We investigate the two- and three-dimensional ferromagnetic Kondo lattice model by unbiased Monte Carlo simulations. A phase diagram for the two-dimensional model is presented, in which the stability of magnetic order and ferromagnetic polarons is examined with respect to the antiferromagnetic superexchange J and temperature. The Monte Carlo simulations reveal that J > 0.02 strengthens individual polarons while small J < 0.02 favors larger clusters and phase separation except for small doping. Lowering the temperature stabilizes ferromagnetic polarons for realistic J > 0.01, while phase separation is only favored for very small J < 0.01. Our Monte Carlo simulations show that low temperatures can lead to diagonal or vertical stripes depending on J. Simulations for three-dimensional systems yield ferromagnetic polarons, which form a `polaron lattice at higher doping levels 0.2 < x < 0.23, when independent polarons do no longer fit into the system. No tendency to phase separation is observed in three dimensions.
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