title: Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states.
abstract: Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn4group. The results are in excellent agreement with previously reported experimental measurements on this system.
authors.affiliation: Science Institute and Faculty of Physical Sciences, University of Iceland VR-III, 107 Reykjavík, Iceland. hj@hi.is and Department of Natural Sciences, University ITMO, St. Petersburg, 197101 Russia.
authors.forename: Sergei
authors.initials: S
authors.lastname: Vlasov
authors.affiliation: Department of Materials and Nanophysics, Royal Institute of Technology (KTH), Electrum 229, SE-16440 Kista, Sweden and Department of Physics, St. Petersburg State University, St. Petersburg, 198504 Russia.
authors.forename: Pavel F
authors.initials: PF
authors.lastname: Bessarab
authors.affiliation: Department of Natural Sciences, University ITMO, St. Petersburg, 197101 Russia and Department of Physics, St. Petersburg State University, St. Petersburg, 198504 Russia.
authors.forename: Valery M
authors.initials: VM
authors.lastname: Uzdin
authors.affiliation: Science Institute and Faculty of Physical Sciences, University of Iceland VR-III, 107 Reykjavík, Iceland. hj@hi.is and Department of Applied Physics, Aalto University, Espoo, FI-00076, Finland.
authors.forename: Hannes
authors.initials: H
authors.lastname: Jónsson