Formation of Magnetization Plateaus in Rare Earth Tetraborides: Exact Diagonalization and Quantum Monte Carlo Studies
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ORIGINAL PAPER
Formation of Magnetization Plateaus in Rare Earth Tetraborides: Exact Diagonalization and Quantum Monte Carlo Studies Pavol Farkaˇsovsky´ 1 · Lubom´ıra Regeciova´ 1 Received: 28 April 2020 / Accepted: 4 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A relatively simple model based on the coexistence of spin and electron subsystems is proposed for a description of magnetization processes in metallic rare earth tetraborides. The model takes into account the Ising interaction between the localized spins, the Hubbard interaction between the itinerant electrons, and the Ising interaction between electron and spin subsystems. To solve this model, a combination of small cluster exact diagonalization calculations and quantum Monte Carlo simulations is used. Particular attention is paid to a description of correlation effects (the Hubbard interaction) on formation and stabilization of magnetization plateaus with fractional magnetizations. It is shown that the Hubbard interaction significantly stabilizes the 1/2 magnetization plateau and simultaneously suppresses the 1/3 magnetization plateau, in accordance with experimental measurements in rare earth tetraborides. Keywords Magnetization plateaus · Shastry-Sutherland lattice · Rare earth tetraborides
1 Introduction In the past decade, a considerable amount of effort has been devoted to understanding of the multitude of anomalous magnetic properties of the so-called Shastry-Sutherland rare earth metal tetraborides. One of the most interesting of them is surely the formation of fascinating sequences of magnetization plateaus with fractional magnetizations. They are observed practically for all members of the metallic RB4 family group (R = Tb, Dy, Ho, Er, Tm, etc.) and form a wide spectrum of magnetization curves in these materials. For instance, a single plateau at onehalf of the saturation magnetization (m/ms = 1/2) has been observed in ErB4 [1]. In T mB4 , in addition to an extended 1/2-plateau a narrow plateau with fractional value of m/ms = 1/8 for temperatures below 4 K has been detected [2, 3], and in T bB4 very complex sequence, consisting of several magnetization plateaus with fractional magnetizations m/ms = 1/2, 4/9.1/3, 2/9, 7/9 is found [4].
Pavol Farkaˇsovsk´y
[email protected] 1
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, Koˇsice, 040 01, Slovakia
It is supposed that the anomalous properties of these systems are caused by the geometrical frustration that leads to an extensive degeneracy in the ground state. Indeed, all above mentioned compounds have the tetragonal structure (space group P4/mbm) with magnetic ions R 3+ located on an Archimedean lattice that is topologically equivalent to the so-called Shastry-Sutherland lattice [5] that exhibits the strong geometrical frustration (see Fig. 1). Moreover, since there are the strong crystal field effects, these compounds can be described in terms of an effective spin-1/2 Shastry-Sutherland model under strong Ising anisotrop
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