The thermodynamics of coupled frustrated ferromagnetic chains is studied within a spin-rotation-invariant Green's-function approach. We consider an isotropic Heisenberg spin-half system with a ferromagnetic in-chain coupling J1<0 between nearest neighbors and a frustrating antiferromagnetic next-nearest-neighbor in-chain coupling J2>0. We focus on the moderate strength of frustration J2<∣J1∣/4 such that the in-chain spin-spin correlations are predominantly ferromagnetic. We consider two interchain couplings (ICs) ${J}_{\ensuremath{\perp},y}$ and ${J}_{\ensuremath{\perp},z}$, corresponding to the two axes perpendicular to the chain, where ferromagnetic as well as antiferromagnetic ICs are taken into account. We discuss the influence of frustration on the ground-state properties for antiferromagnetic ICs, where the ground state is of a quantum nature. The major part of our study is devoted to the finite-temperature properties. We calculate the critical temperature Tc as a function of the competing exchange couplings ${J}_{2},{J}_{\ensuremath{\perp},y},{J}_{\ensuremath{\perp},z}$. We find that for fixed ICs, Tc decreases monotonically with increasing frustration J2, where as ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$ the Tc(J2) curve drops down rapidly. To characterize the magnetic ordering below and above Tc, we calculate the spin-spin correlation functions $\ensuremath{\langle}{\mathbf{S}}_{0}{\mathbf{S}}_{\mathbf{R}}\ensuremath{\rangle}$, the magnetic order parameter M, the uniform static susceptibility ${\ensuremath{\chi}}_{0}$, as well as the correlation length $\ensuremath{\xi}$. Moreover, we discuss the specific heat CV and the temperature dependence of the excitation spectrum ${\ensuremath{\omega}}_{\mathbf{q}}$. As ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$, some unusual frustration-induced features were found, such as an increase of the in-chain spin stiffness (in the case of ferromagnetic ICs) or of the in-chain spin-wave velocity (in the case of antiferromagnetic ICs) with growing temperature.
In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz-Thouless transition from a gapful phase to a gapless spin liquid phase.
Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated S=1/2 antiferromagnetic trimerized quantum Heisenberg spin chain compound Na2Cu3Ge4O12
Abstract We report the magnetization process of S=1/2 S = 1 / 2 Heisenberg antiferromagnetic J1−J1−J2 J 1 - J 1 - J 2 trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction J3 J 3 within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, J′ J ′ s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios α=0.18,β=0.18 α = 0.18 , β = 0.18 , and J1=235 J 1 = 235 K, where α=J2/J1 α = J 2 / J 1 , and β=J3/J1 β = J 3 / J 1 as found for the model compound Na2Cu3Ge4O12 Na 2 Cu 3 Ge 4 O 12 . It is found that a wide 1/3 quantum magnetization plateau state (observed in ground state magnetization) gradually disappears with increasing temperature beyond a crossover temperature Tco T co due to thermal fluctuations. Based on numerical data, the width w(T) of the magnetization plateau is found to follow an exponential behave as ∼e−B/Tco−T ∼ e - B / T co - T , where B is a constant and Tco T co is estimated to be ≈60 ≈ 60