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Motivated by recent experiments on quasi two-dimensional (2D) and quasi-one dimensional (1D) frustrated quantum magnets with
ferromagnetic nearest-neighbor exchange coupling J1 and antiferromagnetic next-nearest-neighbor exchange coupling J2 we investigate the ground-state magnetic ordering of the corresponding J1-J2 spin-½ Heisenberg magnets.
These systems exhibit a zero-temperature phase transition from the ferromagnetic ground state to a ground state with zero magnetization at a critical value of frustration J2c.
For the 2D model we use exact diagonalization (ED) and the coupled cluster method (CCM) to investigate the ground-state magnetic order for J2 > J2c ~ 0.4|J1|. By contrast to previous results, we do not find indications for a magnetically disordered ground state for J2c < J2 < 0.6|J1|, rather our results are in favor of a stable collinear stripe ground-state magnetic long-range order for J2 > 0.4|J1|. For the quasi-1D model, i.e. a system of coupled J1-J2 chains, we study the influence of an inter-chain exchange coupling on the ground state of the model. The spiral correlations at zero field are studied by means of the CCM. The DMRG and ED are used to discuss the fate of multi-magnon bound states in high magnetic fields if inter-chain coupling is taken into account. We find that already a small antiferromagnetic inter-chain coupling may have a significant effect on the ground state in high magnetic fields. Moreover we discuss the thermodynamical properties for J2 < J2c where the ground state is still ferromagnetic, but the frustration influences the thermodynamic quantities. In particular, we examine the low-temperature behavior of the susceptibility χ and the correlation length ξ. In the limit T → 0 both quantities diverge for the 1D as well as for the 2D case. This divergence is exponential, i.e. χ ∼ exp(a/T), ξ ∼ exp(b/T), in D=2, and it follows a power law, χ = cT-2 and ξ = dT-1, in D=1. For the unfrustrated ferromagnets, i.e. for J2=0, the coefficients a,b,c,d are known from previous studies. However, for the frustrated model so far no data were available. We find a linear decrease of the coefficients a,b,c,d with increasing frustration J2. For the 2D ferromagnet the coefficients a and b remain finite at the zero-temperature transition point J2c, i.e. the exponential divergence of χ and ξ is present up to J2c. By contrast, for the 1D ferromagnet both coefficients c and d vanish at J2=J2c indicating that the zero-temperature phase transition is accompanied by a change of the critical behavior of χ and ξ. In addition, we detect the existence of an additional low-temperature maximum in the specific heat when approaching the zero-temperature transition point at J2=J2c. |
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