Interlayer-coupled spin vortex pairs and their response to external magnetic fields

We report on the response of multilayer spin textures to static magnetic fields. Coupled magnetic vortex pairs in trilayer elements (ferromagnetic/nonmagnetic/ferromagnetic) are imaged directly by means of layer-selective magnetic x-ray microscopy. We observe two different circulation configurations with parallel and opposing senses of magnetization rotation at remanence. Upon application of a field, all of the vortex pairs investigated react with a displacement of their cores. For purely dipolar coupled pairs, the individual core displacements are similar to those of an isolated single-layer vortex, but also a noticeable effect of the mutual stray fields is detected. Vortex pairs that are linked by an additional interlayer exchange coupling (IEC), which is either ferromagnetic or antiferromagnetic, mainly exhibit a layer-congruent response. We find that, apart from a possible decoupling at higher fields, these strict IEC vortex pairs can be described by a single-layer model with effective material parameters. This result implies the possibility to design multilayer spin structures with arbitrary effective magnetization.

Figure 1

Vortex configurations in magnetic thin films. (a) Circular single-layer disk, where arrows are indicating the direction of $\mathbf{M}$. Both the sense of the planar magnetization curl (circulation $c$) and the orientation of the central core (polarity $p$) can independently be either in the $+$1 or $-1$ state. (b) Four basic configurations of a stacked vortex pair with respect to the relative orientations of $c$ (FM or AF) and $p$ (PL or AP) in a square-shaped element.

Figure 2

Response of vortex pairs in trilayer disks to external magnetic fields. STXM images showing the layer-specific magnetic orientation (in plane) for different fields applied into the $-x$ direction. The contrast mechanism is sensitive to the $M_{\mathrm{x}}$ component as indicated by the arrows. (a), (b) PDC Co/Cu/NiFe(50) disks with (a) AF and (b) FM configuration at remanence. (c) Co/Ru/NiFe(50) afm IEC disk in AF state, (d) irradiated Co/Ru/NiFe(50):Ne${}^{+}$0.3 fm IEC disk configured FM.

Figure 3

Response of strongly IEC coupled vortex pairs in trilayer squares to external magnetic fields. STXM images and micromagnetic simulations showing the layer-specific magnetic orientation (in plane) for different fields applied into the $-x$ direction. (a) NiFe and (b) Co vortex in an irradiated fm IEC Co/Rh/NiFe(25):Ne${}^{+}$2.0 square. (c) NiFe and (d) Co vortex in an afm IEC Co/Ru/NiFe(25) square. Dotted arrows indicate the qualitative orientation of magnetization.

Figure 4

Comparison of experimental (filled) and simulated (hollow) vortex core displacements in trilayer squares (squares) and disks (circles) upon the application of an external magnetic field $H_x$. In addition, the simulations are performed for a single-layer element with effective material parameters ($\times$). Symbols positioned outside the graphs correspond to an annihilated vortex core.