An effective model of magnetoelectricity in multiferroics RMn2O5

An effective model is developed to explain the phase diagram and the mechanism of magnetoelectric coupling in multiferroics, RMn2O5. We show that the nature of magnetoelectric coupling in RMn2O5 is a coupling between two Ising-type orders, namely, the ferroelectric order in the b-axis, and the.coupled magnetic order between two frustrated antiferromagnetic chains. The frustrated magnetic structure drives the system to a commensurate-incommensurate phase transition, which can be understood as a competition between a collinear order stemming from the “order by disorder” mechanism and a chiral symmetry order. The low-energy excitation is calculated and it quantitatively matches experimental results. Distinct features and the effects of external magnetic field in the electromagnon spectra in the incommensurate phase are predicted. Copyright c © EPLA, 2008 Recently, the search for new spin-electronics materials has led to the discovery of novel gigantic magnetoelectric and magnetocapacitive effects in rare-earth manganites, magnetoelectric multiferroics [1,2]. Unlike the magnetic ferroelectroics studied in the 1960s and 1970s where magnetism and ferroelectricity couple weakly, the magnetism and ferroelectricity in the new materials couple so strongly that the ferroelectricity can be easily manipulated by applying a magnetic field and the magnetic phase can be controlled by applying an electric field [3,4]. This ease of manipulation promises great potential for important technological applications in novel spintronics devices. The physics of the multiferroics involves the interplay between many degrees of freedom, such as charge, spin, orbital and lattice. Tremendous effort has been devoted to decode the fundamental mechanism of the strong coupling between the magnetism and ferroelectricity. Experimentally, two major classes of magnesium oxide multiferroics, have been discovered. The first class is the orthorhombic rare-earth manganites RMnO3 (R=Gd,Tb,Dy, . . .) [5,6], characterized by spiral magnetism strongly coupled with the ferroelectricity. An effective Ginzburg-Landau theory incorporating the space group symmetry and time-reversal symmetry has been constructed to explain the fundamental physics [7]. Microscopically, Dzyaloshinskii-Moriya (a)E-mail: [email protected] spin-orbit interaction is the underlying mechanism of the ferroelectricity [8–10] and an electric current cancellation principle related to spin-orbit coupling can also explain the physics [11]. The second class of materials are the manganese oxides with general formula RMn2O5 (R=Y,Tb,Dy, . . .) [12–15]. These insulating materials consist of linked MnO6 octahedra and MnO5 pyramids with a Pbam space group symmetry. Unlike that in RMnO3, the ferroelectricity in RMn2O5 exists in a collinear magnetic phase, suggesting that a different mechanism is involved in the interaction between the ferroelectricity and magnetism. In this letter, we develop an effective model to explain the phase diagram and the mechanism of magnetoelectric coupling in RMn2O5. Building upon experimental facts and the space group symmetry [4,12–20], we show that the magnetoelectric interaction is between two Ising-type orders, the ferroelectric order in the b-axis and the coupled magnetic order between two frustrated antiferromagnetic chains. The effective model of the magnetism can be derived from a microscopic model with nearest-neighbor magnetic exchange. We show that the effective model nicely captures the phase diagrams of RMn2O5. At high temperature, the commensurate (CM) collinear order is stable due to the “order by disorder” mechanism [21–23] and the existence of an easy axis. As the temperature decreases, a chiral symmetry order replaces the collinear order, and the magnetic structure