Session Y19: Invited Session: Novel Mechanisms of Multiferrocity

Multiferroicity due to Charge Ordering

In this contribution I discuss multiferroicity that is driven by different forms of charge ordering, presenting first the generic mechanisms by which charge ordering can induce ferroelectricity in magnetic systems. In type-I multiferroics [1], ferroelectricity and magnetism have different origins and occur at different temperatures. There is a number of specific classes of materials for which this is relevant. Discussed will be in some detail (i) perovskite manganites of the type (PrCa)MnO3 [2,3], (ii) the complex and interesting situation in magnetite Fe3O4, (iii) strongly ferroelectric frustrated LuFe2O4 and (iv) an example of a quasi-one-dimensional organic system [4]. In type-II multiferroics [1], ferroelectricity is completely due to magnetism, but with charge ordering playing an important role [5], such as (v) multiferroic Ca3CoMnO6, (vi) possible ferroelectricity in rare earth perovskite nickelates of the type RNiO3 [6,7], (vii) multiferroic properties of manganites of the type RMn2O5 [8], (viii) perovskite manganites with magnetic E-type ordering. \\[4pt] [1] J. van den Brink and D. Khomskii, J. Phys.: Condens. Matter 20, 434217 (2008).\\[0pt] [2] D.V. Efremov, J. van den Brink and D.I. Khomskii, Nature Materials 3, 853 (2004).\\[0pt] [3] G. Giovannetti, S. Kumar, J. van den Brink, S. Picozzi, Phys. Rev. Lett. 103, 037601 (2009).\\[0pt] [4] G. Giovannetti, S. Kumar, A. Stroppa, J. van den Brink and S. Picozzi, Phys. Rev. Lett. 103, 266401 (2009). \\[0pt] [5] J. Betouras G. Giovannetti and J. van den Brink, Phys. Rev. Lett. 98, 257602 (2007).\\[0pt] [6] G. Giovannetti, S. Kumar, D. Khomskii, S. Picozzi and J. van den Brink, Phys. Rev. Lett. 103, 156401 (2009).\\[0pt] [7] S. Kumar, G. Giovannetti, J. van den Brink and S. Picozzi, Phys. Rev. B 82, 134429 (2010).\\[0pt] [8] G. Giovannetti and J. van den Brink, Phys. Rev. Lett. 100, 227603 (2008).   

Soft X-ray Observation of electronic contribution to ferroelectric polarization

Multiferroic materials open up new interesting possibilities for devices by enabling the switching of an electric state by magnetic field or {\it vice-versa}. In addition to this functionality, multiferroics are intriguing from a fundamental physics perspective, raising interesting questions concerning coupling of the electric and magnetic order parameters. To date, most coupling mechanisms are understood to occur due to distortions in the crystal lattice. Here we present experimental evidence that in the multiferroics RMn$_2$O$_5$ (where R is a rare earth) there exists a new, purely \emph{electronic} contribution to the ferroelectric polarization, which can exist in the absence of any lattice distortions. This contribution arises due to spin-dependent hybridization of O $2p$ and Mn $3d$ states and was observed through soft x-ray resonant scattering, which has proved to be a very useful tool in the study of the magnetic structure of multiferroics[1]. Through resonant x-ray scattering at the oxygen K-edge, we find that such spin dependent hybridization occurs in both TbMn$_2$O$_5$[2] and YMn$_2$O$_5$[3]. Remarkably, in YMn$_2$O$_5$ we find that the temperature dependence of the integrated intensity of the signal at the oxygen K-edge closely follows the macroscopic electric polarization [3], and hence is proportional to the ferroelectric order parameter. This is in contrast with the temperature dependence observed at the Mn L$_3$ edge, which reflects the Mn magnetic order parameter. Work performed at BNL was supported by the US Department of Energy, Division of Materials Science, under contract No. DE-AC02-98CH10886. \\[4pt] [1] S.B. Wilkins et al., Phys. Rev. Lett. 103, 207602 (2009)\\[0pt] [2] T.A.W. Beale, S. B. Wilkins et al., Phys. Rev. Lett. 105, 087203 (2010)\\[0pt] [3] S. Partzsch, S. B. Wilkins et al., Phys. Rev. Lett. 107, 057201 (2011)   

Dynamic magnetoelectric interaction in multi-orbital Mott insulators

The control of spin textures in magnetic insulators with an applied voltage can be of great importance for dissipationless spintronics. The coupling between spin and charge degrees of freedom in Mott insulators originates from the fluctuations of electron occupancy of strongly correlated orbitals of transition metal ions. Several microscopic mechanisms resulting from the virtual hopping of electrons from a magnetic site to its neighbor, e.g. the ``inverse Dzyaloshinskii-Moriya'' and the Heisenberg exchange striction mechanisms, are responsible for the electric polarization induced by non-centrosymmetric magnetic orders, the excitation of spin waves with the oscillating electric field of a light wave, and other effects recently observed in multiferroic materials. I will discuss a new dynamic magnetoelectric interaction, which describes the electric polarization induced by time-dependent spin textures [1]. Simple symmetry arguments as well as the explicit derivation from an extended Hubbard model of multi-orbital Mott insulators are used to obtain the form of this interaction, which is the electric analogon of the coupling between the scalar spin chirality and magnetic field. It is closely related to the so-called spinmotive force exerted by spins on electrons in magnetic conductors. This interaction makes possible to displace spin textures in ferromagnetic insulators by applying a voltage. It couples the external electric field to the center-of-mass coordinates of topological spin textures in ferromagnetic thin films, such as Skyrmions and magnetic vortices. The effect of this coupling is dramatically amplified in the resonant absorption of circularly polarized light by spin vortices in nanodiscs. \\[4pt] [1] M. Mostovoy, K. Nomura and N. Nagaosa, Phys. Rev. Lett. 106, 047204 (2011).   

Multiferroic vortices: arrested Kosterlitz-Thouless order

The fascinating concept of topological defects permeates ubiquitously our understanding of the early-stage universe, hurricanes, quantum matters such as superfluids and superconductors, and also technological materials such as liquid crystals and magnets. Large-scale spatial configurations of these topological defects have been investigated only in a limited degree. Exceptions include the cases of supercurrent vortices or liquid crystals, but they tend to exhibit either trivial or rather-irregular configurations. Hexagonal REMnO$_{3}$ (RE= rare earths) with RE=Ho-Lu, Y, and Sc, is an improper ferroelectric where the size mismatch between RE and Mn induces a trimerization-type structural phase transition, and this structural transition leads to three structural domains, each of which can support two directions of ferroelectric polarization. We reported that domains in h-REMnO$_{3}$ meet in cloverleaf arrangements that cycle through all six domain configurations, Occurring in pairs, the cloverleafs can be viewed as vortices and antivortices, in which the cycle of domain configurations is reversed. Vortices and antivortices are topological defects: even in a strong electric field they won't annihilate. These ferroelectric vortices/antivortices are found to be associated with intriguing magnetism. The seemingly-irregular configurations of a zoo of multiferroic vortices and antivortices in h-REMnO$_{3}$ can be neatly analyzed in terms of graph theory and this graph theoretical analysis reflects the nature of self-organized criticality in complexity phenomena as well as the condensation and eventual annihilation processes of topological vortex-antivortex pairs. Furthermore, these numerous multiferroic vortices/antivortices can be understood as an arrested Kosterlitz-Thouless phase. \\[4pt] [1] Insulating Interlocked Ferroelectric and Structural Antiphase Domain Walls in Multiferroic YMnO$_{3}$, T. Choi, - - -, S-W. Cheong, Nature Materials 9, 253 (2010). \\[0pt] [2] Self-organization, condensation, and annihilation of topological vortices and antivortices in a multiferroic, S. C. Chae, - - - S.-W. Cheong, PNAS 107,~ 21366 (2010). \\[0pt] [3] Direct observation of the proliferation of ferroelectric dislocation loops and vortex-antivortex pairs, S. C. Chae, - - -, S.-W. Cheong, Phys. Rev. Lett., submitted.   

Interplay between trimerization, ferroelectric, and magnetic order in the hexagonal manganites

The hexagonal manganites h-RMnO$_3$ with R = Sc, Y, In, Dy -- Lu are a model system for multiferroics with pronounced magnetoelectric effects in which the magnetic and ferroelectric order emerge independently (so-called split-order-parameter or type-I multiferroics). In spite of many years of intense investigations the system never seizes to surprise us with novel, unexpected manifestations of its five-fold long-range order (antiferrodistortive, ferroelectric, antiferromagnetic Mn order, and rare-earth order on the 2a and 4b sites). Here I will discuss several such examples: (i) ``Incompatible'' magnetic order of the Mn and rare-earth sublattices according to different symmetry representations in combination with triggered ordering at the 4b site. (ii) The {it absence} of ferroelectric order in h-InMnO$_3$ down to low temperatures in spite of its apparent similarities to, in particular, h-YMnO$_3$. (iii) Observation of a direct and rigid coupling of the ferroelectric to the antiferrodistortive order in annealing experiments at 1300 K. In summary, all these experiments allow us to present a comprehensive model for the microscopic origin of the ferroelectric and the multiple magnetic (re-) ordering in this important group of compounds.