Chemical tuning of magnetic anisotropy and correlations in ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$

We report the temperature and composition dependence of static magnetic susceptibility and Raman spectroscopic measurements on van der Waals antiferromagnets ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$. The end members ${\mathrm{NiPS}}_3$ and ${\mathrm{FePS}}_3$ feature $XY$- and Ising-like magnetism, respectively, enabling chemical tuning of magnetic anisotropy and spin correlations. ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$ shows a turnover from the $XY$ to Ising anisotropy through $x\approx 0.1$. Although the $XY$ anisotropy is rapidly suppressed on introducing Fe content, two-magnon scattering evidences the slow repression of short-range magnetic correlations deep inside the Fe-rich side. Counterintuitively, the two-magnon signal undergoes less renormalization of its energy with increasing $x$ despite the larger spin number and enhanced classical magnetism. The disparate static and dynamic magnetic behaviors indicate the emergence of an exotic spin state in alloy van der Waals magnets.

Figure 1

Magnetic susceptibilities of ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$ as a function of temperature measured at an external field of 1 T parallel (red) and perpendicular (black line) to the $ab$ plane for (a) $x=0$, (b) $x=0.3$, (c) $x=0.42$, (d) $x=0.5$, (e) $x=0.8$, and (f) $x=1$. The vertical axes have the same scale for ease of comparison. The blue dashed lines mark the magnetic transition temperature $T_{\mathrm{N}}$. The inverse triangles on top of the maximum of the magnetic susceptibilities denote the short-range ordering temperature $T^{*}$. The inset in (a) is a zoom of the magnetic susceptibility.

Figure 2

First derivative of the magnetic susceptibility ($d\chi /dT$) with respect to temperature for (a) ${\mu }_{0}H\perp ab$ and (b) ${\mu }_{0}H\parallel ab$. (c) Néel temperature ($T_{\mathrm{N}}$) vs Fe concentration ($x$) determined by a peak of $d\chi /dT$. (d) Temperature and composition dependence of the magnetic anisotropy defined as a ratio of ${\chi }_{\perp }$ to ${\chi }_{\parallel }$.

Figure 3

Field-dependent magnetization of ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$ ($x=0$, 0.3, 0.42, 0.5, 0.8, and 1) for (a) ${\mu }_{0}H\perp ab$ and (b) ${\mu }_{0}H\parallel ab$. The temperature was fixed to $T=2$ K.

Figure 4

Raman spectra of ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$ ($x=0$, 0.3, 0.5, 0.8, and 1) at (a) $T=300$ K and (b) $T=10$ K measured in cross $\left(ab\right)$ polarization. $B_i$ ($i=1–5$) labels symmetry-allowed $B_g$ phonon modes. The asterisks denote forbidden $A_g$ modes, which become intense in the magnetically ordered state of Fe-rich samples. Three ${\mathrm{ZF}}_i$ ($i=1–3$) represent zone-folded phonons and M stands for one-magnon excitation.

Figure 5

Fe-substitution dependence of the phonon frequencies at 10 K. For the mixed samples, the $B_g$ phonons exhibit two- or three-mode behavior.

Figure 6

Normalized intensity of the 380 ${\mathrm{cm}}^{-1}{A}_g$ mode as a function of temperature and composition. The shaded gray area denotes the temperature interval, in which spin-dependent Raman scattering is observed. The solid lines are fits to the expression $I_{\mathrm{s}-\mathrm{RS}}\left(T\right)\sim {|A+B{[1-\left(\frac{T}{T_{\mathrm{N}}}\right)]}^{\gamma }|}^2$ as described in the text.

Figure 7

Temperature- and composition-dependent Raman spectra of ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x{\mathrm{PS}}_3$ for (a) $x=0$, (b) $x=0.3$, (c) $x=0.5$, (d) $x=0.8$, and (e) $x=1$ measured in ($ab$) polarization. (f)–(j) Contour plot of the two-magnon scattering intensity in the temperature-Raman-shift plane after subtracting phonon peaks. The horizontal dotted lines denote the Néel temperature $T_{{\mathrm{N}}^{*}}$ and short-range ordering temperatures $T^{*}$, which are identified from a thermal evolution of the low-energy cutoff and the peak energy.

Figure 8

(a) Normalized two-magnon energy vs normalized temperature for $x=0$, 0.3, 0.5, and 0.8. The vertical dashed line marks the Néel temperature. (b) $x$ dependence of the Néel temperature and short-range ordering temperatures $T_{\mathrm{N}}$ and $T^{*}$ determined by the static magnetic susceptibility $\chi \left(T\right)$ and $T_{{\mathrm{N}}^{*}}$ and $T^{*}$ by the two-magnon scattering. The two-magnon peak energy (black squares) is correlated with the thermal damping temperature of the two-magnon peak (red circles). (c) Ratio $T^{*}/T_{\mathrm{N}}$ extracted from the $\chi \left(T\right)$ and Raman data as a function of $x$.