Ground-state phase diagram and magnetization process of the exactly solved mixed spin-(1,1/2) Ising diamond chain

Abstract

The ground state and magnetization process of the mixed spin-(1,1/2) Ising diamond chain is exactly solved by employing the generalized decoration-iteration mapping transformation and the transfer-matrix method. The decoration-iteration transformation is first used in order to establish a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain in a non-zero magnetic field, which is subsequently exactly treated within the framework of the transfer-matrix technique. It is shown that the ground-state phase diagram includes just four different ground states and the low-temperature magnetization curve may exhibit an intermediate plateau precisely at one half of the saturation magnetization. Our rigorous results disprove recent Monte Carlo simulations of Zihua Xin et al. [Z. Xin, S. Chen, C. Zhang, J. Magn. Magn. Mater. 324 (2012) 3704], which imply an existence of the other magnetization plateaus at 0.283 and 0.426 of the saturation magnetization.

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy

“…Quite recently, Zihua Xin et al [31] have explored another version of the mixed-spin Ising diamond chain with the spin-1 nodal atoms and the spin-1/2 interstitial atoms by employing Monte Carlo simulations. It has been argued that the low-temperature magnetization process of the frustrated mixed spin-(1,1/2) Ising diamond chain might display peculiar magnetization plateaus [31], which have been however refuted by our recent exact calculations based on the generalized decorationiteration transformation [32]. It is worth mentioning, moreover, that the procedure developed in our previous work [32] can be rather straightforwardly adapted to a more general mixed spin-(1,1/2) Ising-Heisenberg diamond chain with the interstitial Heisenberg spins and the nodal Ising spins as well.…”

“…It has been argued that the low-temperature magnetization process of the frustrated mixed spin-(1,1/2) Ising diamond chain might display peculiar magnetization plateaus [31], which have been however refuted by our recent exact calculations based on the generalized decorationiteration transformation [32]. It is worth mentioning, moreover, that the procedure developed in our previous work [32] can be rather straightforwardly adapted to a more general mixed spin-(1,1/2) Ising-Heisenberg diamond chain with the interstitial Heisenberg spins and the nodal Ising spins as well. This classicalquantum Ising-Heisenberg diamond chain is of particular interest, because it enables us to study a mutual competition between the geometric spin frustration and quantum fluctuations by exact means.…”

Absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains

“…The magnetization curves, thus, for the Ising-Heisenberg spin systems share almost all features with the magnetization curves of the small spin clusters, but can contain much more intermediate magnetization plateaus. Various variants of the Ising-Heisenberg chains have been examined: diamond-chain, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] saw-tooth chain, 29,30 orthogonal-dimer chain, [31][32][33] tetrahedral chain, [34][35][36][37][38] and some special examples relevant to real magnetic materials. [39][40][41][42] In the present work, we will rigorously examine a magnetization process of a few quantum Heisenberg spin clusters and Ising-Heisenberg diamond chain, which will not display strict magnetization plateaus on assumption that some constituent spins have different Landé g-factors and may be a XY-anisotropy of the exchange interaction.…”

Exactly solvable spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins

“…[23,24,25]. Of course, individual elements of the transfer matrix (5) are defined through the formula…”