Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Gálisová, Lucia; Strečka, Jozef

doi:10.5488/cmp.14.13002

Cited by 14 publications

(12 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Beside this, other particular case of this model with the ferromagnetic Heisenberg interaction (J H < 0) deserves the attention, since there are some fundamental differences between magnetic behaviour of the hybrid Ising-Heisenberg models with distinct nature of the Heisenberg interaction (see Refs. [29,54,55,58,59]). Finally, several further interesting extensions of the present version of the spin-1/2 Ising-Heisenberg diamond chain also into question.…”

Section: Thermodynamicsmentioning

confidence: 99%

“…It is also worth mentioning that in order to investigate many interesting physical phenomena, various extensions and generalizations of the hybrid Ising-Heisenberg models may be done without loss of their exact solubility. For instance, it is possible to extend the Ising-Heisenberg models by including the next-nearest-neighbour exchange interaction between the Ising spins [50], the Dzyaloshinskii-Moriya anisotropy acting on the decorating Heisenberg spins [51], or to solve exactly the analogous Ising-Heisenberg models with the Heisenberg spins S > 1/2 [29,35,52,53,54,55,56,57,58,59,60,61] that bring a deeper insight into how the magnetic behaviour of the quantum spin systems depends on the magnitude S [35,56,57] of the decorating Heisenberg spins and also allow to examine the effect of other interaction terms such as the axial zero-field splitting parameter [29,52,53,54,55,58,59,60] and/or the biquadratic XXZ interaction [60,61].…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

Gálisová

2012

Physica Status Solidi (b)

View full text Add to dashboard Cite

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...

show abstract

Section: Thermodynamicsmentioning

confidence: 99%

mentioning

confidence: 99%

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

Gálisová

2012

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

“…It is well known that low dimensional magnetic systems have been broadly studied in the literature, both experimentally and theoretically, due to the interesting magnetic and thermodynamic properties they present at zero and finite temperatures as well. Some of these systems have also frustrated spins due to their geometric structure (see, for instance, [9][10][11]). This fact makes the study of molecular magnets more attractive still, because it turns out to be a vast field of quantum phenomena in nanosystems, in particular zero-dimensional magnetic clusters with potential applicability in high-capacity data storage.…”

Section: Introductionmentioning

confidence: 99%

Ground state and thermodynamic properties of spin-1/2 isosceles Heisenberg triangles for V$_6$-like magnetic molecules

Torrico,

Plascak

2020

Preprint

View full text Add to dashboard Cite

The spin-1/2 Hamiltonian for two coupled isosceles Heisenberg triangles, which is well suited for describing the V6-type magnetic molecules, is studied by exact diagonalization. The quantum phase transition diagram, at zero temperature, is obtained as a function of the theoretical parameters. The zero temperature magnetization is also obtained as a function of the external magnetic field. The thermodynamic behavior of the magnetization, entropy, susceptibility, and specific heat, as a function of temperature, are also computed and the corresponding magnetocaloric effect analyzed for various values of the Hamiltonian parameters.

show abstract

“…Recent studies show that the mixed-spin Ising-Heisenberg models defined on decorated planar lattices, containing triangular structures [12][13][14][15][16][17][18], represent suitable candidates for a complex rigorous examination of the frustration phenomenon in 2D. These simplified quantum-classical (hybrid) spin systems can be exactly treated by means of the exact generalized algebraic mapping transformations [19,20], because they admit just local quantum spin fluctuations at decorating lattice sites, while nodal lattice sites are occupied by the Ising spins.…”

Section: Introductionmentioning

confidence: 99%

Frustration phenomenon in the spin-1/2 Ising–Heisenberg planar model of inter-connected trigonal bipyramid structures

Gálisová

2019

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Ground-state and finite-temperature properties of the exactly solvable mixed spin-1/2 Ising-Heisenberg planar model composed of identical trigonal bipyramids that are arranged into a regular archimedean lattice are examined with the aim to clarify the frustration phenomenon at zero and finite temperatures. It is shown that the ground-state spin frustration persists even far above the second-order phase transition. If the interaction ratio between the Heisenberg and Ising exchange interactions is close enough to the ground-state boundaries between the neighboring phases, a remarkable re-entrance of the (non-)frustrated spin arrangement of the Heisenberg spins can be observed around the critical temperature of the model. It is also evidenced that entropy and specific heat show pronounced temperature variations not only around the critical temperature, but also in low-temperature regime if values of the interaction parameters are taken from neighborhood of the ground-state phase transitions, where energies of the neighboring phases are very close.

show abstract

Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Cited by 14 publications

References 35 publications

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

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

Ground state and thermodynamic properties of spin-1/2 isosceles Heisenberg triangles for V$_6$-like magnetic molecules

Frustration phenomenon in the spin-1/2 Ising–Heisenberg planar model of inter-connected trigonal bipyramid structures

Contact Info

Product

Resources

About