Effect of nickel substitution on magnetism in the layered van der Waals ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$

We have grown a series of nickel-substituted single crystals of the layered ferromagnet (FM) ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. The large single-crystalline samples of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ with $x=0–0.84$ were characterized with single-crystal x-ray diffraction, magnetic susceptibility, electrical resistance, and muon spin spectroscopy. We find Fe can be continuously substituted with Ni with only a minor structural variation. In addition, FM order is suppressed from $T_{\mathrm{C}}=212\mathrm{K}$ for $x=0$ down to $T_{\mathrm{C}}=50\mathrm{K}$ for $x=0.3$, which is accompanied by a strong suppression of saturated and effective moments, and Curie-Weiss temperature. Beyond $x=0.3$, the FM order is continuously smeared into a FM cluster-glass phase, with a nearly full magnetic volume fraction. We attribute the observed change in the nature of magnetic order to the intrinsically disordered structure of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and subsequent dilution effects from the Ni substitution.

Figure 1

(a) X-ray diffraction spectrum measured on a single crystal showing $\left(00L\right)$ diffraction peaks. Orange squares denote diffraction peaks from secondary phases and/or flux droplets on the surface of the crystal remnant postgrowth. (b) The structure of the end members, ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Ni}}_3{\mathrm{GeTe}}_2$. The shading of the spheres represents the occupancy of each site, for example, the Fe2 site in ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ has reported 0.85 site occupancy. (c) Ni substitution ($x$ WDS) determined by WDS vs the nominal Ni composition of the ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ crystals. The red line is a second-order polynomial fit to the data $[x_{\mathrm{WDS}}=1.64\left(5\right)x_{\mathrm{nominal}}-0.63\left(6\right)x_{\mathrm{nominal}}^2]$. Inset: A picture of a crucible-limited crystal of a crystal with $x_{\mathrm{WDS}}=0.16$. (d) $c$-lattice parameter vs Ni substitution inferred from $\left(00L\right)$ refinement (solid spheres) and from full single-crystal refinement (open squares). (e) Refined Fe/Ni site occupancy vs $x_{\mathrm{WDS}}$.

Figure 2

(a) Magnetic moment per Fe vs temperature measured on ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ along the $c$ axis at $H=10$ kOe for nickel substitution ranging between $x=0$ and $x=0.84$. (b) Magnetization isotherms measured at $T=2\mathrm{K}$ along the $c$ axis. The solid red lines are fits to Eq. (1). Inset: Blowup of the magnetization isotherms measured on the non-FM samples ($x=0.44–0.84$). (c) The inferred effective moment per Fe vs Ni substitution. (d) Inferred CW temperature vs Ni substitution. (e) Saturated magnetic moment per Fe vs Ni substitution. Open data points were determined from the fit Langevin equation described in Eq. (1). Inset: The average moment per cluster $\mu$ determined from the fitting the $M\left(H\right)$ data to Eq. (1).

Figure 3

(a) $M\left(T\right)/H$ measured at $H=20$ Oe for all compositions ($x=0–0.84$). The arrows correspond to the anomaly observed in the resistance measurement which indicates $T_{\text{C}}$ for the FM samples. Inset: Blowup of the low-temperature $M\left(T\right)/H$ curves for samples with $x=0.37–0.84$ on a semilog plot. (b) Normalized zero-field in-plane resistance vs temperature for the FM samples of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ with $x=0–0.3$ and of the non-FM $x=0.37$ sample. Inset: $dR/dT$ showing a clear anomaly at $T_{\text{C}}$ as marked by the arrows.

Figure 4

TF-$\mu \mathrm{SR}$ asymmetry $A\left(t\right)$ measured in a transverse eternal field $H=50$ Oe, of selected ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ crystals with $x=0$ (a), 0.3 (b), 0.56 (c), and 0.75 (d) below (blue open squares) and above (red open circles) $T_{\text{M}}$. The solid lines are fit the model described in Eq. (2).

Figure 5

(a) The muon relaxation $\lambda$ vs temperature extracted from TF-$\mu \mathrm{SR}$ asymmetry fit to the model in Eq. (2). (b) The magnetic volume fraction $f_{\text{M}}$ vs temperature calculated from the ratio of the paramagnetic and magnetic amplitudes. (c) The local magnetic field experienced by muons stopped at the PM region of the sample. Note the negative field shift down from $H_{\mathrm{ext}}=50$ Oe, which is apparent in all samples above the magnetic transition. The dashed lines indicate $T_{\text{M}}$ $\mu \mathrm{SR}$. Inset: Illustration of the fields sensed by the muons in proximity to a magnetic domain (pink) with a moment of $\mu$.

Figure 6

(a) Early-time TF-$\mu \mathrm{SR}$ asymmetry measured at the lowest $T$ for each sample, with a fit to the model in described in Eq. (2). The asymmetries were vertically stacked by 0.08 for clarity. (b) Static Gaussian field distribution width $\sigma$ at short times $\sigma$ obtained form the fit to Eq. (2) dominated by the early-time asymmetry.

Figure 7

The phase diagram of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{GeTe}}_2$ determined from magnetization and TF-$\mu \mathrm{SR}$ ($T_{\text{M}}$), and resistivity measurements ($T_{\text{C}}$), showing a FM region up to $x=0.3$ which is smeared into a FM spin glass. The violet open squares represent $T_{\mathrm{SRO}}$ which was determined from the minimum in the field at the muon site [Fig. 5]. The solid violet line denotes the fit of the magnetic ordering temperatures to a model described by Eq. (4). The dashed line reflects only the classical dilution effect of disorder $[a=0$ in Eq. (4)].