nmat1804 Cheong Review.indd

In 1865, James Clerk Maxwell proposed four equations governing the dynamics of electric fi elds, magnetic fi elds and electric charges, which are now known as Maxwell’s equations1. Th ey show that magnetic interactions and motion of electric charges, which were initially thought to be two independent phenomena, are intrinsically coupled to each other. In the covariant relativistic form, they reduce to just two equations for the electromagnetic fi eld tensor, succinctly refl ecting the unifi ed nature of magnetism and electricity2. A number of interesting parallels exist between electric and magnetic phenomena, such as the quantum scattering of charge off magnetic fl ux (Aharonov–Bohm eff ect3) and the scattering of magnetic dipoles off a charged wire (Aharonov–Casher eff ect4). Th e formal equivalence of the equations of electrostatics and magnetostatics in polarizable media explains numerous similarities in the thermodynamics of ferroelectrics and ferromagnets, for example their behaviour in external fi elds, anomalies at a critical temperature, and domain structures. Th ese similarities are particularly striking in view of the seemingly diff erent origins of ferroelectricity and magnetism in solids: whereas magnetism is related to ordering of spins of electrons in incomplete ionic shells, ferroelectricity results from relative shift s of negative and positive ions that induce surface charges. Magnetism and ferroelectricity coexist in materials called multiferroics. Th e search for these materials is driven by the prospect of controlling charges by applied magnetic fi elds and spins by applied voltages, and using this to construct new forms of multifunctional devices. Much of the early work on multiferroics was directed towards bringing ferroelectricity and magnetism together in one material5. Th is proved to be a diffi cult problem, as these two contrasting order parameters turned out to be mutually exclusive6–10. Furthermore, it was found that the simultaneous presence of electric and magnetic dipoles does not guarantee strong coupling between the two, as microscopic mechanisms of ferroelectricity and magnetism are quite diff erent and do not strongly interfere with each other11,12. Th e long-sought control of electric properties by magnetic fi elds was recently achieved in a rather unexpected class of materials known as ‘frustrated magnets’, for example the perovskites RMnO3, RMn2O5 (R: rare earths), Ni3V2O8, delafossite CuFeO2, spinel CoCr2O4, MnWO4, and hexagonal ferrite (Ba,Sr)2Zn2Fe12O22 (refs 13–20). Curiously, it is not the strength of the magnetoelectric coupling or high magnitude of electric polarization that makes these materials unique; in fact, the coupling is weak, as usual, and electric polarization is two to three orders of magnitude smaller than in typical ferroelectrics. Th e reason for the high sensitivity of the dielectric properties to an applied magnetic fi eld lies in the magnetic origin of their ferroelectricity, which is induced by complex spin structures, characteristic of frustrated magnets15,21–27. Recent reviews of this rapidly developing fi eld can be found in refs 28–30. Here, we mainly focus on the relationship between magnetic frustration and ferroelectricity, discuss diff erent types of multiferroic materials and mechanisms inducing electric polarization in magnetic states, and outline the directions of the future research in this fi eld.