Magnetic interactions in the multiferroic phase of CuFe${}_{1-x}$Ga${}_x$O${}_2$ ($x=0.035$) refined by inelastic neutron scattering with uniaxial-pressure control of domain structure

We have performed inelastic neutron scattering measurements in the ferroelectric noncollinear-magnetic phase of CuFe${}_{1-x}$Ga${}_x$O${}_2$ (CFGO) with $x=0.035$ under applied uniaxial pressure. This system has three types of magnetic domains with three different orientations reflecting the trigonal symmetry of the crystal structure. To identify the magnetic excitation spectrum corresponding to a magnetic domain, we have produced a nearly “single-domain” multiferroic phase by applying a uniaxial pressure of 10 MPa onto the $\left[1\overline{1}0\right]$ surfaces of a single-crystal CFGO sample. As a result, we have successfully observed the single-domain spectrum in the multiferroic phase. Using the Hamiltonian employed in the previous inelastic neutron scattering study on the “multi-domain” multiferroic phase of CFGO ($x=0.035$) [Haraldsen et al. Phys. Rev. B 82, 020404(R) (2010)], we have refined the Hamiltonian parameters so as to simultaneously reproduce both of the observed single-domain and multidomaim spectra. Comparing between the Hamiltonian parameters in the multiferroic phase of CFGO and in the collinear four-sublattice magnetic ground state of undoped CuFeO${}_2$ [Nakajima et al., Phys. Rev. B 84, 184401 (2011)], we suggest that the nonmagnetic substitution weakens the spin-lattice coupling, which often favors a collinear magnetic ordering, as a consequence of the partial release of the spin frustration.

Figure 1

(a) Crystal structure of CuFeO${}_2$ with a hexagonal basis. (b) Paths of the exchange interactions. For the nearest-neighbor exchange interactions, $J_1$, see Figs. 4a and 4b. (c)–(e) The three types of magnetic domains with the monoclinic bases (${\mathit{a}}_{\mathrm{m}},{\mathit{b}}_{\mathrm{m}}$) and the hexagonal bases ($\mathit{a},\mathit{b}$). Dashed arrows denote $c^{*}$-plane projections of the magnetic modulation wave vectors in each domain.

Figure 2

(a) Calculated and (b) observed intensity map of the magnetic excitation spectra along the $(H,H,\frac{3}{2})$ line in the multi-domain multiferroic phase. (c) Reciprocal-lattice map of the $(H,H,L)$ scattering plane. The dashed arrow denotes the direction of the the $(H,H,\frac{3}{2})$ line.

Figure 3

(a) Calculated and (b) observed intensity map of the magnetic excitation spectra along the $(H,H,\frac{3}{2})$ line in the single-domain multiferroic phase. (c),(d) Profiles of the constant-$E$ scans below 0.5 meV around (c) $H=0.2$ and (d) 0.3.

Figure 4

The relationship among the magnetic structure, the displacements of the oxygen ions and the nearest-neighbor exchange interactions of $J_1^{\left(1\right)}$, $J_1^{\left(2\right)}$, and $J_1^{\left(3\right)}$ in (a) the 4SL phase and (b) the multiferroic phase with the monoclinic bases. (c) Calculated spin arrangements in the multiferroic phase.