Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice with the first (J 1 ), second (J 2 ), third (J 3 ) fourth (J 4 ) and fifth (J 5 ) nearest-neighbour spin couplings are studied by the classical Monte Carlo method. It is shown that switching on J 4 and J 5 interactions (in addition to usually considered J 1 , J 2 and J 3 interactions) changes significantly the picture of magnetization processes found for J 4 = J 5 = 0 and leads to stabilization of new macroscopic magnetic phases (plateaus) with fractional magnetization. In particular, it is found that combined effects of J 4 and J 5 interactions generate the following sequence of plateaus with the fractional magnetization: m/m s =1/9, 1/6, 2/9, 1/3, 4/9, 1/2, 5/9 and 2/3. The results obtained are consistent with experimental measurements of magnetization curves in selected rare-earth tetraborides.attracted much attention after its experimental realization in the SrCu 2 (BO 3 ) 2 compound [2,3]. The observation of a fascinating sequence of magnetization plateaus (m/m s =1/2, 1/3, 1/4 and 1/8) in this material stimulated further theoretical [6,7] and experimental studies [8,9] of the SSL. Some time later, many other Shastry-Sutherland magnets have been discovered. In particular, this concerns an entire group of rare-earth metal tetraborides RB 4 (R = La − Lu). These compounds have the tetragonal crystal symmetry P 4/mbm with magnetic ions R 3+ located on the SSL in with the J 3 interaction is able to generate a number of new magnetization plateaus with the fractional magnetization: m/m s =1/10, 1/9, 1/6, 1/5, 2/5, 4/9, 7/15 and 5/9 in accordance with experimental measurements of magnetization curves in selected rare-earth tetraborides. However, these results can not be considered as definite since the J 4 interaction is the fourth nearest-neighbour interaction only for these values of J 1 and J 2 that satisfy the condition J 1 < J 2 (the case of SrCu 2 (BO 3 ) 2 compound), but not for the case J 1 = J 2 that corresponds to the real situation in rare-earth tetraborides. In this case the J 4 interaction is the fifth nearest neighbor interaction and thus for correct description of situation in rare earth tetraborides it is necessary to

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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