Magnetic properties of the spin‐1/2 Ising–Heisenberg diamond chain with the four‐spin interaction

Abstract

Phone: + 421 55 602 2228A symmetric spin-1/2 Ising-Heisenberg diamond chain with the Ising four-spin interaction is exactly solved by means of the generalized decoration-iteration mapping transformation. The ground state, the magnetization process and thermodynamics are particularly examined for the case of antiferromagnetic pair interactions (Ising and isotropic Heisenberg ones). It is shown that an interplay between pair interactions, the four-spin interaction and the external magnetic field gives rise to several quantum ground states with entangled spin states in addition to some semi-classically ordered ones. Besides, the temperature dependence of the magnetic susceptibility multiplied by the temperature is studied and the interesting triple-peak specific heat curve is also detected when considering the zero-field region rather close to the triple point, where three different ground states coexist.Copyright line will be provided by the publisher 1 Introduction Spin systems with multispin exchange interactions represent objects of scientific interest in the past few years. Research in this field leads to a deeper understanding of many interesting physical phenomena, such as the non-universal critical behaviour [1,2], optical conductivity [3], Raman peaks [4], as well as, deviations from the Bloch T 3/2 law at low temperatures [5,6]. Moreover, the effect of magnetic field on the ground state of quantum systems with cyclic four-spin interaction has been recently particularly examined as well [7,8,9]. Of course, the immense theoretical interest to the spin models with multispin interactions is not purposeless. Multispin interactions have been experimentally observed in real triangular magnetic systems composed of 3 He atoms absorbed on graphite surfaces [10], the hydrogen bonded ferroelectrics PbHPO 4 and PbDPO 4 [11], as well as, the squaric acid crystal (H 2 C 2 O 4 ) [12,13,14] and some copolymers [15]. Recently, it was shown that the cyclic four-spin interaction could also explain the neutron-scattering experiments concerning high-T c compounds such as La 2 CuO 4 [16], La 6 Ca 8 Cu 24 O 41 [17,18], and La 4 Sr 10 Cu 24 O 41 [19].On the theoretical side, in spite of the numerous numerical studies predicting rich phase diagrams [20,21,22,23], a number of important questions concerning the spin ordering and the critical behaviour of quantum Heisenberg models realized by the four-spin interaction, remain unclear due to controversial results obtained by different treatments [24,25,26,27]. From this point of view, the exactly solvable models play an important role in understanding the multispin effects. Of course, the quantum spin models is very difficult to deal with exactly due to a rather cumbersome and sophisticated mathematics, which precludes an exact treatment of the most (even simpleminded) spin systems. Motivated by this fact, a special class of the hybrid Ising-Heisenberg models [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] has been recently proposed, which overcome the afore-mentioned mathematical di...

Magnetocaloric effect in the spin-1/2 Ising-Heisenberg diamond chain with the four-spin interaction

“…Finally, the last two terms determine the magnetostatic Zeeman's energy of the Ising and Heisenberg spins placed in an external magnetic field H oriented along the z-axis. It is worth mentioning that the considered quantum-classical model is exactly solvable within the framework of a generalized decoration-iteration mapping transformation [20][21][22] (for more computational details see our recent works [25] and [7]). As a result, one obtains a simple relation between the partition function Z of the investigated symmetric spin-1/2 Ising-Heisenberg diamond chain with the four-spin interaction and the partition function Z IC of the uniform spin-1/2 Ising linear chain with the nearest-neighbour coupling R and the effective magnetic field H IC…”

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy

“…Owing to this fact, a lot of attention has been also paid to a rigorous treatment of various versions of the spin-1/2 Ising-Heisenberg diamond chain [15][16][17][18][19][20][21][22][23][24][25] and the Ising-Hubbard diamond chain [26][27][28][29].…”

XXZ -Ising model on the triangular kagome lattice with spin 1 on the decorated trimers

“…It was first introduced by Fisher in the 1950s [18] and developed in recent years [19,20]. And it has been widely applied in studying the decorated spin system, in both one [21][22][23] and two [24][25][26][27] dimensions. With this method, the TKL XXZ-Ising model remains solvable when changing the decorated parts with higher spins, which make it serve as an ideal candidate for observing the effects of quantum fluctuations in the mixed spin systems with geometric frustrations.…”