The Magnetic-field-induced Electric Polarization Flop In Multiferroics

Multiferroics are compounds in which the ferroelectric (FE) (or antiferroelectric (AFE)),ferromagnetic (FM) (or antiferromagnetic (AFM)) order and ferroelastic order coexist simultaneously in certain temperature range. The multiferroics researched recently are the materials with both FE order and magnetic order structures, and the coupling effects between these two order structures (Magnetoelectric (ME) effect) triggered a lot of excitement. The materials which have the ME effect-the induction of magnetization by means of an electric field and induction of polarization by means of a magnetic field-are defined as the magnetoelectrics. The first observation of the ME effect triggered a lot of excitement because of the obvious potential of the cross-correlation between the magnetic and electric properties of matter for technical applications. The ferroelectrtomagnets, in which FE ordering and magnetic spin ordering coexist spontaneously at low temperature, have been the object of intensive theoretical and experimental studies from the 60-70's last century for its connection with the finding out this kind of material and theirs some special properties of physics own to ME coupling. By ME coupling, the application of an electric field or FE polarization can change one or more of the parameters governing the magnetic behavior of the system. Correspondingly, being possible magnetostrictive effect or electron-phonon interaction, the fluctuation of spin ordering may lead to a dielectric anomaly and FE relaxation. There exists ME in two type of materials, one of them is spin-order material called magnetoelectrics that may exhibits an induced linear ME effect by external field. This effect is named as the electrically or magnetically induced ME effect. A ferroelectromagnet, however, differs from the magnetoelectrics in that it shows spontaneous ME effects in addition to the ME effects induced by external fields. They are caused by the coexistence in the crystal of spontaneous FE and magnetic moments. An anomalies in the dielectric constants and loss tangent have been observed experimentally in the ferroelectromagnet near the AFM transition temperature, indicative of a coupling between the FE and magnetic ordering, but the nature of the mechanism of ME coupling and the form of interaction is still an important and debated issue.Magnetic ferroelectrics, which are also called as multiferroics belong to the ferroelectromagnets. Some perovskite rare-earth manganites are good cases in point such as RMnO₃ ( R = Gd , Tb,and Dy ) .Experimental results show that FE order appears simultaneously at a magnetic transition in orthorhombically distorted perovskite structure of TbMnO₃ and one can reversibly switch the polarization on and off using an external magnetic field. The magnetically frustrated system MnWO₄ , which is crystallized in a wolframite structure, belongs to another kind of multiferroics. Experimental data show that there exists coupling between the magnetism and dielectric properties, which leads to the dielectric anomaly near its Néel temperature. The magnetoelectric properties of these two kinds of ferroelectromagnets both originate from competing magnetic interactions which produce long - wavelength antiferromagnetic sinusoidal and helicoidal spin order and accordingly lattice modulations through magnetoelastic coupling. This coupling between magnetic order and lattice distortions which produces ferroelectricity gives rise to strong magnetoelectric coupling and the so called magnetic-field-induced-polarization-flop.For the multiferroics we mentioned above, the spin reorientation brings about lattice reorientation and then an electric polarization appears. That is to say the transition to an asymmetric phase is accompanied by the appearance of a spontaneous-polarization, which is the characteristic of the improper ferroelectrics. In the first place,, we use the phenomenological Landau theory of improper FE phase transition to discuss the ME properties of the ferroelectromagnets. For the multiferroics the two first order parameters appear at different temperature, which is differ from the so called improper ferroelectrics and can be seen as one characteristic of the multiferroics. Especially we add the coupling term between the magnetism and the strain-tensor to the Landau free energy, and study the influence of the applied magnetic field on the ferroelectric phase transition. In the second place, based on our theory, the magnetoelectric properties of TbMnO₃ and MnWO₄ are investigated and many interesting experimental phenomenon can be explained, for instance, the appearance of the electric polarization, the so-called magnetic-field-induced electric polarization flop, and temperature dependence of the and electric polarization in several magnetic fields. We argue that the transverse magnetic order parameter (e.g. one of the primary order parameter) is crucial to the FE transition of TbMnO₃ . The appearing of the transverse magnetic moment of Mn is the key to the appearance of polarization, and its rotating is responsible for the magnetic-field-induced polarization flop. When it comes to MnWO₄ , the helicoidal spin order of Mn in the bc plane produces the spontaneous-polarization, and in the high magnetic field the flop of the spiral plane produces the polarization flop.