Possible Quantum Diffusion of Polaronic Muons in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathbf{O}}_7$ Spin Ice

We interpret recent measurements of the zero field muon relaxation rate in the magnetic pyrochlore ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as resulting from the quantum diffusion of muons in the material. In this scenario, the plateau observed at low temperature ($<7\mathrm{K}$) in the relaxation rate is due to coherent tunneling of muons through a spatially disordered spin state and not to any magnetic fluctuations persisting at low temperature. Two further regimes either side of a maximum relaxation rate at $T^{*}=50\mathrm{K}$ correspond to a crossover between tunneling and incoherent activated hopping motion of the muon. Our fit of the experimental data is compared with the case of muonium diffusion in KCl.

Figure 1

Comparison of the diffusion rate (inverse correlation time) ${\tau }_d^{-1}$ of (a) DTO extracted from the data of Ref. 1 by using ${\tau }_d^{-1}={\omega }_0^2{T}_1$, where we have fixed ${\omega }_0=0.3$ Tesla and (b) KCl taken from Ref. 43. The original KCl data may be found in Refs. 35, 36. The fit in panel (a) follows the formula (1) with $\alpha =3$, ${\nu }_0=1/{\tau }_0=2.3\times {10}^{10}{\mathrm{s}}^{-1}$, $E_a=450\mathrm{K}$, ${\nu }_1=1.1\times {10}^{12}{\mathrm{s}}^{-1}{\mathrm{K}}^{1/2}$, and ${\nu }_2=5.5\times {10}^5{\mathrm{s}}^{-1}$. ${\Theta }_D=350\mathrm{K}$ is the estimated Debye temperature (value taken from Ref. 54).