Figure 1

Appearance of ferroelectricity in ${\mathrm{CuFeO}}_2$. (a) Atomic configuration and magnetic structure of ${\mathrm{CuFeO}}_2$. Below temperature $T<T_{N1}$, the crystal structure is the monoclinic space group $C2/m$. The unit cell is drawn with a setting of unique axis $b$ and cell choice 1. Black lines show the unit cell. The left-handed proper screw magnetic structure in ferroelectric phase is illustrated by green arrows at iron ions. When the magnetic chirality is left handed, the electric polarization vector points in the positive direction along the $b$ axis. (b) Magnetic phase diagram of ${\mathrm{CuFe}}_{1-y}{\mathrm{Ga}}_y{\mathrm{O}}_2$ drawn as functions of temperature and the content of Ga ions. Data are taken from Ref. 15. The sample used for the soft x-ray diffraction has 2.2% Ga, indicated by a dash line.Reuse & Permissions

Figure 2

Energy spectra near the Fe $L_{2,3}$ absorption edges. Data on panels (c) to (f) were measured at temperature $T=4.2\mathrm{K}$. Gray lines are guides to eyes. Error bars are smaller than the size of circles. (a) XAS near the Fe $L_3$ and $L_2$ absorption edges obtained in the total electron yield mode. (b) The integrated intensity of superlattice reflection 0 $1-2q$ 0 (circles) for the $E=708.6\mathrm{eV}$ incident beam as a function of temperature. This was measured in two ways, first increasing temperatures from 4 up to 20 K and then decreasing temperatures ($T_{N2}=8.0\mathrm{K}$). Squares show the data adapted from Ref. 12 for ${\mathrm{CuFe}}_{1-y}{\mathrm{Ga}}_y{\mathrm{O}}_2$, $y=0.037$: the integrated intensity for magnetic reflection 0 $q$ $\frac{1}{2}$ observed by neutron scattering ($T_{N2}^{\prime }=7.3\mathrm{K}$). (c)–(f) Integrated intensities of superlattice reflection 0 $1-2q$ 0 for unrotated channels (c) ${\sigma }^{\prime }\sigma$ and (d) ${\pi }^{\prime }\pi$ and for rotated channels (e) ${\pi }^{\prime }\sigma$ and (f) ${\sigma }^{\prime }\pi$ are shown. (g) XAS and intensity of magnetic reflection 0 $1-2q$ 0 calculated using a cluster model. The scale of intensity is normalized so that both maxima are the same. The parameter values used are (in eV): $U_{dd}=7.0$, $U_{dc}(2p)=9.5$, $V(e_g)=2.5$, $10Dq=1.5$, $\Delta =3.0$ (charge transfer energy). The reduction factors of $V$ are $R_c=0.8$, $R_v=0.9$.Reuse & Permissions