Magnetization plateaus and bipartite entanglement of an exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain

Abstract

Spin-1/2 orthogonal-dimer chain composed of regularly alternating Ising and Heisenberg dimers is exactly solved in a presence of the magnetic field by the transfer-matrix method. It is shown that the ground-state phase diagram involves in total six different phases. Besides the ferromagnetic phase with fully polarized spins one encounters the singlet antiferromagnetic and modulated antiferromagnetic phases manifested in zero-temperature magnetization curves as zero magnetization plateau, the frustrated ferrimagnetic and singlet ferrimagnetic phases causing existence of an intermediate one-half magnetization plateau, and finally, the intriguing modulated ferrimagnetic phase with a translationally broken symmetry leading to an unconventional one-quarter magnetization plateau. The quantum character of individual ground states is quantified via the concurrence, which measures a strength of the bipartite entanglement within the pure and mixed states of the Heisenberg dimers at zero as well as nonzero temperatures. The parameter region, where the bipartite entanglement may be in contrast to general expectations reinforced upon increasing of temperature and/or magnetic field, is elucidated. ith six-spin cluster J H ( ) J I ' J I J I J I J I S 2,i-1

Insights into nature of a magnetization plateau of 3d-4f coordination polymer [Dy2Cu2]n from a spin-1/2 Ising-Heisenberg orthogonal-dimer chain

“…It is worthwhile to remark that the partition function, Gibbs free energy and magnetization of the IH-ODC defined through the Hamiltonian (2.1) was exactly calculated under the periodic boundary conditionŝ σ z 1(2), N +1 ≡σ z 1(2),1 in our preceding paper [19]. The calculation procedure used takes advantage of splitting the total Hamiltonian (2.1) into commuting six-spin cluster Hamiltonians involving one horizontal Cu 2+ -Cu 2+ dimer and two enclosing vertical Dy 3+ -Dy 3+ dimers, which allow a straightforward factorization of the partition function into a product of the respective Boltzmann factors.…”

“…The calculation procedure used takes advantage of splitting the total Hamiltonian (2.1) into commuting six-spin cluster Hamiltonians involving one horizontal Cu 2+ -Cu 2+ dimer and two enclosing vertical Dy 3+ -Dy 3+ dimers, which allow a straightforward factorization of the partition function into a product of the respective Boltzmann factors. After tracing out spin degrees of freedom of the horizontal Cu 2+ -Cu 2+ dimer (Heisenberg dimer), the partition function is in fact expressed in terms of four-by-four transfer matrix depending on spin states of two adjacent vertical Dy 3+ -Dy 3+ dimers (Ising dimers) and the whole magnetothermodynamics can be elaborated by making use of the transfer-matrix method (the readers interested in further calculation details are referred to reference [19]). However, all numerical results presented in reference [19] were restricted just to the particular case h H = h I , which corresponds to setting the same Landé g-factors for Cu 2+ and Dy 3+ magnetic ions which is contrary to the expected (typical) values of the gyromagnetic factors g H ≈ 2 for Cu 2+ magnetic ions and g I ≈ 20 for Dy 3+ magnetic ions.…”

“…After tracing out spin degrees of freedom of the horizontal Cu 2+ -Cu 2+ dimer (Heisenberg dimer), the partition function is in fact expressed in terms of four-by-four transfer matrix depending on spin states of two adjacent vertical Dy 3+ -Dy 3+ dimers (Ising dimers) and the whole magnetothermodynamics can be elaborated by making use of the transfer-matrix method (the readers interested in further calculation details are referred to reference [19]). However, all numerical results presented in reference [19] were restricted just to the particular case h H = h I , which corresponds to setting the same Landé g-factors for Cu 2+ and Dy 3+ magnetic ions which is contrary to the expected (typical) values of the gyromagnetic factors g H ≈ 2 for Cu 2+ magnetic ions and g I ≈ 20 for Dy 3+ magnetic ions. Therefore, in the present article we adapt the exact solution for the IH-ODC reported in reference [19] in order to investigate the effect of different 'local magnetic fields' h H h I arising from the difference of the gyromagnetic factors of Cu 2+ and Dy 3+ magnetic ions g H g I .…”

“…Replacement of some of the quantum Heisenberg spins by the classical Ising ones paves the way to an exact solution of the analogous Ising-Heisenberg models by employing exact mapping transformations and the transfer-matrix method [12][13][14]. For instance a few exactly solved versions of the spin- 1 2 Ising-Heisenberg orthogonal-dimer chain [15][16][17][18][19], to be further n (see the text for a full chemical formula) adapted according to crystallographic data reported in reference [21]. Large cyan balls determine crystallographic positions of Dy 3+ magnetic ions, while small green balls stand for crystallographic positions of Cu 2+ magnetic ions (a coloured scheme for atom labeling is presented in the legend); (b) The magnetic structure of the corresponding IH-ODC, in which Dy 3+ magnetic ions are treated as the Ising spins while Cu 2+ magnetic ions are treated as the Heisenberg spins.…”

“…abbreviated as IH-ODC, brought a deeper insight into the magnetization process [15,17,19], magnetocaloric effect [15,17], low-temperature thermodynamics [16][17][18] and bipartite thermal entanglement [16,19] of this frustrated quantum spin chain. Besides, it was demonstrated that the exact solution for the IH-ODC may serve as a useful starting point for the many-body perturbation treatment of the fully Heisenberg counterpart model within a more advanced strong-coupling approach [20].…”