Observation of spin freezing and relaxation at microwave frequencies in the spin ladder compound \(Sr_{14-x}Ca_{x}Cu_{24}O_{41}\)

We report the observation of a frequency (\(\omega \)) and temperature (T) -dependent loss peak in \(\chi''\) and accompanying dispersion in \(\chi'\) from microwave (2-18GHz) measurements of the complex susceptibility \(\tilde{\chi}(\omega, T)=\chi'+i\chi''\) of \(Sr_{14-x}Ca_{x}Cu_{24}O_{41}\). We associate this phenomenon with a rapid decrease of spin disorder and corresponding spin relaxation rate, representing a ``spin freezing transition'' accompanying charge ordering which occurs at temperatures \(\sim 250K\). Our results enable direct quantitative measurements of the spin relaxation rate, and yield information on spin dynamics in these materials and the related compounds \(SrCuO_{2}\) and \(Sr_{2}CuO_{3}\).