Identification of microscopic spin-polarization coupling in the   ferroelectric phase of a magnetoelectric multiferroic CuFe1-xAlxO2
  We have performed synchrotron radiation X-ray and neutron diffraction measurements on magnetoelectric multiferroic CuFe1-xAlxO2 (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 Arima [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 conventional magnetostriction but the variation in the metal-ligand hybridization between the magnetic Fe^3+ ions and ligand O^2- 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 CuFe1-xAlxO2 is the variation in the metal-ligand hybridization with spin-orbit coupling. 
Taro Nakajima, Setsuo Mitsuda, Toshiya Inami, Noriki Terada, Hiroyuki   Ohsumi, Karel Prokes, Andrei Podlesnyak