  Magnetic fields can give rise to a plethora of phenomena in Kitaev spin
systems, such as the formation of non-trivial spin liquids in two and three
spatial dimensions. For the original honeycomb Kitaev model, it has recently
been observed that the sign of the bond-directional exchange is of crucial
relevance for the field-induced physics, with antiferromagnetic couplings
giving rise to an intermediate spin liquid regime between the low-field gapped
Kitaev spin liquid and the high-field polarized state, which is not present in
the ferromagnetically coupled model. Here, by employing a Majorana mean-field
approach for a magnetic field pointing along the [001] direction, we present a
systematic study of field-induced spin liquid phases for a variety of two and
three-dimensional lattice geometries. We find that antiferromagnetic couplings
generically lead to (i) spin liquid phases that are considerably more stable in
field than those for ferromagnetic couplings, and (ii) an intermediate spin
liquid phase which arises from a change in the topology of the Majorana band
structure. Close inspection of the mean-field parameters reveal that the
intermediate phase occurs due to a field-driven sign change in an 'effective'
$z$-bond energy parameter. Our results clearly demonstrate the richness of the
Majorana physics of the antiferromagnetic Kitaev models, in comparison to their
ferromagnetic counterparts.
