The magnetization behaviors and spin configurations of the classical Ising model on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the fascinating magnetization plateaus observed in TmB(4) and other rare-earth tetraborides. The simulations reproduce the 1/2 magnetization plateau by taking into account the dipole-dipole interaction. In addition, a narrow 2/3 magnetization step at low temperature is predicted in our simulation. The multi-step magnetization can be understood as the consequence of the competitions among the spin-exchange interaction, the dipole-dipole interaction, and the static magnetic energy.
PACS 75.10.Hk -Classical spin models PACS 07.55.Db -Generation of magnetic fields; magnets PACS 71.10.Hf -Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems Abstract -The dynamic magnetization behaviors of the classical Ising model on the Shastry-Sutherland lattice with additional long-range interactions are investigated by means of the Glauber dynamics, in order to understand the fascinating magnetization plateaus and the hysteresis loop observed in TmB4. With this algorithm, the experimental 1/n (n = 7, 9, 11) magnetization plateaus as well as the main 1/2 one can be reproduced at low temperatures. Furthermore, the hysteresis loop can also be well explained by the present theory. It is indicated that the formation of domain walls due to the non-equilibrium magnetization process may be responsible for the emergence of the fractional plateaus.
The ordering of the classical Ising model on the Archimedean lattice that is topologically equivalent to the Shastry-Sutherland one is studied in order to understand the fascinating magnetic properties experimentally observed in rare-earth tetraborides such as TmB4. The long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction which is expected to be predominant in these systems is taken into account, and the magnetization plateaus and rich ordering behaviors depending on the Fermi wave vector are investigated in details by Monte Carlo simulation. The experimental 1/2 magnetization step can be qualitatively reproduced and its stability against the change of is confirmed, suggesting that the coupling between conduction electrons and localized moments may play an important role in modulating the magnetization behaviors in these systems.
[Abstract] 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 TmB 4 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.
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