Nominally pure and the vacancy doped systems

For the pure and vacancy-doped systems, the relaxation rate ($\lambda$) at $T\stackrel{<}{\sim}10$ K is temperature independent (Fig.41); this is a characteristic of paramagnetic relaxation. As shown in Fig.42a,b, we also performed longitudinal field (LF) decoupling measurements in the milli-Kelvin regime, and proved the dynamic nature of the relaxation. The LF measurements confirm the absence of a static order in the vacancy doped system.

  

Figure 42: The LF-$\mu$SR spectra of (a) the nominally pure sample and (b) the Mg doped y=1.7% doped system. The solid lines are the fit to the stretched exponential functions, $P_{\mu}(t)=\exp(-(\lambda t)^\beta)$ with (a) $\beta=0.5$ and (b) $\beta=0.72$. (c) The relaxation rate ($\lambda$) as a function of the longitudinal fields applied. The solid lines are the analysis with the T₁ relaxation theory (Eq.33).

As shown in Fig.42c, we have analyzed the LF dependence of the relaxation rate $\lambda$ using the T₁ formula for dilute spin systems (eq.33). The resulting Lorentzian field width (a) and field fluctuation rate ($\nu$) are shown in Table 5. It was suggested that vacancy-doping results in faster field fluctuations ($\nu$) and a larger field width (a) than the nominally pure system shows. Qualitatively, this result may be understood, if muons detect the dipolar fields from unpaired spins in the sample: as susceptibility has indicated, the number of unpaired spins increases upon doping. Therefore, the doped system should exhibit a larger field-width (a) at muon location, if the muons detect the dipolar fields from the doping induced moments. If the interactions between these unpaired spins are also dipolar interactions, the field fluctuation rate ($\nu$) should increase upon doping, as has been observed in the Mg doped systems. A more quantitative discussion, which leads to the estimates shown in Table 5, is given later.

 

$$^{\rm a}$$ Sample Parameter Experiment

$$a\ (\mu s^{-1}) 0.3\sim 3$$ Pure 0.74(4)

$$\nu 18\sim 180$$ 72(12)

$$a\ (\mu s^{-1}) 0.8\sim 6$$ Mg 1.7% 2.0(2)

$$\nu 50\sim 360$$ 600(100)

^a see the discussion later.