Spin-liquid signatures in geometrically frustrated layered kagome compounds $\mathrm{YBa}{\mathrm{Co}}_{4-x}{\mathrm{Fe}}_x{\mathrm{O}}_{7+\delta }$

Experimental detection of spin dynamics of the quantum spin liquid phase, which occurs when the quantum fluctuations lead to fractionalized spin states, remains a challenge. In this paper, we illustrate spin-liquid signatures in the geometrically frustrated layered kagome system $\mathrm{YBa}{\mathrm{Co}}_{4-x}{\mathrm{Fe}}_x{\mathrm{O}}_{7+\delta }$ ($x=0$ and $x=0.6$) over a wide temperature range using micro-Raman spectroscopy. The thermal response of the gapped broad band over a high temperature range possibly marks a spin liquid phase in this system. We report the appearance of sharp spectral features in the high temperature regime with unusual thermal behavior for $\mathrm{YBa}{\mathrm{Co}}_{4-x}{\mathrm{Fe}}_x{\mathrm{O}}_{7+\delta }$ ($x=0.6$). Besides, atypical oscillation of a phonon mode frequency with temperature suggests an unconventional electron-lattice coupling in the doped compound via a strong correlation between their lattice vibration and magnetic spin dynamics.

Figure 1

(a) The layered crystal structure of $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_7$. The atomic arrangements within the individual kagome and triangular lattice planes are shown. (b) The Rietveld refined x-ray diffraction patterns of compounds $\mathrm{YBa}{\mathrm{Co}}_{4-x}{\mathrm{Fe}}_x{\mathrm{O}}_{7+\delta }$ ($x=0$ and 0.6) are measured at room temperature. The experimental and calculated patterns are shown by the open circles and solid red lines, respectively. The difference patterns are shown by the solid blue line at the bottom of each panel. The green bars correspond to the positions of the diffraction peaks for the phase $P31c$.

Figure 2

Raman spectra of $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ (black) and $\mathrm{YBa}{\mathrm{Co}}_{3.6}{\mathrm{Fe}}_{0.4}{\mathrm{O}}_7$ (maroon) at 80 K over the spectral range $50–1000\mathrm{c}{\mathrm{m}}^{-1}$. Calculated Γ point phonon modes of $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_7$ for the space group $P31c$ and $P{6}_{3}mc$ are shown by black and blue bars in the lower part of the figure.

Figure 3

Characteristic Raman response $\left({\chi }^{\prime \prime }\right)$ of (a) $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ and (b) $\mathrm{YBa}{\mathrm{Co}}_{3.4}{\mathrm{Fe}}_{0.6}{\mathrm{O}}_{7+\delta }$ recorded between 80 and 300 K over the spectral range $250–850\mathrm{c}{\mathrm{m}}^{–1}$. (c) The same over the temperature range 220–280 K of the doped compound.

Figure 4

The variation in the integral Raman response of the broad Raman band between 80 and 300 K for $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ (filled green circles) and $\mathrm{YBa}{\mathrm{Co}}_{3.4}{\mathrm{Fe}}_{0.6}{\mathrm{O}}_{7+\delta }$ (dark yellow diamonds). The linear fit to the data points in the low temperature regime is shown by solid lines. To estimate the error bar to the intensity of the broad band, first the sharp Raman peaks are removed manually from the spectra. The normalized difference between the integral intensity of the upper and lower envelope of the broad band at each temperature is taken as the error to intensity of the broad band. The estimated error bars of the data points are within the size of the symbols.

Figure 5

(a) Raman response in $\mathrm{YBa}{\mathrm{Co}}_{3.4}{\mathrm{Fe}}_{0.6}{\mathrm{O}}_7$ at 245 K. The deconvoluted components ($X1$–$X10$) are shown by the black solid lines. The net fitted spectrum is shown by the red solid line. (b) The evolution of the peak positions of $X1–X10$ modes with temperature. The error bars are the standard deviation of the peak positions as obtained from the fitting procedure. The solid lines are a guide to the eyes.

Figure 6

Variation of ${\omega }_{\mathrm{F}}$ (filled circles) and Γ (open triangles) with temperature for (a) $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$, and $\mathrm{YBa}{\mathrm{Co}}_{3.4}{\mathrm{Fe}}_{0.6}{\mathrm{O}}_{7+\delta }$, respectively. The error bar to each data point is the standard deviation of the ${\omega }_{\mathrm{F}}$ as obtained from the fitting procedure. The solid lines are the best fit to the data points as per the equations described in the text. Panels (c) and (d) present the zoomed view of ${\omega }_{\mathrm{F}}$ vs $T$ plot over the temperature range 80–200 K in $\mathrm{YBa}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ and $\mathrm{YBa}{\mathrm{Co}}_{3.4}{\mathrm{Fe}}_{0.6}{\mathrm{O}}_{7+\delta }$, respectively. The solid lines are a guide to the eyes. The value of Δ$T$ is the average thermal periodicity of ${\omega }_{\mathrm{F}}$, as measured between two successive crests and troughs in each panel. (e) The variation of the Fano asymmetry parameter of the peak $P1$ with temperature.