Spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons (original) (raw)
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Journal of physics, 2010
A hybrid lattice-statistical model of doubly decorated two-dimensional lattices, which have localized Ising spins at its nodal sites and itinerant electrons delocalized over decorating sites, is exactly solved with the help of a generalized decoration-iteration transformation. Under the assumption of a quarter filling of each couple of the decorating sites, the ground state constitutes either spontaneously long-range ordered ferromagnetic or ferrimagnetic phase in dependence on whether the ferromagnetic or antiferromagnetic interaction between the localized Ising spins and itinerant electrons is considered. The critical temperature of the spontaneously long-range ordered phases monotonically increases upon strengthening the ratio between the kinetic term and the Ising-type exchange interaction.
Physics Letters A
The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behaviour. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.
Journal of Magnetism and Magnetic Materials, 2016
The generalized decoration-iteration transformation is adapted for the exact study of a coupled spin-electron model on 2D lattices in which localized Ising spins reside on nodal lattice sites and mobile electrons are delocalized over pairs of decorating sites. The model takes into account a hopping term for mobile electrons, the Ising coupling between mobile electrons and localized spins as well as the Ising coupling between localized spins (J ′). The ground state, spontaneous magnetization and specific heat are examined for both ferromagnetic (J ′ > 0) as well as antiferromagnetic (J ′ < 0) interaction between the localized spins. Several kinds of reentrant transitions between the paramagnetic (P), antiferromagnetic (AF) and ferromagnetic (F) phases have been found either with a single critical point, or with two consecutive critical points (P − AF/F − P) and three successive critical points AF/F − P − F/AF − P. Striking thermal variations of the spontaneous magnetization depict a strong reduction due to the interplay between annealed disorder and quantum fluctuations in addition to the aforementioned reentrance. It is shown that the specific heat displays diverse thermal dependencies including finite cusps at the critical temperatures.
International Journal of Modern Physics B, 2008
The mixed-spin Ising model on a decorated square lattice with two different decorating spins of the integer magnitudes S B = 1 and S C = 2 placed on horizontal and vertical bonds of the lattice, respectively, is examined within an exact analytical approach based on the generalized decoration-iteration mapping transformation. Besides the groundstate analysis, finite-temperature properties of the system are also investigated in detail. The most interesting numerical result to emerge from our study relates to a striking critical behaviour of the spontaneously ordered 'quasi-1D' spin system. It was found that this quite remarkable spontaneous order arises when one sub-lattice of the decorating spins (either S B or S C) tends towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further single-ion anisotropy strengthening. The effect of single-ion anisotropy upon the temperature dependence of the total and sublattice magnetization is also particularly investigated.
Journal of Magnetism and Magnetic Materials, 2007
Mixed-spin Ising-Heisenberg model on the decorated triangular lattice is studied by the use of an exact star-triangle map. Within this approach, exact results for the ground-state and finite-temperature behaviour of the antiferromagnetic version of the model are obtained. A particular attention is laid on the effect of exchange anisotropy and next-nearest-neighbour interaction on magnetic behaviour of the system. It was found that the competitive effect between the nearest-neighbour Heisenberg-type, nearest-and next-nearest-neighbour Ising-type interaction, respectively, leads to a remarkable spin frustration in the system. In addition, very weak next-nearestneighbouring coupling is responsible for an interesting reentrant critical behaviour with two or three consecutive critical points.
Physical Review B, 2007
The mixed spin-(1/2, SB, SC) Ising model on a decorated square lattice with two different kinds of decorating spins SB and SC (SB = SC) placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1/2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins SB and SC is examined in particular. If decorating spins SB and SC are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior beared on the spontaneously ordered 'quasi-1D' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.
The European Physical Journal B, 2012
Magnetoelastic properties of the spin-1/2 Ising-Heisenberg model on doubly decorated planar lattices partially amenable to lattice vibrations are examined within the framework of the harmonic approximation and decoration-iteration transformation. It is shown that the mutual interplay between quantum spin fluctuations and local fluctuations of lattice spacings enhances typical quantum features like the quantum reduction of the magnetization in the ground state of the quantum antiferromagnetic phase, while it does not affect the ground-state behaviour of the classical ferromagnetic phase by no means. It also turns out that local fluctuations of lattice spacings are responsible for a much more pronounced reduction of the critical temperature in the quantum antiferromagnetic phase than in the classical ferromagnetic phase. PACS. 05.50.+q Lattice theory and statistics -05.70.Jk Critical point phenomena -75.10.-b General theory and models of magnetic ordering -75.30.Kz Magnetic phase boundaries -75.40.Cx Static properties
Physica A: Statistical Mechanics and its Applications, 2009
Phase transitions of the mixed spin-1/2 and spinS (S ≥ 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple spin-1/2 Ising model on the tetragonal lattice. This mapping correspondence yields for the layered Ising model of mixed spins plausible results either by adopting the conjectured solution for the spin-1/2 Ising model on the orthorhombic lattice [Z.-D. Zhang, Philos. Mag. 87 (2007) 5309-5419] or by performing extensive Monte Carlo simulations for the corresponding spin-1/2 Ising model on the tetragonal lattice. It is shown that the critical behaviour markedly depends on a relative strength of axial zero-field splitting parameter, inter-and intra-layer interactions. The striking spontaneous order captured to the 'quasi-1D' spin system is found in a restricted region of interaction parameters, where the zero-field splitting parameter forces all integer-valued decorating spins towards their 'non-magnetic' spin state.
Journal of Magnetism and Magnetic Materials
The mixed spin-1/2 and spinS Ising model on a decorated planar lattice accounting for lattice vibrations of decorating atoms is treated by making use of the canonical coordinate transformation, the decoration-iteration transformation, and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective single-ion anisotropy and three-site four-spin interaction, which are responsible for the anomalous spin frustration of the decorating spins in virtue of a competition with the equilibrium nearest-neighbor exchange interaction between the nodal and decorating spins. The ground-state and finite-temperature phase diagrams are constructed for the particular case of the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice for which thermal dependencies of the spontaneous magnetization and specific heat are also examined in detail. It is evidenced that a sufficiently strong magnetoelastic coupling leads to a peculiar coexistence of the antiferromagnetic long-range order of the nodal spins with the disorder of the decorating spins within the frustrated antiferromagnetic phase, which may also exhibit double reentrant phase transitions. The investigated model displays a variety of temperature dependencies of the total specific heat, which may involve in its magnetic part one or two logarithmic divergences apart from one or two additional round maxima superimposed on a standard thermal dependence of the lattice part of the specific heat.
Acta Physica Polonica A, 2017
Magnetocaloric properties of the spin-1/2 Ising model on a decorated square lattice in a transverse magnetic field are investigated by the use of a generalized decoration-iteration transformation, which establishes a rigorous mapping correspondence with the zero-field spin-1/2 Ising model on a square lattice. The temperature dependence of the entropy, the isothermal entropy change and the adiabatic temperature change display anomalous singular behavior in a vicinity of a second-order phase transition. The large inverse magnetocaloric effect can be found in the isothermal entropy change within the temperature interval, which is delimited by the critical temperatures at zero and non-zero transverse fields.