Magnetic field dependence of muon spin relaxation in geometrically frustrated ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

Muon spin relaxation has been investigated in the geometrically frustrated antiferromagnet ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a function of magnetic field and temperature. Well above the magnetic ordering temperature of $T_c=1\mathrm{K}$, the field dependence of the muon spin relaxation rate $\left(T_1^{-1}\right)$ originates from field-induced changes in the spectral density of Gd fluctuations. This allows one to determine both the autocorrelation time and magnitude of the fluctuating local magnetic field at the muon. Well below $T_c$ a coherent precession signal is observed, corresponding to a much smaller quasistatic local magnetic field. At low temperatures $T_1^{-1}$ levels off, at a constant value which is much larger than reported recently for a single crystal of ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ [Yaouanc et al., Phys. Rev. Lett. 95, 047203 (2005)]. A magnetic field of $2\mathrm{T}$ completely quenches the low-temperature spin relaxation in the present sample. These results indicate that the ordered state is characterized by low-frequency dynamics which are most likely due to residual crystalline disorder.

Figure 1

Time evolution of the muon spin polarization in ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in a longitudinally applied field of $0.005\mathrm{T}$ at $T=2$ and $0.05\mathrm{K}$ (open squares and filled circles, respectively). The inset shows the behavior at early times on the same vertical scale.

Figure 2

Spin relaxation rate in ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a function of temperature in longitudinally applied magnetic fields of $5\mathrm{mT}$ (filled squares) and $4\mathrm{T}$ (open circles).

Figure 3

Spin relaxation rates $T_1^{-1}$ in ${\mathrm{Gd}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a function of longitudinal magnetic field at 100, 7.5, and $0.1\mathrm{K}$ (see the inset). Note the logarithmic scale on the inset. The solid line is a guide to the eye.