Spin-driven bond order in a $\frac{1}{5}$-magnetization plateau phase in the triangular lattice antiferromagnet CuFeO${}_2$

We have investigated spin-wave excitations in a magnetic-field-induced 1/5-magnetization plateau phase in the triangular lattice antiferromagnet CuFeO${}_2$ (CFO), by means of inelastic neutron-scattering measurements under applied magnetic fields of up to 13.4 T. Comparing the observed spectra with the calculations in which spin-lattice coupling effects for the nearest-neighbor exchange interactions are taken into account, we have determined the Hamiltonian parameters in the field-induced 1/5-plateau phase, which directly show that CFO exhibits a bond order associated with the magnetic structure in this phase.

Figure 1

(a) The $H$-$T$ magnetic phase diagram of CFO (redrawn from Ref. 17). Open and filled symbols denote the transition temperatures (or fields) observed with increasing and decreasing temperature (or field), respectively. (b) A schematic of the experimental setup for the present measurements (top view). The $Q$-$E$ space measured with $E_i=8.6$ meV is shown by a pink shaded area. The observed INS spectra are shown (c) in zero field, (e) under an applied field of 10 T, and (f) under an applied field of 13.4 T. The calculated INS spectra are shown for (d) the 4SL phase $(H=0$ T) and (g) the 5SL phase ($H=13.4$ T). The gray solid lines show the calculated spin-wave dispersion relation on the $(-h,1-h,1/2)$ line. (h)–(j) Schematics showing the oxygen displacements and the splitting of the NN exchange interactions with the magnetic structures in the (h) 4SL, (i) FE-ICM, and (j) 5SL phases. $a_{\mathrm{m}}$ and $b_{\mathrm{m}}$ denote the monoclinic basis.

Figure 2

The (a) observed and (b) calculated spin-wave excitation spectra along the $(h,h,0)$ line in the 5SL phase. The calculated spin-wave dispersion relations are shown by solid gray lines. (c) The magnetic structure in the 5SL phase and the definitions of $J_2$, $J_3$, and $J_z$. Because of the minus sign between the spin angular momentum and the magnetic moment, the direction of the magnetic field is taken to be the $-z$ direction. The gray dashed lines show the magnetic unit cell for the 5SL phase.