Muon Spin Rotation Studies of Spin Dynamics at Avoided Level Crossings in ${\mathrm{LiY}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$

We have studied the ${\mathrm{Ho}}^{3+}$ spin dynamics for ${\mathrm{LiY}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$ via the positive muon (${\mu }^{+}$) transverse field depolarization rate ${\lambda }_{\mathrm{TF}}$ as a function of temperature and magnetic field. We find sharp minima in ${\lambda }_{\mathrm{TF}}(H)$ at fields for which the ${\mathrm{Ho}}^{3+}$ ion system has field-induced (avoided) level crossings. The reduction scales with calculated level repulsions, suggesting that ${\mu }^{+}$ depolarization by slow fluctuations of nonresonant ${\mathrm{Ho}}^{3+}$ spin states is partly suppressed when resonant tunneling opens new fluctuation channels at frequencies much greater than the muon precession frequency.

Figure 1

Calculated magnetic field variation of the hyperfine split ground state electronic energy levels. Inset: closer view of the dominant tunnel splittings (adapted from Ref. 6).

Figure 2

The temperature variation of the depolarization rate at a fixed field of 23 mT. Inset: Temperature dependence of the exponent of the fitted stretched exponential function.

Figure 3

Magnetic field variation of transverse field depolarization rate versus applied field at $T=1.8\mathrm{K}$.

Figure 4

Magnetic field variation of the transverse field depolarization rate ${\lambda }_{\mathrm{TF}}$ in the vicinity of the $n=1$ avoided level crossings at several temperatures. The curves are offset for clarity.