Session U31: Focus Session: Multiferroics II: Theory and LuFe2O4

Spontaneous currents and charge redistribution in Mott insulators

The standard view is that at low energies Mott insulators exhibit only magnetic properties while charge degrees of freedom are frozen out as the electrons become localized by a strong Coulomb repulsion. We demonstrate that this is in general not true: for certain spin textures \textit{spontaneous circular electric currents} or \textit{nonuniform charge distribution} exist in the ground state of Mott insulators. The latter can give a purely electronic mechanism of \textit{multiferroic behaviour}. In addition, low-energy ``magnetic'' states contribute comparably to the dielectric and magnetic functions, leading to interesting phenomena such as the electric field-induced ``ESR'' transitions, rotation the electric field polarization and resonances which may be common for both functions producing a negative refraction index in a window of frequencies.   

First-Principles Study of Large Magnetoelectric Coupling in Triangular Lattices

We investigate, using density functional theory, the magnetoelectric coupling in a frustrated antiferromagnet in which the combination of frustration with magnetic interactions mediated by Anderson superexchange leads to a unconventional and large coupling between polarization and magnetic order. The nature of the superexchange mechanism can be manipulated through induced polarization of the lattice upon application of an electric field, leading to a strong magnetoelectric effect. We demonstrate the effect in a Mn-based triangular lattice that is closely related to the Kagom\'e structure, with modifications to avoid self-compensation of the induced magnetic order. For our study, we employ the VASP software package with LSDA+U for describing electron exchange and correlation effects. A fully noncollinear treatment of the spinors is essential to describe the complex spin structures that the system adopts.   

Trends in spin exchange interactions and ferroelectric polarization in the orthorhombic $R$MnO$_{3}$ series

Recently, magnetic ferroelectricity induced by Heisenberg-type interactions has been theoretically predicted in E-type antiferromagnetic (AFM) HoMnO$_{3}$ \footnote{S. Picozzi et al., Phys. Rev. Lett. (in press)}. In order to fully clarify this unconventional microscopic mechanism, we have studied the structural, magnetic and ferroelectric properties for the entire family of orthorhombic $R$MnO$_{3}$ ($R$= rare earth ions), based on first-principles density functional calculations. The ferromagnetic exchange interaction between nearest-neighbor Mn sites decreases with the ionic radius of $R$ (concomitantly with the in-plane Mn-O-Mn bond angle), whereas the anti-ferromagnetic next-nearest neighbor interaction stays rather constant in the series. The competition of these exchange interactions results in a complicated magnetic phase diagram. The decrease in the Mn-O-Mn angle also affects the hopping integrals between Mn ions (as determined from Wannier functions), so that the calculated electric polarization in E-type AFM $R$MnO$_{3}$ is remarkably reduced throughout the rare earth series.   

First-principles study of magnetoelecric coupling in TbMnO$_3$

At room temperature, the perovskite TbMnO$_3$ forms an orthorhombically distorted lattice with the {\it Pbnm} space group. Below $\sim$27~K the magnetic moments on the Mn atoms develop incommensurate cycloidal order, and simultaneously a polarization appears. We present a first-principles study of this low-temperature phase in which the ordering of the Mn$^{3+}$ moments is forced to be commensurate in a 60-atom supercell, approximating the experimental wavevector. The calculations are based on a non-collinear spin treatment of density-functional theory in the local-density approximation, with the polarization computed using the Berry-phase technique. We confirm that the electric polarization appears only when the spin-orbit coupling is turned on. Both electronic and lattice-mediated contributions to the polarization appear, the latter being dominant. We make a normal-mode analysis of the lattice contribution and discuss the ability of a model based on local Dzyaloshinskii-Moriya interactions to reproduce the computed pattern of forces.   

Magnetoelectric Chains: Quasi-One-Dimensional Multiferroics

Recently discovered pyroxenes represent an example of a multiferroic containing quasi-one dimensional (Q1D) building blocks of zig-zag chains of edge- sharing octahedra along the c-axis of the crystal. This leads us to the natural question: what types of Q1D symmetries would allow for the simultaneous presence of polarizartion and magnetization? Moreover, what kinds of phase transitions can exist between two different Q1D magnetic phases? From this perspective we study quasi- one-dimensional magnetic symmetry in 3D space (magnetic rod groups), enumerate Q1D magnetic point groups that allow for magnetoelectricity and illustrate their role in low-dimensional multiferroic phase transitions.   

Influence of oxygen defects and lattice distortions on the energy gap formation and magnetic properties of multi-ferroic materials

Full potential density functional calculations are performed to study the effects of O-vacancies on the structural parameters and electronic properties of $RMnO_{3-\delta}$, (R=Y, rare-earths). We find that vacancies at the 2a-position of the hexagonal unit cell can introduce a small gap of magnitude 0.2eV. Although significantly lower than the experimentally observed value of 2.5eV, we claim that already such defects, which in general are inevitable in oxides, can introduce the energy gap in addition to the most commonly accepted Coulomb correlation mechanism. Besides, the off-plane O-vacancies modify the magnetic properties of the system and induce small magnetic polarization on the in-plane O-sites and at the interstitials. The electronic structure and magnetic properties modifications as a function of several lattice distortions have been analyzed. We also discuss the mechanisms of the exchange coupling and its most effective path. In addition we compare previously known results of the electronic structure calculations for these systems.   

Domain structure and magnetization reversal in multiferroic LuFe$_2$O$_4$

We report real space magnetic imaging of single crystal multiferroic LuFe$_2$O$_4$ via variable temperature magnetic force microscopy (VT-MFM). The magnetization reversal of LuFe$_2$O$_4$ is investigated in detail with MFM in magnetic fields up to 8 tesla at several temperatures below T$_N$=230 K. Our results suggest that the domain structure and the magnetization reversal of LuFe$_2$O$_4$ are different from those of conventional FM magnets with a uniaxial anisotropy. These unconventional behaviors may originate from the low dimentionality and the unusual spin-charge frustration of LuFe$_2$O$_4$.   

Interplay of charge order and magnetism in LuFe$_{2}$O$_{4}$

Ferroelectricity in LuFe$_{2}$O$_{4}$ may originate from charge order and seems to be coupled the magnetism as well. For both charge order and magnetism, conflicting reports have been published. We have recently grown single crystals exhibiting features in magnetization sharper than previously reported and suggesting an additional transition around 175 K. Neutron scattering experiments have revealed 3D magnetic and charge order. We will present recent synchrotron, calorimetry, and magnetization measurements on these crystals, which indicate a subtle interplay of magnetism, charge order, and structural distortions. Superstructure reflections studied include (1/3,1/3,n and n/2) (exhibiting small systematic deviations away from 1/3), satellites to (0,0,3/2n) and (1/3,1/3,n and n/2), and two other types of reflections. Supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy.   

Three dimensional magnetic correlations in LuFe$_{2}$O$_{4}$

LuFe$_{2}$O$_{4}$ has recently attracted much attention due to a novel electronically driven ferroelectric transition and concomitant indications of coupling between magnetic degrees of freedom and a large spontaneous polarization. To examine the behavior of LuFe$_{2}$O$_{4}$ in further detail, we have performed extensive polarized and unpolarized neutron diffraction experiments on high quality single crystal specimens. These measurements reveal two phase transitions involving magnetic degrees of freedom below 300 K. At 240 K we find the onset of three dimensional ferrimagnetic order. The refined ferrimagnetic spin structure is a symmetry allowed magnetic structure of the parent R-3m space group with a propagation vector of (1/3 1/3 0). Below 175 K many of the magnetic Bragg peaks become significantly broadened and a broad diffuse component to the magnetic scattering becomes evident. In addition, a new set of satellites is observed indexed as (1/3$\pm \delta $ 1/3$\pm \delta $ 3L/2) where $\delta \sim $0.027. Polarized neutron diffraction measurements indicate that these satellites have a substantial magnetic component.   

Optical properties of LuFe$_2$O$_4$

We measured the optical properties of single crystalline LuFe$_2$O$_4$ as a function of temperature and compared the results with recent electronic structure calculations. The 300 K optical gap is found to be ${\sim}$ 0.4 eV. The optical conductivity is very sensitive to temperature and shows a sharp transition at around 170 K structural transition. The Fe$^{2+}$ to Fe$^{3+}$ charge transfer transition (at approximately 1.5 eV) sharpens dramatically at low temperature, a trend that may be connected with the complex charge order of the material. Preliminary high energy magneto-dielectric data will be discussed.   

Effect of oxygen deficiencies on charge ordering in RFe$_{2}$O$_{4-\delta }$ (R=Lu and Y)

Charge ordering (CO) of Fe$^{2+}$ and Fe$^{3+}$ on the triangular lattice in RFe$_{2}$O$_{4-\delta}$ (R=Lu and Y) is suggested to play an important role in the physical properties such as ferroelectricity. Herein, we report changes in the CO structures due to the oxygen deficiencies in RFe$_{2}$O$_{4-\delta}$ by transmission electron microscopy. At room temperature, characteristic superlattice reflections at (1/3 1/3 1/2)-type positions can be observed in the nearly stoichiometric YFe$_{2}$O$_{4-\delta}$, while the diffuse streaks along c*-axis can be seen clearly in the non-stoichiometric YFe$_{2}$O$_{4-\delta}$. It is suggested that the correlations between the Fe-O bilayers are suppressed due to the oxygen vacancies and therefore the two-dimensional charge ordering appears in the non stoichiometric samples at room temperature.   

Ferroelectricity in an Ising Chain Magnet

The concept of magnetism-driven ferroelectricity has recently drawn significant attention. Among the simplest model systems showing this effect are magnetic spiral compounds, and frustrated collinear chain magnets with alternating charge order. While many experimental realizations of the former systems exist, no undisputed examples of the latter have been reported so far. Herein, we report discovery of an experimental realization of this model in an Ising chain compound with an up- up-down-down magnetic order. Unlike in the spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in this system occurs through exchange striction associated with symmetric superexchange coupling. Since the latter can be large, this observation may help identify candidate systems with large magnetoelectric coupling and significant magnetoelectric effects.   

Magnetoelectric effect in Cr$_{2}$O$_{3}$ thin films

Magnetoelectric materials experienced a recent revival as promising components of novel spintronic devices [1, 2, 3]. Since the magnetoelectric (ME) effect is relativistically small in traditional antiferromagnetic compounds like Cr$_{2}$O$_{3}$ (max. $\alpha _{zz}\approx $4ps/m ) and also cross- coupling between ferroic order parameters is typically small in the modern multiferroics, it is a challenge to electrically induce sufficient magnetization required for the envisioned device applications. A straightforward approach is to increase the electric field at constant voltage by reducing the thickness of the ME material to thin films of a few nm. Since magnetism is known to be affected by geometrical confinement thickness dependence of the ME effect in thin film Cr$_{2}$O$_{3 }$is expected. We grow (111) textured Cr$_{2}$O$_{3}$ films with various thicknesses below 500 nm and study the ME effect for various ME annealing conditions as a function of temperature with the help of Kerr-magnetometry. [1] P. Borisov et al. Phys. Rev. Lett. \textbf{94}, 117203 (2005). [2] Ch. Binek, B.Doudin, J. Phys. Condens. Matter \textbf{17}, L39 (2005). [3] R. Ramesh and Nicola A. Spaldin 2007 \textit{Nature Materials} \textbf{6} 21.   

First-principles approach to lattice-mediated magnetoelectric effects

I will present a first-principles scheme for the computation of the magnetoelectric (ME) response of magnetic insulators. The method focuses on the \textit{lattice-mediated} part of the magnetic response to an electric field, which can be expected to be the dominant contribution in materials displaying a strong coupling, thus avoiding the technical difficulties associated to the treatment of a purely electronic ME effect. I will describe results of calcultions for Cr$_{2}$O$_{3}$ and other model magnetoelectric compounds.   

Chirality, Handedness and Pseudovectors

Chirality has been, to our knowledge, universally defined as a symmetry property, namely, lack of mirror symmetry of a physical object (e.g. a molecule) or, more generally, a physical situation (e.g. light propagation). It is understood that the mirror can be followed by a proper rotation and/or translation. The word chirality (Greek: hand), was added by Lord Kelvin after Pasteur noted the physical importance of right- and left-handed molecules, and, in this context, is considered identical to handedness. However, there is another context, equally important, where handedness has a different meaning, namely the handedness associated with the definition of the cross-product of two vectors. We call the former def. 1, the latter, def. 2. We show that the two meanings are essentially different by giving examples which are simultaneously handed (def. 2) and not chiral. These are drawn from light waves, spin spirals and multiferroics. Thus we show that there must be a distinction between chirality and the general idea of handedness.