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

Abstract

The geometric frustration in a class of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chains is investigated by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. The ground state, the magnetization process and the specific heat as a function of the external magnetic field are particularly examined for different strengths of the geometric frustration. It is shown that the increase of the Heisenberg spin value S raises the number of intermediate magnetization plateaux, which emerge in magnetization curves provided that the ground state is highly degenerate on behalf of a sufficiently strong geometric frustration. On the other hand, all intermediate magnetization plateaux merge into a linear magnetization versus magnetic field dependence in the limit of classical Heisenberg spin S → ∞. The enhanced magnetocaloric effect with cooling rate exceeding the one of paramagnetic salts is also detected when the disordered frustrated phase constitutes the ground state and the external magnetic field is small enough.

Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

“…Namely, we considered the pairs of S = 1/2 quantum spins interacting with XXZ interaction arranged in the sawtooth chain in such a way which allows one to use transfer-matrix technique for exact calculations. This result continues the series of investigations of the subject performed earlier for other onedimensional spin systems with Ising and Heisenberg bonds [13][14][15][16][17][18][19][20][21][22][23][24]. These results are not only of academic interest.…”

“…One can mention a formal approach to these problem which is not justified properly yet but in some particular cases demonstrates rather good agreement with experimental data and numerical calculations. The approximation consists in replacement of some or all interaction bonds with Ising ones [13][14][15][16][17][18][19][20][21][22][23][24]. As a result one can obtain an interacting spin system which allows one to calculate all thermodynamic functions analytically.…”

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.…”

Magnetic Grüneisen parameter and magnetocaloric properties of a coupled spin–electron double-tetrahedral chain

“…(9) can be obtained by differentiating Eqs. (6) and (7) with respect to the relevant variable. It should be noted, however, that the resulting expressions for these derivatives are too cumbersume to write them here explicitly.…”

“…Of particular interest is the investigation of the MCE in various one-dimensional (1D) quantum spin systems [4][5][6][7][8][9][10][11][12][13] or hybrid spin-electron models [14][15][16]. The reason is a possibility of obtaining the exact analytical or numerical results as well as a potential use of these models for the explanation of MCE data measured for real magnetic compounds.…”