Scaling collapse of the irreversible magnetization of ferromagnetic thin films*

The irreversible magnetization, \textit{$\Delta $M}, defined as the difference of field-cooled magnetization $M_{FC}$ and zero-field-cooled magnetization $M_{ZFC}$, has been measured for a variety of ferromagnetic thin films as a function of magnetic field $H$ at different temperatures $T$. Isotherms of \textit{$\Delta $M} show maxima\textit{ $\Delta $M}$_{max}$ at characteristic temperature-dependent fields $H_{m}(T)$. At very low and high magnetic fields the values of $M_{FC}$ and $M_{ZFC}$ converge and \textit{$\Delta $M} is observed to approach zero in these limits. If \textit{$\Delta $M/$\Delta $M}$_{max}$ is plotted as a function of $H/H_{m}$ for a given ferromagnetic system, the graphs for different temperatures collapse onto the same curve. This scaling collapse is clearly seen for three different ferromagnetic thin-film systems: polycrystalline gadolinium, phase separated manganites, and single domain Ni nanomagnetic grains embedded in an insulating host. Similar scaling behavior has also been observed in spin-glass material [1]. These results represent a heretofore unrecognized scaling behavior that appears to apply to a broad range of ferromagnetic systems. [1] V. S. Zotev, G. G. Kenning, and R. Orbach, Phys. Rev. B \textbf{66}, 014412 (2006)