Papers by Keyword: Triangular Lattice

Abstract: We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.

Abstract: LiCrO₂ is a triangular lattice antiferromagnetic compound exhibiting geometrically frustrated two dimensional arrangement of Cr ions with T_N = 62 K at which an isostructural transition occurs. We show, using temperature dependent high energy synchrotron X-ray diffraction studies, that upon a nominal 1% Cu doping at the Li site, there are large changes in structural parameters and the (coupled) magnetic and dielectric properties.

Abstract: We have discovered a novel compound Na0.12CrO2Ge0.18Ox•yH2O using a hydrothermal method. Its powder X-ray diffraction reveals a monoclinic unit cell with lattice parameters: a = 7.260 Å, b = 2.950 Å, c = 5.117 Å and β = 103.7°. A Rietveld analysis shows that this compound has a layered structure based on CrO2 sheets consisting of edge-shared CrO6 octahedra. Such a layered structure is commonly seen in many hexagonal Cr oxides such as NaCrO2. A heat treatment at 100 °C modifies the crystal structure without destruction of a layered structure based on Cr triangular-lattice, because H2O molecules among the CrO2 sheets are removed at high temperature. Magnetization measurements reveal a spin-glass behavior below Tg = 3 K.

Abstract: The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J' is considered within the non-linear -model with the use of the renormalization group (RG) approach. For J'  J the asymptotic formula for the Neel temperature TNeel and sublattice magnetization are obtained. RG turns out to be insufficient to describe experimental data since it does not take into account the 2-vortices. Therefore TNeel is estimated using the Monte-Carlo result for the 2D correlation length [10] which has a Kosterlitz-type behavior near the temperature TKT where the vortices are activated.

Abstract: The magnetic phase diagram of Ising spin chains packed into the frustrated triangular lattice is discussed. A structure of a low-temperature phase depends strongly on interactions between the next-to-nearest-neighbor chains because they lift the degeneracy of the triangular AFM Ising model. That is why, a variety of low-temperature phases is observed in CsCoCl3, Ca3Co2O6, and Sr5Rh4O12. On the contrary, the high-temperature phase (honeycomb AFM structure) is unique. The frustrated Ising chain systems demonstrate an unusual and very slow magnetization dynamics. A model of the magnetization dynamics similar to the Glauber theory is developed.

Abstract: A two-dimensional Ising-like model for the triangular spin-chain lattice, where each spin chain is treated as a rigid superspin, is proposed to investigate the dynamics of magnetization in frustrated triangular spin-chain systems. The superspins are assumed to interact with the nearest neighbours and external agency (heat reservoir and external magnetic field) that causes them to change their states randomly with time. A probability of a single spin-flip process is assumed in a Glauber-like form. This technique allows describing the steps in the magnetization curves observed in Ca3Co2O6 and their dependence on the magnetic field sweep rate and temperature.