Pressure-induced polar phases in multiferroic delafossite $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$

The pressure effect on the frustrated magnetic system $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ exhibiting multiferroic behavior has been studied by means of time-of-flight single crystal neutron diffraction combined with a hybrid-anvil-type pressure cell. The nonpolar collinear magnetic ground state (CM1 phase) with propagation vector $\mathit{k}=(0,\frac{1}{2},\frac{1}{2})$ turns into a proper screw magnetic ordering with incommensurate modulation $\mathit{k}=(0,q,\frac{1}{2};q\simeq 0.4)$ and a polar ${21}^{\prime }$ magnetic point group (ICM2 phase), between 3 and 4 GPa. This spin structure is similar to the ferroelectric phase induced by magnetic field or chemical doping under ambient pressure. Above, 4 GPa, a magnetic phase (ICM3) appears, with an incommensurate propagation vector that is unique for the $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ system, $\mathit{k}=(q_a,q_b,q_c;q_a\simeq 0,q_b\simeq 0.34,q_c\simeq 0.43)$. This propagation vector at the general point results in triclinic magnetic symmetry which implies an admixture of both cycloidal and proper screw spin configurations. The ICM3 phase is stable in a narrow pressure range, and above 6 GPa, the spin-density collinear structure (ICM1 phase), similar to the first ordered state at ambient pressure, takes place. Comparing the degree of lattice distortions among the magnetic phases observed at ambient pressure, we discuss the origin of the pressure-induced magnetic phase transitions in $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$.

Figure 1

Temperature vs pressure magnetic phase diagram of CuFeO${}_2$. The data at 7.9 GPa were taken from a previous paper [45]. Solid and dotted lines denote first- and second-order phase transitions, respectively.

Figure 2

(a) Pressure dependence of the diffraction profile along the reciprocal lattice line of $(0,K,\frac{1}{2})$ at 1.5 K in CuFeO${}_2$. (b) At $P=4.3$ and 5.0 GPa, the magnetic peaks appear at the $(0,0.34,0.43)$ and $(0,0.34,0.57)$ positions. Neutron intensity maps on the $(0,K,L)$ plane at 1.5 K and (c) 4.3 GPa, (d) 3.4 GPa, and (e) 2.0 GPa. The arrows in (c)–(e) indicate the observed peak positions.

Figure 3

Temperature dependence of the magnetic diffraction profiles at (a) 2.0, (b) 3.2, and (c) 4.3 GPa. (d) Neutron diffraction profiles along the $(0,K,\frac{1}{2})$ reciprocal lattice line at 3.4 GPa. (e) Temperature variation of the incommensurate $b$ component of the $(0,q,\frac{1}{2})$ propagation vector under pressure.

Figure 4

(a) Results of the magnetic structure refinements. Circles, squares, and triangles denote the structure factors calculated for the proper screw, $bc$-cycloid, and $ab$-cycloid models, respectively. The experimental data measured at 1.5 K and 3.4 GPa were corrected for absorption and the Lorentz factor. The best reliability factor, $R_F=3.45\%$, was obtained for the model with a proper screw spin configuration in the ICM2 phase. ($R_F=6.4\%$ for the $bc$-cycloid and $10.5\%$ for the $ab$-cycloid model.) (b) Illustration of the proper screw magnetic structure. The image shown was depicted using the software vesta [49].