Visualization of the Barkhausen Effect by Magnetic Force Microscopy

By visualization of the Barkhausen effect using magnetic force microscopy we are able to provide detailed information about the physical principles that govern the magnetization reversal of a granular ferromagnetic thin film with perpendicular anisotropy. Individual Barkhausen volumes are localized and distinguished as either newly nucleated or grown by domain wall propagation. The Gaussian size distribution of nucleated Barkhausen volumes indicates an uncorrelated random process, while grown Barkhausen volumes exhibit an inverse power law distribution, which points towards a critical behavior during domain wall motion.

Figure 1

Domain structures of the $\mathrm{L}{\mathrm{a}}_{\mathrm{0.7}}\mathrm{S}{\mathrm{r}}_{\mathrm{0.3}}\mathrm{M}\mathrm{n}{\mathrm{O}}_{\mathrm{3}}$ thin film recorded along the decreasing branch of the major hysteresis loop. (a)–(f) are part of a series consisting of 158 images [10], which have been acquired on the same scan area while slowly ramping the magnetic field (5 or $10\mathrm{m}\mathrm{T}/\mathrm{\text{image}}$). Image parameters (see Ref. 10 for their explanation): Tip coating: 5 nm Fe, scan height $h=24\mathrm{n}\mathrm{m}$, $f_0=195\mathrm{k}\mathrm{H}\mathrm{z}$, $c_z=47\mathrm{N}/\mathrm{m}$, $A_0=\pm 5\mathrm{n}\mathrm{m}$, $U_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}=-0.1\mathrm{V}$, $\Delta f\mathrm{\text{-range}}=0.7\mathrm{H}\mathrm{z}$.

Figure 2

Visualization and localization of individual Barkhausen jumps from consecutive MFM images. (a) and (b) have been recorded from 275–270 mT and 270–265 mT, respectively. The difference image $(\mathrm{c})=(\mathrm{a})–(\mathrm{b})$ visualizes the reversed regions. In the merged image $(\mathrm{d})=(\mathrm{a})+(\mathrm{c})$, their positions with respect to the initial domain pattern can be determined. The arrows indicate examples for an isolated nucleated Barkhausen volume (N) and a Barkhausen volume adjacent to an already existing domain that has been grown by wall propagation (G).

Figure 3

(a) Size distribution for the radii $r_{\mathrm{B}}(N)$ of nucleated Barkhausen volumes. The solid line is a Gaussian fit with a mean value of 73 nm and width of about 10 nm. (b) Size distribution for the areas $a_{\mathrm{B}}(G)$ of Barkhausen volumes grown by wall propagation using logarithmic binning in a double-logarithmic representation. The solid line corresponds to an inverse power law fit with a critical exponent of $\tau =0.54$ and a cutoff area $a_0=6630{\mathrm{n}\mathrm{m}}^2$.