Electron-spin resonance and ferromagnetism in a copper oxide: ${\mathrm{La}}_4$${\mathrm{Ba}}_2$${\mathrm{Cu}}_2$${\mathrm{O}}_{10}$

The electron-spin resonance (ESR) of a copper oxide ${\mathrm{La}}_4$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{10}$, which shows a ferromagnetic transition at around 5 K, has been studied. The ESR spectra show a narrowing with decreasing temperature that is characteristic of the ferromagnetic exchange interaction. The ground state of the ${\mathrm{Cu}}^{2+}$ d hole in the ${\mathrm{La}}_4$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{10}$ compounds is described by the wave function ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$, and it agrees with the results deduced from the structure. The origin of the ferromagnetism is that the d-hole orbits of the ground state are alternately orthogonal to the nearest-neighbor ones.