INTRODUCTION TO MULTIFERROICS Student’s name – Umesh Chandra Thuwal Roll No. – 20109291 Department of Physics IIT Kanpur Abstract Multiferroics are the materials in which ferroic (ferroelectric, ferromagnetic and ferroelastic) ordering coexist. These materials open up the profitable way to control magnetism by an electric field. The coexistence of an electric and magnetic field has been known for the long time, but in the last two decades, some key discoveries generated a lot of interest among researchers in this field. In this report, I provide a general introduction to multiferroics, their different mechanism which support multiferroicity, composite multiferroic and violation of inversion symmetry in multiferroic which leads to multiferroicity, ferrotoroidicity and magnetic monopole in condensed matter. I will also briefly discuss the advantages of multiferroic material and the future of multiferroicity. Introduction In 1994 the term multiferroic was introduced by Hans Schmid [1]. He defined the multiferroic materials as the materials in which two or more ferroic orders such as ferroelectric and ferromagnetism coexist. In a more general context, the multiferroic is defined as the coexistence of any two ferroic (ferroelectric,ferromagnetic, ferroelastic and ferrotoroidic) ordering simultaneously. At present, the researchers have extended this definition to include other long-range order such as antiferromagnetism. Although the term multiferroics was introduced around 90’s but with the introduction of magnetoelectrics, it can be said that the active research in this field was started in the ’50s If we were to talk about the technical merits, ferromagnetic and ferroelectric are different, In multiferroic, both orders may be in a single phase. These material are important for technological implication for mainly two reasons [2]. Firstly, they make it possible to control magnetic bit by electric bit and secondly, the coupling of ferroelectric and ferromagnetic materials might give some novel properties which are not present in either state alone. If in the reading and writing of magnetic bit, an electric voltage is used instead of an electric current (source of magnetic field) the loss of energy will get avoided because long build up is associated with electric current and high energy is needed. Thus multiferroic materials leads to a more smaller, faster and energy efficient data storage which is the demand of future technology. There are many material requirements which are needed to be fulfilled for a material to be called as multiferroic. For instance, ferroelectric material must be non-centrosymmetric to pass spontaneous electric polarisation and there are 31 point groups which allow this. Out of these 13 point groups allow occurrence of both the properties simultaneously. These point groups may lead to large number of possible materials exhibiting multeferroism so it is unlikely that symmetry play an important role in determining whether material will be multiferroic or not. Important term in multiferroics 1.Ferroic Material which shows long rang order with respect to atleast one macroscopic properties and develop a dipole with conjugate field used term ferroic. There are four type of ferroic are shown in figure 1 Ferroelectric material which posseses a spontaneous polarization P that is stable and switched hysteritically by an applied electric field E. Ferromagmetic material possesses a spontaneous magnetization M that is stable and switched hysteritically by an applied magnetic field H. Ferroelastic material shows spontaneous deformation that is stable and switched hysteritically by an applied stress. Ferrotoroidic state with a domain that could be hysterically switched space-time antisymmetric external field (toroidal field). Figure 1. four type of ferroic order, (a) ferroelasticity, (b) ferroelectricity, (c) ferromagnetism, (d) ferrotoroidicity., (a) ferroelasticity exhibit spontaneous strain, σ due to stress (b) spontaneous polarization, P, due to applied electric field , (c) spontaneous magnetization ,M, due to magnetic field (d) ferro-toroidics exhibit a vortex-like alignment of spins with a toroidization due to toroidic field.[3] 2.Magnetoelectric coupling Landau theory describe the magnetoelectric effect in single phase material through expansion of the free energy expression as 1 1 1 F(E, H) = F − PsE − MsH − ∈ ∈ E E − μ μ H H − α E H + β E H H 0 i i i i 2 0 ij i j 2 0 ij i j ij i j 2 ijk i j k 1 + γ H E E 2 ijk i j k Where E and H are electric and magnetic field respectively. Here ∈ and 휇 are the dielectric and magnetic susceptibility. Type 1 and type 2 Multiferroics If the magnetic and ferroelectric ordering in the material occurs independently that means the source of ferroelectric ordering and magnetic ordering are different, denoted as type 1 [2], as shown in figure 2. The coupling between magnetism and ferroelectricity in type 1 multiferroic is usually weak. In general mechanism which driven the multiferroicity in type 1 multiferroic are charge charge ordering mechanism, lone pair mechanism and geometric ferroelectrisity mechanism. If the ferroelectricity and magnetic transition emerges jointly known as the type 2 multiferroic, as shown in figure 2. Coupling between the magnetism and ferroelectricity in type 2 multiferroic is usually larger than type 1. In general spin driven mechanism is responsible for type 2 multiferroic Figure 2 – type 1 and type 2 multiferroic, P, polarization; Si, spin at site i.[2] Multiferroicity due to Different Mechanism As we discussed the ferroelectric and magnetic ordering coexist in these material. Four general mechanism which driven the multiferroicity [2] shown in figure 4. These four mechanism are charge ordering, lone pair, geometric effect and spin driven mechanism. In first three mechanism induced ferroelectrity is independent to magnetic ordering and the multiferroic material are type 1. In spin driven mechanism ferroelectric and magnetic transition occure jointly, type 2 multiferroic. Multiferroicity due to Charge ordering The appearance of ferroelectricity due to charge ordering [4] can be understand using Figure 3. Fig (A) consist of one dimensional chain with same (zero) charge on each site. Fig B shows same one dimensional chain with one set of sites has charge +e and other site has –e, but this arrangement not break the inversion symmetry so no net dipole moment in the arrangement. Another case of charge ordering is when a system dimerizes. Fig C shows, in this type of system strong and weak bond alternate or we can say that sites are equivalent but bonds are not. One can use the terminology, site centred charge ordering (S-CCO) for fig B and bond centred charge ordering (B-CCO) for fig C. but B-CCO arrangement is centrosymmetric thus not ferroelectric. Figure 3 (a) Example of one dimensional neutral chain, (b) S-CCO, (c) B-CCO, (d) linear combination of S-CCO and B-CCO that is ferroelectric. Arrow indicate the polarization which is total zero in (b) and (c), but develops a microscopic moment indicated by red arrow in (d). The dashed lines indicate mirror plane of the system.[4] If combining both type of charge ordering as discussed in figure (B) and figure (C), situation changes. The situation with simultaneous S-CCO and B-CCO are shown in figure (D). In this situation inversion symmetry is broken and each molecule develop a net dipole moment, as a result whole system become ferroelectric. In some material inequivalent bond are due to crystallographic structure and spontaneous charge ordering that can occur below certain temperature press inequivalent in site or the material can contain ion with different valence which after a structural dimerization transition induce ferroelectricity. There is some example of charge ordering multiferroic are perovskite manganites (Pr1−xCaxMnO3), Fe3O4 and LuFe2O4 (frustrated charge order). The value of polarization in 퐿푢퐹푒2푂4 is large in comparision to these other two example. In 퐿푢퐹푒2푂4 valence electron can be distributed non-uniformaly around their host ion in the crystal lattice to form periodic superstructure. Fe atom in 퐿푢퐹푒2푂4 may form a superlattice with an alternating sequence of 퐹푒2+and 퐹푒3+ ions, shown in figure 4 (b). The ferroelectricity in LuFe2O4 is due to a combination of two factors: the bilayer character of the crystal structure, and the frustrated charge ordering leading to the formation of charged planes (e.g., negative charging of the lower layer and positive charging of the upper one). As, generally speaking, in such a situation CO may be very strong, one could in principle expect large spontaneous polarizations. The induced ferroelectricity in these material are independent of magnetic field. Multiferroicity due to lone pair Unbounded valence electron around the host ion. This is mainly observed in BiFeO3 [5]. This is perovskite oxide and most studied multiferroic material because of its high critical temperature In this mechanism the spatial asymmetry is created due to anisotropic distribution of and high ferroelectric polarization. In this material ferroelectricity is not due to the off centering of B site cation (퐹푒3+) rather the main reason for instability was due to the presence of steriochemically active lone pair of A site cation (Bi3+). Two 6s electron of bismuth ion not involved in the bond,thus showing the high polarizability and created a local dipole along [111] plane Figure 4 (a). The ovserved polarization in this ferroelectric marial is very large (100휇퐶/푐푚2). On the other hand the magnetization is guaranteed by B site magnetic 퐹푒3+(푑5) ions. Due to the independent origin of ferroelectric and magnetic ordering this is type 1 multiferroic. Multiferroicity due to geometric effect Geometric constraints and size effect can cause an instability in material [2]. Such type of mechanism is driven by steric effect rather than the usual change in chemical bond leads to ionic shift that result to a polar distortion and geometric ferroelectricity Figure 4(c). For example in h − RMnO3 (R = Sc, Y, In or Dy − Lu) a unit cell trimerizing lattice distortion 2 derives the force of the ferroelectric order at 푇푐 ≥ 1200퐾 with polarization 5.6 휇퐶/푐푚 .