Splitting of the second magnetization peak in the superconductorTl2Ba2CaCu2O8+x

Abstract

We show that transition states during spin flips, besides interspin exchange and on-site anisotropy, are necessary for a complete description of monatomic spin chains, and study the dynamical spin system using kinetic Monte Carlo method based on transition-state theory. Using experimental parameters of the monatomic Co spin chains on Pt surfaces, we produce the experimental hysteresis loop at 10 K and show that there is no hysteresis loops at 45 K. There is a phase crossover from the long-range ferromagnetism at low temperature to disordered magnetic states at high temperature. Our systematical simulation shows that the chain-length dependence of the long-range ferromagnetism is very weak and even approaches to zero when the chain length becomes large enough. The crossover temperature is a monotonously increasing function of the sweeping rate of changing magnetic field. The simulations are justified because the quantum effect can be ignored except for very low temperatures. Our theory explains the ferromagnetism of finite one-dimensional spin chains with large magnetic anisotropy such as the monatomic Co chains on Pt surfaces.