Multiferroic Materials | Basic Physics for IIT JAM PDF Download

Materials that are both ferroelectric and magnetic–multiferroics–are rare.  This is because in most ferroelectrics, such as BaTiO₃, the ferroelectricity is driven by a hybridization of empty d orbitals with occupied p orbitals of the octahedrally coordinated oxygen ions.  This mechanism requires empty d orbitals and thus cannot lead to multiferroic behavior.  There are consequently very few ferroelectrics that exhibit long range magnetic order, and rarer still are materials where these
two disparate order parameters exist and exhibit significant coupling.  Multiferroics have been of particular interest recently both to understand the fundamental aspects of the novel mechanism that gives rise to th
is magnetic-ferroelectric coupling, as well as because of the intriguing possibility of using these coupled order parameters in novel device applications.  In particular,

recent "proof of principle" work has shown that it is possible to control the magnetic phase with an applied electric field, and control the electric polarization with an applied magnetic field.
The hexagonal HoMnO₃ system of particular interest here is a prototype multiferroic.  The holmium-oxygen displacements give rise to a ferroelectric moment along the crystallographic c axis at very high tem
peratures (T_C = 875 K), while the Mn moments order at 72 K.  The order parameters are naturally coupled through the Ho-Mn exchange and ani
sotropy interactions.  The crystal structure is shown in the figure, where we see that the Mn spin system has the added interest that the moments occupy a fully frustrated triangular lattice.

Side view of crystal structure 

Top View

Purple spheres represent holmium ions, blue spheres oxygen ions arranged octahedrally with the Mn ions in the middle.
The Mn spins order at 72 K, and then the magnetic structure undergoes a spin reorientation transition at 40 K (in zero applied field).  At both of these transitions there are anomalies in the dielectric constant, demonstrating that there is strong coupling between the magnetic and ferroelectric order parameters.


Magnetic order parameters for HoMnO₃;  (left) isometric plot of the [1,0,1] magnetic Bragg peak and (right) integrated intensities vs. T for two different magnetic peaks.  The magnetic structure changes three times in evolving to the ground state.  All three magnetic structures are non-collinear, and possess different chiral symmetries as shown below.  The transition at ~8K includes the development of magnetic order for the holmium moments as well as a change in the magnetic structure of the Mn spins.


Three magnetic structures for the Mn spins.
The application of a magnetic field (along the c-axis) broadens and moves the spin-reorientation transition in temperature, as shown by the data below.  The data allow the phase boundary to be mapped in the (H,T) plane.  At low T additional transitions are observed, which are also hysteretic.

Field dependence of the magnetic intensities at intermediate T (left) and low T (right)

Phase diagram as a function of (H,T) determined from neutron diffraction measurements.
The spin dynamics of this system turns out to be particularly interesting.  Inelastic neutron scattering measurements reveal the planar nature of the spin system, and have established the basic model for the magnetic interactions in the system. The non-collinear spin structure gives rise to three different "flavors" of bosons.  The single-ion anisotropy of the (ferroelectric) holmium rare earth ions couples to the Mn spins, and in our view plays a critical role in both the spin reorientation transitions (much like that found in Nd₂CuO₄) and in the multiferroic behavior.

Spin-wave dispersion relations at 20 K for two in-plane directions in reciprocal space, and along the c-axis (inset) where no significant dispersion is observed, indicating that the system is 2d in nature.  The solid curves are fits to a 2d Heisenberg model.  Dashed lines indicate two (dispersionless) crystal field levels of Ho at 1.5 and 3.1 meV. The scan shown is for Q=1.3,0,0, where the apparent sloping background is actually due to the holmium crystal field level at lower energy.