Fluctuating fractionalized spins in quasi-two-dimensional magnetic ${\mathrm{V}}_{0.85}\mathrm{P}{\mathrm{S}}_3$

Quantum spin liquid (QSL), a state characterized by exotic low energy fractionalized excitations and statistics, is still elusive experimentally and may be gauged via indirect experimental signatures. A remnant of the QSL phase may reflect in the spin dynamics as well as quanta of lattice vibrations, i.e., phonons, via the strong coupling of phonons with underlying fractionalized excitations. Inelastic light scattering (Raman) studies on ${\mathrm{V}}_{1–x}\mathrm{P}{\mathrm{S}}_3$ single crystals evidence the spin fractionalization into Majorana fermions deep into the paramagnetic phase reflected in the emergence of a low frequency quasielastic response, along with a broad magnetic continuum marked by a crossover temperature $T^{*}\sim 200$ K from a pure paramagnetic state to a fractionalized spin regime qualitatively gauged via dynamic Raman susceptibility. We found further evidence of anomalies in the phonons’ self-energy parameters, in particular, phonon line broadening and line asymmetry evolution at this crossover temperature, attributed to the decaying of phonons into itinerant Majorana fermions. This anomalous scattering response is thus indicative of fluctuating fractionalized spins suggesting a phase proximate to the quantum spin liquid state in this quasi-two-dimensional magnetic system.

Figure 1

Crystal structure of $\mathrm{VP}{\mathrm{S}}_3$ plotted using vesta as viewed along (a) an arbitrary direction, (b) the $a$ axis, (c) the $b$ axis, and (d) the $c$ axis; thick gray solid lines connecting the vanadium atoms represent a 2D honeycomb lattice formation. Red, blue, and green spheres represent vanadium, phosphorus, and sulphur, respectively.

Figure 2

(a) Temperature evolution of the Raman response ${\chi }^{\prime \prime }(\omega ,T)$ [measured raw Raman intensity/$1+n(\omega ,T)$]. The inset shows the phonons’ subtracted Raman response. Labels $\mathrm{P}1-\mathrm{P}15$ represent phonon modes. (b) Temperature dependence of the phonons’ subtracted Raman conductivity ${\chi }^{\prime \prime }(\omega ,T)/\omega$. (c) Temperature dependence of ${\chi }^{\mathrm{dyn}}\left(T\right)$ obtained from the Kramers-Kronig relation. The solid blue line is the power-law fit ${\chi }^{\mathrm{dyn}}\sim T^{\alpha }$. Background colored shading reflects different magnetic phases. (d) The main panel shows integrated raw spectra intensity in the energy range $1–\sim 95$ meV; the blue solid line shows fitting by a combined bosonic and fermionic function, $\left[a+b\left\{1+n({\omega }_b,T)\right\}\right]+c{\left\{1-f({\omega }_f,T)\right\}}^2$. Solid green and red lines show temperature dependence of bosonic and fermionic function. The inset shows the magnetic contribution to the Bose-corrected integrated intensity and $T^{*} (\sim 200$ K) represents the temperature where spin fractionalization starts building up. The pink solid line represents fitting by the two-fermion scattering function $a+b{\left[1-f(\omega ,T)\right]}^2$, where $f(\omega ,T)=1/[1+e^{\hslash {\omega }_f/k_{B}T}]$ is the Fermi distribution function.

Figure 3

(a,b) show the temperature evolution of the Bose-corrected spectra, i.e., Raman response ${\chi }^{\prime \prime }(\omega ,T)$ and Raman conductivity ${\chi }^{\prime \prime }(\omega ,T)/\omega$ in the low frequency region LFR $(1-9.0$ meV), respectively. (c) Temperature dependence of ${\chi }_{\mathrm{LFR}}^{\mathrm{dyn}}\left(T\right)$ obtained from the Kramers-Kronig relation. The solid blue line is the power-law fit ${\chi }_{\mathrm{LFR}}^{\mathrm{dyn}}\sim T^{\alpha }$. Background colored shading reflects different magnetic phases. $\left(\mathrm{d}-\mathrm{f}\right)$ Mode frequency evolution as a function of temperature for the modes P2, P4, P6, P7, P9, and P10. Red solid lines are a guide to the eye. $T^{*} (\sim 200$ K) represents the temperature where spin fractionalization starts building up.

Figure 4

(a) Shows the raw Raman spectrum in the frequency range of $\sim 45–360\mathrm{c}{\mathrm{m}}^{-1}$ showing the evolution of the asymmetry for the modes P2, P6, and P7. (b) Shows the evolution of the phonon modes P2, P6, and P7 (as the inset) normalized asymmetry gauged via slope. Background colored shading reflects different magnetic phases. $\left(\mathrm{c}-\mathrm{e}\right)$ show the linewidth for the modes P2, P4, P6, P7, P9, and P10. Red solid lines are a guide to the eye. $T^{*} (\sim 200$ K) represents the temperature where spin fractionalization starts building up.

Figure 5

(a) Resistivity as a function of temperature; inset shows $\ln \left(\rho \right)$ vs $1/T$. (b) Molar magnetic susceptibility ${\chi }_{\mathrm{mol}}$ in ZFC mode with $H\parallel ab$ plane and $H\parallel c$ axis along with the respective derivatives.

Figure 6

Raw spectra of bulk ${\mathrm{V}}_{0.85}\mathrm{P}{\mathrm{S}}_3$ along with peak labels at different temperatures within the spectral range of $5–760\mathrm{c}{\mathrm{m}}^{-1}$. Low frequency region (LFR) is shaded in purple.

Figure 7

Temperature-dependent evolution of features (frequency and FWHM) of the phonon modes. Some of the phonons were fitted with the anharmonic model as mentioned in the text indicated by solid red and blue lines which are a guide to the eye. Dotted vertical lines represent $T_N (\sim 60$ K) and crossover temperature $T^{*} \left(\sim 200\mathrm{K}\right)$.

Figure 8

Variation of the phonon self-energy parameter $A$ with phonon frequencies.