Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation

Transitions between magnetic states of a system coupled to a heat bath can occur by exceeding the energy barrier, but as temperature is lowered quantum mechanical tunneling through the barrier becomes the dominant transition mechanism. A method is presented for estimating the onset temperature for tunneling in a system with an arbitrary number of spins using the second derivatives of the energy with respect to the orientation of the magnetic vectors at the first order saddle point on the energy surface characterizing the over-the-barrier mechanism. An application to a monomer and a dimer of molecular magnets containing a Mn 4 group is presented and the result found to be in excellent agreement with reported experimental measurements.

Section: Over-the-barrier Transitionsmentioning

confidence: 99%

Calculations of the onset temperature for tunneling in multispin systems

Vlasov¹,

Bessarab²,

Uzdin³

et al. 2017

“…The dividing surface separating the orientations that correspond to the A and B states can be represented as a continous curve F (θ, φ) = 0. The MEP between the stable states was found using the geodesic nudged elastic band method [24], a generalization of the frequently used NEB method for atomic rearrangements [33]. The exact position of the first order saddle point was determined with the climbing image algorithm [34].…”

Section: Modelmentioning

confidence: 99%

“…While robust methods are available for finding MEPs in complex magnetic systems [24,25], the visualization of the transition mechanism is in general a difficult task. To simplify the problem, one can consider a projection of the multidimensional surface on a two-dimensional surface, where the energy is given by a two-parameter function specifying the orientation of the magnetic moments in the system.…”

Section: Introductionmentioning

confidence: 99%

Thermal stability of magnetic states in submicron magnetic islands

Liashko¹,

Lobanov²,

Uzdin³

et al. 2017

The lifetime of magnetic states in single domain micromagnetic islands is calculated within the harmonic approximation to transition state theory. Stable magnetic states, minimum energy paths between them and first order saddle points determining the activation energy are analyzed and visualized on two-dimensional energy surfaces. An analytical expression is derived for the pre-exponential factor in the Arrhenius rate expression for the reversal of the magnetic moment when the external field is directed either along the anisotropy axis or perpendicular to it.

“…If both the initial and final states of the transition are known, the minimum energy path on the energy surface connecting the two local energy minima can be found and thereby the first-order saddle point -the highest energy point on that path. The nudged elastic band (NEB) method is commonly used for this task [19][20][21]. A more challenging task is to find saddle points on the energy ridge given only the initial state minimum.…”

Section: Introductionmentioning

confidence: 99%

Instantons describing tunneling between magnetic states at finite temperature

Vlasov¹,

Bessarab²,

Uzdin³

et al. 2017

A method is presented for finding instantons in magnetic systems -optimal paths corresponding to tunneling from one magnetic state to another at a finite temperature. The method involves analytical continuation of the energy to allow for complex values of the angle variables. First, a set of discretization points are placed equally spaced on a chosen energy contour. Then, an estimate of the corresponding temperature is obtained using Landau-Lifshitz dynamics in imaginary time along the contour. Finally, the distribution of the discretization points as well as the energy are systematically refined by converging on the nearest stationary point of the Euclidean action, thereby obtaining a discrete representation of the closest instanton at the given temperature. The method is illustrated with an application to a system consisting of a single spin subject to uniaxial anisotropy and transverse external magnetic field. First-order and second-order crossovers from over-the-barrier mechanism to tunneling are found depending on the applied field, and the difference in the dependence of the instanton temperature on the energy illustrated for the two cases. By comparing the Boltzmann factors for over-the-barrier and tunneling transitions, the crossover temperature between the two mechanisms is estimated for both first-and second-order crossover.