Phase diagram of ${\mathrm{BiFeO}}_3/{\mathrm{LaFeO}}_3$ superlattices studied by x-ray diffraction experiments and first-principles calculations

Combining structural and functional measurements, we have mapped the phase diagram of ${\mathrm{BiFeO}}_3/{\mathrm{LaFeO}}_3$ superlattices grown by off-axis sputtering on (110)${}_o {\mathrm{DyScO}}_3$ substrates. The phase diagram displays three distinct regions as a function of ${\mathrm{BiFeO}}_3$ fraction, with a ${\mathrm{BiFeO}}_3$-like ferroelectric phase and a ${\mathrm{LaFeO}}_3$-like paraelectric phase at its extremities, and a complex intermediate region, as supported by first-principles calculations. This intermediate region shows unusual, mixed functional behavior, most likely due to competing phases driven by substitution with a same-size central ion and the specific boundary conditions imposed by the superlattice structure. In the ${\mathrm{BiFeO}}_3$ rich superlattices, scaling of the ferroelectric-to-paraelectric transition temperature with the ${\mathrm{BiFeO}}_3$ thickness could provide an alternate route for studying ferroelectric size effects in ${\mathrm{BiFeO}}_3$.

Figure 1

(a) Schematic representation of the superlattices with $m{\mathrm{BiFeO}}_3$ and $n{\mathrm{LaFeO}}_3$ (pseudocubic) lattice units, and $p$ periods in the full superlattice. (b) Specular x-ray diffraction from a typical superlattice on (110)${}_o {\mathrm{DyScO}}_3$ confirming high crystalline quality.

Figure 2

(a) Evolution of average out-of-plane lattice parameter with overall ${\mathrm{BiFeO}}_3$ fraction for two series of superlattices with 12 and 20 unit cell periods, respectively. (b),(c) Reciprocal space maps around the (332)${}_o$ reflection of ${\mathrm{DyScO}}_3$ for superlattices with a large and a small out-of-plane average lattice parameter, showing that the superlattices are fully strained throughout the phase diagram. (d) Evolution of the dielectric constant with overall ${\mathrm{BiFeO}}_3$ fraction for the same two series of superlattices and the DFPT model. The dielectric constant peaks on the ${\mathrm{BiFeO}}_3$-rich side of the lattice parameter step.

Figure 3

Out-of-plane lattice parameter from PBEsol + $U$ calculations for superlattices with varying fraction of ${\mathrm{BiFeO}}_3$. For ${\mathrm{BiFeO}}_3$ fractions below 0.8 the $Pnma$-like (initial structure $a^{-}{a}^{-}{c}^{+}$) phase is favored over the $R3c$-like (initial structure $a^{-}{a}^{-}{a}^{-}$) phase (inset), resulting in a sharp change of lattice parameter.

Figure 4

Polarization-voltage (P-V) dependence showing (a) normal ferroelectric behavior for a (9/3)20 superlattice, (b) paraelectric behavior for a (5/7)20 superlattice, and (c) mixed ferroelectric-paraelectric behavior for a (6/6)20 superlattice. (d) Capacitance-voltage measurement for the same superlattice showing complex behavior with a quadruple-humped curve.

Figure 5

(a) Synchrotron XRD measurement along the specular rod, showing the presence of half-order (cell doubling) peaks. (b) Temperature dependence of such half-order peaks. The peaks reappear at the same position upon cooling.

Figure 6

Evolution with temperature of the difference between the average lattice parameter and the paraelectric lattice parameter (obtained from a linear fit of the high temperature data) for (a) (16/4)12, (b) (5/5)24, and (c) (12/4)15 superlattices, showing two distinct out-of-plane lattice parameters. (d) The transition temperature $T_C$ scales linearly with the ${\mathrm{BiFeO}}_3$ sublayer thickness. The error bars are a measure of the observed thermal hysteresis.

Figure 7

Schematic phase diagram of ${\mathrm{BiFeO}}_3/{\mathrm{LaFeO}}_3$ superlattices on (110)${\mathrm{DyScO}}_3$ substrates. (a) Room temperature phase diagram as a function of ${\mathrm{BiFeO}}_3$ fraction. There are three distinct regions: a ${\mathrm{BiFeO}}_3$-like region, a ${\mathrm{LaFeO}}_3$ region, and a rich and complex intermediate region. (b) Phase diagram as a function of ${\mathrm{BiFeO}}_3$ thickness per period for a ${\mathrm{BiFeO}}_3$ fraction of 0.8. The transition temperature scales linear with ${\mathrm{BiFeO}}_3$ thickness.