Formation of magnetization plateaus in the 3D Ising model with the long-range RKKY interaction: application to rare-eart
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Formation of magnetization plateaus in the 3D Ising model with the long-range RKKY interaction: application to rare-earth tetraborides Lubom´ıra Regeciov´a and Pavol Farkaˇsovsk´ ya Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Koˇsice, Slovakia
Received 9 March 2020 / Received in final form 5 May 2020 Published online 15 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The standard Metropolis algorithm and the parallel tempering method are used to study the influence of the long-range RKKY interaction on the formation of magnetization plateaus in the 3D Ising model with magnetically coupled Shastry-Sutherland layers. It is shown that depending on the Fermi momentum kF the model exhibits the rich spectrum of magnetic solutions which is demonstrated by the appearance of the large number of magnetization plateaus on the magnetization curves. In particular, the following set of individual fractional magnetization plateaus with macroscopic stability regions is observed: m/ms = 1/8, 1/7, 1/6, 1/5, 2/9, 1/4, 1/3, 3/8, 2/5, 5/12, 3/7, 1/2, 5/9 and 2/3. In the regime of kF ∼ 2π/1.24, corresponding to the real situation in T mB4 , we have confirmed the existence of the magnetization plateau with m/ms = 1/8, the nature of which was intensively discussed in recent experimental works. Since the change of kF can be induced by doping, our results provide predictions of the complete sequences of magnetization plateaus that could appear in tetraboride solid solutions. And finally, the current results are confronted with our previous ones obtained for the two-dimensional Ising model with the RKKY interaction in order to reveal the role of system dimension on the formation of magnetization plateaus.
1 Introduction The formation of fascinating sequences of magnetization plateaus with fractional magnetization has been in the centre of experimental as well as theoretical investigation of metallic rare-earth tetraborides (RB4 ) for decades. The RB4 compounds crystalize in tetragonal structure with space group P4/mbm (Fig. 1a) with layers of magnetic ions R3+ formed an Archimedean lattice (Fig. 1b) topologically equivalent to the so-called Shastry-Sutherland lattice (see Fig. 1c). This lattice was proposed almost 40 years ago by Shastry and Sutherland [1] as a purely theoretical example of a two-dimensional frustrated spin system. It can be depicted as a square lattice with four anti-ferromagnetic couplings J and one additional diagonal anti-ferromagnetic coupling J 0 , as shown in Figure 1b. Although all members of the metallic RB4 family share very similar structure, their magnetization curves are completely different. Low temperature magnetization measurements have shown that the fractional magnetization plateaus are formed at m/ms = 1/8 and 1/2 in the T mB4 [2,3], at m/ms = 1/2 in the ErB4 [4], at m/ms = 1/3, 4/9 and 3/5 in the HoB4 [4] and at m/ms = 2/9, 1/3, 4/9, 1
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