Evolution of the spin dynamics in the van der Waals system $M_2{\mathrm{P}}_2{\mathrm{S}}_6$ ($M_2=\mathrm{Mn}{}_2$, MnNi, ${\mathrm{Ni}}_2$) series probed by electron spin resonance spectroscopy

In this paper we report a detailed ESR spectroscopic study of the single-crystalline samples of the van der Waals compounds ${\mathit{M}}_{\text{2}}{\mathrm{P}}_{\text{2}}{\mathrm{S}}_{\text{6}}$ (${\mathit{M}}_{\text{2}}={\mathrm{Mn}}_{\text{2}}$, MnNi, ${\mathrm{Ni}}_{\text{2}}$), performed at an excitation frequency of 9.56 GHz, in a broad range of temperatures above the magnetic order, and at different orientations of the magnetic field with respect to the sample. Analyzing temperature and angular dependencies of the resonance field and of the linewidth of the ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ compound we have observed a significant change of the spin dynamics from the dominance of the 3D-like fluctuations close to the magnetic order to a relative increase of the 2D-like spin fluctuations at higher temperatures. Such a behavior, which is opposite to the development of the low-D signatures in the previously studied ${\mathrm{Cr}}_{\text{2}}{\mathrm{Ge}}_{\text{2}}{\mathrm{Te}}_{\text{6}}$ compound, can be explained by the difference in the type of magnetic order in ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ and ${\mathrm{Cr}}_{\text{2}}{\mathrm{Ge}}_{\text{2}}{\mathrm{Te}}_{\text{6}}$. On the other hand, ${\mathrm{MnNiP}}_2{\mathrm{S}}_6$ compound exhibits angular dependencies of the linewidth typical for the system with 3D-like spin correlations in the whole measurement temperature range, however the 2D-like correlations can be seen in the temperature dependencies of the resonance field and the linewidth. ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, in turn, does not show any 2D signatures. This suggests that varying the Ni content in ${\left({\mathrm{Mn}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{P}}_2{\mathrm{S}}_6$ one can control the exchange interaction, possibly also in the third dimension.

Figure 1

Temperature dependence of the ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ESR spectra at a fixed excitation frequency $\nu =9.56\mathrm{GHz}$ for $\mathbf{H}\parallel ab$ plane (a) and $\mathbf{H}\perp ab$ plane (b).

Figure 2

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$: Temperature dependence of the linewidth at $\nu =9.56\mathrm{GHz}$ for $\mathbf{H}\parallel ab$ plane (closed circles) and $\mathbf{H}\perp ab$ plane (closed squares). The respective temperature dependence of the resonance field is shown in the inset. Differently colored temperature ranges indicate four regimes of the spin dynamics discussed in Sec. 4a.

Figure 3

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$: Angular dependence of the linewidth at $\nu =9.56\mathrm{GHz}$ at four different temperatures: 80 K, 100 K, 200 K, and 300 K. Solid-red lines are fits to the data as described in the text.

Figure 4

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$: Angular dependence of the resonance field $H_{\mathrm{res}}$ at $\nu =9.56\mathrm{GHz}$ at four different temperatures: 80 K, 100 K, 200 K, and 300 K. Dashed-red lines are fits to the data as described in the text.

Figure 5

Temperature dependence of the ${\mathrm{MnNiP}}_2{\mathrm{S}}_6$ ESR signal at a fixed excitation frequency $\nu =9.56\mathrm{GHz}$ for $\mathbf{H}\parallel ab$ plane (a) and $\mathbf{H}\perp ab$ plane (b).

Figure 6

${\mathrm{MnNiP}}_2{\mathrm{S}}_6$: Temperature dependence of the linewidth at $\nu =9.56\mathrm{GHz}$ for $\mathbf{H}\parallel ab$ plane (blue circles) and $\mathbf{H}\perp ab$ plane (red squares). The respective temperature dependence of the resonance field is shown in the inset.

Figure 7

${\mathrm{MnNiP}}_2{\mathrm{S}}_6$: Angular dependence of the linewidth at $\nu =9.56\mathrm{GHz}$ at four temperatures: 80 K, 100 K, 200 K, and 300 K. Solid-red lines are fits to the data as described in the text.

Figure 8

${\mathrm{MnNiP}}_2{\mathrm{S}}_6$: Angular dependence of the resonance field $H_{\mathrm{res}}$ at $\nu =9.56\mathrm{GHz}$ at four different temperatures: 80 K, 100 K, 200 K, and 300 K. Dashed-red lines are fits to the data as described in the text.

Figure 9

${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$: (a) Temperature dependence of the ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ESR signal at a fixed excitation frequency $\nu =9.56\mathrm{GHz}$ for H $\left|\right|$ $\mathit{ab}$ plane orientation. Dashed-red lines are the fits using the function described in Eq. (1). (b) Temperature dependence of the linewidth at $\nu =9.56\mathrm{GHz}$ for $\mathbf{H}\parallel ab$ plane (blue circles) and $\mathbf{H}\perp ab$ plane (red squares).