Relating spin-polarized STM imaging and inelastic neutron scattering in the van der Waals ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$

Van der Waals (vdW) ferromagnets have enabled the development of heterostructures assembled from exfoliated monolayers with spintronics functionalities, making it important to understand and ultimately tune their magnetic properties at the microscopic level. Information about the magnetic properties of these systems comes, so far, largely from macroscopic techniques, with little being known about the microscopic magnetic properties. Here, we combine spin-polarized scanning tunneling microscopy and quasiparticle interference imaging with neutron scattering to establish the magnetic and electronic properties of the metallic vdW ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. By imaging domain walls at the atomic scale, we can relate the domain wall width to the exchange interaction and magnetic anisotropy extracted from the magnon dispersion as measured in inelastic neutron scattering, with excellent agreement between the two techniques. From comparison with density functional theory calculations we can assign the quasiparticle interference to be dominated by spin-majority bands. We find a dimensional dichotomy of the bands at the Fermi energy: bands of minority character are predominantly two-dimensional in character, whereas the bands of majority character are three-dimensional. We expect that this will enable new design principles for spintronics devices.

Figure 1

Sample characterization. (a) Intensity of neutrons scattered at the atomic Bragg peak as a function of temperature. The signal will consist of the structural peak and the magnetic signal due to the ferromagnetic order. The red line represents a power-law fit to the data giving a ferromagnetic transition temperature of $215\mathrm{K}$. (b) Magnetization $M$ of the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ crystal used for the STM measurements. Zero-field-cooled (ZFC), field-cooled (FC), and field-warmed (FW) measurements are shown. The transition temperature $T_{\mathrm{c}}$ is found to be $T_{\mathrm{c}}=218\mathrm{K}$ and is extracted by fitting a Curie-Weiss law to the high temperature data. (c) A low-temperature magnetization $M$ vs. field $H$ loop recorded in the ferromagnetic phase. Inset: Close up of a $50\mathrm{mT}$ window around zero field. (d) TEM image of the layered structure of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. Inset: Side view of the crystal structure. (e) Schematic of the STM tunnel junction experimental setup. Inset: The ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ crystal structure. (f) A topographic STM image of the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ surface ($V_s=30\mathrm{mV}, I_s=1\mathrm{nA}$). Inset: Typical STS spectrum recorded on the surface of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ ($V_s=100\mathrm{mV}, I_s=1\mathrm{nA}$).

Figure 2

Identification of defects. (a) Top view of a $3\times 3$ supercell of a monolayer of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. (b) Simulated STM topography of the supercell in (a). (c) STM topography of a region of the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ surface containing no defects. (d) Top view of supercell in (a) with a Te atom removed. (e) Simulated STM topography of the supercell in (d). (f) STM topography of the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ surface, showing a Te-site defect. (g) Same supercell as in (a), with an Fe atom removed, corresponding to $y=0.14$ (i.e., ${\mathrm{Fe}}_{2.86}\mathrm{GeTe}2)$. (h) Simulated STM topography of the supercell in (g). (i) STM topography of the ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ surface, showing an Fe-site defect. STM images (c), (f), and (i) taken with $V_s=50\mathrm{mV}, I_s=50\mathrm{pA}$. Simulated images (b), (e), and (h) calculated for constant current and $V_s=100\mathrm{mV}$.

Figure 3

Magnon dispersion and magnetic imaging. (a) Inelastic neutron scattering measurement of the spin-wave dispersion of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ around $\mathbf{q}=(H,H,-2)$ for $H=-0.2...0.2$. The green line represents a parabolic fit to the data. The fit results in $J\approx 43\left(10\right)\mathrm{meV}$ and $K\approx 0.6\left(1\right)\mathrm{meV}$ (see main text for details). (b) A ferromagnetic domain wall imaged using spin-polarized STM ($V_s=100\mathrm{mV}, I_s=125\mathrm{pA}$). The domain wall runs diagonally through the image. (c) The same area as in (b) imaged with a spin-polarized tip with the opposite spin polarization from that used in (b) ($V_s=100\mathrm{mV}, I_s=125\mathrm{pA}$). (d) A line profile $z\left(x\right)$ taken through the difference of images (b) and (c) perpendicular to the domain wall. The red line shows the expected profile from the neutron scattering measurement. (e) The height difference $\mathrm{\Delta }z$ recorded between oppositely polarized areas as a function of applied bias voltage. (f) dI/dV spectra (blue curve) recorded on either side of the domain wall shown in (b) and (c) ($V_s=400\mathrm{mV}, I_s=250\mathrm{pA}, V_{\mathrm{mod}}=3\mathrm{mV}$). The spectroscopy set point was chosen at a bias voltage where the domain wall was not visible. The resulting spin polarization determined from the dI/dV spectra is also shown (red curve).

Figure 4

Quasiparticle interference imaging. (a)–(c) Six-fold symmetrized FFT of the differential conductance $\tilde{g}(\mathbf{q},V)$ and calculated constant energy contours, showing majority (red) and minority (blue) spin bands averaged over 16 $k_z$ values from 0 to $2\pi /c$, at (a) $0\mathrm{mV}$, (b) $-60\mathrm{mV}$, and (c) $-300\mathrm{mV}$. Corresponding scattering vectors are marked on the experimental data and band-structure calculation. (d) $\tilde{g}(\mathbf{q},V)$ as a function of bias $V$ for $\mathbf{q}$ along $\mathrm{\Gamma }$-K and $\mathrm{\Gamma }$-M taken from similar $\tilde{g}(\mathbf{q},V)$ measurements to (a)–(c), averaged between $q_x/q_y=\pm 0.378{\mathrm{nm}}^{-1}$ for $\mathrm{\Gamma }$-K/$\mathrm{\Gamma }$-M. Points fitted to the band dispersions along both directions are also plotted, with parabolic fits to the highest four energy points for each direction giving an average effective mass of $m^{*}=5.3\pm 0.8m_e$ ($\mathrm{\Gamma }$-M: $4.5m_e, \mathrm{\Gamma }$-K: $6.1m_e$). (e) Second derivative with respect to $\mathbf{q}$ of the differential conductance map, $\frac{{\partial }^2\tilde{g}(\mathbf{q},V)}{\partial q^2}$, as a function of bias for $\mathbf{q}$ along $\mathrm{\Gamma }$-K and $\mathrm{\Gamma }$-M. The $\tilde{g}(\mathbf{q},V)$ data were smoothed along the $\mathbf{q}$-direction with a window of $5.060{\mathrm{nm}}^{-1}$ before calculating the second derivative. (f) DFT calculation of the band structure of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, showing majority (red) and minority (blue) spin bands averaged over 16 $k_z$ values from 0 to $2\pi /c$.

Figure 5

Spin-polarized quasiparticle interference. (a) SP-STM image ($30\mathrm{mV}, 100\mathrm{pA}, 41\times 20{\mathrm{nm}}^2$) recorded with the tip polarized parallel to the sample by applying a $200\mathrm{mT}$ field along the sample $c$ axis. (b) Image of the same location with the same tip after the magnetization of the tip was reversed relative to the sample by applying a $200\mathrm{mT}$ field antiparallel to the sample $c$ axis. Slight differences in the topographic contrast can be observed. (c) The difference of (a) and (b). Subsurface Fe clusters become apparent in the difference image. (d) The quasiparticle interference pattern recorded at the Fermi level ($V=0\mathrm{V}$). (e) Difference of the Fourier transform of topographies ($V_{\mathrm{s}}=30\mathrm{mV}, I_{\mathrm{s}}=100\mathrm{pA}$) recorded with opposite relative tip and sample spin orientations. Red vectors show up more intensely when the magnetization of tip and sample are parallel, and blue regions when they are antiparallel with respect to each other, showing the different spin-character of the bands.