Incommensurate magnetic structure, Fe/Cu chemical disorder, and magnetic interactions in the high-temperature multiferroic $\mathrm{YBaCuFeO}{}_5$

Motivated by the recent observations of incommensurate magnetic order and electric polarization in ${\mathrm{YBaCuFeO}}_5$ up to temperatures $T_{N2}$ as high as 230 K [B. Kundys et al., Appl. Phys. Lett. 94, 072506 (2009); Y. Kawamura et al., J. Phys. Soc. Jpn 79, 073705 (2010)], we report here for the first time a model for the incommensurate magnetic structure of this material, which we complement with ab initio calculations of the magnetic exchange parameters. Using neutron powder diffraction, we show that the appearance of polarization below $T_{N2}$ is accompanied by the replacement of the high-temperature collinear magnetic order by a circular inclined spiral with propagation vector ${\mathbf{k}}_i=(1/2,1/2,1/2\pm q)$. Moreover, we find that the polarization approximately scales with the modulus of the magnetic modulation vector $q$ down to the lowest temperature investigated $(\sim 3$ K). Further, we observe occupational Fe/Cu disorder in the ${\mathrm{FeO}}_5\text{−}{\mathrm{CuO}}_5$ bipyramids, although a preferential occupation of such units by Fe-Cu pairs is supported by the observed magnetic order and by density functional calculations. We calculate exchange coupling constants for different Fe/Cu distributions and show that, for those containing Fe-Cu dimers, the resulting magnetic order is compatible with the experimentally observed collinear magnetic structure $\mathrm{[}{\mathbf{k}}_c=(1/2,1/2,1/2),T_{N2}>T>T_{N1}=440$ K]. Based on these results, we discuss possible origins for the incommensurate modulation and its coupling with ferroelectricity.

Figure 1

Models for the crystal structure of ${\mathrm{YBaCuFeO}}_5$ used for the Rietveld fits of the RT NPD data recorded on HRPT (see also Table 1). (a) Centrosymmetric $\left(P4/mmm\right)$ with a single Fe/Cu site. (b) Centrosymmetric $\left(P4/mmm\right)$ with Fe/Cu sites split. (c) Noncentrosymmetric $\left(P4mm\right)$ with perfect Fe/Cu order along c. (d) Noncentrosymmetric $\left(P4mm\right)$ with partial Fe/Cu order. The contour plots are Fourier difference maps of the $(x$, 1/2, $z)$ plane showing the neutron scattering density not reproduced by each of the models.

Figure 2

NPD pattern measured on HRPT at RT. Red crosses: observed data. Black lines: Rietveld fit obtained using the model 4 of Table 1. The vertical ticks indicate the positions of the Bragg reflections for the crystal (upper row) and the commensurate AFM magnetic structure with ${\mathbf{k}}_c=(1/2,1/2,1/2)$ [lower row, see also Fig. 5].

Figure 3

(a) 2D contour plot showing the temperature dependence of the NPD patterns for ${\mathrm{YBaCuFeO}}_5$ measured on DMC. The patterns at 1.5 and 300 K are shown separately. (b) Temperature dependence of the integrated intensity of the (1/2, 1/2, 1/2) magnetic reflection and its incommensurate satellites. (c) Portion of the NPD patterns showing these reflections for our sample (210 and 1.5 K) and a sample prepared according to Ref. [13] (1.5 K). (d) Temperature dependence of the ${\mathrm{Fe}}^{3+}$ magnetic moment. (Inset) Angle $\theta$ between the magnetic moment direction $\left(T_{N1}<T<T_{N2}\right)$ and the spiral plane $\left(T<T_{N2}\right)$ with the c axis.

Figure 4

Red dots: dc magnetic susceptibility of ${\mathrm{YBaCuFeO}}_5$ measured at 1 T by heating after cooling in zero field. Black open squares: incommensurate modulation vector $q$ (in reciprocal lattice ${\mathrm{c}}^{*}$ units). Blue dotted/continuous lines: normalized electric polarization measured by applying an electric field of $\pm 300$ V. In order to use the same axis as $q$, the polarization values have been normalized to their saturation value $(\sim 0.64$ $\mu \text{C}$/${\mathrm{cm}}^2$, see Fig. 9) and further divided by a constant value of $\sim 10.2$.

Figure 5

Magnetic structures of ${\mathrm{YBaCuFeO}}_5$. (a) Colinear magnetic order at 230 K. (b) Two views of the circular spiral order at 1.5 K. For clarity, only one crystal cell within the ab plane is shown. Gold and blue arrows denote ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Cu}}^{2+}$ magnetic moments, respectively.

Figure 6

NPD pattern measured on DMC at 1.5 K. Red crosses: observed data. Black lines: Calculated intensities. The vertical ticks indicate the positions of the Bragg reflections for the crystal (upper row), the CM magnetic structure with ${\mathbf{k}}_c=(1/2,1/2,1/2)$ (intermediate row), and the ICM magnetic structure with ${\mathbf{k}}_c=(1/2,1/2$, 1/$2\mp q)$ (lower row).

Figure 7

Three-dimensional view of the supercell with a = $\surd 2$ $\mathrm{a}{}_c$ and c = 2$\mathrm{c}{}_c$ used in the ab initio calculations (left upper panel) and its projection on the $\mathbf{ab}$ plane (right upper panel) for one of the ${\mathrm{Fe}}^{2+}/{\mathrm{Cu}}^{3+}$ distributions considered. Note that the $\mathbf{a}$ and $\mathbf{b}$ axes are rotated by $\frac{\pi }{4}$ with respect to those in Fig. 1. Panels from (a) to (j) show the projection on the $\mathbf{ac}$ plane of the considered supercells with different orderings of ${\mathrm{Fe}}^{2+}$ ions (golden square pyramids) and ${\mathrm{Cu}}^{3+}$ (blue square pyramids) and their energies relative to that of structure (a). For clarity, ${\mathrm{Ba}}^{2+}$ and ${\mathrm{Y}}^{3+}$ ions are not shown. The blue and red frames surround, respectively, the low-energy and high-energy sets mentioned in Sec. VII A.

Figure 8

Phase diagrams obtained using the spiral ansatz (2) for configurations (a), (b), (d), and (e). Positive/negative signs of the $J$'s correspond to AFM/FM interactions, respectively. The blue region corresponds to the commensurate collinear structure shown in the left panel of Fig. 3. The red region and the yellow region indicate, respectively, an incommensurate spiral state and a commensurate noncollinear state. The green dot indicates the values of the NNN couplings in Table 1. Brown, blue, and back labels indicate Fe-Fe, Cu-Cu, and Fe-Cu couplings, respectively. The results for configuration (c) are not displayed due to the large number of inequivalent NNN couplings.

Figure 9

Temperature dependence of the electric polarization (blue dots) and estimations using the angle $\theta$ between c and the spiral plane and the modulus of the magnetic modulation vector $q$ as described in the text (red diamonds and black open dots).

Figure 10

(Left) Selected regions of the 230 K neutron powder diffraction pattern of ${\mathrm{YBaCuFeO}}_5$ measured at DMC with $\lambda =2.458$ Å. Red crosses indicate experimental data, and continuous lines the fits carried out using the models for the magnetic structure schematized in the right panel. The irreps describing the different magnetic orders in the space groups P4/mmm and P4mm are also indicated.

Figure 11

(Right) Variation of ${\mathrm{Chi}}^2$ as a function of the phase between the magnetic moments at the 1 (blue) and 2 (red) sites. (Left) Fits of the 1.5-K data recorded on DMC with $\lambda =2.458$ Å using some representative values of the phases. Red crosses: experimental data. Black continuous lines: calculated patterns. The three rows of ticks indicate the positions of Bragg reflections of (up to down) the nuclear, the AFM commensurate, and the AFM ICM phases. Particularly unstable fits [“spikes” in (a) marked as (2) and (5)] are obtained for values of the phase giving rise to spirals with uniform pitch ($2\pi /5$ and $7\pi /5)$.