Spin wave excitations in the pyrovanadate $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$

The pyrovanadate $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ belongs to the orthorhombic ($Fdd2$) class of crystals with noncentrosymmetric crystal structure. Recently, the compound has been identified to be a magnetic multiferroic with a substantial electric polarization below the magnetic transition temperature $T_C$ = 35 K. Here we report the results of our inelastic neutron-scattering (INS) studies on a polycrystalline sample of $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$. Our INS data clearly show the existence of dispersive spin wave excitations below $T_C$ with a zone-boundary energy of 11 meV at 5 K. We have analyzed the data using linear spin wave theory, which shows good agreement between the experiment and calculation. The analysis is consistent with the third-nearest-neighbor exchange interaction playing a dominant role in the magnetism of the material.

Figure 1

(a) Various spin exchange interactions in $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ in a conventional unit cell according to model I. (b) The helical honeycomb network (model II) of spin exchange comprising $J_1$ and $J_2$ only.

Figure 2

(a) 2D map of the scattering intensity of $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ as a function of energy transfer ($\hslash \omega$) and momentum transfer ($|\vec{Q}|$) obtained at 5 K. The color scale shows the scattering intensity $S\left(\right|\vec{Q}|, \omega$) in absolute units, mb/sr/meV/f.u. (b) The scattering intensity as a function of momentum transfer with phonon-scattering corrections applied to the data with the intensity being summed over the energy range 8–12 meV at 5 K. The inset in (b) shows the same data without phonon correction.

Figure 3

Scattering intensity (without phonon correction) as a function of energy transfer for the window of momentum transfer 0–3 Å${}^{-1}$ recorded at different temperatures.

Figure 4

(a, b) The 2D color plots of the neutron-scattering intensity as obtained from phonon-corrected measured experimental data (at 5 K) and simulated by the spinw package, respectively. (c, d) The experimental and simulated scattering intensity as a function of energy transfer for the $|\vec{Q}|$ range 0–3 Å${}^{-1}$ and as a function of momentum transfer summed over 3–6 meV, respectively.

Figure 5

Simulated 2D color plot for neutron-scattering intensity [(a) and (b)] as well as its energy variation [(c) and (d)] considering the Heisenberg interaction terms $J_1$ and $J_2$ only (model II). For (a) and (c) we have considered $J_1>J_2$, while for (b) and (d) it is $J_1<J_2$, using the values quoted in Table 1.