In this work it is established that for regularities of the magneto-optical response from curved magnetic nanosructures, a crossover occurs at certain scales. At scales less than characteristic length the normalized value of magneto-optical hysteresis loop for transverse magneto-optical Kerr effect does not depend on incident angle of electromagnetic radiation. For curved nanostructures at scales of the order or large than characteristic length and at certain incident angles, hysteresis loops were observed that are inherent in magnetic vortex structures. For systems based on nanometers thick cobalt films deposited on various nanostructured substrates the characteristic length is of about of 100 nm. On the basis of the experimental data the energy consumption for the formation of vortex structures is estimated.
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