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Ground state and constrained domain walls in multilayers
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Image of FIG. 1.
FIG. 1.

Calculation of the DW width from the calculated magnetization angle at layer depth . The drawn line is a fit to the data (엯). The dashed line is the tangent at . The horizontal arrow indicates the DW width.

Image of FIG. 2.
FIG. 2.

Angle of the magnetization against the layer depth for the simulation with and . This simulation is a clear example of the F state. For small , the magnetization in the Fe layer is fully aligned with the applied external field and . Only at large , twisting occurs in the layers and is reduced.

Image of FIG. 3.
FIG. 3.

Three-dimensional view of the data of Fig. 2. For clarity, the data are plotted only for , showing half of a Gd layer (thick arrows) and half of a Fe layer (thin). The magnetic field is parallel to the axis. At the interface, the Fe layer is off the axis and the Gd layer is off the axis.

Image of FIG. 4.
FIG. 4.

vs for the simulation with and . This simulation illustrates the twisted ground state. Even at small , decreases rapidly with and DWs are formed in both Fe and Gd layers. at relatively small , but for all . Note that the twisting is more pronounced at low in the top and bottom layer, as recently reported by Haskel et al. (see Ref. 15).

Image of FIG. 5.
FIG. 5.

Angle at the boundary as a function of external field. Open symbols correspond to and solid symbols to . Circles and triangles correspond to simulations using and , respectively.

Image of FIG. 6.
FIG. 6.

Data extracted of the twisted state simulation with and and the F state simulation with and . The angle of the magnetic moment at the center , the interface angle , the twist in the DW , and the width of the DW are plotted vs the applied field . The figure highlights the different behavior of the Fe and the Gd layers. Open circles (T–Gd) correspond to the Gd layer of the twisted state simulation; Closed circles (T–Fe) correspond to the Fe layer of the T state simulation. Open diamonds (F–Gd) represent the Gd layer of the F state simulation and closed diamonds (F–Fe) represent the Fe layer of the F state simulation.

Image of FIG. 7.
FIG. 7.

Data extracted of the F state simulation with and . Data have been taken in a decreasing field, followed by an increasing field. Note the hysteretic behavior at small fields. axis symbols are the same as in Fig. 6.

Image of FIG. 8.
FIG. 8.

The simulation of multilayers for various . The simulations for and are identical above . For clarity, only the data for the Gd layers are shown. axis symbols are the same as in Fig. 6.

Image of FIG. 9.
FIG. 9.

Sketch of the DW overlap. The DW width is reduced from the top to the bottom panel. The surface tension of the overlapping DWs enhances the reduction of the twist.

Image of FIG. 10.
FIG. 10.

Phase diagram as a function of the total Fe magnetization (bottom axis) and the total Gd magnetization (left axis). The drawn lines indicate the boundaries between the G (open squares), the twisted (gray triangles) and the F (gray circles) states. The corresponding layer thicknesses are given on the top and right axes.


Generic image for table
Table I.

Material parameters for Fe and Gd.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Ground state and constrained domain walls in Gd∕Fe multilayers