  The competing spin orders and fractional magnetization plateaus of classical
Heisenberg model with long-range interactions on a Shastry-Sutherland lattice
are investigated using Monte Carlo simulations, in order to understand the
fascinating spin ordering sequence observed in TmB4 and other rare-earth
tetraborides. The simulation reproduces the experimental 1/2 magnetization
plateau at low temperature by considering multifold long range interactions. It
is found that more local long range interactions can be satisfied in the 1/2
plateau state than those in the 1/3 plateau state, leading to the stabilization
of the extended 1/2 plateau. A mean-field theory on the spin ground states in
response to magnetic field is proposed, demonstrating the simulation results.
When the energies of the Neel state and the collinear state are degenerated,
the former state is more likely to be stabilized due to the competitions among
the local collinear spin orders. The present work provides a comprehensive
proof of the phase transitions to the Neel state at nonzero temperature, in
complimentary to the earlier predictions for the Fe-based superconductors.
