Domain walls in a dipole-coupled transverse magnetic island chain

Abstract

I analyze the nonlinear Hamiltonian equations of motion for a one-dimensional chain of transverse magnetic nano-islands, seeking solutions for different types of static domain-walls (DWs) connecting uniform static states. The system of elongated magnetic islands oriented transverse ($y$-direction) to the chain direction ($x$-direction) experiences an applied magnetic field transverse to the chain. The macro-spin model includes dipole interactions between islands, their uniaxial and easy-plane anisotropies, and Oersted energy of the applied field. DWs can form most easily between pairs of degenerate uniform states, described by their local magnetizations as oblique, $y$-parallel, and $y$-alternating. The DWs between oblique states are well-described with scalar $\varphi^4$ theory. General DW structures are found via a numerical energy relaxation scheme. At some anisotropy and field parameters, nearest-neighbor dipole interactions drive antiferromagnetic order inside the DW itself. The variety of DWs present in the model might be exploited for their sensitivity to parameter changes in detectors or switching technology.

Figures (20)

• Figure 1: Part of a system of magnetic islands elongated transverse to the chain, with the dipoles in a uniform oblique state due to the competition among dipolar energy, shape anisotropy, and Oersted energy.
• Figure 2: Regions in the anisotropy-applied field coordinates $(k_1,b)$ where the different uniform states are stable in the NN model. In relaxation simulations, point A produced the smooth oblique--oblique DW in Fig. \ref{['oblq-nn-k090-b41']}; point B produced the oblique--oblique DW with AFM order in Fig. \ref{['obliq-nn-af-k090-b02']}.
• Figure 3: For the NN model with parameters at point A in Fig. \ref{['nn-phases']}, a DW between oblique states and the fitting of the tangent line at its center. This is a case where the maximum magnetic field for oblique states is $b_{\rm max}=4.20$ . The width is $w=2h$ where $h=6.5$ is the half-width, measured in units of the island spacing, $a$. The $\varphi^4$ theory, Eq. (\ref{['hbeta']}), gives $h=6.32$ for this situation.
• Figure 4: For the NN model, DWs between oblique states for a low value of anisotropy, $k_1=0.90$, for a range of transverse applied field $b$. Points are the relaxation simulation; curves are the $\varphi^4$ theory using fitted widths. The system size is $N=200$, and the view is zoomed into the center where the DW is. There is an obvious trend in the DW width as $b$ approaches the maximum, where the system will go into a $y$-par state.
• Figure 5: For the NN model, DW half-widths between oblique states for a low value of anisotropy, $k_1=0.90$, as a function of transverse applied field $b$. Points are relaxation simulation data while the curves are the $\varphi^4$ theory, Eq. (\ref{['hbeta']}). The insert shows a linear dependence of $\beta^2=h^{-2}$ on $b$ until $b$ reaches $b_{\rm max}$.