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arXiv:1506.02933 · Physical Review B

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

Vadim Ohanyan, Onofre Rojas, Jozef Strečka, Stefano Bellucci A

Published Dec 16, 2015• 27 citations
arXivHTMLPDF

Abstract

We examine the general features of the noncommutativity of the magnetization operator and Hamiltonian for small quantum spin clusters. The source of this noncommutativity can be a difference in the Land\'e $g$ factors for different spins in the cluster, $XY$ anisotropy in the exchange interaction, and the presence of the Dzyaloshinskii-Moriya term in a direction different from the direction of the magnetic field. As a result, zero-temperature magnetization curves for small spin clusters mimic those for the macroscopic systems with the band(s) of magnetic excitations, i.e., for the given eigenstate of the spin cluster the corresponding magnetic moment can be an explicit function of the external magnetic field yielding the nonconstant (nonplateau) form of the magnetization curve within the given eigenstate. In addition, the $XY$ anisotropy makes the saturated magnetization (the eigenstate when all spins in cluster are aligned along the magnetic field) inaccessible for finite magnetic field magnitude (asymptotical saturation). We demonstrate all these features on three examples: a spin-1/2 dimer, mixed spin-(1/2,1) dimer, and a spin-1/2 ring trimer. We consider also the simplest Ising-Heisenberg chain, the Ising-$XYZ$ diamond chain, with four different $g$ factors. In the chain model the magnetization curve has a more complicated and nontrivial structure than that for clusters.

DOI
10.1103/physrevb.92.214423

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We examine the general features of the noncommutativity of the magnetization operator and Hamiltonian for small quantum spin clusters. The source of this noncommutativity can be a difference in the Land'e ggg factors for different spins in the cluster, XYXYXY anisotropy in the exchange interaction, and the presence of the Dzyaloshinskii-Moriya term in a direction different from the direction of the magnetic field. As a result, zero-temperature magnetization curves for small spin clusters mimic those for the macroscopic systems with the band(s) of magnetic excitations, i.e., for the given eigenstate of the spin cluster the corresponding magnetic moment can be an explicit function of the external magnetic field yielding the nonconstant (nonplateau) form of the magnetization curve within the given eigenstate. In addition, the XYXYXY anisotropy makes the saturated magnetization (the eigenstate when all spins in cluster are aligned along the magnetic field) inaccessible for finite magnetic field magnitude (asymptotical saturation). We demonstrate all these features on three examples: a spin-1/2 dimer, mixed spin-(1/2,1) dimer, and a spin-1/2 ring trimer. We consider also the simplest Ising-Heisenberg chain, the Ising-XYZXYZXYZ diamond chain, with four different ggg factors. In the chain model the magnetization curve has a more complicated and nontrivial structure than that for clusters.
The exactly solvable spin-1/2 Ising-Heisenberg distorted diamond chain in the presence of the external magnetic field is investigated for the case of antiferromagnetic Ising and ferromagnetic XXZ Heisenberg interactions. The influence of quantum fluctuations and the distortion on the ground state, magnetic and thermal properties of the model are studied in detail.In particular, it is established that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and 1/3 of the saturation magnetization. It is demonstrated that the temperature dependence of the specific heat reveals up to four distinct peaks at zero magnetic field and up to five distinct peaks at a weak magnetic field. The physical origin of all observed additional peaks of the specific heat has been clarified on the grounds of dominating thermal excitations. We have shown that the quantum fluctuations give rise to an effective geometrical frustration in this chain.
The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.
The zero temperature non-plateau magnetization is a peculiar property of quantum spin chain and sometimes appear due to different giro-magnetic factor. Here we illustrate the non-plateau magnetization property driven by XY-anisotropy in Ising-XYZ diamond chain. Two particles with spin-1/2 are bonded through the XYZ coupling, which is responsible for the emergence of non-plateau magnetization. These two quantum operator spins are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. This model exhibits a quite unusual non-plateau magnetization at zero temperature, we also discuss the phase diagram at zero temperature. Furthermore, owing to the non-plateau magnetization property, we focus our discussion on magnetocaloric effect of this model, illustrating isentropic curves as well as the Gr\uneisen parameters, showing the regions where the model exhibits an efficient magnetocaloric effect. Due to the existence of two phases very close to each other the strong XY-anisotropy, we obtain a peculiar behavior of magnetocaloric effect, observing a wider interval in the magnetic field, where the magnetocaloric effect is efficient.
We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H CB, H CE and H CS were obtained, in which the H CB and H CE correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H CS correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ℏ ω σ,k (σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [ℏ ω 3,k (H CB)]min = 0, [ℏ ω 2,k (H CE)]max = 0 and [ℏ ω 2,k (H CS)]min = 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.
Ground state of the mixed spin-(1,1/2) Ising-Heisenberg distorted diamond chain in the presence of the external magnetic field is rigorously studied in the frustrated case of ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions.The influence of quantum fluctuations, magnetic field, and the distortion of diamond cells on the ground state are examined in detail.It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-half of the saturation magnetization.
In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strengths on the entanglement properties of the S=12S=\frac{1}{2}S=21​ antiferromagnetic linear chain tetramer compound NaCuAsO4\mathrm{Na}\mathrm{Cu}\mathrm{As}{\mathrm{O}}_{4}NaCuAsO4​. The entanglement gap temperature TE{T}_{E}TE​ is found to have a nonmonotonic dependence on the value of $\ensuremath{\alpha}$, the exchange coupling inhomogeneity parameter. We next determine the variation of TE{T}_{E}TE​ as a function of SSS for a spin dimer, a trimer, and a tetrahedron. The temperature TE{T}_{E}TE​ is found to increase as a function of SSS but the scaled entanglement gap temperature tE{t}_{E}tE​ goes to zero as SSS becomes large. Last, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.