Boundary Vortices for Thin Ferromagnetic Films

Action minimization and sharp‐interface limits for the stochastic Allen‐Cahn equation

“…In micromagnetics, for example, one is interested in thermally activated switching of the magnetization. There is a regime -involving submicron-scale, soft thin films, commonly used for magnetoresistive memory devices -in which the magnetic behavior is dominated by "boundary vortices" [24,28,29]. We wonder whether thermally activated switching in this regime can be described by minimizing a suitable action involving the nucleation and motion of boundary vortices.…”

Moving boundary vortices for a thin-film limit in micromagnetics

“…The next lemma is a generalization of lemma 4.3 in [16]. It is the key lemma for the proof of Theorem 2.1.…”

“…Another result from [16] we will need is concerned with the behavior of the initial data. Choose a function ω ∈ C ∞ ([0, ∞)) with 0 ≤ ω ≤ 1, ω(s) = s for 0 ≤ s ≤ , such that for any δ ∈ (0, e −e ], two points x 1δ , x 2δ ∈ ∂ can be found with the following properties:…”

Effective anisotropy of thin nanomagnets: Beyond the surface-anisotropy approach

“…15,16,17,18,19,20,21. The important length scale is the magnetic exchange length ℓ = A/4πM 2 S where A is the exchange constant and M S is the saturation magnetization.…”

“…In the case h/R ≪ 1 and ℓ 2 ≪ 2h R | ln(h/2R)| the magnetization develops edge defects, including fractional vortices. 13,20,21 This problem has a boundary constraint and an interior penalty. It is relevant for typical Permalloy (Ni 80 Fe 20 , Py) disks where we have h ∼ 20nm, 2R ∼ 100nm and ℓ ∼ 5.3nm.…”