Exchange coupling with the multiferroic compound ${\text{BiFeO}}_3$ in antiferromagnetic multidomain films and single-domain crystals

The exchange coupling observed between a soft ferromagnetic layer and the antiferromagnetic multiferroic compound ${\text{BiFeO}}_3$ (BFO) is investigated. Results obtained on BFO ferroelectric and antiferromagnetic multidomain films and monodomain single crystals are compared. A significant interface coupling occurs in the two systems whose anisotropy however differs significantly. In thin film based heterostructures, the measured twofold anisotropy of the FM layer imposed by the magnetic field during deposition is well accounted for using a double macrospin model describing the role of uncompensated spins, pinned or reversible, in the vicinity of the interface. In contrast, no macroscopic bias is observed in thin films deposited on BFO single crystals where the anisotropy direction is imposed by the underlying antiferromagnetic structure. This highlights the fundamental difference between exchange coupling with a single domain antiferromagnet and with a much more magnetically disordered multidomain state.

Figure 1

(Color online) Orientation and projections of the polarization $P$ and the magnetic moments in single-domain crystals of ${\text{BiFeO}}_3$. (a) Representation in the pseudocubic system of the (111) plane containing the three possible $⟨101⟩$ cycloid propagation vectors assuming a polarization $P$ along [111] in a single crystalline platelet of BFO. The magnetic moments are contained in one of the {121} planes. (b) Sketch of the magnetic moments $M$ (long arrows) forming a cycloid in the $\left(11\overline{2}\right)$ plane; the moments depicted by the dark or light arrows illustrate the AF coupling from one plane to the next. Due to the canting, the induced local moment $m$ (shorter and broader arrows) is zero over a modulation period. (c) On the (010) plane covered by the ferromagnet, from left to right: For $P$ along [111] $\left(P_{\left[111\right]}\right)$ and for $q$ parallel to $\left[\overline{1}10\right]$ $\left(q_{\left[\overline{1}10\right]}\right)$, the projection of the canted moment $m$ is modulated along [100]; it is along the diagonal [101] for $q_{\left[10\overline{1}\right]}$ and along [001] for $q_{\left[01\overline{1}\right]}$. Taking into account all possible orientations of the polarization in the single crystal among the eight $⟨111⟩$ ones, projection of $m$ on the surface plane modulated along the $⟨100⟩$ or $⟨110⟩$ directions, imposed by the propagation vector.

Figure 2

(Color online) Epitaxial BFO films on (001) ${\text{SrTiO}}_3$ (STO) and projections. (a) Representation in the pseudocubic system of the {111} easy magnetization plane of a single AFM domain in a thin films of BFO. The (111) magnetic planes are perpendicular to the spontaneous polarization $P$, depicted here along [111]. No preferential orientation is expected for the magnetization within the (111) plane, as sketched by the circular rotative arrow whereas an antiferromagnetic coupling is imposed from one plane to the next. (b) Collection of ten possible individual AFM domains. In each case, the orientations have arbitrary chosen. The dotted arrows depict the projection of the electric polarization on the (001) plane, always along $⟨110⟩$ directions. The black arrows correspond to the projection of the magnetic moments whose strength is imposed by the orientation of the spin in the {111} planes. The isolated drawing, giving rise to twin elliptical-like structures, rotated by $90°$ one from another, results from the averaging of the entire set of possible coupled projections for $P$ and $M$.

Figure 3

(Color online) (a) Longitudinal ferromagnetic hysteresis cycle (MOKE) of a Permalloy layer deposited on a single-domain BFO crystal: along the easy direction (dots) and along the hard direction (squares). (b) Polar plot of the evolution of $M_R/M_S$ and $H_{switch}$ of a Py or single-domain BFO crystal. For readability, values are added on the circle lines in addition to the usual vertical scale. The angle is defined between the applied field $H$ and the [100] direction of BFO. The deposition field ${\vec{H}}_{dep}$ is represented by the large arrow.

Figure 4

Longitudinal ferromagnetic hysteresis loop (MOKE) of a CoFeB layer deposited on a BFO or STO film along the easy (dots) and hard (squares) directions.

Figure 5

(Color online) (a) Polar plot of the evolution of $H_E$ (squares) and $H_C$ (open circles) in a CoFeB/BFO (001) heterostructures, field grown. The angle is defined between the applied field and the [100] direction of BFO. For readability, values are added on the circle lines in addition to the usual vertical scale. The deposition field ${\vec{H}}_{dep}$ is represented by a large arrow. For comparison, the bias field and the corresponding coercive field when assuming a sine dependence for the unidirectional exchange coupling are shown by black solid lines. The wide gray solid lines are the results of the model described in the text. (b) Magnetization vectors ${\vec{M}}^F,{\vec{M}}^{BFO}$, deposition ${\vec{H}}_{dep}$ and applied $\vec{H}$ fields, angles and anisotropies in the simulations of CoFeB/BFO(001) bilayers.

Figure 6

(Color online) Longitudinal (along the applied field, continuous line) and transverse (perpendicular to the applied field, dotted line) hysteresis loops of $M^F$ and $M^{BFO}$ as measured (dots) and simulated (lines). Loops are obtained at $0°$ (easy axis) at $45°$ (intermediate direction) and at $90°$ (hard axis) from $H_{dep}$.