Diamagnetic impurity effects on the Néel temperature in La2CuO4 and related materials

To investigate why the sensitivity of the Néel temperature T_N of the antiferromagnetic (AF) layered copper perovskites (typically La₂CuO₄) to diamagnetic impurities such as Zn is reportedly much larger than in the AF members of the K₂NiF₄ family, we first treat the effect of a concentration c of impurities on the uncorrelated electronic states in the coherent potential approximation (CPA). Then we consider the Heisenberg hamiltonian as the large correlation limit of the Hubbard hamiltonian for a single band of impurity-modified electronic states. The correlation effects are treated variationally. The model is solved explicity by using a rectangular density of states, and we obtain the c-dependent exchange J, staggered moment S_q, spin wave velocity and transverse susceptibility at zero temperature. We take into consideration several recently proposed formulae for T_N in the clean limit, and include the impurity effects by exploiting the results obtained, in order to test their predictions against the experimental T_N(c) data for La₂Cu_1−cZn_cO₄. Our results suggest that, to explain the difference between the K₂NiF₄ and the La₂ CuO₄ families, one should consider both the sign and the magnitude of the difference I≡ε^B−ε^A between impurity (B) and host (A) ionic potentials. The slowly decreasing trend of T_N(c) in the K₂NiF₄ family is reproduced if I is negative and sizeable, or positive but very small, while the quick decrease typical of the copper perovskites requires a positive and rather large I. For reasonable values of the interaction parameters, among the several models we compare, only the model of Chakravarty, Halperin and Nelson is able to semi-quantitatively reproduce the non-linear behaviour of T_N(c) reported for La₂Cu_1−cZn_cO₄, provided the spin stiffness is assumed to scale with c as appropriate to Fermi liquids.