Magnetic structure and spin-wave excitations in the multiferroic magnetic metal-organic framework ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$

We report the magnetic diffraction pattern and spin-wave excitations in ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$ measured using elastic and inelastic neutron scattering. The magnetic structure is shown to be a $G$-type antiferromagnet with moments pointing along the $b$ axis. By comparison with simulations based on linear spin-wave theory, we have developed a model for the magnetic interactions in this multiferroic metal-organic framework material. The interactions form a three-dimensional network with antiferromagnetic nearest-neighbor interactions along three directions of $J_1=-0.103\left(8\right)$ meV, $J_2=-0.032\left(8\right)$ meV, and $J_3=-0.035\left(8\right)$ meV.

Figure 1

Simplified low temperature $Cc$ crystallographic structure of ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$ showing the Mn ions linked together via formate ion bridges, colored red, yellow, and cyan for the three nearest-neighbor magnetic interactions. The network is composed of quasicubes with a $G$-type antiferromagnetic ordering of the Mn moments. (Dimethylammonium ions, which sit within these quasicubes, have been omitted for clarity.)

Figure 2

Powder diffraction data for ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$ from Bank 2 ($13-{21}^{\circ }$) on GEM. The main figure shows a refinement of the nuclear and magnetic intensity, with tick marks showing the positions of the nuclear and magnetic peaks; the inset shows a refinement of the magnetic model alone to the difference between data above and below the Néel temperature.

Figure 3

Inelastic neutron scattering measured from ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$ on LET, with an incident energy of $E_i=2.76$ meV. (a) A cut along the elastic line for $-0.25<E<0.25$ meV as a function of temperature, shows the appearance of the magnetic Bragg peaks (001), (110), and ($20\overline{1}$) below $T_{\mathrm{N}}$. The black tick marks are located according to the crystallographic cell at $T=7$ K. (b)–(d) Color-coded inelastic neutron scattering intensity maps, energy transfer against momentum transfer $Q$, in arbitrary units, measured at $T=5$, 8, and 20 K. All three maps are on the same color scale shown by the color bar. (e) A cut through the magnetic scattering for $0.3<\left|Q\right|<0.7$ Å${}^{-1}$ as a function of temperature using the same color key as in (a).

Figure 4

(a) ${\chi }^2$ map for an energy cut at $1.2<\left|Q\right|<1.4$ Å${}^{-1}$ through the inelastic neutron scattering data from ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{NH}}_2{\left[{\mathrm{Mn}(\mathrm{HCO}}_2\right)}_3]$ shown in (b) compared to SpinW simulations as a function of ${log}_{10}(J_1/J_2)$ vs $J_3$. (c)–(f) SpinW simulations for different $J_1$, $J_2$, and $J_3$ values corresponding to positions (i), (ii), (iii), and (iv) shown in the map in (a).

Figure 5

(a) Compares an energy cut through the inelastic neutron scattering data from ${(\mathrm{CD}}_3{)}_2{\mathrm{ND}}_2{\left[{\mathrm{Mn}(\mathrm{DCO}}_2\right)}_3]$ at $1.2<\left|Q\right|<1.4$ Å${}^{-1}$ with the same cuts through the simulations in Figs. 4–4; while (b) compares the different simulated results (dashed lines) to cuts along $\left|Q\right|$ for $0.78<E_T<0.88$ meV (red), $0.6<E_T<0.7$ meV (yellow), $0.35<E_T<0.45$ meV (green), and $0.15<E_T<0.25$ meV (blue). These cuts have been offset vertically for clarity. The horizontal bar in (a) represents the instrumental energy resolution.