Ferrimagnetic spin-1/2 chain of alternating Ising and Heisenberg spins in arbitrarily oriented magnetic field

Abstract

The ferrimagnetic spin-1/2 chain composed of alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field is exactly solved using the spin-rotation transformation and the transfer-matrix method. It is shown that the low-temperature magnetization process depends basically on a spatial orientation of the magnetic field. A sharp stepwise magnetization curve with a marked intermediate plateau, which emerges for the magnetic field applied along the easy-axis direction of the Ising spins, becomes smoother and the intermediate plateau shrinks if the external field is tilted from the easy-axis direction. The magnetization curve of a polycrystalline system is also calculated by performing powder averaging of the derived magnetization formula. The proposed spin-chain model brings an insight into high-field magnetization data of 3d-4f bimetallic polymeric compound Dy(NO 3 )(DMSO) 2 Cu(opba)(DMSO) 2 , which provides an interesting experimental realization of the ferrimagnetic chain composed of two different but regularly alternating spin-1/2 magnetic ions Dy 3+ and Cu 2+ that are reasonably approximated by the notion of Ising and Heisenberg spins, respectively.

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg distorted diamond chain

“…6(a) exhibits two abrupt magnetization jumps closely connected 9 with an existence of two intermediate magnetization plateaus: the zero plateau corresponding to the AF ground state and 10 the one-half plateau corresponding to the MD ground state. In accordance with this statement, temperature dependences 11 of the total magnetization shown in Fig. 6(b) asymptotically tend towards zero, one-half or unity as temperature goes to which can be achieved in the zero-temperature asymptotic limit on assumption that the magnetic field is fixed exactly at 14 the critical value corresponding to the field-induced transitions AF ↔ MD and MD ↔ SPA, respectively (see dotted lines in 15 Fig.…”

“…(5). For this purpose, 11 it is quite advisable to pass to the matrix representation of the cell HamiltonianĤ k in the basis spanned over four available 12 states of two Heisenberg spins σ z k,1 and σ z k,2 : 13 | ↑, ↑⟩ k = |↑⟩ k,1 |↑⟩ k,2 , | ↓, ↓⟩ k = |↓⟩ k,1 |↓⟩ k,2 , | ↑, ↓⟩ k = |↑⟩ k,1 |↓⟩ k,2 , | ↓, ↑⟩ k = |↓⟩ k,1 |↑⟩ k,2 , 14 whereas | ↑⟩ k,i and | ↓⟩ k,i denote two eigenvectors of the spin operatorσ z k,i with the respective eigenvalues σ z k,i = 1/2 and 15 −1/2. After a straightforward diagonalization of the cell HamiltonianĤ k one obtains the following four eigenvalues:…”

“…It should be also mentioned that the two ground states FRU and AF coexist together at the point [0, 0] 9 forJ + = 4. 10 The general form of the ground-state phase diagram can be obtained in theJ + -h plane when the scale of theJ + -axis is 11 expressed in terms of the interaction ratioĨ 2 = I 2 /I 1 between both Ising coupling constants (see Fig. 3).…”

“…In the present article, we have rigorously examined the ground state and thermodynamics of the mixed spin-(1,1/2) 8 Ising-Heisenberg distorted diamond chain within the transfer-matrix method. In particular, our attention was focused on 9 how the parallelogram distortion affects the magnetization process, susceptibility and specific heat of the mixed spin-(1,1/2) 10 Ising-Heisenberg distorted diamond chain with the antiferromagnetic Ising interactions and either the antiferromagnetic 11 or ferromagnetic XXZ Heisenberg interaction. Under this circumstances, the magnetic properties of the mixed spin-(1,1/2) 12 Ising-Heisenberg distorted diamond chain are substantially influenced by a geometric spin frustration.…”

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

“…Despite a certain oversimplification, some exactly solved IsingHeisenberg spin chains afford a plausible quantitative description of the magnetic behavior of real spin-chain materials [7][8][9][10][11][12][13][14]. Owing to this fact, a lot of attention has been also paid to a rigorous treatment of various versions of the spin-1/2 Ising-Heisenberg diamond chain [15][16][17][18][19][20][21][22][23][24][25] and the Ising-Hubbard diamond chain [26][27][28][29].…”