Muon spin relaxation study of spin dynamics in the extended kagome systems ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7+\delta } (\delta =0,0.1)$

We present muon spin relaxation ($\mu \mathrm{SR}$) measurements of the extended kagome systems ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7+\delta }$ ($\delta =0,0.1$), comprising two interpenetrating kagome sublattice of $\mathrm{Co}{\left(\mathrm{I}\right)}^{3+}$ ($S=3/2$) and a triangle sublattice of $\mathrm{Co}{\left(\mathrm{II}\right)}^{2+}$ ($S=2$). The zero- and longitudinal-field $\mu \mathrm{SR}$ spectra of the stoichiometric compound ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ unveil that the triangular subsystem orders at $T_N=101$ K. In contrast, the muon spin relaxation rate pertaining to the kagome subsystem shows persistent spin dynamics down to $T=20$ K and then a sublinear decrease $\lambda \left(T\right)\sim T^{0.66\left(5\right)}$ on cooling towards $T=4$ K. In addition, the introduction of interstitial oxygen ($\delta =0.1$) is found to drastically affect the magnetism. For the fast-cooling experiment ($>10$ K/min), ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ enters a regime characterized by persistent spin dynamics below 90 K. For the slow-cooling experiment (1 K/min), evidence is obtained for the phase separation into interstitial oxygen-poor and oxygen-rich regions with distinct correlation times. The observed temperature, cooling rate, and oxygen content dependencies of spin dynamics are discussed in terms of a broad range of spin-spin correlation times, relying on a different degree of frustration between the kagome and triangle sublattices as well as of oxygen migration.

Figure 1

(a) Sketch of the spin topology in the stoichiometric material ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$. Orange and blue spheres represent two inequivalent Co atoms arranged on the triangular (solid orange lines) and kagome layers (solid blue lines). There are three crystallographically different oxygen sites (red small spheres) in the lattice. (b) Crystal structure of the oxygen-excess material ${\mathrm{YBaCo}}_4{\mathrm{O}}_8$. The cyan and light green spheres indicate the edge-sharing octahedral Co sites in the triangular and kagome planes, respectively. Introducing interstitial oxygen atoms leads to a conversion of the oxygen tetrahedra into octahedra.

Figure 2

(a) ZF- and (b) LF-$\mu \mathrm{SR}$ spectra of ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ at various temperatures. The temperature-dependent LF-$\mu \mathrm{SR}$ spectra were recorded in a 2000 G longitudinal field to decouple the contribution of static field. LF-$\mu \mathrm{SR}$ spectra of ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ measured at constant temperatures (c) $T=2$ K and (d) $T=30$ K in a magnetic field $H=0–4000$ G. The solid lines represent fits of the data as described in the text.

Figure 3

(a) Temperature dependence of the initial asymmetry of ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ extracted from the ZF- (full circles) and LF-$\mu \mathrm{SR}$ (open squares) spectra. (b) Temperature dependence of the stretching exponent and the slow relaxing fraction of the sample obtained from the ZF data. (c) Temperature dependence of the slow muon spin-relaxation rate ${\lambda }_s$ for the ZF data (full circles) and the muon relaxation rate ${\lambda }_{\mathrm{LF}}$ for the LF data (open squares). The solid curve is a fit to a power law ${\lambda }_s\left(T\right)\sim T^{0.66\left(5\right)}$. (d) Temperature dependence of the fast muon spin-relaxation rate ${\lambda }_f$ taken from the ZF-$\mu \mathrm{SR}$ spectra. The shaded bars denote the magnetic transition temperature.

Figure 4

Temperature dependence of the $\mu \mathrm{SR}$ spectra taken at TRIUMF for ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ at various temperatures following (a) fast cooling ($>10$ K/min) from 290 to 1.55 K and (b) slow cooling (1 K/min) from 290 to 2.2 K. LF-$\mu \mathrm{SR}$ spectra of ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ measured at $T=2$ K on (c) fast cooling and (d) slow cooling in a magnetic field $H=0–2000$ G. The solid lines represent fits of the data as described in the text.

Figure 5

(a) Temperature dependence of the normalized initial asymmetry of ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ extracted from the $\mu \mathrm{SR}$ spectra. (b) Muon relaxation rate ${\lambda }_f$ and (c) ${\lambda }_s$ of ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ as a function of temperature, obtained from the $\mu \mathrm{SR}$ spectra. (d) Temperature dependence of the fast relaxing fraction of the sample. The inset shows the change of the exponent with temperature.

Figure 6

Field dependence of the longitudinal relaxation rate of ${\mathrm{YBaCo}}_4{\mathrm{O}}_7$ measured at $T=2$ K (full triangles) and 30 K (inverse full triangles) and ${\mathrm{YBaCo}}_4{\mathrm{O}}_{7.1}$ recorded at $T=2$ K in the fast (full squares) and slow (open squares) cooling processes. An external field is plotted in a logarithmic scale.