In order to investigate field fluctuations in the charge doped system, we performed longitudinal field measurements. The results are shown in Fig. 43. The zero-field (ZF) spectrum exhibited a Gaussian decay, which seemed to be the Gaussian Kubo-Toyabe function in the slow fluctuation regime (see section 3.1). However, the LF dependence of the relaxation didn't follow the predictions of the Gaussian Kubo-Toyabe theory. If the Gaussian behavior in the zero-field were due to almost static Gaussian field distribution, the relaxation should have been decoupled in a LF200 G, while in fact, the relaxation was present up to LF=2 kG. There are two unconventional behaviors presented in this result:

- (1)
- The weak LF dependence of the relaxation suggests persistent
dynamics in the spin system, even though the temperature (
*T*=50 mK) is well below the glass temperature (). - (2)
- There has been no theories which allow the coexistence of the
zero-field
*Gaussian*decay and fast field fluctuations. In the framework of the conventional Kubo-Toyabe theory, fast fluctuation induces either an exponential function (dense spin system) or a square-root exponential function (dilute spin system), but never a Gaussian decay (see Chapter 3).