Ferromagnetic Domain Walls in finite systems: mean-field critical exponents and applications

The distribution of magnetic moments in finite ferromagnetic bodies was first investigated by Landau and Lifshitz in a famous paper [\textit{Phys. Z. Soviet Union}, \textbf{8}, 153 (1935)], where they obtained the domain structure of a ferromagnetic crystal at low temperatures, in the regime of saturated magnetization. In this article, we investigate the general properties of ferromagnetic domain walls of uniaxial crystals from the view point of the Landau free energy. We present the basic ideas at an introductory level, for non-experts. Extending the formalism to the vicinity of the Curie temperature, where a general qualitative description by the Landau theory of phase transitions can be applied, we find that domain walls tend to suppress the layers, leading to a continuous vanishing of the domain structure with anomalous critical exponents. In the saturated regime, we discuss the role of domain walls in mesoscopic systems and ferromagnetic nanojunctions, relating the observed magnetoresistance with promising applications in the recent area of spintronics.