Formation of Magnetization Plateaus in Rare Earth Tetraborides: Exact Diagonalization and Quantum Monte Carlo Studies

Ground state and thermodynamic properties of the coupled double-Ising model: application to rare-earth tetraborides

“…Moreover, both subsystems are coupled by the anisotropic spin-dependent interaction of the Ising type. In these points the model accords with the previous ones [19][20][21]. However, to model the most realistically situation in rare-earth compounds we have considered there instead the same spins in both subsystems, different combination of mixed spins: S = 1, 3/2 and 2 in the spin subsystem and s = 1/2 in the electron subsystem, which corresponds to real rare-earth compounds (S(Ho 3+ ) = 2, S(Er 3+ ) = 3/2 and S(Tm 3+ ) = 1).…”

“…Unfortunately, the reduction of the 1/3 plateau phase and the stabilization of the 1/2 plateau phase due to the spin-electron Ising coupling is still too small to reach the accordance between the theoretical and experimental results and therefore a further generalization of the model is needed. The subsequent numerical studies that we have performed on the generalized model [20,21], which considers instead the Ising coupling a more realistic Heisenberg coupling and instead the noninteracting electrons, the interacting electrons (within the Hubbard model) showed that both the Hubbard as well as Heisenberg interaction stabilize the 1/2 plateau and suppress the 1/3 plateau, but their effects are still not sufficiently strong to suppress completely the 1/3 plateau, which stability region is comparable with one of the 1/2 plateau phase. To remove this discrepancy we have proposed in our very recent paper [22] a new simple, but realistic spin-electron model.…”

Phase Diagram Mapping out the Complex Magnetic Structure of Single Crystals of (Gd, Er)B4 Solid Solutions

“…We also point out that the pristine ErB 4 compound exhibits a strong Ising-type singleion anisotropy with an easy magnetization axis along the c-axis [4]. On the other hand, the single-ion anisotropy of Gd is considered small, and GdB 4 can be described as a noncollinear Heisenberg antiferromagnet with the easy axis along the (110) direction [29].…”

“…Therefore, the partial substitution of Er by Gd has an impact on the magnetic anisotropy of the Gd 1−x Er x B 4 solid solution. Such a little but important variation in ionic radii, along with the difference in the magnetic moments between Gd and Er, may, in turn, influence the geometrically frustrated exchange interaction and the exchange couplings, with these effects playing fundamental roles in stabilizing distinct magnetic states [4]. This point is currently under investigation.…”

“…A very well-known geometrical frustrated system is the Shastry-Sutherland lattice, which can be realized in a group of layered compounds [3]. The Shastry-Sutherland model has also been realized in systems displaying magnetization plateaus in the presence of a magnetic field [3][4][5].…”