arXiv:1001.1222v2 [cond-mat.str-el] 26 May 2010 Thermodynamics of a two-dimensional frustrated spin- 1 2 Heisenberg ferromagnet M. H¨ artel and J. Richter Institut f¨ ur Theoretische Physik, Otto-von-Guericke-Universit¨ at Magdeburg, D-39016 Magdeburg, Germany D. Ihle Institut f¨ ur Theoretische Physik, Universit¨ at Leipzig, D-04109 Leipzig, Germany S.-L. Drechsler Leibniz-Institut f¨ ur Festk¨ orper- und Werkstoffforschung Dresden, D-01171 Dresden, Germany (Dated: November 12, 2018) Using the spin-rotation-invariant Green’s function method we calculate the thermodynamic quan- tities (correlation functions 〈 S 0 S R 〉 , uniform static spin susceptibility χ , correlation length ξ , and specific heat C V ) of the two-dimensional spin-1 / 2 J 1 - J 2 Heisenberg ferromagnet for J 2 < J c 2 ≈ 0 . 44 | J 1 | , where J c 2 is the critical frustrating antiferromagnetic next-nearest neighbor coupling at which the ferromagnetic ground state gives way for a ground-state phase with zero magnetization. Examining the low-temperature behavior of χ and ξ , in the limit T → 0 both quantities diverge exponentially, i.e., χ ∝ exp( b/T ) and ξ ∝ exp( b/ 2 T ), respectively. We find a linear decrease in the coefficient b with increasing frustration according to b = − π 2 ( J 1 + 2 J 2 ), i.e., the exponential divergence of χ and ξ is present up to J c 2 . Furthermore, we find an additional low-temperature maximum in the specific heat when approaching the critical point, J 2 → J c 2 . present paper we will focus on the region of weak frus- tration J$_{2}$ < J c $_{2}$. Although for J$_{2}$ < J c 2 the ground state remains fer- romagnetic, the frustrating J$_{2}$ may influence the ther- modynamics substantially, in particular near a zero- temperature transition. This has been demonstrated for the one-dimensional (1D) frustrated ferromagnet in Ref. 28, where a change in the low-temperature behav- ior of the susceptibility and the correlation length as well as an additional low-temperature maximum in the spe- cific heat have been found when approaching the zero- temperature critical point from the ferromagnetic side. The Hamiltonian of the system considered in this paper is given by where ( S$_{i}$ ) 2 = 3 / 4, and 〈 i,j 〉 denotes NN and [ i,j ] denotes NNN bonds. The unfrustrated 2D ferromag- net ( J$_{2}$ = 0) has been widely investigated, e.g., by the modified spin-wave theory, 29 renormalization group approaches, 30,31 the quantum Monte Carlo method, 32–35 and by a spin-rotation-invariant second-order Green’s function method (RGM). 35–39 However, in presence of frustration ( J$_{2}$ > 0) the choice of appropriate methods for studying temperature dependent quantities of this system is restricted due to frustration and dimension- ality. For instance, the powerful quantum Monte Carlo method is not applicable due to the minus sign problem, whereas finite-temperature density matrix renormaliza- tion group studies are restricted to 1D systems. So far, only a few theoretical papers deal with the ther- modynamics of the model for J$_{2}$ > 0, see, e.g., Refs. 13,16 and 17, where finite lattices of N = 16 and N = 20 On the other hand, some materials considered as 2D spin-1/2 ferromagnets, such as K$_{2}$CuF$_{4}$, Cs$_{2}$CuF$_{4}$, Cs$_{2}$AgF$_{4}$, La$_{2}$BaCuO$_{5}$, and Rb$_{2}$CrCl$_{4}$, 23–27 might have also a weak frustrating NNN interaction J$_{2}$ < J c $_{2}$. In contrast to the previous investigations of the 2D J$_{1}$ - J$_{2}$ model with ferrromagnetic J$_{1}$ 13–18,21 which have consid- ered predominantly the case of strong frustration, in the Low-dimensional quantum magnets have attracted much attention during the last decades. 1,2 They are pre- destined to study the influence of strong thermal and quantum fluctuations. Much attention has been paid to the theoretical investigation of the two-dimensional (2D) spin-1 / 2 J$_{1}$ - J$_{2}$ quantum Heisenberg antiferromag- net which may serve as a canonical model to study the interplay of frustration effects and quantum fluc- tuations (see, e.g., Ref. 3). An additional motivation to study this model comes from the experimental side. 4 Very recently, several quasi-2D magnetic materials with a ferromagnetic nearest-neighbor (NN) coupling J$_{1}$ < 0 and a frustrating antiferromagnetic next-nearest neigh- bor (NNN) coupling J$_{2}$ > 0 have been investigated ex- perimentally, e.g., Pb$_{2}$VO(PO$_{4}$)$_{2}$, 5–8 (CuCl)LaNb$_{2}$O$_{7}$, 9 SrZnVO(PO$_{4}$)$_{2}$, 8,10,11 and BaCdVO(PO$_{4}$)$_{2}$. 7,10,12 The quite large frustrating J$_{2}$ drives these materials out of the ferromagnetic phase. The experimental findings have stimulated several theoretical studies of the ground-state and thermodynamic properties of the J$_{1}$ - J$_{2}$ model with J$_{1}$ < 0 and frustrating J$_{2}$ > 0. 13–21 It was found that the ferromagnetic ground state for the spin-1 / 2 model breaks down at J$_{2}$ = J c 2 ≈ 0 . 4 | J$_{1}$ | . 13–18,21,22 Note that for the classical model (spin s → ∞ ) the corresponding transition point is at J$_{2}$ = 0 . 5 | J$_{1}$ | . PACS numbers: I. INTRODUCTION H = J$_{1}$ ∑ 〈 i,j 〉 S$_{i}$S$_{j}$ + J$_{2}$ ∑ [ i,j ] S$_{i}$S$_{j}$ ; J$_{1}$ < 0 ; J$_{2}$ ≥ 0 , (1)