Figure 1

Temperature $\left(T\right)$ versus magnetic field $\left(B\right)$ phase diagram of $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ with $B$ applied along the $c$ axis. Open and filled symbols represent the data points in the cooling (or $B$-decreasing) and warming (or $B$-increasing) runs, respectively. Diamond, square, triangle, and inverse triangle data points were obtained by measurements of magnetization, dielectric constant, electric polarization, and magnetostriction, respectively. Upper inset: Crystal structure of $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$. Lower insets: Schematic illustrations of magnetic structures on ${\mathrm{Fe}}^{3+}$ sites at (left) the collinear-commensurate $(1∕4)$ and (right) the collinear-commensurate $(1∕5)$ states. White and black circles correspond to up and down spin states, respectively. Inversion symmetry is broken at the noncollinear-incommensurate phase (gray area).Reuse & Permissions

Figure 2

Temperature profiles of (a) magnetic susceptibility parallel (${\chi }_{\Vert }$, gray line) and perpendicular (${\chi }_{\perp }$, black line) to the $c$ axis, (b) dielectric constant parallel (${\epsilon }_{\Vert }$, gray line) and perpendicular (${\epsilon }_{\perp }$, black line) to the $c$ axis, and (c) magnetostriction parallel (gray line) and perpendicular (black line) to the $c$ axis in $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$.Reuse & Permissions

Figure 3

(Color online) Wave number of modulated magnetic structure (a), magnetization (b), and magnetostriction parallel (c) and perpendicular (d) to the $c$ axis, and electric polarization perpendicular to the $c$ axis (e) of $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ as a function of magnetic field at selected temperatures. Magnetic field was applied along the $c$ axis. The data of Fig. 3a were taken from Ref. 16.Reuse & Permissions