Radio-frequency magnetic susceptibility of spin ice crystals Dy\(_{2}\)Ti\(_{2}\)O\(_{7}\) using tunnel diode resonator

Spin ice compound, Dy$_2$Ti$_2$O$_7$, has shown complex frequency - dependent magnetic behavior at low temperatures. While the DC measurements show conventional paramagnetic behavior, finite frequency susceptibility shows two regimes, - complex kagom\'e ice behavior at around 2 K and spin collective behavior above 10 K, depending on the frequency. Conventional AC susceptometry is limited to frequencies in a kHz range, but to get an insight into the possible Arrhenius activated behavior and characteristic relaxation times, higher frequencies are desired. We used self-oscillating tunnel-diode resonator (TDR) to probe magnetic susceptibility at 14.6 MHz, in the presence of a DC magnetic field and down to 50 mK. We found an unusual non-monotonic field dependence of the lower transition temperature, most likely associated with different spin configurations in a kagom\'e ice and an activated behavior of the upper transition, which has now shifted to 50 K range. This work was supported by the U.S. DOE BES MSED and was performed at the Ames Laboratory, Iowa State University under contract DE-AC02-07CH11358. The work at Princeton university was supported by DOE BES grant number DE-FG02-08ER46544.