  Magnetism of Cu$_2$(OH)$_3$Br single crystals based on a triangular lattice
is studied by means of magnetic susceptibility, pulsed-field magnetization, and
specific heat measurements. There are two inequivalent Cu$^{2+}$ sites in an
asymmetric unit. Both Cu$^{2+}$ sublattices undergo a long-range
antiferromagnetic (AFM) order at $T\rm_N$ = 9.3 K. Upon cooling, an anisotropy
crossover from Heisenberg to $XY$ behavior is observed below 7.5 K from the
anisotropic magnetic susceptibility. The magnetic field applied within the $XY$
plane induces a spin-flop transition of Cu$^{2+}$ ions between 4.9 T and 5.3 T.
With further increasing fields, the magnetic moment is gradually increased but
is only about half of the saturation of a Cu$^{2+}$ ion even in 30 T. The
individual reorientation of the inequivalent Cu$^{2+}$ spins under field is
proposed to account for the magnetization behavior. The observed spin-flop
transition is likely related to one Cu site, and the AFM coupling among the
rest Cu spins is so strong that the 30-T field cannot overcome the anisotropy.
The temperature dependence of the magnetic specific heat, which is well
described by a sum of two gapped AFM contributions, is a further support for
the proposed scenario.
