Magnetic Field tuning of low energy spin dynamics in the single-atomic magnet Li$_2$(Li$_{1-x}$Fe$_x$)N

We present a systematic 57Fe-Moessbauer study on highly diluted Fe centers in Li2(Li1-xFex)N single-crystals as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Below 30 K the Fe centers exhibit a giant magnetic hyperfine field of E_A = 70.25(2)T parallel to the axis of strongest electric field gradient Vzz = -154.0(1) V/A2. Fluctuations of the magnetic hyperfine field are observed between 50K and 300K and described by the Blume two-level relaxation model. From the temperature dependence of the uctuation rate an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal activation barrier of E_A = 570(6)K and an attempt frequency nu_0 = 309(10) GHz. Moessbauer spectroscopy studies with applied transverse magnetic fields up to 5T reveal a large increase of the uctuation rate by more than one order of magnitude. In longitudinal magnetic fields a splitting of the uctuation rate into two branches is observed consistent with a Zeeman induced modifcation of the energy levels. The experimental observations are qualitatively reproduced by a single-ion effective spin Hamiltonian analysis assuming a Fe1+ d7 charge state with unquenched orbital moment and a J = 7=2 ground state. It is demonstrated that a weak axial single-ion anisotropy D of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.