Graded index confined spin waves in a mixed Bloch-Néel domain wall

Abstract

We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle $\ensuremath{\alpha}$ $(0<\ensuremath{\alpha}<\ensuremath{\pi}/2 \mathrm{radians})$ between domains. The model is obtained from the linearized Bloch equations of motion and under reasonable assumptions that can apply to the scenario of a thick (80 nm) magnetic patch, which simplifies the calculations without a high impact on the model accuracy. The model shows that there is a clear dependence of the local wave number of the confined spin wave on the local angle of domain magnetization with respect to the wall and on the excitation magnetic field frequency. From this model, we can define a local mode index in the wall as a function of such angle and excitation frequency. Therefore, the model can be applied to 1D propagating modes, although it also has physical implications for 2D scenarios where a domain wall merges with a saturated magnetic region. Micromagnetic simulations are in good agreement with the predictions of the model. Our model can also give insight on the effects that curved edge structures may have on the propagating characteristics of spin waves bounded in domain walls.