  The theoretical inception of the Kitaev honeycomb model has had defining
influence on the experimental hunt for quantum spin liquids, bringing
unprecedented focus onto the synthesis of materials with bond-directional
interactions. Numerous Kitaev materials, which are believed to harbor ground
states parametrically close to the Kitaev spin liquid, have been investigated
since. Yet, in these materials the Kitaev interaction often comes hand in hand
with off-diagonal $\Gamma$ interactions -- with the competition of the two
potentially giving rise to a magnetically ordered ground state. In an attempt
to aid future material investigations, we study the phase diagram of the
spin-1/2 Kitaev-$\Gamma$ model on the honeycomb lattice. Employing a
pseudofermion functional renormalization group approach which directly operates
in the thermodynamic limit and captures the joint effect of thermal and quantum
fluctuations, we unveil the existence of extended parameter regimes with
emergent incommensurate magnetic correlations at finite temperature. We
supplement our study with additional calculations on a finite cylinder geometry
to investigate the impact of periodic boundary conditions on the incommensurate
order, thereby providing a new perspective on previous numerical studies on
finite systems.
