magnetic field is applied. Exploiting the inelastic phonon gap of graphene, we can directly access the buried vdW interface to the Fe$_3$GeTe$_2$ by scanning tunnelling spectroscopy. Systematically analyzing the Faraday-like screening of the tip electric field by the graphene, we demonstrate the tunability of the constitutional interface dipole, as well as the Zeeman effect, by tip gating. Our findings are supported by density functional theory and electrostatic modelling.

Figures (16)

• Figure 1: Orbital moments in Fe$_3$GeTe$_2$ and scanning tunnelling microscopy experiment of the graphene/Fe$_3$GeTe$_2$ heterostructure.(a) Top view of the monolayer Fe$_3$GeTe$_2$ unit cell, highlighting the two inequivalent Fe sites. (b) First Brillouin zone of Fe$_3$GeTe$_2$ with indicated symmetry points and lines. (c) Spin-resolved band structure of bulk Fe$_3$GeTe$_2$, calculated by density functional theory including spin-orbit coupling, with color-coded majority (red) and minority (blue) bands. Near $\Gamma$ only dispersive bands cross the Fermi energy $E_{\rm F}$, while at K/K' several band extrema are located close to $E_{\rm F}$. (d) Zoom into the shaded region in panel c, calculated without (left) and with (right) spin-orbit coupling. The latter calculation shows out-of-plane orbital magnetic moments $m_{z}^\mathrm{BO}$ near the K/K' points. (e) Optical micrograph of a graphene/Fe$_3$GeTe$_2$ heterostructure. Outlines of the respective flakes are indicated. (f) Schematic side view of the heterostructure and the scanning tunnelling microscopy setup. There are two parallel tunnelling channels, from the tip to graphene (black arrow) and to Fe$_3$GeTe$_2$ (orange arrow). The tip-sample distance $h$ and graphene-Fe$_3$GeTe$_2$ distance $d$ are indicated. $V_{\rm s}$ is the sample bias and $I_{\rm t}$ the tunnelling current. At the graphene/Fe$_3$GeTe$_2$ vdW interface, a charge transfer dipole gives rise to an internal electric field $\vec{ {E}_\mathrm{FGT}}$, which results in a canting of the Fe spins at the interface (indicated by the red arrows at the Fe-II sites), due to the Rashba effect and Dzyaloshinskii–Moriya interaction (see main text for details). (g) Schematic of non-collinear spin arrangement in the Fe-I sublattice, where a canting of localized spins $\vec{S}_i$ results in a conical spin structure. The ensuing scalar spin chirality gives rise to a chiral orbital moment $m_z^\mathrm{CO}\sim \vec{S}_1\cdot(\vec{S}_2\times \vec{S}_3)$shindou2001orbitaltatara2003quantumbulaevskii2008electronicdos2016chirality.
• Figure 2: Tunnelling through the inelastic gap of graphene.(a) STM topography of the graphene/Fe$_3$GeTe$_2$ heterostructure surface ($V_\mathrm{s}=-50\,\rm mV$, $I_\mathrm{t}=70\,\rm pA$), simultaneously revealing atomic resolution of the graphene lattice and a longer-range modulation stemming from the partial occupancy of the Fe-II sites in Fe$_3$GeTe$_2$. Inset: Zoom into the graphene lattice (scan size $2.5\rm\,nm$). (b) Fourier transform of the topography in panel a. The hexagonal patterns of graphene (black circles), Fe$_3$GeTe$_2$ (orange circles), and their moiré pattern (red circles) are clearly visible. (c) Spatially averaged tunnelling spectrum of the heterostructure (blue solid line, $V_\mathrm{s}=500\,\rm mV$, $I_\mathrm{t}=200\,\rm pA$). Below the inelastic threshold, i.e., for $|eV_\mathrm{s}|<\hbar \omega$ where $\omega$ is a typical phonon frequency of graphene, an inelastic tunnelling gap is observed (vertical dotted lines), while outside this range the linear dispersion of the graphene Dirac cone is visible. Within the inelastic gap, a significant conductivity is measured, in contrast to the findings for graphene/hBN heterostructures (grey dashed line, data from Ref. decker2011local). The graphene is close to charge neutrality in both cases. For better comparison, both data sets are normalized at $eV_{\rm s}=-500\rm\,meV$. (d) Schematic diagram of the tunnelling processes. With its gapless spectrum, Fe$_3$GeTe$_2$ dominates the tunnelling current within the inelastic gap of the graphene.
• Figure 3: Giant orbital Zeeman effects at the graphene/Fe$_3$GeTe$_2$ interface.(a) Tunnelling spectra (differential conductance in arbitrary units) for different out-of-plane $B$ fields (normal to surface). For clarity, curves are offset by 0.2 arb. units each. In the inelastic gap of graphene (shaded region), two peaks emerge with increasing $B$ field, as indicated by arrows and symbols. Tip stabilization parameters: $V_{\rm s}=300\rm\,mV$ and $I_{\rm t}=1\rm\,nA$. (b) Zoom into the inelastic-gap region, revealing both a continuous increase of the two peaks' intensities and shifts to higher energy as a function of applied $B$ field. Curves are offset by 0.2 arb. units each. Dashed arrows are guides to the eye. Tip stabilization parameters: $V_{\rm s}=50\rm\,mV$ and $I_{\rm t}=0.5\rm\,nA$. (c) Symbols: Peak positions (horizontal axis) as function of applied $B$ field (vertical axis). The solid lines are linear fits, yielding effective Landé $g$-factors $g_1\approx30$ (circles) and $g_2\approx230$ (squares). Inset: Schematic decomposition of the observed peak shifts into a splitting and a shifting contribution. The former arises from the band orbital moments (BOM) induced by the topological nodal line gap, while the latter has its origin in the chiral orbital moments (COM) induced by spin canting. For more details, see main text.
• Figure 4: Tuning the orbital Zeeman effects at the graphene/Fe$_3$GeTe$_2$ interface by electric fields.(a) Differential conductance spectra (in arbitrary units) for different tunnelling setpoints. The inelastic gap is cut out, and the curves for different setpoints are offset vertically for clarity. The Dirac point energy $E_{\rm D}$ (black dots) is extracted from the crossing points of line fits to the linear graphene spectrum above/below the vertical dashed lines, revealing a shift to higher values as the setpoint is increased. The dashed arrow is a guide to the eye. Remnant features due to Fe$_3$GeTe$_2$ near the edge of the inelastic gap do not shift with setpoint, as indicated by red dotted lines. The tip stabilization voltage was $V_\mathrm{s}=150\rm\,mV$ for all setpoints. (b) Dirac point energies $E_{\rm D}$ (filled circles, extracted from panel (a)) plotted as function of the change in tip-sample distance $\delta h$ (see upper inset). Error bars are propagated from the fits of the Dirac spectrum in panel (a). The red curve is a fit to the data points, using the capacitor model in the lower inset (Eqs. \ref{['eq:ngr']} and \ref{['eq:E_D']} in the Methods section). (c) Differential conductance spectra (in arbitrary units) of the Fe$_3$GeTe$_2$-derived peaks in the inelastic gap of graphene for different tunnelling setpoints (curves are vertically offset for clarity. All spectra are recorded at a fixed external field of $B=2\rm\,T$. (d) Energy positions of the peaks in panel c as a function of setpoint current (Extended Data Fig. \ref{['Fig-SI-peak-extraction2']}).
• Figure S1: Fourier-filtered topography of graphene, Fe$_3$GeTe$_2$ and their moiré lattice.(a) STM topography (constant-current image at $V_\mathrm{s}=-50\,\rm mV$, $I_\mathrm{t}=70\,\rm pA$), measured on the heterostructure shown in Fig. \ref{['Fig2']}a (b) Fourier-filtered graphene lattice. (c) Fourier-filtered Fe$_3$GeTe$_2$ lattice. (d) Fourier-filtered moiré lattice. The images in panels b to d were generated by inverse FFT of the Fourier transform image of panel a, selecting only the corresponding spots, as marked by the black, orange and red circles in Fig. \ref{['Fig2']}b, respectively.