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Register a new userMicroscopic polarization and magnetization fields: Including spin effects
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We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons. We include a general spin orbit coupling and Zeeman interaction term to account for the modifications to the dynamics upon treating the electrons as spinful particles. We find a contribution to the magnetization due to the intrinsic angular momentum of the electrons. Additionally, the charge current gains a component transverse to both this intrinsic magnetization and the electric field of the crystal lattice. The microscopic polarization and magnetization fields are introduced throughout an extended system using a set of orthogonal orbitals associated with each site. As well free charge and current density fields are introduced associated with charge movement from site to site. The sites act as natural expansion points for the microscopic fields allowing for the evaluation of multipole moments associated with the polarization and magnetization fields. Associated with the dipole moments are the respective macroscopic polarization and magnetization fields, from which we can extract various response tensors. We focus on topologically trivial insulators in the limit of uniform fields to recover the magnetoelectric polarizability (MP) tensor, which contains the accepted expression for the orbital magnetoelectric polarizability (OMP) tensor as well as an added explicitly spin dependent contribution. This general framework can then be extended to finite frequency responses.
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This chapter takes a microscopic view of quantum tunneling of magnetization (QTM) in single-molecule magnets (SMMs), focusing on the interplay between exchange and anisotropy. Careful consideration is given to the relationship between molecular symmetry and the symmetry of the spin Hamiltonian that dictates QTM selection rules. Higher order interactions that can modify the usual selection rules are shown to be very sensitive to the exchange strength. In the strong coupling limit, the spin Hamiltonian possess rigorous $D_{2h}$ symmetry (or $C_{infty}$ in high-symmetry cases). In the case of weaker exchange, additional symmetries may emerge through mixing of excited spin states into the ground state. Group theoretic arguments are introduced to support these ideas, as are extensive results of magnetization hysteresis and electron paramagnetic resonance measurements.
We demonstrate magnetization switching in out-of-plane magnetized TaCoFeBMgO nanowires by current pulse injection along the nanowires, both with and without a constant and uniform magnetic field collinear to the current direction. We deduce that an effective torque arising from spin-orbit effects in the multilayer drives the switching mechanism. While the generation of a component of the magnetization along the current direction is crucial for the switching to occur, we observe that even without a longitudinal field thermally generated magnetization fluctuations can lead to switching. Analysis using a generalized Neel-Brown model enables key parameters of the thermally induced spin-orbit torques switching process to be estimated, such as the attempt frequency and the effective energy barrier.
The gyromagnetic relation - i.e. the proportionality between the angular momentum $vec L$ (defined by an inertial tensor) and the magnetization $vec M$ - is evidence of the intimate connections between the magnetic properties and the inertial properties of ferromagnetic bodies. However, inertia is absent from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the Gilbert equation and the Bloch equation contain only the first derivative of the magnetization with respect to time). In order to investigate this paradoxical situation, the lagrangian approach (proposed originally by T. H. Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic equation generalized to the inertial regime is obtained. It is shown how both the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert equation are recovered at the kinetic limit, i.e. for time scales above the relaxation time $tau$ of the angular momentum.
We construct a microscopic optical potential including breakup effects for elastic scattering of weakly-binding projectiles within the Glauber model, in which a nucleon-nucleus potential is derived by the $g$-matrix folding model. The derived microscopic optical potential is referred to as the eikonal potential. For $d$ scattering, the calculation with the eikonal potential reasonably reproduces the result with an exact calculation estimated by the continuum-discretized coupled-channels method. As the properties of the eikonal potential, the inaccuracy of the eikonal approximation used in the Glauber model is partially excluded. We also analyse the $^6$He scattering from $^{12}$C with the eikonal potential and show its applicability to the scattering with many-body projectiles.
A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Mobius ribbon, for which the central curve is a circle about which the line segment executes a $180^circ$ twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Mobius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.
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