Couplings of the gadolinium spin system. (a) The interaction of the different heat baths in an extended three-temperature model. After infrared laser excitation of the valence electrons, the whole system equilibrates by exchanging energy and momentum, indicated by the double arrows. The 5d and 4f spin systems couple via inter- and intra-atomic exchange, where the intra-atomic exchange Jint=130 meV is much larger than the largest (nearest neighbour) inter-atomic exchange Jij=5.9 meV. In thermal equilibrium, the combination of inter- and intra-atomic exchange interactions mediates spin order in the 4f system via the delocalized 5d valence bands...
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