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Article Dans Une Revue Physical Review B Année : 2020

Path sampling for lifetimes of metastable magnetic skyrmions and direct comparison with Kramers' method

Christoph Vogler
  • Fonction : Auteur
Joo-Von Kim
  • Fonction : Auteur
Robert L Stamps
  • Fonction : Auteur
Dieter Suess
  • Fonction : Auteur

Résumé

We perform a direct comparison between Kramers' method in many dimensions, i.e., Langer's theory, adapted to magnetic spin systems, and a path sampling method in the form of forward flux sampling, as a means to compute the collapse rates of metastable magnetic skyrmions. We show that a good agreement is obtained between the two methods. We report variations of the attempt frequency associated with skyrmion collapse by three to four orders of magnitude when varying the applied magnetic field by 5% of the exchange strength, which confirms the existence of a strong entropic contribution to the lifetime of skyrmions. This demonstrates that in complex systems, the knowledge of the rate prefactor, in addition to the internal energy barrier, is essential in order to properly estimate a lifetime. The rate of decay of metastable states is a ubiquitous problem in physics. Thermal activation processes across an energy barrier are found within fields as diverse as solid state physics (Josephson junctions), chemical reactions, electrical circuit theory (phase-locked loops), laser physics, and magnetization switching in ferromagnets [1,2]. In the context of magnetic data storage, information is stored in the form of 0 and 1 bits, corresponding to uniformly magnetized grains pointing along opposite directions. New challenges arise in the necessity to design small magnetic structures capable of retaining a given state against fluctuations for an average lifetime of 10 years at room temperature [3]. The ability to precisely predict that lifetime is therefore crucial. The rate of such thermally activated processes can be described by an Arrhenius law [4], k = τ −1 = f 0 e −β E , (1) in which β = (k B T) −1 , E is the internal energy barrier, and the prefactor f 0 , commonly referred to as the attempt frequency, corresponds to a fundamental fluctuation rate. Estimating the stability of magnetic structures is often synonymous with accessing internal energy barriers, while assuming a typical value of the prefactor in the GHz range [5-8]. Hence, it is generally accepted that β E ∼ 50 at room temperature is a sufficient and necessary condition in order to achieve the desired stability. In recent years, magnetic skyrmions [9,10] have emerged as potential candidates for spintronics applications in data storage and logic devices [11-15]. Magnetic skyrmions are particlelike spin textures carrying an integer topological * louise.desplat@gmail.com charge. They are stabilized by the introduction of a characteristic length scale in a system via competing interactions. In particular, the existence of chiral skyrmions in noncentrosymmetric bulk magnets and thin magnetic films with broken inversion symmetry is made possible by the Dzyaloshinskii-Moriya interaction (DMI) [16-19]. Isolated skyrmions typically live on the ferromagnetic (FM) background as metastable excitations, but, under the effect of thermal fluctuations, will eventually collapse back to the uniformly magnetized state. The problem of their thermal stability has so far yielded vastly different theoretical predictions depending on the system of interest [20-22], particularly concerning the order of magnitude of the attempt frequency. Experimentally, extreme variations of f 0 were observed for small variations of the applied magnetic field in the case of the decay of the skyrmion lattice [3]. The apparent lack of consensus between the results is in part due to the difficulty in calculating the rate constants of rare events. For structures with lifetimes well above the nanosecond range, direct Langevin simulations [23], where one integrates the stochastic dynamics of the spin system at each time step, becomes unrealistic. In that case, a possible approach is the use of a form of reaction rate theory [1,4], which allows a direct calculation of the rate prefactor by considering details of the fluctuations about the metastable state A and the saddle point (SP) S along the reaction coordinate. Numerical implementations of this method [24,25] combined with a path finding scheme [26,27] have previously been used to obtain lifetimes of magnetic skyrmions [21,22,28,29]. While this is a computationally optimal solution, reaction rate theory is based on many assumptions concerning the damping regime, the energy landscape, and the density of states of the system. Additionally, whenever we are faced with several mechanisms 2469-9950/2020/101(6)/060403(5) 060403-1
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Dates et versions

hal-03005540 , version 1 (14-11-2020)

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Louise Desplat, Christoph Vogler, Joo-Von Kim, Robert L Stamps, Dieter Suess. Path sampling for lifetimes of metastable magnetic skyrmions and direct comparison with Kramers' method. Physical Review B, 2020, 101 (6), pp.060403(R). ⟨10.1103/physrevb.101.060403⟩. ⟨hal-03005540⟩
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