Frustrated Ising model on the Cairo pentagonal lattice

Order and disorder, crossovers, and phase transitions in dipolar artificial spin ice on the Cairo lattice

We study the thermodynamic properties of the magnetic dipolar spin ice on a 2D pentagonal Cairo lattice by using the numerical Metropolis and the complete enumeration methods. We use the model of point Ising-like dipoles considering long-range interactions with up to 100 nearest neighbors and with periodic boundary conditions. There are two explicit peaks both in the temperature behavior of the heat capacity and in the magnetic susceptibility. The low-temperature peak is caused only by long-range interactions and is not present in the model where each dipole interacts only with four nearest neighbors. The height of the peak depends logarithmically on the quantity of dipoles, which indicates a phase transition. The nature of the low-temperature phase transition is related to the transformation from order to disorder in orthogonal sublattices while maintaining the spin ice state and the spin ice rule in the sublattice of crosses. The high-temperature heat capacity peak is associated with the melting of spin ice, i.e., with the crossover from spin ice to paramagnetic chaos. Its height is constant and does not depend on the quantity of dipoles. It is shown that the choice of the radius of the dipole-dipole interaction has a significant effect on the statistical properties of the model. The model may even show the appearance of the long-range order and the phase transition in the case of long-range interaction or its absence in the case of short-range interaction.

Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

Tomonaga-Luttinger Spin Liquid and Kosterlitz-Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition

In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz–Thouless transition from a gapful phase to a gapless spin liquid phase.

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

To investigate the influence of geometric frustration on the properties of low-energy configurations of systems of ferromagnetic nanoislands located on the edges of the Cairo lattice, the model of interacting Ising-like magnetic dipoles is used. By the method of complete enumeration, the densities of states of the Cairo pentagonal lattices of a finite number of Ising-like point dipoles are calculated. The calculated ground and low-energy states for systems with a small number of dipoles can be used to solve the problem of searching for the ground states in a system with a relatively large number of dipoles. It is shown that the ground-state energy of the Cairo pentagonal lattices exhibits nonmonotonic behavior on one of the lattice parameters. The lattice parameters can be used to control the degree of geometric frustration. For the studied lattices of a finite number of Ising dipoles on the Cairo lattice in the ground-state configurations, a number of closed pentagons is observed, which are different from the obtained maximum closed pentagons. The magnetic order in the ground-state configurations obeys the ice rule and the quasi-ice rules.

Dimer Physics in the Frustrated Cairo Pentagonal Antiferromagnet Bi_{2}Fe_{4}O_{9}

The research field of magnetic frustration is dominated by triangle-based lattices but exotic phenomena can also be observed in pentagonal networks. A peculiar noncollinear magnetic order is indeed known to be stabilized in Bi_{2}Fe_{4}O_{9} materializing a Cairo pentagonal lattice. We present the spin wave excitations in the magnetically ordered state, obtained by inelastic neutron scattering. They reveal an unconventional excited state related to local precession of pairs of spins. The magnetic excitations are then modeled to determine the superexchange interactions for which the frustration is indeed at the origin of the spin arrangement. This analysis unveils a hierarchy in the interactions, leading to a paramagnetic state (close to the Néel temperature) constituted of strongly coupled dimers separated by much less correlated spins. This produces two types of response to an applied magnetic field associated with the two nonequivalent Fe sites, as observed in the magnetization distributions obtained using polarized neutrons.

Synthesis, structure and magnetic ordering of the mullite-type Bi2Fe(4-x)CrxO9 solid solutions with a frustrated pentagonal Cairo lattice

Highly homogeneous mullite-type solid solutions Bi2Fe(4-x)CrxO9 (x = 0.5, 1, 1.2) were synthesized using a soft chemistry technique followed by a solid-state reaction in Ar. The crystal structure of Bi2Fe3CrO9 was investigated using X-ray and neutron powder diffraction, transmission electron microscopy and (57)Fe Mössbauer spectroscopy (S.G. Pbam, a = 7.95579(9) Å, b = 8.39145(9) Å, c = 5.98242(7) Å, RF(X-ray) = 0.022, RF(neutron) = 0.057). The ab planes in the structure are tessellated with distorted pentagonal loops built up by three tetrahedrally coordinated Fe sites and two octahedrally coordinated Fe/Cr sites, linked together in the ab plane by corner-sharing forming a pentagonal Cairo lattice. Magnetic susceptibility measurements and powder neutron diffraction show that the compounds order antiferromagnetically (AFM) with the Néel temperatures decreasing upon increasing the Cr content from TN ∼ 250 K for x = 0 to TN ∼ 155 K for x = 1.2. The magnetic structure of Bi2Fe3CrO9 at T = 30 K is characterized by a propagation vector k = (1/2,1/2,1/2). The tetrahedrally coordinated Fe cations form singlet pairs within dimers of corner-sharing tetrahedra, but spins on the neighboring dimers are nearly orthogonal. The octahedrally coordinated (Fe,Cr) cations form antiferromagnetic up-up-down-down chains along c, while the spin arrangement in the ab plane is nearly orthogonal between nearest neighbors and collinear between second neighbors. The resulting magnetic structure is remarkably different from the one in pure Bi2Fe4O9 and features several types of spin correlations even on crystallographically equivalent exchange that may be caused by the simultaneous presence of Fe and Cr on the octahedral site.

Thermodynamic description of the Ising antiferromagnet on a triangular lattice with selective dilution by a modified pair-approximation method

The pair-approximation method is modified in order to describe systems with geometrical frustration. The Ising antiferromagnet on a triangular lattice with selective dilution (Kaya-Berker model) is considered and a self-consistent thermodynamic description of this model is obtained. For this purpose, the Gibbs free energy as a function of temperature, concentration of magnetic atoms on the selected sublattice, and external magnetic field is derived. In particular, the phase diagram is constructed and a comparison of different methods is presented. The thermodynamic quantities are discussed in the context of their physical validity, and the improvement in the description introduced by the modified method is emphasized.