Impurity-doping-induced ferroelectricity in the frustrated antiferromagnet $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$

Dielectric responses have been investigated on the triangular-lattice antiferromagnet $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ and its site-diluted analogs $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ ($x=0.01$ and 0.02) with and without the application of the magnetic field. We have found a ferroelectric behavior at zero magnetic field for $x=0.02$. At any doping level, the onset field of the ferroelectricity always coincides with that of the noncollinear magnetic structure while the transition field dramatically decreases to zero field with Al doping. The results imply the further possibility of producing the ferroelectricity by modifying frustrated spin structure in terms of site doping and external magnetic field.

Figure 1

(Color online) Temperature profiles of (a) ac susceptibility measured with magnetic fields parallel and perpendicular to the $c$ axis (magnified data are also plotted separately), (b) in-plane dielectric constant, and (c) electric polarization perpendicular to the $c$ axis for $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ $(x=0.02)$. The arrows in (a) and (b) indicate the thermal scan direction of the measurement. Two opposite poling electric fields are used for the polarization measurement ($E>0$ and $E<0$). (d) Schematic crystal structure of delafossite $\mathrm{Cu}\mathrm{Fe}\left(\mathrm{Al}\right){\mathrm{O}}_2$.

Figure 2

(Color online) Magnetic field dependence of magnetization at various temperatures for $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ with (a) $x=0.00$, (b) $x=0.01$, and (c) $x=0.02$. Arrows indicate the field-scan direction of the measurement. In the measurement for $x=0.01$, the sample was warmed up to $20\mathrm{K}$ and cooled down without magnetic field, prior to each field-increasing run.

Figure 3

(Color) Temperature dependence of electric polarization perpendicular to the $c$ axis at various magnetic fields for $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$, (a) $x=0.00$, (b) $x=0.01$, (c) $x=0.02$. The arrows in (a) and (b) indicate the thermal scan direction of the measurement. After a proper poling procedure, each measurement was made in a warming run unless indicated by the arrows (see the text). (d) Magnetic-field dependence of polarization at $5\mathrm{K}$ obtained from the above scans.

Figure 4

Temperature $\left(T\right)$ versus the magnetic-field $\left(H\right)$ phase diagram of $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ for (a) $x=0.00$, (b) $x=0.01$, and (c) $x=0.02$ $(H\Vert c)$. Circle, triangle, square, and diamond data points were obtained by measurements of electric polarization, dielectric constant, magnetization ($T$ dependence), and magnetization ($H$ dependence), respectively. Open and filled symbols represent the anomalies in the increasing and decreasing $T$ or $H$ runs, respectively. Spontaneous electric polarization, i.e., the ferroelectricity (FE) was observed in the noncollinear spin order (NC) state (the shadowed area). In the hatched area, the magnetic structure depends on the hysteresis. The CM-4 phase remains in a field-increasing or temperature-increasing run, otherwise the NC phase shows up in this area.