Structural and magnetic properties of isovalently substituted multiferroic BiFeO${}_3$: Insights from Raman spectroscopy

Raman spectra, supplemented by powder x-ray diffraction and magnetization data of isovalently $A$- and $B$-site substituted ${\mathrm{BiFeO}}_3$ in the ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ ($0\le x\le 1$), ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$ ($0\le x\le 0.2$), and ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ ($0\le x\le 0.3$) series, are presented. A good agreement between the structural transitions observed by x-ray diffraction and the vibrational modes observed in the Raman spectra is found over the whole substitutional ranges, and in particular we find spectroscopic signatures of a $\mathrm{Pb}{\mathrm{ZrO}}_3$-type structure for ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{FeO}}_3$. Mode assignments in the substituted materials are made based on Raman spectra of the end-members ${\mathrm{BiFeO}}_3$ and $\mathrm{La}{\mathrm{FeO}}_3$. Moreover, by comparing spectra from all samples with $R3c$ structure, the phonon assignment in ${\mathrm{BiFeO}}_3$ is revisited. A close connection between the degree of octahedral tilt and the Raman shift of the $A_1$ oxygen $a^{-}{a}^{-}{a}^{-}$ tilt mode is established. An explanation for the strong second-order scattering observed in ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ and ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$ is suggested, including the assignment of the previously mysterious ${\mathrm{BiFeO}}_3$ mode at 620 ${\mathrm{cm}}^{-1}$. Finally, the magnetization data indicates a transition from a cycloidal modulated state towards a canted antiferromagnet with increasing $A$-site substitution, while ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ with $x=0$ and $0.15$ exhibit an anomalous closing of the hysteresis loop at low temperatures. For low $A$-site substitution levels ($x\le 0.1$) the decreasing Raman intensity of the Fe derived modes correlates with the partial destruction of the spin cycloid as the substitution level increases.

Figure 1

PXRD data for (a) ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ series and (b) ${\mathrm{Bi}}_{0.5}{\mathrm{La}}_{0.5}{\mathrm{FeO}}_3$, ${\mathrm{Bi}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{FeO}}_3$ (both $Pnma$ symmetry), and ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{Fe}}_{0.7}{\mathrm{Mn}}_{0.3}{\mathrm{O}}_3$ ($Imma$) from bottom to top. Peaks from the impurity phase ${\mathrm{Bi}}_2{\mathrm{Fe}}_4{\mathrm{O}}_9$ are indicated by $*$ for the ${\mathrm{BiFeO}}_3$ ($x=0$) sample in (a).

Figure 2

Raman spectra of ${\mathrm{BiFeO}}_3$ in the spectral range (a) 130–1700 ${\mathrm{cm}}^{-1}$ and (b) 50–700 ${\mathrm{cm}}^{-1}$ at two different spots. The first-order $\Gamma$-point phonons are visible in (a) below 620 ${\mathrm{cm}}^{-1}$. A strong two-phonon spectrum can be seen at higher wave numbers. A closer look at the first-order phonon is given in (b), together with mode symmetries taken from Ref. 33 and predominantly involved atomic species taken from the first-principle study in Ref. 42. The modes are numbered according to ascending frequency. In addition, as they overlap closely with the polar Bi offset and antiphase oxygen-octahedra distortion respectively,[42] the two lowest $A_1$ modes are labeled according the main atomic species involved in the vibration. The mode within square brackets was not observed in our spectra, but is included for completeness.[33] The additional modes in the upper spectrum arises as a consequence of the LO-TO splitting of the oblique phonons when the laser light impinges at an angle with the [111] pseudocubic direction.

Figure 3

Raman spectra of $\mathrm{La}{\mathrm{FeO}}_3$ in the spectral range (a) 130–1700 ${\mathrm{cm}}^{-1}$ and (b) 50–700 ${\mathrm{cm}}^{-1}$. The Raman allowed first-order $A_g+B_{2g}$ phonons in the $ac$ plane can be labeled according to the respective atomic motions as either $A$-site modes (A), oxygen tilt (T), oxygen bending (B), or oxygen stretch (S) modes as indicated in (b). Besides the first-order scattering, strong second-order scattering can be observed above 900 ${\mathrm{cm}}^{-1}$ in (a). Notice the broad background beneath the B and T modes arising from IR-active LO vibrations.[34, 44, 45] These bands becomes Raman active via the Fröhlich interaction and their respective overtones and combinations are the origin of the strong second-order scattering.[34]

Figure 4

Raman spectra for ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$ in the spectral range (a) 150–1700 ${\mathrm{cm}}^{-1}$ and (b) 50–375 ${\mathrm{cm}}^{-1}$. The $R3c$ structure is clearly observed up until $x=0.1$, while a $Pnma$ structure is seen for $x\ge 0.175$. A mixed phase region is found for the intermediate substitution range, indicating phase coexistence on the micron scale. To the right of (b) we indicate the structural phases that each spectrum belongs to. To improve viewing, the individual spectra have been scaled and translated along the $y$ axis.

Figure 5

Raman spectra for ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ in the spectral range (a) 150–1700 ${\mathrm{cm}}^{-1}$ and (b) 50–375 ${\mathrm{cm}}^{-1}$. The spectra indicates a $R3c$ structure below $x\le 0.15$. From the high resolution spectra in (b), a centrosymmetric $Pnma$ structure can be deduced for $x\ge 0.5$, while the low frequency mode at 60 ${\mathrm{cm}}^{-1}$ indicates an antiferroelectric structure between $x=0.175$ and $x=0.4$, see Sec. 5. To the right of (b) we indicate the structural phases that each spectrum belongs to. Stars are used in the biphasic $x=0.15$ sample to highlight the Raman active modes characteristic of the $\mathrm{Pb}{\mathrm{ZrO}}_3$-type phase. To improve viewing, the individual spectra have been scaled and translated along the $y$ axis.

Figure 6

Raman spectra for ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ and ${\mathrm{BiFeO}}_3$ in the spectral range 150–1700 ${\mathrm{cm}}^{-1}$. The transition from $R3c$ to $Imma$ symmetry is clearly visible in the decrease in spectral features above $x=0.15$. To the right we indicate the structural phases that each spectrum belongs to, although a phase coexistence in the $x=0.15$ sample, in accord with results from neutron diffraction,[21] can be deduced from the observable, but weak, second-order scattering. To improve viewing, the individual spectra have been scaled and translated along the $y$ axis.

Figure 7

Comparison of the low frequency spectra in the $R3c$ structures of ${\mathrm{BiFeO}}_3$, ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$, ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$, and ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{FeO}}_3$ collected at 80 K. Dashed lines shows phonon positions in ${\mathrm{BiFeO}}_3$ and are used to facilitate comparison between samples. The LO-TO splitting is visible as a two peak structure in the $E\left(1\right)$ mode and as the shoulder of the $A_1\left(1\right)$ mode for the $E\left(2\right)$ mode. To improve viewing, the individual spectra have been scaled and translated along the $y$ axis.

Figure 8

(a) Position of the $A_1\left(2\right)\left(\mathrm{O}\right)$ mode as a function of $A$-site substitution for the BFO, Tb5, Tb10, La10, La15, and Sm10 samples. The shift due to Tb substitution is significantly larger than that from La substitution as is expected from the increased octahedral distortion in ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$. (b) Shows the same Raman shifts, now as a function of the octahedral tilt angle. The near linear dependence, with a slope of 18 ${\mathrm{cm}}^{-1}$/deg, indicates a close connection between the frequency of the $A_1\left(2\right)\left(\mathrm{O}\right)$ mode and the octahedral distortion in the $R3c$ structure. The tilt angles were extracted from room temperature neutron diffraction studies,[15, 21] however, no reliable data on the La containing materials could be found.

Figure 9

Band assignments in the $Pnma$ phases of $\mathrm{La}{\mathrm{FeO}}_3$, ${\mathrm{Bi}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{FeO}}_3$, and ${\mathrm{Bi}}_{0.5}{\mathrm{La}}_{0.5}{\mathrm{FeO}}_3$ collected at 80 K. The labeling of A, T, B, and S is explained in Fig. 3. LO denotes the Raman-inactive longitudinal phonons whose overtones and combination bands are the source of the second-order scattering,[34, 46] see text for details. To improve viewing, the individual spectra have been scaled and translated along the $y$ axis.

Figure 10

Comparison between ${\mathrm{PbZrO}}_3$ at 273 K (top) and ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}\mathrm{Fe}{\mathrm{O}}_3$ at 80 K (bottom). Notice the similarity in spectral features shared between the two compounds as indicated by the arrows and dashed lines, including the presence of low-frequency antiferroelectric modes below 100 ${\mathrm{cm}}^{-1}$. The Raman spectrum of ${\mathrm{PbZrO}}_3$ was reproduced from the spectrum found by Pasto and Condrate.[52]

Figure 11

Raman spectra in the region of second-order scattering in ${\mathrm{BiFeO}}_3$, ${\mathrm{Bi}}_{0.95}{\mathrm{Tb}}_{0.05}{\mathrm{FeO}}_3$, ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{FeO}}_3$, and $\mathrm{La}{\mathrm{FeO}}_3$. The second-order scattering is attributed to overtones and combination modes of the first-order modes M1, M2, and M3. In total there are six expected peaks in the second-order scattering: 2M1, 2M2, 2M3, M1+M2, M1+M3, and M2+M3. The dashed lines indicates the position of the first and five of the expected second-order modes in ${\mathrm{BiFeO}}_3$, while the sixth 2M2 peak is hinted in the line shape between the M1+M3 and M2+M3 modes. The ${\mathrm{Bi}}_{0.95}{\mathrm{Tb}}_{0.05}{\mathrm{FeO}}_3$ spectrum is very similar to the ${\mathrm{BiFeO}}_3$ spectrum except from a shift in the M1 related modes and resonant enhancement of the M3 mode. ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{FeO}}_3$ shows a distinct double peak structure in the first-order M3 mode and the overtone 2M3, denoted by M3${}^{\prime }$. The M1 and 2M1 peaks are also visible, while the decrease in spectral features indicates the absence of the M2 mode. The M1+M3 and M1+M3${}^{\prime }$ peaks forms a featureless band with just one visible peak, marked with a star. The resonant enhancement of the M3 mode in ${\mathrm{Bi}}_{0.95}{\mathrm{Tb}}_{0.05}{\mathrm{FeO}}_3$ and ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{FeO}}_3$ is very similar to what is observed in $B$-site substituted $\mathrm{La}{\mathrm{FeO}}_3$,[34] and leads us to assign the M3 mode to a formally Raman-silent $A_2$ LO mode. A common mechanism behind the different second-order peak suggests a LO assignment of all of the M1, M2, and M3 modes.

Figure 12

Magnetization versus field at 300 K for ${\mathrm{Bi}}_{1-x}{\mathrm{Tb}}_x{\mathrm{FeO}}_3$ with $x=0.05$, 0.1, and 0.2. The lower right inset shows field cooled magnetization versus temperature curves for the $x=0.05$, 0.1, 0.15, and 0.2 samples using an applied field of 500 Oe. The inset in the upper left corner shows magnetization versus field at 10 K for the $x=0.05$ and 0.2 samples.

Figure 13

Magnetization versus field at 10 and 300 K for ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{FeO}}_3$ with $x=0.1$ and $0.2$. The inset shows field cooled magnetization versus temperature curves for the same samples using an applied field of 500 Oe.

Figure 14

Magnetization versus field at 10 and 300 K for ${\mathrm{Bi}}_{0.9}{\mathrm{Sm}}_{0.1}{\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_3$ with $x=0$ and $0.15$. The lower right inset shows field cooled magnetization versus temperature curves for the $x=0$, $0.15$, and $0.3$ samples using an applied field of 500 Oe. The inset in the upper left corner shows magnetization versus field at 10 K for the $x=0.3$ sample.