Magnetic excitations in the quasi-two-dimensional ferromagnet ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ measured with inelastic neutron scattering

${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ is an itinerant ferromagnet composed of two-dimensional layers weakly connected by van der Waals bonding that shows a variety of intriguing phenomena. Inelastic neutron scattering measurements on bulk single crystals of ${\mathrm{Fe}}_{2.75}{\mathrm{GeTe}}_2$ were performed to quantify the magnetic exchange interaction energies and anisotropy. The observed inelastic excitations, which extend to a maximum energy of $\sim 75$ meV, are indicative of dominant in-plane correlations with negligible magnetic interactions between the layers. A spin gap of 3.7 meV is observed, allowing a measure of the magnetic anisotropy. The excitations are damped, reflective of both the magnetic site occupancy reduction of 25% on one Fe sublattice and the itinerant interactions. A minimal model is employed to describe the excitation spectra and extract magnetic exchange interaction values. The temperature evolution of the excitations are probed and correlations shown to persist above $T_c$, further supporting the low-dimensional nature of the magnetism.

Figure 1

(a) Structural/magnetic unit cell of ${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$. Arrows indicate the magnetic moments on the Fe ions. The nearest neighbor Fe1-Fe1 ($J_1$) (red) and next nearest neighbor Fe1-Fe2 ($J_2$) (blue) interactions are shown. (b) The qausi-2D layered structure is highlighted. (c) Top-down view of the hexagonally arranged magnetic Fe ions in the $ab$ plane. (d) ${\mathrm{Fe}}_{2.75}{\mathrm{GeTe}}_2$ flux grown single crystals.

Figure 2

(a) INS measurements with $E_i=120\mathrm{meV}$ that captured the full range of observable magnetic excitations. The slice covers $-0.1\le K\le 0.1$ and $10\le L\le 10$ r.l.u. (b) Constant energy cuts at 60, 70, 80, 90 and 100 meV, with an energy range of $\pm 5$ meV. Cuts covers $-0.1\le K\le 0.1$ and $-10\le L\le 10$ r.l.u. (c) Inelastic scattering in the $\left(H0L\right)$ plane at 6 meV, $\pm 2$ meV and $-0.1\le K\le 0.1$ r.l.u., and (d) 50 meV, $\pm 5$ meV and $-0.15\le K\le 0.15$ r.l.u. (e)–(h) Inelastic scattering in the $(HH,K-K)$ plane at constant energies of 10, 30, 40, and 65 meV, with an energy range of $\pm 5$ meV and $-10\le L\le 10$ r.l.u. All measurements were performed at 10 K.

Figure 3

(a) INS measurements with $E_i=10$ meV around the magnetic zone center. The ranges were $-2\le L\le 2$ r.l.u., $-0.075\le K\le 0.075$ r.l.u. (b) Cut through the magnetic zone center of $(0,0,0)$ at low energy (circles) compared to model calculations (line) to define the spin-gap energy of 3.7(2) meV. The ranges were $-2\le L\le 2$ r.l.u., $-0.075\le H\le 0.075$ r.l.u., and $-0.075\le K\le 0.075$ r.l.u..

Figure 4

Comparison of INS data with a spin wave model. (a) Constant energy data with $E_i=50$ meV (circles) compared to the model (solid lines). The dotted lines show the background. (b) Energy dispersion from $E_i=50$ meV and (c) $E_i=120$ meV compared to model simulations. (d) Data and (e) model of a constant energy slice of 60 meV in the $(H,K)$ plane.

Figure 5

Temperature dependence of inelastic scattering centered at 15 meV in the range 13.5 to 16.5 meV for (a) 10 K, (b) 160 K, and (c) 295 K. (d) Cut through $(H,H)=0$ in the range $-0.05$ to $0.05$ r.l.u. and over the $L$ range $-3$ to 3 r.l.u. All the data shown have been corrected with the Bose factor. Incident energy was $E_i=30\mathrm{meV}$.