Anisotropy of Neel “orange-peel” coupling in magnetic multilayers

Abstract

Highlights:-"Orange-peel" coupling between two ferromagnetic layers is calculated for an arbitrary orientation of the layers magnetizations -"Orange-peel" coupling changes sign when the magnetizations rotate from in-plane orientation to out-of-plane orientation Abstract: We calculate the energy of the magnetostatic interaction between two ferromagnetic films with uniform magnetization and correlated interfaces (the "orange-peel" effect). The "orange-peel" coupling is anisotropic: the interaction is ferromagnetic when the films are magnetized in-plane; and it is antiferromagnetic when magnetization is out-of-plane. The interaction anisotropy can be used to distinguish the "orange-peel" effect from the interlayer exchange coupling.The magnetostatic interaction of two magnetic layers appears due to the roughness of their interfaces. The roughness produces a stray field. This field acts on the neighboring film leading to the so-called "orange-peel" interlayer interaction [1][2][3][4][5][6][7][8]. Often the "orange-peel" (OP) coupling is comparable to the interlayer exchange interaction [5,[9][10][11][12][13][14], which appears due to spin currents of conduction electrons [15]. These two interaction mechanisms should be distinguished in certain cases.This can be done by studying the angular dependencies of the interlayer coupling energy. The exchange interaction is isotropic and depends on the mutual orientation of magnetizations ex~( 1 2 ), where 1,2 are layers magnetic moments. In the present manuscript we will show that "orange-peel"interaction is anisotropic and obeys the relation op~⊥ 1⊥ 2⊥ − || 1|| 2|| , where 1,2⊥ are the out-of-plane magnetizations components, 1,2|| are the in-plane components, ⊥ and || are positive and of the same order.Consider a system of two ferromagnetic films with rough surfaces (see Fig. 1). We assume that these surfaces are correlated and can be described by the same function ( ), where = ( , ) is the in-plane coordinate vector. Often the correlation between the film interfaces naturally appears during the films growth [16]. Therefore, this assumption is quite relevant. The ferromagnetic films are separated by a non-magnetic spacer of thickness . We also assume that both layers are uniformly

Stripe structures in phase separated magnetic oxides

“…In the case of bending perturbation in (25) the solution is more complicated. We follow the approach proposed in [39]. We calculate the Coulomb energy assuming that the bending is small δ b ≪ d, l and 2π/k.…”

Studying of the Interlayer Interaction in Magnetic Multilayers (FM/I/FM) Measuring the FMR Peak Asymmetry

“…In previous sections we did not discuss the origin of the interlayer coupling. There are a few possible types of the interaction: 1) the interlayer exchange coupling [6][7][8][9][10][11] ; 2) the magneto-dipole "orange-peel" (OP) effect [12][13][14][15][16][17]; 3) and the coupling due to pin-holes.…”

“…The MTJ consists of two ferromagnetic (FM) layers separated by an insulating (I) spacer. An interaction between the layers in the MTJ defines a system ground state [6][7][8][9][10][11][12][13][14][15][16][17]. It influences a susceptibility of magnetic field sensors based on MTJ systems.…”

Strontium Ferromolybdate-Based Magnetic Tunnel Junctions

“…Here, the magnetostatic anisotropy constant with an absolute value up to |K| = 1.32 × 10 6 J/m 3 will be negative, corresponding to a parallel alignment of the magnetizations in the two FM layers. The out-of-plane magnetization induces an anti-FM interaction between the layers due to a stray field resulting from the uniformly charged curved surface [24]. For arbitrary orientations of magnetization, the offset field is given by [24]:…”

“…The out-of-plane magnetization induces an anti-FM interaction between the layers due to a stray field resulting from the uniformly charged curved surface [24]. For arbitrary orientations of magnetization, the offset field is given by [24]:…”