The magnetic properties of RMn2O5 multiferrroics as obtained by unpolarized and polarized neutron diffraction experiments are reviewed. We discuss the qualitative features of the magnetic phase diagram both in zero magnetic field and in field and analyze the commensurate magnetic structure and its coupling to an applied electric field. The origin of ferrolectricity is discussed based on calculations of the ferroelectric polarization predicted by different microscopic coupling mechanisms (exchange striction and cycloidal spin-orbit models). A minimal model containing a small set of parameters is also presented in order to understand the propagation of the magnetic structure along the c-direction.
The scope of magnetic neutron scattering has been expanded by the observation of electronic Dirac dipoles (anapoles) that are polar (parity-odd) and magnetic (time-odd). A zero-magnetization ferromagnet Sm0.976Gd0.024Al2 with a diamond-type structure presents Dirac multipoles at basis-forbidden reflections that include the standard (2, 2, 2) reflection. Magnetic amplitudes measured at four such reflections are in full accord with a structure factor calculated from the appropriate magnetic space group.
The key physical property of multiferroic materials is the existence of a coupling between magnetism and polarization, i.e. magnetoelectricity. The origin and manifestations of magnetoelectricity can be very different in the available plethora of multiferroic systems, with multiple possible mechanisms hidden behind the phenomena. In this Review, we describe the fundamental physics that causes magnetoelectricity from a theoretical viewpoint. The present review will focus on the main stream physical mechanisms in both single phase multiferroics and magnetoelectric heterostructures. The most recent tendencies addressing possible new magnetoelectric mechanisms will also be briefly outlined.
This paper presents results of a recent study of multiferroic CCO by means of single crystal neutron diffraction. This system has two close magnetic phase transitions at $T sub{N1}=24.2$ K and $T sub{N2}=23.6$ K. The low temperature magnetic structure below $T sub{N2}$ is unambiguously determined to be a fully 3-dimensional proper screw. Between $T sub{N1}$ and $T sub{N2}$ antiferromagnetic order is found that is essentially 2-dimensional. In this narrow temperature range, magnetic near neighbor correlations are still long range in the ($H,K$) plane, whereas nearest neighbors along the $L$-direction are uncorrelated. Thus, the multiferroic state is realized only in the low-temperature 3-dimensional state and not in the 2-dimensional state.
Various phenomena related to inhomogeneous magnetoelectric interaction are considered. The interrelation between spatial modulation of order parameter and electric polarization, known as flexoelectric effect in liquid crystals, in the case of magnetic media appears in a form of electric polarization induced by spin modulation and vice versa. This flexomagnetoelectric interaction is also related to the influence of ferroelectric domain structure on antiferromagnetic vector distribution, and to the magnetoelectric properties of micromagnetic structures. The influence of inhomogeneous magnetoelectric interaction on dynamic properties of multiferroics, particularly magnon spectra is also considered.
We have investigated the temperature evolution of the magnetic structures of HoFeO$_3$ by single crystal neutron diffraction. The three different magnetic structures found as a function of temperature for hfo are described by the magnetic groups Pb$$n$2_1$, Pbn$2_1$ and Pbn$2_1$ and are stable in the temperature ranges $approx$ 600-55~K, 55-37~K and 35$>T>2$~K respectively. In all three the fundamental coupling between the Fe sub-lattices remains the same and only their orientation and the degree of canting away from the ideal axial direction varies. The magnetic polarisation of the Ho sub-lattices in these two higher temperature regions, in which the major components of the Fe moment lie along $x$ and $y$, is very small. The canting of the moments from the axial directions is attributed to the antisymmetric interactions allowed by the crystal symmetry. They include contributions from single ion anisotropy as well as the Dzyaloshinski antisymmetric exchange. In the low temperature phase two further structural transitions are apparent in which the spontaneous magnetisation changes sign with respect to the underlying antiferromagnetic configuration. In this temperature range the antisymmetric exchange energy varies rapidly as the the Ho sub-lattices begin to order. So long as the ordered Ho moments are small the antisymmetric exchange is due only to Fe-Fe interactions, but as the degree of Ho order increases the Fe-Ho interactions take over whilst at the lowest temperatures, when the Ho moments approach saturation the Ho-Ho interactions dominate. The reversals of the spontaneous magnetisation found in this study suggest that in hfo the sums of the Fe-Fe and Ho-Ho antisymmetric interactions have the same sign as one another, but that of the Ho-Fe terms is opposite.