  We investigate the low temperature magnetic phases in TmB_4, a metallic
quantum magnet on the geometrically frustrated Shastry-Sutherland lattice,
using co-ordinated experimental and theoretical studies. Our results provide an
explanation for the appearance of the intriguing fractional plateau in TmB_4
and accompanying magnetic hysteresis. Together with observation of the bump in
the half-plateau, our results support the picture that the magnetization
plateau structure in TmB_4 is strongly influenced by the zero-field modulated
phases. We present a phenomenological model to explain the appearance of the
modulated phases and a microscopic Hamiltonian that captures the complete
magnetic behavior of TmB_4.
