Spin-cycloid instability as the origin of weak ferromagnetism in the disordered perovskite ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_3$

Powder neutron diffraction and magnetometry studies have been conducted to investigate the crystallographic and magnetic structure of ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_3$. The compound stabilizes in the $Imma$ orthorhombic crystal symmetry in the measured temperature range of 5 to 380 K, with a transition to antiferromagnetic order at $T_{\mathrm{N}}\approx 240$ K. The spin cycloid present for BiFeO${}_3$ is found to be absent with 50% Mn${}^{3+}$ cation substitution, leading to $G$-type antiferromagnetic order with an enhanced out-of-plane canted ferromagnetic component, evident from measurable weak-ferromagnetic hysteresis. Structural modifications do not solely explain this behavior, indicating that modified electron exchange interactions must be taken into account. A classical spin simulation was developed to investigate the effect of random substitution in a disordered pseudocubic perovskite. The calculations took into account the nearest-neighbor, next-nearest-neighbor, and Dzyaloshinskii-Moriya interactions, along with the local spin anisotropy. Using this framework to extend the established Hamiltonian model for BiFeO${}_3$, we show that only certain types of perturbations at a magnetic defect and the surrounding molecular fields trigger a simultaneous collapse of cycloidal order and the emergence of the long-range weak-ferromagnetic component. By adopting values for the Mn molecular fields appropriate for $\mathit{RE}$MnO${}_3$ ($\mathit{RE}=$ rare earth), simulations of BiMn${}_{0.5}$Fe${}_{0.5}{\mathrm{O}}_3$ exhibit the key magnetic properties of our experimental observations.

Figure 1

Refinement results of (a) high-resolution neutron and (b) laboratory x-ray diffraction performed at $T=300$ K. The system has been refined to the $Imma$ crystal symmetry. Expected peak positions are indicated by vertical black markers. A small Bi${}_2$${\mathrm{O}}_3$ impurity peak is marked with a star. The peak marked by a # is attributed to $\sim$1% second-order neutron contamination. The red markers in (a) represent reflections corresponding to an additional in-phase BO${}_6$ rotation present in the related $Pnma$ space group, none of which are apparent in the diffraction signal.

Figure 2

(a) Magnetic hysteresis measurements reveal a measurable weak ferromagnetic moment. (b) Field-cooled and zero-field-cooled temperature-dependency measurements show the transition to magnetic order occurs below $T_{\mathrm{N}}=240\mathrm{K}$. (c) The magnetic susceptibility indicates primarily antiferromagnetic order, with a negative intercept determined by fitting the Curie-Weiss law in the paramagnetic region.

Figure 3

Rietveld refinement of neutron diffraction data collected at 5 K. Inset: A closer examination of the (101) half-order magnetic reflection reveals no satellite peaks, indicating a collapse of the cycloid spin structure. The expected positions of additional peaks due to a BiFeO${}_3$-type spin cycloid are shown as blue dashed lines. A small Bi${}_2$${\mathrm{O}}_3$ impurity peak is marked with a star.

Figure 4

Rietveld refinement results of the neutron diffraction temperature-dependency study performed from 5 to 350 K. (a) The magnetic moment of the Fe/Mn follows a general trend from $T_{\mathrm{N}}\approx 240$ K to a maximum of 2${\mu }_{\mathrm{B}}/$ion at low temperatures. (b) Orthorhombic lattice parameters indicate no deviation from the behavior of a normal anharmonic solid. The $b$-direction pseudocubic equivalent $b*=b/\sqrt{2}$ is plotted for legibility of all three crystal axes.

Figure 5

(a) An illustration of the relevant pseudocubic directions rotated into the frame of reference, and a determination of one of the planes in which the spins rotate, formed by the electric polarization ($P$) and cycloid propagation vector (${\tau }_2$). The crystal and magnetic structures of (b) BiFeO${}_3$ ($R3c$) and (c) ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_3$ ($Imma$) are visualized in a pseudocubic plane (O atoms are not shown). The red axes show the pseudocubic directions, whereas the colored axes represent the respective rhombohedral and orthorhombic cells. While both systems are well described by a pseudocubic cell, the cycloidal rotation of the spin moments present in BiFeO${}_3$ was not detected in ${\mathrm{Bi}}_{0.8}{\mathrm{La}}_{0.2}{\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_3$, where the results are consistent with a uniform canted structure along a high-symmetry direction.

Figure 6

Results for the undoped case. (a) Hysteresis along the cycloid propagation ($1\overline{1}0$). (b) Line profiles of spin orientation, revealing cycloidal propagation in the (111) direction. (c) Simulated lattice grid showing a cycloidal structure on top of antiferromagnetic order. (d) Simulated reciprocal-space map of the AFM ($\frac{1}{2}$ $\frac{1}{2}$ $\frac{1}{2}$) reflection.

Figure 7

Reciprocal-space maps of the antiferromagnetic ($\frac{1}{2}$ $\frac{1}{2}$ $\frac{1}{2}$) reflection, illustrating the effect of varying [(a), (c), (e)] $\delta$-type and [(b), (d), (f)] $\epsilon$-type perturbations upon the spin structure. Whereas the $\delta$ type features a cycloid threshold minimum of 0.5, the $\epsilon$ type features an intermediary region around 1.0.

Figure 8

Effect of increasing the anisotropy pertubation upon the simulated magnetic hysteresis at 50% Mn substitution.

Figure 9

(a) Temperature dependency of AFM $G$-type staggered magnetization with increasing $\delta$-type perturbation strength. (b) A mean-field treatment matches well with our results for low to moderate perturbations, but for stronger perturbations it fails to provide realistic results.

Figure 10

(a) Simulated hysteresis and (b) magnetic transition for relative experimental energies for simulation 2 which, in absence of Mn doping, give a cycloid length of 18 unit cells. (c) Simulation 1 hysteresis and (d) magnetic transition for absolute energy ratios. The simulation units have been rescaled assuming $|\overrightarrow{S_{\text{Fe}}}|=2.5$ and $|J_{\text{Fe-Fe}}|=4.38\mathrm{meV}=50\mathrm{K}=76\mathrm{T}/\mathrm{gS}$.