Charge and spin order in $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Fe}{\mathrm{O}}_3$: Idle spins and frustration in the charge-disproportionated state

The perovskite $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Fe}{\mathrm{O}}_3$ undergoes a remarkable sequence of charge-disproportionation (CD) and charge-transfer (CT) transitions on cooling due to competing electronic instabilities: $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}\mathrm{F}{\mathrm{e}}^{3.5+}{\mathrm{O}}_3\to \mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}{\mathrm{Fe}}^{3+}{}_{0.67}{\mathrm{Fe}}^{4.5+}{}_{0.33}{\mathrm{O}}_3\left(\mathrm{CD}\mathrm{phase}\right)\to \mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.25}{\mathrm{Bi}}^{5+}{}_{0.25}\mathrm{F}{\mathrm{e}}^{3+}{\mathrm{O}}_3\left(\mathrm{CT}\mathrm{phase}\right)$. The accompanying changes in charge and spin ordering have been determined from neutron diffraction and physical property measurements. The CT phase adopts a simple $G$-type antiferromagnetic structure of $\mathrm{F}{\mathrm{e}}^{3+}$ spins but the CD phase adopts an unusual charge and magnetic arrangement in which $\mathrm{F}{\mathrm{e}}^{3+}$ spins are antiferromagnetically ordered but the $\mathrm{F}{\mathrm{e}}^{4.5+}$ moments have no long-range order due to magnetic frustration and form a spin glass at low temperatures.

Figure 1

Zero-field and field-cooled magnetization data and resistivity data collected as a function of temperature from $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Fe}{\mathrm{O}}_3$.

Figure 2

Refined structures of the three phases of $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Fe}{\mathrm{O}}_3$ showing the Fe spin orders in the two low-temperature phases.

Figure 3

Observed, calculated, and difference plot for the refinement of $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Fe}{\mathrm{O}}_3$ against neutron powder diffraction data collected at: (a) 300 K. The red tick marks correspond to contributions from the high-temperature phase $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}\mathrm{F}{\mathrm{e}}^{3.5+}{\mathrm{O}}_3$. The unindexed featured marked with the asterisk is a contribution from a trace of $\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3$ ($<0.2\%$ by weight). (b) 240 K. The upper set of tick marks correspond to magnetic reflections and the lower to nuclear reflections of the CD phase $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}{\mathrm{Fe}}^{3+}{}_{0.67}{\mathrm{Fe}}^{4.5+}{}_{0.33}{\mathrm{O}}_3$. The feature marked with the asterisk contains a small contribution from the CT phase $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.25}{\mathrm{Bi}}^{5+}{}_{0.25}\mathrm{F}{\mathrm{e}}^{3+}{\mathrm{O}}_3$ (see Supplemental Material) [16]. (c) 5 K. From top to bottom the tick marks correspond to magnetic and nuclear reflections of the CT phase $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.25}{\mathrm{Bi}}^{5+}{}_{0.25}\mathrm{F}{\mathrm{e}}^{3+}{\mathrm{O}}_3$ and magnetic and nuclear reflections of the CD phase $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}{\mathrm{Fe}}^{3+}{}_{0.67}{\mathrm{Fe}}^{4.5+}{}_{0.33}{\mathrm{O}}_3$.

Figure 4

(a) Field-cooled $M$/$H$ curve collected from $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}{\mathrm{Fe}}^{3+}{}_{0.67}{\mathrm{Fe}}^{4.5+}{}_{0.33}{\mathrm{O}}_3$. (b) Relative orientations of the magnetic moments in the $ac$ plane of $\mathrm{C}{\mathrm{a}}_{0.5}{\mathrm{Bi}}^{3+}{}_{0.5}{\mathrm{Fe}}^{3+}{}_{0.67}{\mathrm{Fe}}^{4.5+}{}_{0.33}{\mathrm{O}}_3$.