μSR study of spin dynamics in LiY${}_{1-x}$Ho${}_x$F${}_4$

We present zero-field positive muon spin relaxation (μSR) measurements for LiY${}_{1-x}$Ho${}_x$F${}_4$ samples with $x$ $=$ 0.0017, 0.0085, 0.0406, and 0.0855. We characterize the dynamics associated with the formation of the (F-μ-F)${}^{-}$ complex by comparing our data with Monte Carlo simulations to determine the concentration range over which the spin dynamics are determined primarily by the Ho${}^{3+}$-μ interaction rather than by the F-μ interaction. Simulations show that F-μ-F oscillations should evolve into a Lorentzian Kubo--Toyabe decay for an increasing static magnetic field distribution Γ (i.e., increasing $x$), but the data do not show this behavior, consistent with the recently reported existence of strong magnetic fluctuations in this system at low temperatures. Anisotropy in the field distribution is shown to cause small errors of the order of 10% from behavior predicted for an isotropic distribution. Finally, numerical calculations show that values of Γ calculated in the single-ion limit greatly exceed the values extracted from curve fits, suggesting that strong correlations play an important role in this system.

Figure 1

Temperature evolution of the depolarization curves for samples with (a) $x$ $=$ 0.0017 and (b) $x$ $=$ 0.0854. Solid lines are fits to Eq. (2). In (b) $G_{\mathrm{F}\mu \mathrm{F}}(t)$  $=$ 1 for the curves at $T$ $=$ 1.6 and 6 K. In (a) the curve for $T$ $=$ 50 K would be nearly identical to $T$ $=$ 20 and 14 K. Curves have been offset for clarity.

Figure 2

Temperature dependence of the fit parameters ${\lambda }_{\mathit{ZF}}$ (left axis), ${\omega }_D$ (right axis), and β (inset) for the $x$ $=$ 0.0017 sample (muon polarization parallel to $c$ axis).

Figure 3

Simulated evolution of the FμF depolarization with increasing magnetic disorder Γ. Simulated data (symbols) are fitted with (solid lines) Eq. (2) for 1 and 4 G, and Eq. (3) for 16, 50 and 80 G.

Figure 4

Low-temperature depolarization curves for samples with $x$ $=$ 0.0017, 0.0085, 0.0406, and 0.0854 (muon polarization parallel to the $c$ axis). Solid lines are fits to Eq. (2); $G_{\mathrm{F}\mu \mathrm{F}}$ ($t$) $=$ 1 for $x$ ⩾ 0.0085. The curves have been offset for clarity.

Figure 5

Measured (open squares) evolution of the muon depolarization with increasing longitudinal field at low temperature and simulated (solid lines) FμF data over the same field range with magnetic disorder Γ $=$ 8 G.