Magnetization plateaus and phase diagrams of the Ising model on the Shastry–Sutherland lattice

Deviren, Şeyma Akkaya

doi:10.1016/j.jmmm.2015.06.022

Cited by 5 publications

(2 citation statements)

References 46 publications

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“…The existence of the magnetization plateau at only 1/3 and its absence at 1/2 (as observed for example in ErB 4 and TmB 4 ) indicates that it is necessary to go beyond the classical Ising limit to reach the correct description of the magnetization processes in rare-earth tetraborides. The subsequent analytical [10][11][12][13] and numerical [9,[14][15][16][17] studies of various extensions of the Ising model with the third, fourth and even fifth nearest neighbors showed that the generalized model is able to describe some of the individual plateaus observed in rare-earth materials, but it is questionable if it is the intrinsic property of a model, or only a consequence of the large number of variables (fitting parameters) that enter to the model as interaction parameters.…”

Section: Introductionmentioning

confidence: 99%

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

Farkašovský¹,

Regeciová²

2022

J. Phys.: Condens. Matter

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A combination of the standard Metropolis algorithm and the parallel tempering method is used to study ground-state and thermodynamic properties of the coupled double Ising (CDI) model on the Shastry-Sutherland lattice (SSL). This model is derived from the complex spin-electron model, in which electrons described by the Hubbard model and spins described by the Ising model interact via the anisotropic spin-dependent interaction of the Ising type, under the following three conditions: (i) the Hubbard interaction between electrons in the conduction band is sufficiently large; (ii) the number of conduction electrons is equal to the number of the lattice points; (iii) there is the easy axis spin anisotropy in the system. The model is solved numerically for the selected combinations of spins from the electron ($s=1/2$) and spin ($S=1,3/2,2$) Ising branch which represent very realistically the situation in TmB$_4$, ErB$_4$ and HoB$_4$ compounds, where in addition all three conditions are simultaneously satisfied. It is shown that the interlpay between the electron and spin branch of the CDI model leads to the suppression of the 1/3 magnetization plateau (the main magnetization plateau found in the ordinary Ising model on the SSL) and the stabilization of magnetization plateaus with $m\sim 1/2$, which is in perfect agreement with the experimental measurements in TmB$_4$ and ErB$_4$ compounds. A nice correspondence between theoretical and experimental results is also obtained for the temperature dependence of the specific heat capacity, where the low-temperature peak corresponding to the electron branch of the CDI model is followed by high-temperature peak of the spin branch. This opens a new route for exploring the physics of other complex spin-electron systems in which the above-mentioned conditions (i)-(iii) are fulfilled.

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Section: Introductionmentioning

confidence: 99%

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

Farkašovský¹,

Regeciová²

2022

J. Phys.: Condens. Matter

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“…Thus, the study of the Ising limit was the first natural step towards the complete understanding of magnetization processes in rare-earth tetraborides. The subsequent analytical [6,7,8,9] and numerical [10,11,12,13] studies showed that the basic version of the Ising model on the Shastry-Sutherland lattice, with nearest and next-nearest neighbor interactions and its extensions, up to the 5th nearest neighbors, are able to describe some of the individual plateaus observed in rare-earth materials, as well as the partial sequences consisting of two or even three right magnetization plateaus, but not the complete sequences. These theoretical works point to the fact that for the correct description of magnetization processes in rare-earth tetraborides one has to consider the long-range interactions.…”

Section: Introductionmentioning

confidence: 99%

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

Regeciová

Farkašovský

2019

Eur. Phys. J. B

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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

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Dynamic phase transitions and dynamic phase diagrams of the Ising model on the Shastry-Sutherland lattice

Deviren

2016

Journal of Magnetism and Magnetic Materials

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Magnetization plateaus and phase diagrams of the Ising model on the Shastry–Sutherland lattice

Cited by 5 publications

References 46 publications

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

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

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

Dynamic phase transitions and dynamic phase diagrams of the Ising model on the Shastry-Sutherland lattice

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