Magnetic phase diagram of the Ising model with the long-range RKKY interaction

Abstract

The standard Metropolis algorithm and the parallel tempering method are used to examine magnetization processes in the Ising model with the long-range RKKY interaction on the Shastry-Sutherland lattice. It is shown that the Ising model with RKKY interaction exhibits, depending on the value of the Fermi wave vector k F , the reach spectrum of magnetic solutions, which is manifested in the appearance of new magnetization plateaus on the magnetization curve. In particular, we have found the following set of individual magnetization plateaus with fractional magnetization m/m s =1/18, 1/9, 1/8, 1/5, 1/4, 1/3, 3/8, 5/12, 1/2, 3/5, 2/3, which for different values of k F form various sequences of plateaus, changing from very complex, appearing near the point k F = 2π/1.2, to very simple appearing away this point. Since the change of k F can be induced by doping (the substitution of rare-earth ion by other magnetic ion that introduces the additional electrons to the conduction band) the model is able to predict the complete sequences of magnetization plateaus, which could appear in the tetraboride solid solutions.In the past decade, a considerable amount of effort has been devoted to understanding the underlying physics that leads to anomalous magnetic properties of metallic Shastry-Sutherland magnets [1,2,3,4]. However, in spite of an impressive research activity, the properties of these systems are far from being understood. In particular, this concerns the entire group of rare-earth metal tetraborides RB 4 (R = La − Lu) that exhibits the strong geometrical frustration. These compounds have the tetragonal crystal symmetry P 4/mbm with magnetic ions R 3+ located on an Archimedean lattice (see Fig.1a) that is topologically equivalent to the so-called Shastry-Sutherland lattice [5] (see Fig. 1b). It is supposed that the anomalous properties of these systems Figure 1: The real structure realized in the (001) plane of rare-earth tetraborides (a), which is topologically identical to the Shastry-Sutherland lattice (b). J 1 , J 2 , J 3 , J 4 and J 5 denote the first, second, third, fourth and fifth nearest neighbors on the real Archimedean lattice.are caused by the geometrical frustration that leads to an extensive degeneracy in the ground state. The most famous manifestation of the geometrical frustration in the above-mentioned tetraborides is the observation of the fascinating sequence of magnetization plateaus with the fractional magnetization. For example, for ErB 4 the magnetization plateau has been found at m/m s = 1/2 [2, 3], for T bB 4 at m/m s =2/9, 1/3, 4/9, 1/2 and 7/9 [4], for HoB 4 at m/m s =1/3, 4/9 and 3/5 [2] and for T mB 4 at

Evolution of field-induced metastable phases in the Shastry-Sutherland lattice magnet TmB4

“…Considerable efforts have been dedicated to models of TmB 4 with competing further neighbor (i.e. Ruderman-Kittel-Kasuya-Yoshida) interactions, which can be parametrized to produce long-range ordered phases in both 1/2 and 1/8 plateaus [18][19][20][21][22][23][24][25][26][27][28]. Experiments are usually interpreted in terms of simple structures implied by idealized values of the plateau magnetization (e.g., [31,36]).…”

“…1 [17]. The 1/2 plateau can be explained by calculations of the ground state of frustrated Ising models on a SSL [18][19][20][21][22][23][24][25][26][27][28] but the 1/8 plateau is more difficult to rationalize. It appears in some models, but interpretations in terms of complex structures at domain walls [17] or incommensurate modulated magnetic order [29,30] have also been proposed.…”