  The appearance of nontrivial phases in Kitaev materials exposed to an
external magnetic field has recently been a subject of intensive studies. Here,
we elucidate the relation between the field-induced ground states of the
classical and quantum spin models proposed for such materials, by using the
infinite density matrix renormalization group (iDMRG) and the linear spin wave
theory (LSWT). We consider the $K \Gamma \Gamma'$ model, where $\Gamma$ and
$\Gamma'$ are off-diagonal spin exchanges on top of the dominant Kitaev
interaction $K$. Focusing on the magnetic field along the $[111]$ direction, we
explain the origin of the nematic paramagnet, which breaks the
lattice-rotational symmetry and exists in an extended window of magnetic field,
in the quantum model. This phenomenon can be understood as the effect of
quantum order-by-disorder in the frustrated ferromagnet with a continuous
manifold of degenerate ground states discovered in the corresponding classical
model. We compute the dynamical spin structure factors using a matrix operator
based time evolution and compare them with the predictions from LSWT. We, thus,
provide predictions for future inelastic neutron scattering experiments on
Kitaev materials in an external magnetic field along the $[111]$ direction. In
particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone
mode which results from the lifting of a continuous degeneracy via quantum
fluctuations.
