Theoretical Analysis of the Reduction of Neel Temperature in La${}_2$(Cu${}_{1-x}$Zn(or Mg)${}_x)$O${}_4$

Using Tyablikov’s decoupling approximation, we calculate the initial suppression rate of the Neel temperature, $R_{IS}=-lim_{x-> 0} T^{-1}{N} dT{N}/dx$, in a quasi two-dimensional diluted Heisenberg antiferromagnet with nonmagnetic impurities of concentration $x$. In order to explain an experimental fact that $R_{IS}^{(Zn)}=3.4$ of the Zn-substitution is different from $R_{IS}^{(Mg)}=3.0$ of the Mg-substitution, we propose a model in which impurity substitution reduces the intra-plane exchange couplings surrounding impurities, as well as dilution of spin systems. The decrease of 12% in exchange coupling constants by Zn substitution and decrease of 6% by Mg substitution explain those two experimental results, when an appropriate value of the interplane coupling is used.