Optimal Control of Magnetization Reversal in a Monodomain Particle by Means of Applied Magnetic Field.

A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. An optimal control path minimizing the energy cost of the reversal is identified and used to derive the time-dependent direction and amplitude of the optimal switching field. The minimum energy cost of the reversal scales inversely with the switching time for fast switching, follows exponential asymptotics for slow switching, and reaches the lower limit proportional to the energy barrier between the target states and to the damping parameter at infinitely long switching time. For a given switching time, the energy cost is never smaller than that for a free macrospin. This limitation can be bypassed by adding a hard anisotropy axis that activates the internal torque in the desired switching direction, thereby significantly reducing the energy cost. A comparison between the calculated optimal control path and minimum energy path reveals that optimal control does not translate to the minimization of the energy barrier but signifies effective use of the system's internal dynamics to aid the desired magnetic transition.

Duplication, Collapse, and Escape of Magnetic Skyrmions Revealed Using a Systematic Saddle Point Search Method.

Various transitions that a magnetic Skyrmion can undergo are found in calculations using a method for climbing up the energy surface and converging onto first order saddle points. In addition to collapse and escape through a boundary, the method identifies a transition where the Skyrmion divides and forms two Skyrmions. The activation energy for this duplication process can be similar to that of collapse and escape. A tilting of the external magnetic field for a certain time interval is found to induce the duplication process in a dynamical simulation. Such a process could turn out to be an important avenue for the creation of Skyrmions in future magnetic devices.

Lifetime of racetrack skyrmions.

The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls-skyrmions-driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.

Magnetic exchange force microscopy: theoretical analysis of induced magnetization reversals.

In magnetic exchange force microscopy a magnetic tip is scanned over the surface of a solid and an image representing the exchange interaction recorded. Sudden changes in the image corresponding to magnetization switching can be monitored as a function of the tip-surface distance thereby giving important information about the lifetime of metastable magnetic states and how it is affected by the exchange interaction. Here, theoretical calculations are carried out to study the tip-surface interaction and determine the mechanism and rate of transitions in a magnetic exchange force microscopy experiment, and comparison made with reported experimental data on an Fe cluster interacting with an antiferromagnetic Fe overlayer on a W(001) surface. The activation energy was determined from calculations of minimum energy paths and the pre-exponential factor in the Arrhenius rate expression evaluated from harmonic transition state theory, extended to account for zero modes. A noncollinear extension of the Alexander-Anderson model was used to describe the magnetic properties of an atomic scale representation of the system. The calculations reveal how the tip size, tip-surface distance and magnetic field affect the lifetime of the magnetic states.

Spin relaxation signature of colossal magnetic anisotropy in platinum atomic chains.

Recent experimental data demonstrate emerging magnetic order in platinum atomically thin nanowires. Furthermore, an unusual form of magnetic anisotropy - colossal magnetic anisotropy (CMA) - was earlier predicted to exist in atomically thin platinum nanowires. Using spin dynamics simulations based on first-principles calculations, we here explore the spin dynamics of atomically thin platinum wires to reveal the spin relaxation signature of colossal magnetic anisotropy, comparing it with other types of anisotropy such as uniaxial magnetic anisotropy (UMA). We find that the CMA alters the spin relaxation process distinctly and, most importantly, causes a large speed-up of the magnetic relaxation compared to uniaxial magnetic anisotropy. The magnetic behavior of the nanowire exhibiting CMA should be possible to identify experimentally at the nanosecond time scale for temperatures below 5 K. This time-scale is accessible in e.g., soft x-ray free electron laser experiments.

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states.

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 Mn4 group. The results are in excellent agreement with previously reported experimental measurements on this system.

Size and shape dependence of thermal spin transitions in nanoislands.

Theoretical calculations of thermal spin transitions in nanoscale clusters on a surface are presented. The mechanisms for magnetization reversal are identified and the activation energy and pre-exponential factor for the rate are evaluated using a recently developed harmonic transition state theory and a Heisenberg-type Hamiltonian. A maximum is found in the pre-exponential factor as a function of cluster size corresponding to a crossover from a uniform rotation mechanism to temporary domain wall formation. As the islands grow, the energy barrier increases up to a limit where the domain wall is fully established. For larger islands, the minimum energy path becomes flat resulting in a significant recrossing correction to the transition state theory estimate of the rate. The parameters of the Hamiltonian are chosen to mimic Fe clusters on a W(110) surface, a system that has previously been studied extensively in the laboratory and the calculated results are found to be in close agreement with the reported measurements.