Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice: effects of long-range interactions

Abstract

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

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.…”

DMRG study of exciton condensation in the extended Falicov-Kimball model

“…On the other hand, it should be noted that the original version of the model, as well as its extensions discussed above, represent a too crude approximation of real rare-earth compounds, since we neglect all nonlocal Coulomb interactions, that can change this picture. For a correct description of these materials one should take into account at least the following nonlocal Coulomb interaction terms [39]:…”

“…In this article we focus our attention on the properties of the EI phase induced by local hybridization 𝑉 in the one dimension. Although it is generally known that there is no nonvanishing 𝑃 𝑑 𝑓 = 𝑑 + 𝑓 expectation value in the limit of vanishing hybridization (no spontaneous hybridization), the studies that we performed in the past years on various extensions of the original Falicov-Kimball model showed that it is possible to dramatically enhance excitonic correlations in the limit of small, but finite 𝑉 by additional interactions/factors [36][37][38][39]. The effects of most important interactions are discussed in this review.…”

“…(Colour online) n 0 , n d , n T and n un d = n d − n T as functions of E f calculated for four different values of U ch (U ch = 0, 0.2, 0.4, 0.5) at U nn = U ch , U = 1, V = 0.1, L = 100 and n f + n d = 1[39].…”