Crystal growth and anisotropic magnetic properties of quasi-two-dimensional ${(\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$

We report the crystal growth by chemical vapor transport together with a thorough structural and magnetic characterization of the quasi-2D magnets ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ with $x_{\text{Ni}}=\text{0,}\text{0.3,}\text{0.5,}\text{0.7,}\text{0.9}$, and 1. As-grown crystals exhibit a layered morphology with weak van der Waals interactions between layers parallel to the crystallographic $ab$ plane of the monoclinic structure in the space group $C2/m$ (No. 12). Magnetization measurements reveal an antiferromagnetic ground state for all grown crystals. In the ordered state, the magnetization along different crystallographic directions is in agreement with an Ising anisotropy for $0\le x\le 0.9$ and only for ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ a different behavior is observed which is in line with an anisotropic Heisenberg or $XXZ$ model description. This striking abrupt change of anisotropy at a critical Ni concentration is coupled to a change in the width of the maximum in the magnetization around $T_{\text{max}}$. Furthermore, all intermediate compounds $0<x\le 0.9$ exhibit an anisotropic magnetization already in the paramagnetic state similar to the parent compound ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$.

Figure 1

As-grown single crystal of (a) ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (b) (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, and (c) ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$. An orange square in the background corresponds to $1\text{mm}\times 1\text{mm}$ for scale. Electron microscopy images of a (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystal in topographic mode (SE detector) in (d) and in chemical contrast mode (BSE detector) in (e).

Figure 2

Elemental maps and SEM(SE) image of a crystal of (a) ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ($x=0$), (b) (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ($x=0.3$), and (c) ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ($x=1$). The elemental maps are color coded based on the relative intensity of the characteristic x-ray K line. Brighter regions correspond to higher relative intensity.

Figure 3

Crystal structure of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$. Exemplary relative occupancies of the $T$ sites by Fe and Ni as well as the disorder ratio are according to the structural parameters obtained from scXRD for (${\mathrm{Fe}}_{0.3}{\mathrm{Ni}}_{0.7}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ (see Table 2). The site occupancies are reflected by spheres with different colored sections depending on the relative occupancies with white corresponding to an empty site, and brown, blue, and red to the elements according to the legend. Panel (a) shows the $bc$ plane, (b) shows the $ac$ plane, and (c) shows the $ab$ plane. Each ${\mathrm{S}}_6$ octahedron either hosts a transition metal atom or a ${\mathrm{P}}_2$ dumbbell in its center, as indicated by the yellow octahedron. Less than half of the occupied atomic sites correspond to the minority transition element $2a$ and P $8j$ sites.

Figure 4

$0kl$ section of reciprocal space measured by scXRD on (${\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ with (a) $x=0$, (b) $x=0.3$, (c) $x=0.5$, (d) $x=0.7$, (e) $x=0.9$, and (f) $x=1$. Significant streaking in $l$ direction (perpendicular to the $ab$ planes) is observable in (a), (d), and (f).

Figure 5

pXRD patterns of the members of the ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ substitution series from Cu $K_{\alpha 1}$ radiation ($\lambda =1.5406$ Å) in red and corresponding Le Bail fits in black. All patterns are normalized to the main reflection.

Figure 6

Evolution of the lattice parameters (top: $a$ and $b$; bottom: $c$ and $\beta$) of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ as function of the degree of Ni substitution. Squares correspond to the values extracted from scXRD and circles show the values extracted from pXRD by Le Bail fits. The dashed lines illustrate an ideal linear evolution based on the lattice parameters of ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ and ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ from pXRD. Error bars are smaller than the symbols.

Figure 7

Normalized magnetization as function of temperature $M{H}^{-1}\left(T\right)$ for a field of 1 T applied along three different crystallographic directions for (a) ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (b) (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (c) (${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (d) (${\mathrm{Fe}}_{0.3}{\mathrm{Ni}}_{0.7}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (e) (${\mathrm{Fe}}_{0.1}{\mathrm{Ni}}_{0.9}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, and (f) ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$. The $M{H}^{-1}$ axes have the same scale for best comparability. The insets in (e) and (f) show a zoomed-in view on the thermal evolution of $M{H}^{-1}$ of (${\mathrm{Fe}}_{0.1}{\mathrm{Ni}}_{0.9}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ and ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, respectively. The orange dotted lines indicate the Néel temperature $T_{\text{N}}$ for each compound. The green dashed lines in (a), (b), (c), (d), and (f) denote the isotropic temperature of the maximum of $M{H}^{-1}\left(T\right)T_{\text{max}}$. For (e) (${\mathrm{Fe}}_{0.1}{\mathrm{Ni}}_{0.9}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, $T_{\text{max}}$ is found to be anisotropic and accordingly the yellow line indicates $T_{\text{max}}$ for $\mathit{H}\parallel a$ and $\mathit{H}\parallel b$, while the turquoise line marks $T_{\text{max}}$ for $\mathit{H}\parallel c\text{*}$.

Figure 8

Evolution of the Néel temperature $T_{\text{N}}$ and the temperature of the maximum in $M{H}^{-1}\left(T\right)T_{\text{max}}$ as function of the degree of Ni substitution in ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ single crystals. The specific values of $T_{\text{N}}$ and $T_{\text{max}}$ are given in Table 3.

Figure 9

Field dependent magnetization $M\left(H\right)$ at 1.8 K for magnetic fields applied along three different crystallographic directions for (a) ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (b) (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (c) (${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (d) (${\mathrm{Fe}}_{0.3}{\mathrm{Ni}}_{0.7}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (e) (${\mathrm{Fe}}_{0.1}{\mathrm{Ni}}_{0.9}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, and (f) ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$. The $M$ axes have the same scale for best comparability. The inset in (f) shows a zoomed-in view on $M\left(H\right)$ of ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ demonstrating a nonlinear evolution of $M$ as function of ${\mu }_{0}H$ for $\mathit{H}\parallel a$.

Figure 10

First derivative of the thermal evolution of the normalized magnetization (as shown in Fig. 7) as function of $T$ for (a) ${\mathrm{Fe}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (b) (${\mathrm{Fe}}_{0.7}{\mathrm{Ni}}_{0.3}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (c) (${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (d) (${\mathrm{Fe}}_{0.3}{\mathrm{Ni}}_{0.7}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, (e) (${\mathrm{Fe}}_{0.1}{\mathrm{Ni}}_{0.9}{)}_2{\mathrm{P}}_2{\mathrm{S}}_6$, and (f) ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, for three different directions of an applied magnetic field of ${\mu }_{0}H=1$ T. Néel temperatures ($T_{\text{N}}$) and temperatures of the maximum in $M{H}^{-1}\left(T\right)$ ($T_{\text{max}}$) are marked by a dashed line and arrows, respectively.