Nonmagnetic impurities in two- and three-dimensional Heisenberg antiferromagnets.

In this paper we study in a large-S expansion effects of substituting spins by non-magnetic impurities in twoand threedimensional Heisenberg antiferromagnets in a weak magnetic field. In particular, we demonstrate a novel mechanism where magnetic moments are induced around non-magnetic impurities when magnetic field is present. As a result, Curie-type behaviour in magnetic susceptibility can be observed well below the Neel temperature, in agreement with what is being observed in La2Cu1−xZnxO4 and Sr(Cu1−xZnx)2O3 compounds. PACS Numbers: 75.10.Jm, 75.10.-b, 75.40.Mg Typeset using REVTEX 1 Recently, there has been increasing interests in the effects of substituting Cu by nonmagnetic ions (Zn) in high-Tc cuprates, where interesting effects were discovered for compounds in the underdoped regime [1]. In particular, magnetic susceptibility measurement [2] and other experiments [3] seem to indicate that local magnetic moments are generated as Cu ions were replaced by Zn, both in the underdoped high-Tc Yttrium and Bismuth compounds [2,3], and for undoped Lanthanum compound [4]. Based on RVB theories of the t−J model, Nagaosa and Ng [5] have constructed explanations on how local magnetic moments can be generated in these compounds in the disordered phase of two-dimensional antiferromagnets. Their theory is believed to be applicable to the underdoped regime of high-Tc compounds. However the theory is not applicable to the La compound where Curie-type behaviour is observed in magnetic susceptibility at temperatures well below the Neel temperature where long-range antiferromagnetic order exists. More recently, similar experiment on the two-leg ladder compound Sr(Cu1−xZnx)2O3 also indicates formation of local magnetic moments in the spin-gap phase as Cu ions are replaced by Zn ions [6]. The compound was found to order antiferromagnetically at low temperature at x ∼ 0.07 [7]. Surprisingly, Curie behaviour in magnetic susceptibility remains even below the Neel-ordering temperature [7], indicating that formation of magnetic moments around non-magnetic impurities is a general phenomenon in Neel state of quantum antiferromagnets. In the presence of long-range antiferromagnetic order, the low temperature properties of clean antiferromagnets can be understood at least qualitatively using a semi-classical theory (1/S expansion). In this paper we shall generalize this approach to include the effects of non-magnetic impurities in the presence of a uniform magnetic field. Notice that in the absence of magnetic field, a similar study has been performed by Bulut et. al. [8] where no ’free’ magnetic moments were found to be induced around non-magnetic impurities. We shall show that local magnetic moments can be induced by non-magnetic impurities once magnetic field is applied on the system through a novel mechanism. Notice that strictly speaking, thermal fluctuations destroy long-range magnetic order at two dimension at any finite temperature. Thus our analysis at two dimension can only be applied to layered