Aspects of the FM Kondo Model: From Unbiased MC Simulations to Back-of-an-Envelope Explanations

Summary. Effective models are derived from the ferromagnetic Kondo lattice model with classical corespins, which greatly reduce the numerical effort. Results for these models are presented. They indicate that double exchange gives the correct order of magnitude and the correct doping dependence of the Curie temperature. Furthermore, we find that the jump in the particle density previously interpreted as phase separation is rather explained by ferromagnetic polarons. Manganites [1] are often described by the ferromagnetic Kondo lattice model, which is considered to explain some of their features, e.g., the transition from antiferromagnetic to ferromagnetic order with doping [2]. The application of the model is motivated by the fact, that crystal field splitting divides the five d-orbitals into two eg and three t2g orbitals, where the latter are energetically favored in the case of manganites. All three t2g orbitals are singly occupied and rather localized. Due to a strong Hund’s rule coupling, these electrons are aligned in parallel and form a core spin with length S = 3/2. The filling of the eg orbitals is determined by doping and these electrons can hop from one Mn ion to the next via the intermediate oxygen. Hund’s rule coupling leads to a ferromagnetic interaction between the itinerant eg electrons and the t2g core spin. The core spins interact through super exchange leading to a weak antiferromagnetic coupling between them. In this chapter, we derive effective models for the ferromagnetic Kondo lattice model and introduce suitable Markov chain Monte Carlo (MC) algorithms. The presented results, were not obtainable by simple analytic considerations, are partly found by this MC method and partly by use of the Wang-Landau algorithm [3].