Competing Exchange Interactions and Multiferroic Behavior of a Molecule-Based Magnet

Multiferroic behavior sensitively depends on the microscopic interactions between spins. The molecule-based magnet (NH₄)₂FeCl₅ (H₂O) exhibits a complex magnetic-field or pressure versus temperature phase diagram with three multiferroic phases observed by magnetization, neutron diffraction, and Raman spectroscopy measurements. Both low-field phases contain spin cycloids with electric polarization P along the a axis produced by the inverse Dzyalloshinskii-Moriya interaction. Above the spin-reorientation transition at roughly 4 T, the spins form a canted antiferromagnetic state and P rotates to the c axis. The electric polarization at high fields is believed to be caused by p-d orbital hybridization. We evaluate the magnetic interactions in the low-field multiferroic phase by comparing inelastic neutron scattering spectra of a single crystal with a simple Heisenberg model containing five exchange interactions mediated by intermolecular hydrogen and halogen bonds. Two competing exchange interactions in every bc plane produce a cycloid with spins in the ac plane, helicity S_i x S_j along the b axis, and ordering wavevector Q = (0, 0, 0.23) r.l.u. along the c axis. Using this wavevector as a constraint, we obtain excellent agreement between the observed and predicted inelastic spectra at zero field. With some small but clear differences, the zero-field exchange and anisotropy parameters also provide excellent agreement with the inelastic neutron-scattering spectra of the high-field phase. The resulting exchange and anisotropy parameters are compared with the predictions of first-principle calculations.