2007 # Effective anisotropy of thin nanomagnets: Beyond the surface-anisotropy approach

**Abstract:** We study the effective anisotropy induced in thin nanomagnets by the nonlocal demagnetization field (dipole-dipole interaction). Assuming a magnetization independent of the thickness coordinate, we reduce the energy to an inhomogeneneous onsite anisotropy. Vortex solutions exist and are ground states for this model. We illustrate our approach for a disk and a square geometry. In particular, we obtain good agreement between spin-lattice simulations with this effective anisotropy and micromagnetic simulations.

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“…For thin nanodots the easy-plane anisotropy parameter A (r) is negative being practically a constant. The in-plane anisotropy parameter B(r) is coordinate-dependent: it vanishes in the disk center and it is sharply localized near the disk edge [20]. One can see that for the easy-plane uniform state nanodot with φ = const, θ = π/2, the second (in-plane) energy term in (1) vanishes after integration and makes no important contribution.…”

mentioning

confidence: 84%

“…For thin nanodots the easy-plane anisotropy parameter A (r) is negative being practically a constant. The in-plane anisotropy parameter B(r) is coordinate-dependent: it vanishes in the disk center and it is sharply localized near the disk edge [20]. One can see that for the easy-plane uniform state nanodot with φ = const, θ = π/2, the second (in-plane) energy term in (1) vanishes after integration and makes no important contribution.…”

mentioning

confidence: 84%

“…Probably the simplest way which gives physical insight how the dipolar interaction secures the stability of curling ground state is to use a local approach [20]. In this approach the dipolar interaction can be reduced approximately to an on-site anisotropy energy which in the case of a cylindrical nanodot has the form…”

mentioning

confidence: 99%

“…This corresponds to the exchange length ℓ = $\sqrt{A/4\pi M_S^2}$ ≈ 5.3 nm; the mash size is 2 nm. The second type is original spin–lattice SLASI simulator 55, based on discrete LLG equations (2) for the lattice spins, where the 3D spin distribution is supposed to be independent on z coordinate. Comparison of different approaches is plotted on Figure 1.…”

confidence: 99%

“…in the vortex, configuration [5]. Similarity between the effects of the stray field and the surface anisotropy is not casual: Effective surface anisotropy in thin nanomagnets is known to be induced by the dipolar interaction [8,9].…”

confidence: 99%