Influence of the Incommensurability in ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ Family Compounds

We study the influence of the structural modulation on the low energy physics of the ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ oxides, using ab initio determination of the on-site and nearest-neighbor effective parameters. The structural modulations appear to be the key degree of freedom responsible for the low energy properties, such as the electron localization, the formation of dimers in the $x=0$ compound, or the antiferromagnetic order in the $x=13.6$ compound.

Figure 1

Energy of the hole orbital as a function of its position along the chain. (a) For $x=0$, (b) for $x=13.6$.

Figure 2

Exchange $J$ and hopping $t$ integrals as a function of the position of the fragment along the chain. (a) $J$ for $x=0$, (b) $J$ for $x=13.6$, (c) $t$ for $x=0$, (d) $t$ for $x=13.6$.

Figure 3

Orbital-energy differences as a function of the fourth coordinate $\tau$, (a) for $x=0$, (b) for $x=13.6$. The solid line represents the fit.

Figure 4

Localization of the magnetic electrons along the chain, as a function of the number $n$ of holes transferred to the ladders. (a) For $x=0$, (b) for $x=13.6$. The number of sites considered in both cases corresponds to a better approximation of the compound unit cells than the $10/7$ ratio, that is, $c_{ch}/c_{la}=3.9235/2.7268\simeq 100/69.5$ for $x=0$ and $c_{ch}/c_{la}=3.90136/2.73607\simeq 77/54$ for $x=13.6$. Dots stand for ZR singlets and the ellipsoids delimit spin clusters, which are magnetically very stable (with at most one second-neighbor frustrated interaction).