Equilibrium and metastable nanoscale domains in ultrathin magnets

Full text: Magnetic domain structures (DS) of ultrathin films of thickness, d<lex (the exchange length) exhibit novel features: a sharp thickness dependence of domain sizes and strong reconstruction of magnetization distributions in domains related to anisotropy changes which are essential for an understanding of magnetism on the nanoscale length. The evolution of magnetic DSs and the properties of nanoscaled domains in ultrathin films and wedges with thickness dependent anisotropy are still an open problem. In such samples the reorientation phase transition from the perpendicular to in-plane magnetization state takes place with the increasing film thickness above the critical one. During the transition the DS period decreases in several orders of magnitude in a very narrow film thickness range, e.g., as the Co-film thickness increases from d=1 nm to dl=1.79 nm the magnetization distribution transforms from large domains with sizes and geometry determined mainly by coercivity rather than magnetostatic forces into nanosized sinusoidal-like domains at d∼dl [1]. In this work we analytically and by micromagnetic simulations describe magnetization distributions in films of different thickness and anisotropy. Applying the thermodynamic approach we show that depending on the coercivity field distribution the out-of-equilibrium domains can significantly differ in sizes from the equilibrium ones. Moreover, sizes and geometry of metastable domains depend on magnetic and thermal sample history, e.g. in experiments [2] small metastable 'frozen' by coercivity domains with the period close to the minimal one (pmin∼8πlex2/d, [1]) remained in the film after removal of the applied in-plane magnetic field. In the ultrathin regime (d<lex) the relationship between the periods of metastable (p) and equilibrium (p0) domains is given by ln p/p0=± πhcp/d , where hc=Hc/4πMs is the normalized coercive field, Ms is the magnetization of saturation, and the sign is related with the direction of magnetization process in which the metastable domains were created. Thus, any potential barriers (related with coercivity, sample morphology, shape, and coverage) on the DS energy landscape can affect the domain sizes. The difference in the total energies of the equilibrium and metastable domains is typically less than 1%. However, even such a small energy difference leads to a significant difference in the sizes of equilibrium and out-of-equilibrium domains. Metastable magnetization states can also appear in laterally size limited ultrathin magnets. New types of equilibrium and metastable domain-like magnetization distributions in nanodisks and nanowires we found by micromagnetic simulations. The metastable states could easily be switched by a small external field and therefore used as medium for high density perpendicular recording with highest frequencies. The critical disk radius and wire width under which the magnetization distributions become out-of-plane ones were found by simulations and analytically. The work was supported by Marie Curie Fellowships for 'Transfer of Knowledge' ('NANOMAG-LAB', N 2004-003177) and the Polish State Committee for Scientific Research (Grant No. 4 T11B 006 24). [1] M. Kisielewski et. al., Phys. Rev. B (2004) 69, 184419. [2] M. Kisielewski et. al., J. Appl. Phys. (2003) 93, 6966