${}^{31}\mathrm{P}$ NMR investigation of quasi-two-dimensional magnetic correlations in $T_2{\mathrm{P}}_2{\mathrm{S}}_6$ ($T$=Mn, Ni)

We report the anomalous breakdown in the scaling of the microscopic magnetic susceptibility—as measured via the ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) shift $K$—with the bulk magnetic susceptibility $\chi$ in the paramagnetic state of ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$. This anomaly occurs near $T_{\max }\sim 117$ K the maximum in $\chi \left(T\right)$ and is therefore associated with the onset of quasi-two-dimensional (quasi-2D) magnetic correlations. The spin-lattice relaxation rate divided by temperature ${\left(T_{1}T\right)}^{-1}$ in ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ exhibits broad peaklike behavior as a function of temperature, qualitatively following $\chi$, but displaying no evidence of critical slowing down above the Néel temperature $T_N$. In the magnetic state of ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, NMR spectra provide good evidence for ${60}^{\circ }$ rotation of stacking-fault-induced magnetic domains, as well as observation of the spin-flop transition that onsets at 4 T. The temperature-dependent critical behavior of the internal hyperfine field at the P site in ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ is consistent with previous measurements and the two-dimensional anisotropic Heisenberg model. In a sample of ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, we observe only two magnetically split resonances in the magnetic state, demonstrating that the multiple-peaked NMR spectra previously associated with ${60}^{\circ }$ rotation of stacking faults is sample-dependent. Finally, we report the observation of a spin-flop-induced splitting of the NMR spectra in ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$, with an onset spin-flop field of ${\mu }_0{H}_{\mathrm{sf}}=14$ T.

Figure 1

(a) Local environment of the magnetically inequivalent P sites in ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ [37]. Mn are shown in purple, S(1) in orange, S(2) in yellow, and P in pale pink. Black vectors represent the magnetic moments on the Mn sites [27], and blue vectors represent the calculated dipolar hyperfine field at the P sites due to the Mn magnetic moments [38]. (b) Optical microscope image of ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystal B on a mm grid.

Figure 2

${}^{31}\mathrm{P}$ NMR frequency spectra as a function of temperature from ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystal B for (left) $H_0\parallel c^{*}$ and (right) $H_0\perp c^{*}$ with nominal ${\mu }_0{H}_0=7$ T.

Figure 3

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ magnetic susceptibility $\chi$ (solid lines) and NMR shift ${}^{31}\mathrm{K}$ (markers) a function of temperature for (a) $H_0\parallel c^{*}$ and (b) $H_0\perp c^{*}$. The axes have been scaled to highlight the deviation from scaling below approximately 150 K and clearly outside of the experimental uncertainties below $T_{\max }$. The raw shift $K_{\mathrm{raw}}$ was extracted from Gaussian fits to the data in Fig. 2, with respect the ${}^{31}\mathrm{P}$ in 85% ${\mathrm{H}}_3{\mathrm{PO}}_4$ in water. The shift $K=K_{\mathrm{raw}}-K_d$, where $K_d$ is the contribution from bulk magnetic effects as discussed in the text. To convert the susceptibility to CGS units (${\text{cm}}^3\text{mol}{\text{Mn}}^{-1}$), divide by $4\pi \times {10}^{-6}$ [40].

Figure 4

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ NMR shift ${}^{31}\mathrm{K}$ as a function of out-of-plane angle $\theta$ (black circles), where $\theta =0^{\circ }$ indicates $H_0\parallel c^{*}$. The grey curve is a fit to Eq. (1) as described in the text, which yields the fit parameters $K_{c^{*}}=0.053\%\pm 0.002$% and $K_{ab}=0.098\%\pm 0.001$%. The raw shift $K_{\mathrm{raw}}$ (salmon hexagons) and the contribution from bulk magnetic effects $K_d$ (green diamonds) are shown for completeness.

Figure 5

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ NMR shift ${}^{31}\mathrm{K}$ as a function of magnetic susceptibility $\chi$ with temperature as an implicit parameter. Lines are fits to extract the hyperfine coupling $A$ and orbital shift $K_0$ as summarized in Table 1.

Figure 6

Full width at half maximum (FWHM) of the ${}^{31}\mathrm{P}$ resonances for ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ and ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ as a function of temperature in the paramagnetic state. ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ data are from Ref. [35] ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ data are from single-peak fits to the spectra in Fig. 2.

Figure 7

${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6{}^{31}\mathrm{P}$ NMR spectra offset by (a) out-of-plane angle $\theta$ ($\theta =0^{\circ }$ corresponds to $H_0\parallel c^{*}$) and (b) in-plane angle $\phi$ in the magnetic state at $T=70$ K ($\phi =0^{\circ }$, degrees does not correspond to a particular in-plane crystalline axes, see text for further discussion). (c) Resonance frequencies vs $\theta$ extracted from multi-peak fits to the spectra in (a). (d) Resonance frequencies vs $\phi$ extracted from (b) by the same method. (e) In-plane rotation resonance frequencies from (d) offset by $-{60}^{\circ }, 0^{\circ }$, and ${60}^{\circ }$. The markers/colors in (d) and (e) were chosen by hand to indicate the unique resonances.

Figure 8

Temperature dependence of the internal field $B_{\mathrm{int}}$ obtained from NMR spectra of ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ measured for $H_0\perp c^{*}$ in the magnetic state. The light purple line is the fit to Eq. (7) as described in the text. Error bars indicate $\sigma$ of the distribution of internal fields, uncertainties of peak value of $B_{\mathrm{int}}$ are smaller than the marker size.

Figure 9

Magnitude of the component of the internal magnetic field parallel to the applied external field as a function of ${\mu }_0{H}_0$, showing evidence of the spin-flop transition, which begins at (a) 14 T in the case of ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ with $H_0$ aligned approximately along $a$ and (b) 4 T in the case of ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ for $H_0$ aligned along approximately with $c^{*}$.

Figure 10

In-plane angular dependence of the ${}^{31}\mathrm{P}$ magnetic peak splitting $\mathrm{\Delta }f$ as a function of in-plane angle $\phi$ for ${\mathrm{Ni}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystal A at $T=150\pm 2$ K and ${\mu }_0{H}_0=5$ T. Open red circles represent experimental data and the blue curve is a fit to Eq. (3) to extract the internal field $B_{\mathrm{int}}$. The inset shows the raw frequency-swept spectra. Note that the magnet was in persistent mode for these measurements, and the field likely drifted enough to shift the spectra from one measurement to the next, but this has no effect on the splitting.

Figure 11

(a) ${\left(T_1\right)}^{-1}$ vs temperature from ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystal A. (b) Spin-lattice relaxation rate divided by temperature ${\left(T_{1}T\right)}^{-1}$ as a function of temperature for the same sample. The Néel temperature $T_N$ is marked with a dashed vertical line.

Figure 12

Parameters $T_{2g}^{-1}, T_{2^{\prime }}^{-1}$, and $B_{\mathrm{int}}$ extracted from fits to the echo-decay curves as a function of temperature for ${\mathrm{Mn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$. The inset shows an example echo-decay curve (crystal B, $H_0\perp c^{*}, T=295$ K).