Si-doped system

Recent technical development at TRIUMF made it possible to measure small specimens, such as $\sim 5\,{\rm mm}\times 5\,{\rm mm}$ single crystal. We measured such single crystals of Cu(Ge_1-ySi_y)O₃ (y=2 %), using the newly developed `low background apparatus', which has an additional particle counter (veto-counter) on the beam path, behind the sample. If a muon misses the sample and hits the veto-counter, it makes a rejection signal so that this event is thrown away. This way, background-free measurements of small crystals has become possible.

A single crystal of Si-doped system Cu(Ge_1-ySi_y)O₃ (y=2 %) was synthesized at Laboratoire de Chimie des Solides, Université Paris-Sud (Orsay, France), using the floating zone method. A single crystalline rod ($\phi\sim 3$ mm; long-axis = c-axis) was cleaved to a thickness of $\sim 1$ mm and tiled, so that the surface area across the muon beam becomes large. We used three such sliced pieces for our measurements.

  

Figure 59: (a) Zero-field $\mu$SR spectra of the Si 2% doped crystal, and (b) the same spectra with longer time range. The solid lines are the fit with the function described in the text (eq.59). The line drawn on the 5.5 K data is a fit with Gaussian Kubo-Toyabe function from nuclear dipolar fields.

In Fig.59, $\mu$SR spectra of the Si 2% doped system are shown. A spontaneous muon spin precession was observed, indicating the Néel order of the moments. We analyzed the spectra with the functional form:

The first term of eq.59 corresponds to the `1/3-component' in polycrystalline measurements; in a single crystal, the direction of the local field depends on the crystal orientation (see Fig.15 in Chapter 3), so that the muon spin component which does not show a precession could be any amplitude ($A_{1/3}\equiv\cos^2\theta$ defined in Fig.15 of Chapter 3). The time-dependent part of the muon spin polarization seems to have two sub-components; one precession signal (the second term of eq.59) and relaxation (the third term).

In Fig.60, we show the precession frequency (f) and the relaxation rate ($\Delta$) as a function of temperature. It was found that relaxation rate ($\Delta$) scales with the precession frequency (f), as shown in the inset of Fig.60. Since the frequency (f) is proportional to the size of the ordered moments, this scaling result indicates that the relaxation (the third term of eq.59) is caused by a distributed local field which reflects the moment size.

A power-law fit ($\approx (T_{\rm N}\!-\!T)^\beta$) to the frequency (f) and the relaxation rate ($\Delta$) found $T_{\rm N}=5.02(2)$ K and $\beta=0.24(2)$.The exponent ($\beta$) is consistent with that of the antiferromagnetic Bragg peak intensity observed in (Cu_1-xZn_x)GeO₃ [161].

  

Figure 60: Temperature dependence of the precession frequency (f) and the relaxation rate ($\Delta$). The dashed line is a power-law fit described in the text. The inset is the ratio $f/\Delta$, which was found to be temperature independent.