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arXiv:1703.04573 · Physical review. B./Physical review. B

Thermodynamics of frustrated ferromagnetic spin- 12 Heisenberg chains: Role of interchain coupling

P. Müller, Johannes Richter, Dieter Ihle

Published Apr 5, 2017• 15 citations
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Abstract

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 ${J}_{1}<0$ between nearest neighbors and a frustrating antiferromagnetic next-nearest-neighbor in-chain coupling ${J}_{2}>0$. We focus on the moderate strength of frustration ${J}_{2}<|{J}_{1}|/4$ 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 ${T}_{c}$ as a function of the competing exchange couplings ${J}_{2},{J}_{\ensuremath{\perp},y},{J}_{\ensuremath{\perp},z}$. We find that for fixed ICs, ${T}_{c}$ decreases monotonically with increasing frustration ${J}_{2}$, where as ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$ the ${T}_{c}({J}_{2})$ curve drops down rapidly. To characterize the magnetic ordering below and above ${T}_{c}$, 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 ${C}_{V}$ 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.

DOI
10.1103/physrevb.95.134407

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Abstract. We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic nextnearest-neighbor bonds J2> 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T −2 at J2 < |J1|/4 to χ ∝ T −3/2 at the quantum-critical point J2 = |J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat Cv(T) for J2 � |J1|/8, indicating its strong influence on the low-energy spectrum. Introduction: In low-dimensional frustrated quantum magnets thermal and quantum fluctuations strongly influence the low-temperature physics [1,2]. Special attention has been paid to one-dimensional (1D) J1-J2 quantum Heisenberg magnets, see Ref. [3] and references therein. Recent experimental studies have shown that edge-shared chain cuprates, such as LiVCuO4, Li(Na)Cu2O2, Li2ZrCuO4, and Li2CuO2 [4–13], represent a family of quantum magnets for
The thermodynamic quantities (spin-spin correlation functions $\ensuremath{\langle}{\mathbf{S}}_{0}{\mathbf{S}}_{n}\ensuremath{\rangle}$, correlation length $\ensuremath{\xi}$, spin susceptibility $\ensuremath{\chi}$, and specific heat CV{C}_{V}CV​) of the frustrated one-dimensional J1{J}_{1}J1​-J2{J}_{2}J2​ Heisenberg ferromagnet with arbitrary spin quantum number SSS below the quantum critical point, i.e., for J2<∣J1∣/4{J}_{2}<|{J}_{1}|/4J2​<∣J1​∣/4, are calculated using a rotation-invariant Green-function formalism and full diagonalization as well as a finite-temperature Lanczos technique for finite chains of up to N=20N=20N=20 sites. The low-temperature behavior of the susceptibility $\ensuremath{\chi}$ and the correlation length $\ensuremath{\xi}$ are well described by $\ensuremath{\chi}=\frac{2}{3}{S}^{4}\left(|{J}_{1}|\ensuremath{-}4{J}_{2}\right){T}^{\ensuremath{-}2}+A{S}^{5/2}{\left(|{J}_{1}|\ensuremath{-}4{J}_{2}\right)}^{1/2}{T}^{\ensuremath{-}3/2}$ and $\ensuremath{\xi}={S}^{2}\left(|{J}_{1}|\ensuremath{-}4{J}_{2}\right){T}^{\ensuremath{-}1}+B{S}^{1/2}{\left(|{J}_{1}|\ensuremath{-}4{J}_{2}\right)}^{1/2}{T}^{\ensuremath{-}1/2}$ with $A\ensuremath{\approx}1.1\ensuremath{\cdots}1.2$ and $B\ensuremath{\approx}0.84\ensuremath{\cdots}0.89$. The vanishing of the factors in front of the temperature at J2=∣J1∣/4{J}_{2}=|{J}_{1}|/4J2​=∣J1​∣/4 indicates a change of the critical behavior of $\ensuremath{\chi}$ and $\ensuremath{\xi}$ at $T\ensuremath{\rightarrow}0$. The specific heat may exhibit an additional frustration-induced low-temperature maximum when approaching the quantum critical point. Such a maximum appears for S=1/2S=1/2S=1/2 and S=1S=1S=1, but was not found for S>1S>1S>1.
We calculate the thermodynamic quantities (correlation functions ⟨S0Sn⟩⟨{\mathbf{S}}_{0}{\mathbf{S}}_{n}⟩⟨S0​Sn​⟩, correlation length $\ensuremath{\xi}$, spin susceptibility $\ensuremath{\chi}$, and specific heat CV{C}_{V}CV​) of the frustrated one-dimensional spin-half ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg ferromagnet, i.e., for J2<0.25∣J1∣{J}_{2}<0.25|{J}_{1}|J2​<0.25∣J1​∣, using a rotation-invariant Green's-function formalism and full diagonalization of finite lattices. We find that the critical indices are not changed by J2{J}_{2}J2​, i.e., $\ensuremath{\chi}={y}_{0}{T}^{\ensuremath{-}2}$ and $\ensuremath{\xi}={x}_{0}{T}^{\ensuremath{-}1}$ at $T\ensuremath{\rightarrow}0$. However, the coefficients y0{y}_{0}y0​ and x0{x}_{0}x0​ linearly decrease with increasing J2{J}_{2}J2​ according to the relations ${y}_{0}=(1\ensuremath{-}4{J}_{2}/|{J}_{1}|)/24$ and ${x}_{0}=(1\ensuremath{-}4{J}_{2}/|{J}_{1}|)/4$, i.e., both coefficients vanish at J2=0.25∣J1∣{J}_{2}=0.25|{J}_{1}|J2​=0.25∣J1​∣ indicating the zero-temperature phase transition that is accompanied by a change in the low-temperature behavior of $\ensuremath{\chi}$ $(\ensuremath{\xi})$ from $\ensuremath{\chi}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ $(\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}1})$ at J2<0.25∣J1∣{J}_{2}<0.25|{J}_{1}|J2​<0.25∣J1​∣ to $\ensuremath{\chi}\ensuremath{\propto}{T}^{\ensuremath{-}3/2}$ $(\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}1/2})$ at J2=0.25∣J1∣{J}_{2}=0.25|{J}_{1}|J2​=0.25∣J1​∣. In addition, we detect the existence of an additional low-temperature maximum in the specific heat when approaching the critical point at J2=0.25∣J1∣{J}_{2}=0.25|{J}_{1}|J2​=0.25∣J1​∣.
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We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.
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