Exact Results of the Ising-Heisenberg Model on the Diamond Chain with Spin-1/2

Abstract

Magnetic properties of a diamond chain consisting of spin-1/2 Ising-and Heisenbergtype atoms are investigated using the generalized decoration-iteration technique that removes all the Heisenberg-type atoms from the diamond chain and substitutes these atoms by new effective couplings. Exact results for the magnetization, enthalpy, Gibbs free energy, specific heat, entropy and susceptibility are obtained for zero and nonzero external magnetic field. Numerical results for the ground-state phase diagram are investigated in detail.

Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain

“…It should be at first pointed out that all the obtained results are rather general as they hold for an arbitrary quantum spin number S of the Heisenberg spins and also independently of whether ferromagnetic or antiferromagnetic interactions J H and J I are considered. It is also noteworthy that some particular cases of the investigated model system have already been examined by the present authors in earlier papers [32][33][34][35]. More specifically, the present results reduce to those acquired for the IsingHeisenberg diamond chains with two particular spin values S = 1/2 and 1, which have undergone a rather detailed analysis in references [32][33][34].…”

“…In addition, the spin-1, spin-3/2, and spin-5/2 Heisenberg model with the diamond chain topology might prove its usefulness in elucidating magnetic properties of polymeric coordination compounds M 3 (OH) 2 (M = Ni, Co, Mn) [28,29], [Ni 3 (fum) 2 (µ 3 -OH) 2 Unfortunately, the rigorous theoretical treatment of geometrically frustrated quantum Heisenberg models is very difficult to deal with due to a non-commutability of spin operators involved in the Heisenberg Hamiltonian, which is also a primary cause of the presence of quantum fluctuations. Owing to this fact, we have recently proposed a novel class of the geometrically frustrated Ising-Heisenberg diamond chain models [32][33][34][35], which overcome this mathematical difficulty by introducing the Ising spins at the nodal sites and the Heisenberg dimers on the interstitial decorating sites of the diamond chain. This simplified quantum model can be examined within the framework of exact analytical approach based on the generalized decoration-iteration transformation [36][37][38], because the nodal Ising spins represent a barrier for quantum fluctuations that are consequently restricted to elementary diamond-shaped units.…”

“…The main purpose of this work is to provide the exact solution for the generalized version of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain [32][33][34][35], which should bring a deeper insight into how the magnetic properties depend on the quantum spin number S of the Heisenberg spins. The exact analytical solution for this extended version of the Ising-Heisenberg diamond chain will be attained by combining the Kambe projection method [45] with the generalized decorationiteration mapping transformation [36][37][38] and the transfer-matrix technique [46,47].…”

Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

“…Unfortunately, searching for the exact solution for the geometrically frustrated quantum Heisenberg models often fails due to a non‐commutability between spin operators involved in their Hamiltonians. Owing to this fact, we have recently proposed a special class of geometrically frustrated Ising–Heisenberg models on diamond‐like decorated lattices 32–38, which can be examined within the framework of an exact analytical approach based on the generalised decoration–iteration transformation 39–41. These simplified quantum models overcome the afore‐mentioned mathematical difficulty by introducing the Ising spins at nodal lattice sites and the Heisenberg dimers on interstitial decorating sites of the considered planar lattice.…”

“…It is worth mentioning that the mixed‐spin Ising–Heisenberg models with diamond‐like decorations turn out to be very useful testing ground for elucidating many quantum properties of low‐dimensional magnetic materials, in spite of the fact that the monomer–dimer interaction is considered as the Ising‐type interaction. Indeed, these rather simple spin models shed light on diverse quantum features to appear in the ground state 32–35, 38, the magnetisation process 34, 37, 38, the thermodynamics 34, 37, as well as, the critical behaviour 36. Note that kinetically frustrated diamond chain models constituted by nodal Ising spins and mobile electrons delocalised over the interstitial decorating sites have been particularly examined as well 42–44.…”