Energy relaxation between low lying tunnel split spin-states of the single molecule magnet Ni$_4$

We have developed integrated magnetic sensors to study quantum tunneling of magnetization (QTM) in single molecule magnet (SMMs) single crystals. These sensors incorporate a microstrip resonator (30~GHz) and a micro-Hall effect magnetometer. They have been used to investigate the relaxation rates between the 2 lowest lying tunnel split spin-states of the SMM Ni$_4$ ($S=4$). EPR spectroscopy at 30~GHz and 0.4~K and concurrent magnetization measurements of several Ni$_4$ single crystals are presented. EPR enables measurement of the energy splitting between the 2 lowest lying superposition states as a function of the longitudinal and transverse fields. The energy relaxation rate is determined in two ways. First, in cw microwave experiments the change in spin-population together with the microwave absorption directly gives the relaxation time from energy conservation in steady-state. Second, direct time-resolved measurements of the magnetization with pulsed microwave radiation have been performed. The relaxation time is found to vary by several orders of magnitude in different crystals, from a few seconds down to smaller than 100~$\mu$s. We discuss this and the form of the relaxation found for different crystals and pulse conditions.