Spin-lattice coupling mediated multiferroicity in ${\left({\mathrm{ND}}_4\right)}_2{\mathrm{FeCl}}_5·{\mathrm{D}}_2\mathrm{O}$

We report a neutron diffraction study of the multiferroic mechanism in ${\left({\mathrm{ND}}_4\right)}_2{\mathrm{FeCl}}_5·{\mathrm{D}}_2\mathrm{O}$, a molecular compound that exhibits magnetically induced ferroelectricity. This material exhibits two successive magnetic transitions on cooling: a long-range order transition to an incommensurate (IC) collinear sinusoidal spin state at $T_N=7.3$ K, followed by a second transition to an IC cycloidal spin state at $T_{FE}=6.8$ K, the latter of which is accompanied by spontaneous ferroelectric polarization. The cycloid structure is strongly distorted by spin-lattice coupling, as evidenced by the observations of both odd and even higher-order harmonics associated with the cycloid wave vector, and a weak commensurate phase that coexists with the IC phase. The second-order harmonic appears at $T_{FE}$, thereby providing unambiguous evidence that the onset of the electric polarization is accompanied by a lattice modulation due to spin-lattice interaction. The neutron results, in conjunction with the negative thermal expansion and large magnetostriction observed in Ref. [19], indicate that spin-lattice coupling plays a critical role in the ferroelectric mechanism of ${\left({\mathrm{ND}}_4\right)}_2{\mathrm{FeCl}}_5·{\mathrm{D}}_2\mathrm{O}$.

Figure 1

(a) Crystal structure of ($\mathrm{N}{\mathrm{H}}_4$)${}_2{\mathrm{FeCl}}_5·{\mathrm{H}}_2\mathrm{O}$. (b) IC collinear sinusoidal spin structure at 7 K in the paraelectric phase. (c) IC cycloidal-spiral spin structure at 4 K in the ferroelectric phase, as viewed along the $b$ axis (three unit cells along $c$-axis are plotted). Only magnetic Fe ions are shown in (b) and (c) for the purpose of clarity.

Figure 2

$L$ scans along both (0 0 $L$) and (2 0 $L$) with the intensity plotted on a logarithmic scale. (a) (0 0 $L$) scan measured at 1.5 K and 10 K. The primary IC satellites (0 0 $n\pm k_{z1}$) and the second- (0 0 $n\pm 2k_{z1}$), third- (0 0 $n\pm 3k_{z1}$), and fifth-order (0 0 $\mathrm{n}\pm 5k_{z1}$) harmonic peaks are marked by *(black), **(pink), $†$(green), and $‡$(blue), respectively ($n$ is an integer). (b) (2 0 $L$) scan measured at 1.5 K reveals the coexistence of IC and commensurate phases. The primary IC satellites (2 0 $n\pm k_{z1}$), third- (2 0 $n\pm 3k_{z1}$), and fifth-order (2 0 $n\pm 5k_{z1}$) harmonic peaks and the commensurate peak (2 0 $n\pm k_{z2}$) are marked by *(black), $†$(green), $‡$(blue), and $♯$ (cyan), respectively. Neutron data have been normalized to beam monitor count, and the error bars are statistical in nature and represent one standard deviation.

Figure 3

Temperature dependence of (a) the specific heat, (b) integrated intensity of the (0 0 0.77) magnetic peak, and (c) integrated intensity of the (0 0 2.46) second-order harmonic peak. The inset in (c) shows $L$ scans of (0 0 2.46) at selected temperatures. The solid lines in (b) and (c) are fits of the order-parameter data to the power law as described in the text. (d) Temperature dependence of IC propagation vector $k_{z1}$ determined from (0 0 1-$k_{z1}$), and (0 0 2+$2k_{z1}$). The error bar in (d) represents statistical error from the fitting, not the systematic error.

Figure 4

Polarized neutron data measured in the horizontal field configuration, $P_0\parallel Q$. (a) $L$-scan along [0 1 $L]$ measured at 1.5 K comparing the spin-flip (SF, $-+$) and non-spin-flip (NSF, ++) scatterings with the intensity plotted on a logarithmic scale. (b) Comparison of the 1.5 K SF and NSF data suggests the hybrid nature of the (0 0 2.46) second-order harmonic peak. Comparison of 1.5 K and 10 K data of (0 0 2.46) from (c) the SF channel and (d) NSF channel, respectively.