Strong spin triplet contribution of the first removal state in the insulating regime of Bi$_2$Sr$_2$Ca$_{1- x}$Y$_x$Cu$_2$O$_{8+\delta}$

The experimental dispersion of the first removal state in the insulating Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+\delta}$ regime of is found to differ significantly from that of other parent materials: oxyclorides and ${\rm La_2CuO_4}$. For Y-contents of $0.92\geq x \geq0.55$ due to nonstoichiometric effects in the Bi–O layers, the hole concentration in the CuO$_2$-layers is almost constant and on the contrary the crystal lattice parameters $a,b,c$ change very strongly. This ($a,b$) parameter increase and $c$ parameter decrease results in an unconventional three peak structure at $(0,0);(\pi/2,\pi/2);(\pi,\pi)$ for $x=0.92$. We can describe the experimental data only beyond the framework of the $3$-band $p{-}d$-model involving the representations of a new triplet counterpart for the Zhang–Rice singlet state.