Identification of microscopic spin-polarization coupling in the ferroelectric phase of magnetoelectric multiferroicCuFe1−xAlxO2

Abstract

We have performed synchrotron radiation x-ray and neutron diffraction measurements on magnetoelectric multiferroic ${\text{CuFe}}_{1\ensuremath{-}x}{\text{Al}}_{x}{\text{O}}_{2}$ $(x=0.0155)$, which has a proper helical magnetic structure with incommensurate propagation wave vector in the ferroelectric phase. The present measurements revealed that the ferroelectric phase is accompanied by lattice modulation with a wave number $2q$, where $q$ is the magnetic modulation wave number. We have calculated the Fourier spectrum of the spatial modulations in the local electric polarization using a microscopic model proposed by T. Arima [J. Phys. Soc. Jpn. 76, 073702 (2007)]. Comparing the experimental results with the calculation results, we found that the origin of the $2q$-lattice modulation is not the conventional magnetostriction but the variation in the metal-ligand hybridization between the magnetic ${\text{Fe}}^{3+}$ ions and ligand ${\text{O}}^{2\ensuremath{-}}$ ions. Combining the present results with the results of a previous polarized neutron diffraction study [Nakajima et al., Phys. Rev. B 77, 052401 (2008)], we conclude that the microscopic origin of the ferroelectricity in ${\text{CuFe}}_{1\ensuremath{-}x}{\text{Al}}_{x}{\text{O}}_{2}$ is the variation in the metal-ligand hybridization with spin-orbit coupling.