The effect of confinement and defects on the thermal stability of skyrmions

The stability of magnetic skyrmions against thermal fluctuations and external perturbations is investigated within the framework of harmonic transition state theory for magnetic degrees of freedom. The influence of confined geometry and atomic scale non-magnetic defects on the skyrmion lifetime is estimated. It is shown that a skyrmion on a track has lower activation energy for annihilation and higher energy for nucleation if the size of the skyrmion is comparable with the width of the track. Two mechanisms of skyrmion annihilation are considered: inside the track and escape through the boundary. For both mechanisms, the dependence of activation energy on the track width is calculated. Non-magnetic defects are found to localize skyrmions in their neighborhood and strongly decrease the activation energy for creation and annihilation. This is in agreement with experimental measurements that have found nucleation of skyrmions in presence of spin-polarized current preferably occurring near structural defects

Energy surface and lifetime of magnetic skyrmions

The stability of skyrmions in various environments is estimated by analyzing the multidimensional surface describing the energy of the system as a function of the directions of the magnetic moments in the system. The energy is given by a Heisenberg-like Hamiltonian that includes Dzyaloshinskii-Moriya interaction, anisotropy and external magnetic field. Local minima on this surface correspond to the ferromagnetic and skyrmion states. Minimum energy paths (MEP) between the minima are calculated using the geodesic nudged elastic band method. The maximum energy along an MEP corresponds to a first order saddle point on the energy surface and gives an estimate of the activation energy for the magnetic transition, such as creation and annihilation of a skyrmion. The pre-exponential factor in the Arrhenius law for the rate, the so-called attempt frequency, is estimated within harmonic transition state theory where the eigenvalues of the Hessian at the saddle point and the local minima are used to characterize the shape of the energy surface. For some degrees of freedom, so-called 'zero modes', the energy of the system remains invariant. They need to be treated separately and give rise to temperature dependence of the attempt frequency. As an example application of this general theory, the lifetime of a skyrmion in a track of finite width for a PdFe overlayer on a Ir(111) substrate is calculated as a function of track width and external magnetic field. Also, the effect of non-magnetic impurities is studied. Various MEPs for annihilation inside a track, via the boundary of a track and at an impurity are presented. The attempt frequency as well as the activation energy has been calculated for each mechanism to estimate the transition rate as a function of temperature

Skyrmions in antiferromagnets

Calculations of skyrmions in antiferromagnets (AFMs) are presented, and their properties compared with skyrmions in corresponding ferromagnets (FMs). The rates of skyrmion collapse and escape through the boundary of a track, as well as the binding to and collapse at a non-magnetic impurity, are calculated as a function of an applied magnetic field. The activation energy for skyrmion annihilation is the same in AFMs and corresponding FMs in the absence of an applied magnetic field. The pre-exponential factor in the Arrhenius rate law is, however, different because skyrmion dynamics is different in the two systems. An applied magnetic field has opposite effects on skyrmions in the two types of materials. In AFMs, the rate of collapse of skyrmions as well as the rate of escape through the edge of a magnetic strip decreases slightly with increasing field, while these rates increase strongly for a skyrmion in the corresponding FMs when the field is directed antiparallel to the magnetization in the center of the skyrmion. A non-magnetic impurity is less likely to trap a skyrmion in AFMs, especially in the presence of a magnetic field. This, together with the established fact that a spin polarized current moves skyrmions in AFMs in the direction of the current, while in FMs skyrmions move at an angle to the current, demonstrates that skyrmions in AFMs have several advantageous properties over skyrmions in FMs for memory and spintronic devices.Peer reviewe

Toward room-temperature nanoscale skyrmions in ultrathin films

Breaking the dilemma between small size and room-temperature stability is a necessary prerequisite for skyrmion-based information technology. Here we demonstrate by means of rate theory and an atomistic spin Hamiltonian that the stability of isolated skyrmions in ultrathin ferromagnetic films can be enhanced by the concerted variation of magnetic interactions while keeping the skyrmion size unchanged. We predict film systems where the lifetime of sub-10 nm skyrmions can reach years at ambient conditions. The long lifetime of such small skyrmions is due to exceptionally large Arrhenius pre-exponential factor and the stabilizing effect of the energy barrier is insignificant at room temperature. A dramatic increase in the pre-exponential factor is achieved thanks to the softening of magnon modes of the skyrmion, thereby increasing the entropy of the skyrmion with respect to the transition state for collapse. Increasing the number of skyrmion deformation modes should be a guiding principle for the realization of nanoscale, room-temperature stable skyrmions.</p

Toward room-temperature nanoscale skyrmions in ultrathin films

Breaking the dilemma between small size and room-temperature stability is a necessary prerequisite for skyrmion-based information technology. Here we demonstrate by means of rate theory and an atomistic spin Hamiltonian that the stability of isolated skyrmions in ultrathin ferromagnetic films can be enhanced by the concerted variation of magnetic interactions while keeping the skyrmion size unchanged. We predict film systems where the lifetime of sub-10 nm skyrmions can reach years at ambient conditions. The long lifetime of such small skyrmions is due to exceptionally large Arrhenius pre-exponential factor and the stabilizing effect of the energy barrier is insignificant at room temperature. A dramatic increase in the pre-exponential factor is achieved thanks to the softening of magnon modes of the skyrmion, thereby increasing the entropy of the skyrmion with respect to the transition state for collapse. Increasing the number of skyrmion deformation modes should be a guiding principle for the realization of nanoscale, room-temperature stable skyrmions.QN/Akhmerov Grou