  Magneto-optical spectroscopy in fields up to 30 Tesla reveals anomalies in
the equilibrium and ultrafast magnetic properties of the ferrimagnetic
rare-earth-transition metal alloy TbFeCo. In particular, in the vicinity of the
magnetization compensation temperature, each of the magnetizations of the
antiferromagnetically coupled Tb and FeCo sublattices show triple hysteresis
loops. Contrary to state-of-the-art theory, which explains such loops by sample
inhomogeneities, here we show that they are an intrinsic property of the
rare-earth ferrimagnets. Assuming that the rare-earth ions are paramagnetic and
have a non-zero orbital momentum in the ground state and, therefore, a large
magnetic anisotropy, we are able to reproduce the experimentally observed
behavior in equilibrium. The same theory is also able to describe the
experimentally observed critical slowdown of the spin dynamics in the vicinity
of the magnetization compensation temperature, emphasizing the role played by
the orbital momentum in static and ultrafast magnetism of ferrimagnets.
