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		Inverse Melting of Magnetic Domain Structures in Ultrathin Films V. Zablotskii1,2 A. Maziewski1 and T. Polyakova2 1 Institute of Experimental Physics, University of Bialystok, Lipowa 41, 15-424 Bialystok, Poland. 2 Donetsk National University 83055, Donetsk, Ukraine.    Inverse freezing and inverse melting are processes where a more symmetric phase is found at lower temperatures than at higher temperatures [1]. Such inverse transitions were recently observed in physical systems of different nature: vortex matter in high-Tc superconductors [2,3] and domain patterns of ultrathin films [4]. In the former the qualitative picture of the phase transitions can be described as follows: the competition between the vortex-vortex interaction energy (which sets the ordering of the system), and entropy term, TS, that drives disordering, depends on the temperature of the system. In a system with a temperature-independent lateral interaction between the particles, a temperature decrease makes the entropy decrease and leaves the internal energy unchanged. Then, the main contribution to the free energy comes from the internal energy and the minimum of the free energy is reached for the ordered phase. Therefore, the lowering of the temperature causes phase transitions from a disordered phase to an ordered phase or phase transition to the lower-symmetry ordered phase. However, in a vortex system, due to the temperature dependence of the interaction energy, the internal energy also decreases considerably, when temperature is lowered. The swift drop of the internal energy leads to the situation when the disorder term prevails at low temperatures and the free-energy minimum corresponds to a disordered state. The entropy decreasing is overwhelmed by the drop of the internal energy, and then a disorder sets in as if the lateral interaction were switched off. Therefore, the vortex system can undergo a phase transition from an ordered structure to a disordered state with a decrease of temperature. The necessary condition for this effect is the existence of a minimum in the temperature dependence of the normalized interaction potential Eint/kBT[3]. We describe an inverse transition effect in ultrathin magnetic films that are magnetized perpendicular to the film plane. Magnetization state of such a film represents stripe domains with opposite perpendicular magnetization. The key parameters controlling the domain structure (DS) geometry and period are the characteristic length, lc=s/4p MS2 (the ratio between the domain wall and demagnetization energies), and quality factor Q =K/2p MS2(K is the first anisotropy constant). These quantities are temperature dependent and lc(T) plays a role of the interacting potential, like the vortex-vortex potential in the vortex systems. Thus, for films with a pronounced nonmonotonic temperature dependence of l one can expect counter thermodynamic behavior: the inverse phase sequence and cooling-induced disordering. Indeed, on changing temperature the existing domain structure should adopt itself under the new magnitudes of lc and Q. For zero-field case there are two possibilities: i) DS exactly follows the new values of the parameters, conserving the equilibrium DS period; ii) DS keeps a constant period and becomes metastable.Such a metastable state can be fixed by domain wall coercivity and/or by the topological laws restricting the domain wall reconstruction (to delete or create an additional wall one should overcome an energy barrier which is proportional to s ). The metastability degree grows with the temperature. Close to the Curie point lc rapidly changes due to the temperature dependence of the magnetization saturation and the uniaxial anisotropy constant. At the Curie point lc falls to zero, but depending on the competition between K (T), Ms(T) and A(T) ( the exchange constant) dependencies the characteristic length can has a non-monotonic temperature dependence. As above explained this leads to the inverse melting transition. During the transition because of drastic changes of the DS period with the thickness the domain size can vary in several orders of magnitude for a narrow range of film thickness changes (about 2 - 2.1 ML). In the present work we apply the thermodynamic approach to analyze the possible temperature dependencies of the DS period and phase transitions between different domain states. Phase diagrams for magnetization states of ultrathin films are calculated. In the frameworks of this approach the inverse melting of domain structures is well described. One can expect a similar effect in other physical systems exhibiting a nonmonotonic temperature dependence of the interaction potential. The work was supported by Marie Curie Fellowships for "Transfer of Knowledge" ("NANOMAG-LAB", N 2004-003177). [1] A. L. Greer Nature 404, 134 (2000). [2] Avraham N. et al., Nature, 411 (2001) 451; Physica C, 369 (2002) 36. [3] A. Tarasenko, V. Zablotskii and L. Jastrabik Europhys. Letters 62, 63 (2003). [4] O. Portmann, A. Vaterlaus, and D. Pescia, Nature 422, 701 (2003).