  Context. In chemically peculiar Ap/Bp stars with large-scale organised
magnetic fields with a simple centred dipole configuration, the ratio between
the maximum and the minimum of the mean magnetic field modulus is of the order
of 1.25. Values of 2 or more are observed only for very few Ap/Bp stars and are
indicative of a very unusual magnetic field geometry. Aims. Determining the
magnetic field structure of Ap/Bp stars is bound to provide a different insight
into the physics and the origin of the magnetic fields in early-type stars. In
this respect, the Bp star HD 57372 is of particular interest because strongly
variable magnetically split lines are observed in HARPS and APOGEE spectra.
Methods. We obtained and analysed measurements of the mean magnetic field
modulus and of the mean longitudinal magnetic field using near-infrared spectra
and optical polarimetric spectra distributed over the stellar rotation period.
Results. The mean magnetic field modulus <B> of HD 57372, as estimated from
absorption lines that are split via the Zeeman effect and resolved in both
optical and near-infrared spectra, is found to vary by an extraordinary amount
of about 10 kG. The exceptional value of 3 for the ratio between the maximum
and the minimum of the field modulus is indicative of a very unusual geometry
of HD 57372's magnetic field. All observable quantities are found to vary in
phase with the photometric period of 7.889 days. This includes the longitudinal
magnetic field <Bz>, which varies from -6 kG up to 1.7 kG in FORS2 spectra as
well as the metal line strengths, whose equivalent widths change by up to 50%
of their mean values over the course of the rotation period. The B8 temperature
class of HD 57372 also places it among the hottest stars known to exhibit
resolved, magnetically split lines.
