We report a comprehensive specific heat and inelastic neutron scattering study to explore the possible origin of multiferroicity in HoCrO ₃ . We have performed specific heat measurements in the temperature range 100 mK–290 K and inelastic neutron scattering measurements were performed in the temperature range 1.5–200 K. From the specific heat data we determined hyperfine splitting at 22.5(2) μ eV and crystal field transitions at 1.379(5) meV, 10.37(4) meV, 15.49(9) meV and 23.44(9) meV, indicating the existence of strong hyperfine and crystal field interactions in HoCrO ₃ . Further, an effective hyperfine field is determined to be 600(3) T. The quasielastic scattering observed in the inelastic scattering data and a large linear term γ = 6.3 ( 8 ) mJ mol ⁻¹ K ⁻² in the specific heat is attributed to the presence of short range exchange interactions, which is understood to be contributing to the observed ferroelectricity. Further the nuclear and magnetic entropies were computed to be, ∼17.2 Jmol ⁻¹ K ⁻¹ and ∼34 Jmol ⁻¹ K ⁻¹ , respectively. The entropy values are in excellent agreement with the limiting theoretical values. An anomaly is observed in the peak position of the temperature dependent crystal field spectra around 60 K, at the same temperature an anomaly in the pyroelectric current is reported. From this we could elucidate a direct correlation between the crystal electric field excitations of Ho ³⁺ and ferroelectricity in HoCrO ₃ . Our present study, along with recent reports, confirm that HoCrO ₃ , and R CrO ₃ ( R = rare earth) in general, possess more than one driving force for the ferroelectricity and multiferroicity.

We re-investigate the magnetically frustrated, diamond-lattice-antiferromagnet spinels FeAl${}_{2}$O${}_{4}$ and MnAl${}_{2}$O${}_{4}$ using magnetization measurements and diffuse scattering of polarized neutrons. In FeAl${}_{2}$O${}_{4}$, macroscopic measurements evidence a ``cusp'' in zero field-cooled susceptibility around 13 K. Dynamic magnetic susceptibility and memory effect experiments provide results that do not conform with a canonical spin-glass scenario in this material. Through polarized neutron-scattering studies, absence of long-range magnetic order down to 4 K is confirmed in FeAl${}_{2}$O${}_{4}$. By modeling the powder averaged differential magnetic neutron-scattering cross section, we estimate that the spin-spin correlations in this compound extend up to the third nearest-neighbor shell. The estimated value of the Land\'e $g$ factor points towards orbital contributions from Fe${}^{2+}$. This is also supported by a Curie-Weiss analysis of the magnetic susceptibility. MnAl${}_{2}$O${}_{4}$, on the contrary, undergoes a magnetic phase transition into a long-range ordered state below $$\approx${}$40 K, which is confirmed by macroscopic measurements and polarized neutron diffraction. However, the polarized neutron studies reveal the existence of prominent spin fluctuations co-existing with long-range antiferromagnetic order. The magnetic diffuse intensity suggests a similar short-range order as in FeAl${}_{2}$O${}_{4}$. Results of the present work support the importance of spin-spin correlations in understanding magnetic response of frustrated magnets like $A$-site spinels which have predominant short-range spin correlations reminiscent of the ``spin-liquid'' state.

We demonstrate spin-spiral-induced ferroelectricity in epitaxial TbMnO${}_{3}$ films grown on YAlO${}_{3}$ substrates down to a film thickness of 6nm. The ferroelectric polarization is identified by optical second-harmonic generation. Using x-ray resonant magnetic scattering we directly prove the existence of a noncollinear magnetic structure in the ferroelectric phase and thus bulk-like multiferroicity. The electric-field-induced reversal of the magnetic domains along with the reversal of the ferroelectric polarization evidences the rigid coupling of magnetic and ferroelectric order and hence a ``giant'' magnetoelectric effect in the films.

The magnetic excitation spectrum of the magnetocaloric compound ${\mathrm{MnFe}}_4{\mathrm{Si}}_3$ has been investigated by means of polarized and unpolarized inelastic neutron scattering on single crystals. Spectra were collected in the ferromagnetic phase ($T_C\approx 305\mathrm{K}$), as well as in the paramagnetic state, in order to understand the nature of the magnetism in ${\mathrm{MnFe}}_4{\mathrm{Si}}_3$. Spin-wave measurements at 1.5 K reveal a strong anisotropy of the magnetic exchange interactions along the (h00) and (00l) reciprocal directions of the hexagonal system, which also manifests itself in the $q$-dependent linewidths in the paramagnetic state. The correlation lengths indicate a short-range order, while the average linewidth is of the order of $k_B{T}_C$ pointing to a behavior typical of many ferromagnets. In addition, the in- and out-of-plane spin fluctuations are found to be isotropic around $T_C$ and can be suppressed by a magnetic field of 2 T.