Magnetic field induced antiferromagnetic cone structure in multiferroic ${\mathrm{BiFeO}}_3$

Neutron diffraction measurements were performed under high magnetic fields up to 17 T in a multiferroic ${\mathrm{BiFeO}}_3$ single crystal, in which an intermediate magnetic (IM) phase has been found between the cycloid and canted antiferromagnetic phases [S. Kawachi et al., Phys. Rev. Mater. 1, 024408 (2017)]. We clearly found that the incommensurate magnetic peaks, which split perpendicular to the magnetic field in the cycloid phase, rotate by 90 deg to align parallel to the field in the IM phase. The magnetic structure in the IM phase can be best described by an antiferromagnetic cone (AF cone) structure. The transition from the cycloid to AF cone is of first order and the direction of the magnetic wave vector and the easy plane of the cycloidal component are rotated by 90 deg without changing the cycloidal modulation period, whereas the transition from the AF cone to canted antiferromagnetic phase is gradual and the cone angle becomes smaller gradually without changing the modulation period. Interestingly, the cycloidal component as well as the cone angle in the IM phase shows a large hysteresis between the field increasing and decreasing processes. This result, combined with the magnetostriction with a large hysteresis previously reported in the IM phase, suggests a strong magnetoelastic coupling.

Figure 1

(a) Cycloid structure at ambient and low magnetic fields, (b) AF cone structure predicted for the intermediate phase theoretically [16], and (c) CAFM structure. The red arrows represent the Fe moments in a triangular plane perpendicular to [1, 1, 1] direction. In the plot the rotation plane includes [1, 1, 1] direction. The blue arrows represent the Fe moments in the adjacent plane along [1, 1, 1]. The modulation pitches shown in (a) and (b) and the canting angle in (c) are exaggerated for clarity. (d) Magnetic field-temperature phase diagram. The circles and triangles represent the transition fields between the cycloid and AF cone structure observed in the field increasing and decreasing processes, respectively. The squares represent the transition fields between the AF cone and CAFM structure. Closed and open symbols correspond to the data obtained with neutron diffraction and magnetization measurements, respectively. The magnetization data are from Ref. [16].

Figure 2

Configurations of neutron diffraction experiments in vertical magnetic field with [1, 1, 1]-[1, $-$1, 0] scattering plane (a) and horizontal magnetic field with [1, 1, 1]-[1, 1, $-2]$ scattering plane (b). The filled circles represent magnetic Bragg peaks around (1/2, 1/2, 1/2). The ellipsoid represents the instrumental resolution function schematically. Slightly canted ferromagnetic component in the AF cone and CAFM phases should cause magnetic signal which overlaps to the nuclear Bragg peaks, although the ferromagnetic Bragg peak is not shown here.

Figure 3

Orientation of the magnetic domains with $H\parallel$ [1, 1, $-2]$ observed using neutron diffraction. (a) The peak profile along (1/$2\pm h$, 1/$2\mp h$, 1/2) as a function of magnetic field measured in the field increasing process. (b) Integrated intensities of commensurate and incommensurate magnetic peaks as a function of magnetic field. D1, D2, and D3 represent three magnetic domains shown in the inset of (d). (c) Magnetic field dependence of incommensurability ($\delta$) of the incommensurate magnetic Bragg peaks at (1/$2\pm \delta$, 1/$2\mp \delta$, 1/2), (1/$2\mp \delta$, 1/2, 1/$2\pm \delta$), and (1/2, 1/$2\pm \delta$, 1/$2\mp \delta$). (d) Angle between the cycloidal plane and the scattering plane ($\theta$) as a function of magnetic field. The inset shows the six magnetic incommensurate peaks (filled circles) and $\theta$.

Figure 4

Contour plots of the magnetic intensities at (1/$2\pm h$, 1/$2\pm h$, 1/$2\mp 2h$) with $H\parallel$[1, 1, $-2]$ during magnetic field increasing (a) and decreasing (b) processes at 250 K. (c) and (d) The results at 290 K. Two broken lines show the field region where incommensurate peaks are observed.

Figure 5

Integrated intensities of the commensurate (CM) and two incommensurate magnetic (ICM) peaks as a function of magnetic field at 250 K (a) and 290 K (b). Filled and open circles represent the intensities measured during the field increasing and decreasing processes, respectively. (c) and (d) Cone angle as a function of magnetic field at 250 and 290 K, respectively. (e) and (f) Incommensurability (${\delta }^{\prime }$) as a function of magnetic field at 250 and 290 K, respectively.