Quantum Spin Memory Using Inverse Copper Oxide Cluster—Spin Configurations Unpredicted from Ligand Field Theory

Abstract

In quantum mechanics, 3d orbital can be expressed using quantum wave function. Though five 3d orbitals have the same radial quantum wave function, they have different angular quantum wave functions. In molecular orbital (MO) calculation, Gaussian-type quantum wave function is applied, instead of Slater-type quantum wave function. $$3{d}_{{x}^{2}-{y}^{2}}$$ and $$3{d}_{{z}^{2}}$$ orbitals are expressed by the superposition of $${x}^{2}$$ , $${y}^{2}$$ and $${z}^{2}$$ components. Ligand field theory is constructed in semi-quantum manner, based on point charge. Though one specific spin configuration can be predicted, the correct orbital energy diagram cannot be predicted. For example, in OCuO cluster, ligand field theory predicts that highest orbital energy is given in $$3{d}_{{3x}^{2}-{r}^{2}}$$ orbital. However, in fact, the orbital has lower orbital energy than other 3d orbitals. Two spin configurations: (1) $$3{d}_{{3x}^{2}-{r}^{2}}$$ type and (2) $$3{d}_{{z}^{2}-{x}^{2}}$$ type are here given. Next, we consider realistic model, inverse Cu4O4 cluster, where oxygen atoms are allocated at edges of square, instead of copper atom. As same as OCuO cluster, two spin configurations are given. In $$3{d}_{{z}^{2}-{x}^{2}}$$ type spin configuration, there is no orbital overlap between copper and oxygen atoms. In other words, $$3{d}_{{z}^{2}-{x}^{2}}$$ type electron works as barrier to oxygen electron. The effect is called “Barrier Effect”. Further, in $$3{d}_{{z}^{2}-{x}^{2}}$$ type spin configuration, quintet and singlet spin states are almost degenerated. When controlling the total energy difference, inverse Cu4O4 cluster can be applied for quantum spin memory.