Magnetic-field-induced change of magnetoelectric coupling in the hybrid multiferroic ${\left(\mathrm{N}{\mathrm{D}}_4\right)}_2[\mathrm{FeC}{\mathrm{l}}_5·{\mathrm{D}}_2\mathrm{O}]$

In this paper, we elucidate the changes of magnetoelectric coupling mechanism in different zones of the rich magnetic field-temperature $\left(B\text{−}T\right)$ phase diagram of the molecular multiferroic ${\left(\mathrm{N}{\mathrm{H}}_4\right)}_2\left[\mathrm{FeC}{\mathrm{l}}_5·{\mathrm{H}}_2\mathrm{O}\right]$, which represents one of the rare cases where improper ferroelectricity has been observed in a hybrid material. We have recently proposed a mechanism of multiferroicity in zero magnetic field in the deuterated form of this material from a detailed determination of its crystal and magnetic structures. The proposed magnetic structure at zero magnetic field corresponds to a cycloidal spin arrangement that gives rise to a ferroelectric polarization through the spin current mechanism induced via the inverse Dzyaloshinskii-Moriya interaction. In this paper, we present a single-crystal neutron diffraction study under external magnetic field, aimed at elucidating the evolution of the magnetic structure under applied magnetic field, and determine the mechanism of magnetoelectric coupling, which allows us to describe an unprecedented change from spin current to spin-dependent $p\text{−}d$ hybridization mechanism.

Figure 1

(a) $Q$ scans along the [0, 3, ξ] direction as a function of an increasing magnetic field applied along the crystallographic $a$ axis recorded at 2 K. (b) Integrated intensities of the $(0,3,-0.23)$, (0, 3, 0.23), and (0, 3, 0) reflections (in blue, red, and green, respectively; open and filled symbols represent increasing and decreasing magnetic field, respectively; roman numerals indicate phases).

Figure 2

Magnetic structures at 2 K and at different magnetic fields applied along the crystallographic $a$ axis: at zero field (left), at 3.5 (middle), and at 6 T (right).

Figure 3

Dependence of the component of electric polarization along the crystallographic $c$ axis for a magnetic field applied along the $a$ axis. The symbols correspond to the measurements reported by Ackermann et al. (data taken from Ref. [24]), while the continuous line represents a calculation of the polarization predicted by the $p\text{−}d$ hybridization model, assuming a linear dependence with B of the component of the magnetic moment along the $a$ axis, together with a constant value for the component in the $bc$ plane.