Universality of density waves in p-doped La2CuO4 and n-doped Nd2CuO4+y

The contribution of $O^{2-}$ ions to antiferromagnetism in $L{a}_{2-x}A{e}_{x}Cu{O}_4$ ($Ae=Sr,Ba)$ is highly sensitive to doped holes. In contrast, the contribution of $C{u}^{2+}$ ions to antiferromagnetism in $N{d}_{2-x}C{e}_{x}Cu{O}_{4+y}$ is much less sensitive to doped electrons. The difference causes the precarious and, respectively, robust antiferromagnetic phase of these cuprates. The same sensitivities affect the doping dependence of the incommensurability of density waves, $\delta (x)$. In the hole-doped compounds this gives rise to a doping offset for magnetic and charge density waves, ${\delta }_{m,c}^p(x)\propto \sqrt{x-x_{0p}^N}$. Here $x_{0p}^N$ is the doping concentration where the N'{e}el temperature vanishes, $T_N(x_{0p}^N) = 0$. No such doping offset occurs for density waves in the electron-doped compound. Instead, excess oxygen (necessary for stability in crystal growth) of concentration $y$ causes a different doping offset in the latter case, ${\delta }_{m,c}^n(x)\propto \sqrt{x-2y}$. The square-root formulas result from the assumption of superlattice formation through partitioning of the $Cu{O}_2$ plane by pairs of itinerant charge carriers. Agreement of observed incommensurability $\delta (x)$ with the formulas is very good for the hole-doped compounds and reasonable for the electron-doped compound. The deviation in the latter case may be caused by residual excess oxygen.