Experimental

In order to obtain the spin-lattice relaxation rate 1/T₁ we measured the magnetization recovery and fitted the sum of exponentials to it, which we discussed in section . One of these fits is shown in figure . The experimental spin echo intensity m(t) was obtained by integrating the spin echo signal which was the answer of the spin system to a pulse sequence as shown in figure . We were exclusively working with slow irradiation (see section ) because all attempts with fast irradiation showed ambiguous or sometimes simply bad results. t denotes the recovery time.

  

Figure: The magnetization recovery of the ¹¹B in CaB₆. The solid line is a fit with the function for slow irradiation as we found it in section .

In order to guarantee the régime of slow irradiation the characteristic duration of the comb has to be of the order of the recovery time, during which the magnetization recovers about 10%. In our case that is a value between 1 and 10 seconds. As lower the temperature was, as longer the comb had to be.^4.2 At temperatures below 0.8 K this started to cause some troubles, because the irradiation of the comb acted as a heating on the sample. For a short time the temperature of the substrate was up to 20% higher than it was regulated to, but the thermal contact of the sample with the cooling liquid was that good, that the temperature could be stabilized within 20 seconds. This is only of the order of some 0.5 to 1 percent of the relaxation time at these temperatures and we decided to neglect that effect.

Measuring in the slow irradiation régime has the additional advantage that we don't have to worry about the width in frequency of the pulses. But with a quadrupole splitting as big as it is in VaB₆ this was a minor problem anyway.

At the lowest temperatures we had to measure relaxation rates of some thousand seconds. It would obviously take too long to determine such a relaxation by simply measuring every point of the relaxation curve. But there are several methods to shorten that procedure. We decided to use the fact that in the high-temperature limit the echo intensity increases like 1/T (see [#!slichter!#]). In measuring the totally recovered spin echo intensity at a higher temperature and not changing anything in the experimental setup afterwards, it is possible to extrapolate the totally recovered spin echo intensity towards lower temperatures and we don't have to wait for the total recovery (see figure ). To be sure that there is no significant change in the behaviour of at low temperatures we rescaled the magnetization recoveries with T₁ from the fit and compared the curves (see figure ).

  

Figure: A measurement of a very long relaxation rate. It would be impossible to measure the last two points at 10⁷ s. Since these points are crucial for the fit, we extrapolated the echo intensity with a 1/T-law.

  

Figure: The comparison of the different magnetization recovery curves. The different curves are rescaled with T₁(T). They coincide and show that the procedure we applied seems to work.