NMR Studies in Hexaborides Diplomarbeit in experimenteller Festkörperphysik.

In figure

we display a ¹¹B field-sweep NMR-spectrum for CaB₆ at a fixed frequency of 71.96 MHz. This spectrum has been taken at a temperature of 0.16 K, far below T_</I>B. In figure we display a ¹¹B field-sweep NMR-spectrum for CaB₆ at the same frequency. This spectrum has been taken at a temperature of 15.05 K, far above $T_\mathrm{B} \approx 5$ K. Please note the fact, that the spectrum does not show the same temperature régimes as the relaxation rate shows. In both spectra the quadrupole splitting is 440 Gauss or 600 kHz. Within the resolution obtainable from field sweeps we observed no Knight shift of the relatively narrow central line.

In our fits to the spectra it has been observed that the width of the central line and the width of the wings do not coincide. This behaviour has already been found in other substrates (private communication with B. Ambrosini).

Figure: ¹¹B NMR-spectrum for CaB₆ at a fixed frequency of 71.96 MHz and at a temperature of 0.16 K. The solid line is a fit to the data with the central line at 5.195 T

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**Figure:** ¹¹B NMR-spectrum for CaB₆ at a fixed frequency of 71.96 MHz and at a temperature of 15.05 K. The solid line is a fit to the data with the central line at 5.195 T
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In order to measure the Knight shift more accurately we had to increase the resolution. This could only be done in performing some frequency sweeps at a fixed field. In figure we show a ¹¹B NMR frequency-sweep spectrum for CaB₆ at a fixed field of 5.195 T. It has been taken at a temperature around T_</I>B. In figure we display an other ¹¹B NMR frequency-sweep spectrum for CaB₆ at the same field and at a temperature far below T_</I>B. In both spectra the central line is at $(70.963\pm 0.002)$ MHz. Therefore a possible Knight shift is smaller than 0.005%. In a solid there are many other effects from which one would expect a shift of that magnitude. For that reason it does not make sense to increase the resolution even further. The quadrupole frequency showed up to be $(600\pm 3)$ kHz at both temperatures.

Figure: ¹¹B NMR-spectrum for CaB₆ at a fixed field of 5.195 T and at a temperature of 3.04 K. The solid line is a fit to the data with the central line at 70.963 MHz.

$\includegraphics[width=12cm]{eps_figures/fittedfrequencysweep28.6.eps}$

Figure: ¹¹B NMR-spectrum for CaB₆ at a fixed field of 5.195 T and at a temperature of 0.16 K. The solid line is a fit to the data with the central line at 70.963 MHz.

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In figure and figure we show frequency sweeps at the ¹¹B site in LaB₆ and SrB₆. The data for the complete spectra and for the central line are compared in figure . Note the very good coincidence of the width of the central line. In figure the intensity of the single curves is rescaled in order to have the same intensity of the central line. The figure shows that there is almost no temperature dependence of the Knight shift. A different line shape has only been found at 0.16 K.


Figure: ¹¹B NMR-spectrum for LaB₆ at a fixed field of 5.195 T and at a temperature of 1.53 K. The solid line is a fit to the data with the central line at 70.962 MHz.

$\includegraphics[width=10cm]{eps_figures/fittedfreqsweepLaB6dilution.eps}$


Figure: ¹¹B NMR-spectrum for SrB₆ at a fixed field of 5.195 T and at a temperature of 3.17 K. The solid line is a fit to the data with the central line at 70.962 MHz.

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Figure: ¹¹B NMR-spectra for CaB₆, SrB₆ and LaB₆ at a fixed field of 5.195 T. All central lines coincide very well at 70.963 MHz (even the metallic LaB₆ has no Knight shift at the ¹¹B site). The quadrupole splitting differs due to the different lattice constant.

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Figure: ¹¹B NMR-spectra for CaB₆ at a fixed field of 5.195 T. The central lines at all temperatures coincide at 70.963 MHz. Only the lowest temperature has a slight shift towards lower frequencies, but the effect is very small.

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The summary of all the data obtained by frequency sweeps is plotted in the figures and . Neither the central line nor the quadrupole splitting show any significant temperature dependence. The ratio of the quadrupole frequencies coincide nicely with the theoretical values of [#!schwarz!#]. Surprisingly there was a completely different experimental ratio given in [#!schwarz!#].


Figure: Larmor frequencies of the ¹¹B nuclei in the substrates CaB₆, SrB₆ and LaB₆ at a fixed field of 5.195 T.

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Figure: Quadrupole frequencies of the ¹¹B nuclei in the substrates CaB₆, SrB₆ and LaB₆ at a fixed field of 5.195 T.

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Finally we display the $\tau$ -dependence of the CaB₆ spectrum in figure . $\tau$ denotes the delay between the two pulses of an echo sequence. In the next section we will give some evidence that this is a T₂ effect.


Figure: The $\tau$ -dependence of the shape of the central line.

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NMR Studies in Hexaborides Diplomarbeit in experimenteller Festkörperphysik.

Results