Ferromagnetic resonance force microscopy studies of arrays of micron size permalloy dots

The dynamic magnetic properties of micron-sized permalloy disks have been investigated using magnetic resonance force microscopy. From local spectroscopy data, information about the global sample properties is obtained. The experimental results are in good agreement with theoretical predictions, which account for magnetostatic modes with quantized in-plane wave vector. Ferromagnetic resonance spectral features due to the permalloy dots in close proximity to the micromagnetic probe tip provide two-dimensional images of the sample.

Figure 1

The sample consisted of a patterned array of 50-nm-thick, $1.5\text{−}\mathrm{\mu }\mathrm{m}\text{−}\mathrm{diam}$ ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ disks separated by a center-to-center distance of $1.8\mathrm{\mu }\mathrm{m}$.

Figure 2

The $\mathrm{SmCo}$ micromagnetic tip used for these experiments was manually attached to the end of a $450\text{−}\mathrm{\mu }\mathrm{m}\text{−}\mathrm{long}$ and $30\text{−}\mathrm{\mu }\mathrm{m}\text{−}\mathrm{wide}$ lightly boron doped $(\approx {10}^{15}{\mathrm{cm}}^{-3})$ silicon cantilever. The tip was shaped using a focused ion beam mill.

Figure 3

(Color online) An FMRFM spectrum obtained at a microwave frequency $f_{\mathrm{mw}}=7.7\mathrm{GHz}$; the amplitude of the microwave excitation was modulated at the cantilever resonance frequency with a depth of 60%. The tip-sample separation was $0.4\mathrm{\mu }\mathrm{m}$. The applied magnetic field $\vec{H}$ is aligned along the film normal parallel to the tip magnetization. For each magnetostatic mode, a sketch of the expected lateral variation of transverse moment excited by the microwaves at the particular applied field is also indicated.

Figure 4

FMRFM spectra measured at $f_{\mathrm{mw}}=7.7\mathrm{GHz}$ with 60% amplitude modulation at the cantilever resonance frequency for various tip-sample separations. $\vec{H}$ is aligned along the film normal antiparallel to the tip magnetization. The spectra have been vertically offset for clarity.

Figure 5

Comparison of the experimentally determined resonance fields of the modes $m=1,\dots ,5$ for different microwave frequencies (symbols) with theoretical results (solid lines).

Figure 6

(Color online) Images obtained at a tip-sample separation of $150\mathrm{nm}$ and a microwave frequency of $f_{\mathrm{mw}}=7.7\mathrm{GHz}$ 60% amplitude modulated at the cantilever frequency are shown. The lower right-hand panel shows the FMRFM spectrum obtained with the tip located over the center of the permalloy dot [indicated by the star in panels (a)–(c)]. Panels (a)–(c) show the cantilever response obtained in lateral scans over an area $2.5\mathrm{\mu }\mathrm{m}\times 2.5\mathrm{\mu }\mathrm{m}$ at three external fields: $H=11960$, $11980$, and $12040\mathrm{Oe}$. The external magnetic field was aligned parallel to the moment of the tip.

Figure 7

(Color online) Images obtained at a tip-sample separation of $150\mathrm{nm}$ and a microwave frequency of $f_{\mathrm{mw}}=7.7\mathrm{GHz}$ 60% amplitude modulated at the cantilever frequency are shown. The lower right-hand panel shows the FMRFM spectrum obtained with the tip located over the center of the permalloy dot [indicated by the star in panels (a)–(c)]. Panels (a)–(c) show the cantilever response obtained in lateral scans over an area $2.5\mathrm{\mu }\mathrm{m}\times 2.5\mathrm{\mu }\mathrm{m}$ at three external fields: $H=-12640$, $-12600$, and $-12525\mathrm{Oe}$. The external magnetic field was aligned antiparallel to the moment of the tip.