(a) Atomic structure of the Fe/PbTiO3 superlattice. The planar (thin black curve) and macroscopic averaged electrostatic potential (thick red curve) along the  direction of (b) the Fe/PbTiO3 superlattice and (c) the corresponding free-standing PbTiO3 slab. The polarization direction of PbTiO3 film is pointing leftward.
(a) Relative displacements of M-O (M = Pb, Ti) at each PbTiO3 atomic plane in the Fe/PbTiO3 superlattice. The arrow marks the direction of the polarization in PbTiO3 film. (b) The layer by layer magnetic moment of the Fe film in the paraelectric (PE) and ferroelectric (FE) states for the Fe/PbTiO3 superlattice. The moments of the corresponding free-standing Fe slab are also shown in the blue triangle curve. The midpoint of the ferromagnetic layer defined as zero. Note that layer number −4 and 4 correspond to the right and left interfaces illustrated in Fig. 1(a), respectively. The horizontal line denotes the bulk moment values.
Contour plot in the (010) plane of the charge density difference at the left interface for the Fe/PbTiO3 superlattice as the ferroelectric polarization direction (a) pointing leftward and (b) pointing rightward. Charge gain is given by solid red lines and charge loss by dotted black lines. The charge density difference is obtained by subtracting the charge densities of freestanding Fe and PbTiO3 slabs from the total charge density of the Fe/PbTiO3 superlattice. The interval of contours is 0.002 e/Å3.
Orbital-resolved DOS for interfacial atoms in Fe/PbTiO3 superlattice: (a) Ti 3 d, (b) Fe 3 d, and (c) O 2 p. Majority- and minority-spin DOS are shown in the upper and lower panels, respectively. The solid red and dashed blue lines denote DOS of atoms at the right and left interfaces, respectively. Shaded plots are the DOS projected on bulk Fe 3 d orbitals (b), on Ti 3 d (a) and O 2 p orbitals (c) in the central TiO2 monolayer of PbTiO3 which can be regarded as bulk. The vertical line indicates the Fermi energy.
Contour plot in the (010) plane of the induced spin density at the left interface for the Fe/PbTiO3 superlattice as the ferroelectric polarization direction (a) pointing leftward and (b) pointing rightward. Spin increment is given by solid red lines and spin decrement by dotted black lines. The induced spin density is obtained by subtracting the spin densities of free-standing Fe and PbTiO3 slabs from the total spin density in the Fe/PbTiO3 superlattice. The interval of contours is 0.004 e/Å3.
Cohesive energies in J/m2 and bond lengths in Å for Fe/PbTiO3 interface. L and R in brackets indicate the left and right interfaces, respectively.
Magnetic moments in of M (M = Fe, Ti) atoms in the ferroelectric Fe/PbTiO3 superlattice. () is the total moment of the M atoms at the left (right) surface side. is the difference between the magnetic moments at the right and left interfaces, and is the total moment difference. The polarization of the PbTiO3 film is pointing leftward.
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