Nanomagnetic systems and transitions between magnetic states are currently an active topic of research. Spintronics is, in particular, a new branch of science and technology where spin degrees of freedom and spin currents are used in an analogous way as electron current in electronic devices. The development of techniques for constructing magnetic systems with near atomic-scale precision opens the possibility of using quantum coherence in magnetic states for quantum computing devices. Quantum mechanical tunneling from one magnetic state to another is an important topic in that context. In this thesis, the tunneling between magnetic states is studied from the point of view of instanton theory. An instanton is an optimal tunneling path, corresponding to a solution to the equation of motion in imaginary time. A method for finding instantons in magnetic systems at finite temperature is presented. It is used to find the crossover temperature from over-the-barrier transition mechanism to tunneling. In some cases, the crossover is abrupt, a first order transition, while in other cases it is more gradual, a second order transition. The latter is referred to as thermally assisted tunneling. A test problem including a single spin with an easy axis and applied transverse magnetic field is studied where the crossover changes from first to second order as the strength of the applied magnetic field is increased. The instanton is used to estimate the crossover temperature as well as the activation energy for thermally activated tunneling as a function of temperature. A general expression is presented for the crossover temperature in second-order transitions where the only input is the second derivative of the energy of the system with respect to the orientation of the magnetic moments at the first order saddle point in the energy surface. The over-the-barrier transition rate and crossover temperature for tunneling are estimated for a monomer and dimer of a molecular magnet containing a Mn4 group and the results found to agree well with experimental data. An application to the annihilation of a magnetic skyrmion shows that a crossover temperature for tunneling can be obtained at over 1 K for a certain range of values for the parameters in the Hamiltonian.

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