Spontaneous flexoelectric/flexomagnetic effect in nanoferroics

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Flexoelectricity in soft materials and biological membranes (2014, background): “: þ1 713 743 4502; et al., 2007; Eliseev et al., 2009, 2011; Maranganti and Sharma, 2009; Majdoub et al., 2008a,b, 2009a,b; Sharma et al., 2010, 2012; Gharbi et al., 2011; Kalinin and Meunier, 2008; Dumitrica et al., 2002).”
Piezoelectric thin-film superlattices without using piezoelectric materials (2010, methodology): “(6) Neglecting the effect of charge density as suggested by Askar and Lee (1970), the total electric enthalpy density can be written as”
Flexoelectric Effect in Solids (2013, background): “Flexomagnetism Symmetry-wise, the same coupling between strain gradient and polarization is also allowed between strain gradient and magnetization [32].”
Fundamentals of flexoelectricity in solids (2013, methodology): “11 Such a conclusion is compatible with a result by Eliseev et al [52], who argued that the electrode-adjacent variation of the spontaneous polarization causes a bending of a ferroelectric plate depending on the boundary condition for the polarization.”
Size-dependent piezoelectricity (2012, background): “Although there are some developments in this direction (Tagantsev, 1986; Maranganti et al., 2004; Sharma, 2007, Eliseev et al., 2009), these theories also suffer from the use of different inconsistent second order gradients of deformation, as well as ignoring the possible couple-stress effect.”