Magnetic normal modes of bicomponent permalloy/cobalt structures in the parallel and antiparallel ground state

Two-dimensional arrays of bicomponent structures made of cobalt and permalloy elliptical dots with thickness of 25 nm, length 1 μm, and width of 225 nm, have been prepared by a self-aligned shadow deposition technique. Brillouin light scattering has been exploited to study the frequency dependence of thermally excited magnetic eigenmodes on the intensity of the external magnetic field, applied along the easy axis of the elements. Several modes have been observed while sweeping the field along the major and minor hysteresis loops, encompassing both the parallel and the antiparallel alignment of the magnetization in adjacent permalloy and cobalt dots. Micromagnetic simulations based on the dynamic matrix method enabled us to successfully reproduce the measured evolution of the frequencies with the field, as well as to identify the spatial profiles of the modes. A marked difference in the field dependence of the frequency of some modes has been observed for parallel and antiparallel magnetization configurations, suggesting the possibility of tuning the dynamic response in a reprogrammable way. The role of both static and dynamic magnetic coupling in determining the mode frequency is discussed in detail by studying the frequency evolution as a function of the gap size between the dots.

Figure 1

Major (full points) and minor (open points) normalized MOKE hysteresis loop for the bicomponent Py/Co dots array measured with the external field applied along the dots long axis. The dashed curve represents the first derivative of the upper branch of the major loop with respect to $H$. Arrows indicate the field range of the parallel (P) and antiparallel (AP) alignment of the Py and Co magnetizations. Inset shows the SEM image of the array together with an enlarged image of the bicomponent unit of the Py/Co elliptical dots. The coordinate axis and the direction of the applied field H, as applied for MOKE, MFM, and BLS measurements, are also indicated.

Figure 2

MFM images of the bicomponent Py/Co dots for different values of the applied magnetic field which are indicated by greek letters along both the major and minor hysteresis loop. The rectangular dashed area enclosed a couple of Py/Co elliptical dots as the basic unit of the bicomponent dot array.

Figure 3

Dependence of the magnetic eigeinmode wave frequency on the applied field strength. Filled dots are experimental frequencies measured by BLS on sweeping the applied magnetic field from positive to negative saturation (i.e., following the upper branch of the hysteresis loop). Dashed curves are the calculated mode frequencies obtained by DMM and the labels indicate the modes nomenclature based on their spatial profiles. Black (blue) curves represent the calculated modes localized into Py (Co) dots. The normalized major hysteresis loop is also plotted for showing the transition fields (vertical dashed lines) occurring during the reversal process of the dots. Arrows mark the field regions of the different relative alignment of the magnetization for the Py and Co dots (P or AP). Inset shows a representative BLS spectrum measured at $H$ = 0 Oe along the upper branch of the major $M-H$ loop.

Figure 4

Calculated spatial distribution of the in-plane dynamic magnetization [Im$\left(\delta m_y\right)$, imaginary part] for different modes observed in the BLS spectra at the field values indicated on the top of the figure. In the top two lines the magnetization distribution in the top (Co) and bottom (Py) dots, as calculated by the micromagnetic simulations, is also shown, for both the AP and P states.

Figure 5

Full points are the frequencies measured along the minor hysteresis (also shown in the figure). The frequencies measured along the major hysteresis loop of Fig. 3 are also plotted as open points, for the sake of comparison.

Figure 6

Calculated frequency evolution of modes detected in the BLS spectra vs the gap size $d$ for two different values of applied magnetic field. Left panel: $H$ = −500 Oe (AP state). Right panel: $H$  = +500 Oe (P state). Red (black) curves represent the calculated frequencies for modes localized into the Py (Co) dots. Horizontal dotted lines shown in the right panel represent the calculated frequency values for noninteracting (isolated) Py and Co dots.

Figure 7

Panels (a) and (d) show the profile of the averaged internal field in the Py dot in the P $(H$ = +500 Oe) and AP $(H$ = −500 Oe) states, respectively at $d$ = 10 nm (black lines) and $d$ = 50 nm (red-dashed lines). Panel (g): As in panels (a) and (d), but in the Co dot in the P state. Blue dashed lines in panels (a), (d), and (g) give the magnitude of the external magnetic field. Panels (b) and (e): Spatial profiles $\left[\mathrm{Im}\left(\delta m_y\right)\right]$ of the F(Py) mode in the P and AP ground states, respectively, at $d$ = 10 nm. Panels (c) and (f): Corresponding spatial profiles $\left[\mathrm{Im}\left(\delta m_y\right)\right]$ at $d$  = 50 nm. Panel (h): Spatial profile $\left[\mathrm{Im}\left(\delta m_y\right)\right]$ of the F(Co) mode in the P state at $d$ = 10 nm. Panel (i): As in panel (h), but at $d$ = 50 nm. Panels (b), (c), (e), (f), (h), and (i) also depict the spatial profiles in the micromagnetic cells placed in the central line of either the Py or the Co dot.