  In this study, we present a complete experimental and theoretical
investigation of the fundamental exciton Zeeman splitting in wurtzite InP
nanowires. We determined the exciton gyromagnetic factor, $g_{exc}$, by
magneto-photoluminescence spectroscopy using magnetic fields up to 29 T. We
found that $g_{exc}$ is strongly anisotropic with values differing in excess of
50\% between the magnetic field oriented parallel and perpendicular to the
nanowire long axis. Furthermore, for magnetic fields oriented along the
nanowire axis, $g_{exc}$ is nearly three times larger than in bulk zincblende
InP and it shows a marked sublinear dependence on the magnetic field, a common
feature to other non-nitride III-V wurtzite nanowires but not properly
understood. Remarkably, this nonlinearity originates from only one Zeeman
branch characterized by a specific type of light polarization. All the
experimental findings are modeled theoretically by a robust approach combining
the $k \cdot p$ method with the envelope function approximation and including
the electron-hole interaction. We revealed that the nonlinear features arise
due to the coupling between Landau levels pertaining to the A (heavy-hole like)
and B (light-hole like) valence bands of the wurtzite crystal structure. This
general behavior is particularly relevant for the understanding of the spin
properties of several wurtzite nanowires that host the set for the observation
of topological phases potentially at the base of quantum computing platforms.
