This presentation contains two lectures given by E This presentation contains two lectures given by E. Dagotto to his class of Solid State II (2009) at the Dept. of Physics of the University of Tennessee. The subjects are (i) Multiferroics and (ii) Oxide interfaces.

Multiferroics (1) Electric and magnetic ordering in solids are usually considered separately: effects such as ferroelectricity are caused by charges while magnetism is caused by spins. (2) However, in a few cases these two orders are strongly coupled. If this is the case, then it may occur that using an electric field E, we can induce a finite magnetization M. Or using a magnetic field H, we can generate a finite electric polarization P. Or, if a material has both orders, namely nonzero P and M, using H we could control P or using E we can control M. (3) For instance, in GMR we could control the orientation of relative magnetizations via electric fields.

There are two types of multiferroics: Proper (or type I) multiferroics. In these cases the two phenomena of P and M occur for different reasons, but there is still a (weak) coupling between them. A famous example is BiFeO3, with TFE=1100K and TAF=643K. (2) Improper (or type II) multiferroics. New developments. Here both orders are deeply coupled to one another. But unfortunately critical temperatures are small. In spite of this problem for applications, they are the most interesting intelectualy.

Reviews Sang Cheong and Maxim Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nature Materials 6, 13 (2007). R. Ramesh and Nicola Spaldin, Multiferroics: progress and prospects in thin films, Nature Materials 6, 21 (2007). D. Khomskii, Physics 2, 20 (2009). Special issue of Journal of Physics: Condensed Matter, vol 20, number 43, 29 Oct 2008.

Recent efforts have opened a new line of research: the multiferroic manganites New spiral magnetic phase, which is also FE Kimura et al.,Nature 426, 55 (2003). See also Cheong and Mostovoy, Nat. Phys. 6, 13 (2007), and others.

Magnetic fields rotate the direction of polarization

But can current theory explain spiral phases But can current theory explain spiral phases? The standard DE model with JAF coupling and Jahn-Teller distortions does NOT have a spiral phase JAF E-phase vs. Spiral T. Hotta et al., PRL 90, 247203 (2003)

Are there spirals or FE states in the phase diagram of CMR materials Rich phase diagram, including metallic and insulating phases, with spin, charge, and orbital order, but no FE o spiral. T CE-type Spin/charge/orbital order Cheong et al. A-type AF orbital order

“Standard’’ model for Mn oxides Mobile carriers interacting with localized spins: S=3/2 (localized) 3d orbitals 5 fold degenerate Large JHund

Double exchange models for manganites J AF H Mn 4+ Mn 3+ t2g eg + JH is the largest coupling JAF/t ~ 0.1 (still relevant) + e-ph coupling + disorder

Likely, we need magnetic frustration to generate a spiral order. In a Heisenberg model with J1 (NN) and J2 (NNN) couplings, there are competing tendencies. This leads to “frustration”. A compromise between the two possible AF states could be a spiral. This has been observed in many spin systems, but only recently in more sophisticated models as those for manganites.

Lattice GdFeO3 distortions induce a small NNN J2 S. Dong et al Lattice GdFeO3 distortions induce a small NNN J2 S. Dong et al., PRB 78, 155121 (2008) J1 is AF, and J2 is also AF (different along a and b: J2b/J2a~2)

Double exchange model for multiferroics Large JH DE Super-exchange Elastic energy JT distortions

Phase diagram including JT distortions A, E, and spiral states are insulators. Wavevectors q’s of TbMO3 and DyMO3 are part of spiral phase

MC phase diagram now contains the three observed phases A-Spiral-E 12x12 MC, J2a~0 P small since DM interaction is only 1 meV/Angstrom A S E

Spiral order may cause FE via Dzyaloshinskii-Moriya mechanism I Spiral order may cause FE via Dzyaloshinskii-Moriya mechanism I. Sergienko et al., PRL 97, 227204 (2006); Mostovoy et al. HDM= g Tokura et al.

How to generate FE without spirals Prediction of FE in the E-AF phase (I. Sergienko et al., PRL 97, 227204 (2006))

Next challenge: doped multiferroics FM C G CE T x W ? PM T: temperature W: Bandwidth R1-xAxMnO3

Phase diagram at n=0.75 (S. Dong et al., in preparation) Techniques: MC 8x8 and 16x16, and T=0 optimization. New phases!

New phases found at n=0. 75 (MC and variational; S. Dong et al New phases found at n=0.75 (MC and variational; S. Dong et al., in preparation) DM non-ferroelectric C1/4E3/4 (Hotta et al.) DM ferroelectric FE phase (Dong et al.) Fragile? Realistic JAF?

New phases at n=0.75 Both phases have the same S(q) and are Insulators. FE induced via DM interaction. P still small, similar to TbMnO3 Since caused by DM interaction. TC x4 larger than in spiral phase.

========================

New playground: oxide interfaces LTO STO Scanning transmission electron microscopy Ohtomo et al, Nature 419 (‘02) See also Mannhart, Triscone, Hwang, Tokura, Ramesh, Bozovic, … Pulsed laser deposition, Molecular beam epitaxy… z LaTiO3 SrTiO3 For list of references see Science 318, 1076 (2007)

Oxide multilayers interfaces: what are they good for? (1) Potential applications in the new field of “oxide electronics”. New functionalities? (2) New two-dimensional phases at oxide interfaces? (3) Reduction of the influence of quenched disorder in the doping process, contrary to chemical doping. (4) Can CMR, stripes be artificially made? Can Tc’s be enhanced?

Molecular beam epitaxy takes place in high vacuum or ultra high vacuum (10−8 Pa). The most important aspect of MBE is the slow deposition rate (typically less than 1000 nm per hour), which allows the films to grow epitaxially. The slow deposition rates require proportionally better vacuum to achieve the same impurity levels as other deposition techniques. In solid-source MBE, ultra-pure elements such as gallium and arsenic are heated in separate until they begin to slowly sublimate. The gaseous elements then condense on the wafer, where they may react with each other. In the example of gallium and arsenic, single-crystal gallium arsenide is formed. The term "beam" means that evaporated atoms do not interact with each other or vacuum chamber gases until they reach the wafer, due to the long mean free paths of the atoms. During operation, RHEED (Reflection High Energy Electron Diffraction) is often used for monitoring the growth of the crystal layers. A computer controls shutters in front of each furnace, allowing precise control of the thickness of each layer, down to a single layer of atoms. Intricate structures of layers of different materials may be fabricated this way. Such control has allowed the development of structures where the electrons can be confined in space, giving quantum wells or even quantum dots. Such layers are now a critical part of many modern semiconductor devices.

Exotic results already found The interface between two insulators can be a metal The interface between two insulator can be a superconductor In general, the properties of the ensemble can be drastically different from the properties of the individual building blocks

Reviews C. H. Ahn et al., Review of Modern Physics 78, 1185 (2006)

SMO/LMO/SMO/LMO MC, DMRG, Poisson equation, one orbital, large W I. Gonzalez et al., JPCM 20, 264002 (2008) MC, DMRG, Poisson equation, one orbital, large W LaMnO3/CaMnO3 layers. Both AF insulating, but combination is FM metallic. See also S. Yunoki et al., PRB 76, 064532 (2007); PRB 78, 024405 (2008).

Large-bandwidth manganite superlattices (LMO)2n(SMO)n Bhattacharya et al., PRL 100, 257203 (08)

LMO-CMO Simulation done on a 4x4x8 cluster, at T=0, optimizing numerically the classical t2g spins and the oxygen coordinates. R. Yu et al., in progress. Clear CE spin pattern at the center, but Z=3 anomalous Very stable intermediate n=0.5 region, but phases at each layer cannot be simply read from phase diagram.

Are there spirals or FE states in the phase diagram of CMR materials Rich phase diagram, including metallic and insulating phases, with spin, charge, and orbital order, but no FE o spiral. T CE-type Spin/charge/orbital order Cheong et al. A-type AF orbital order

Results cannot be simply read from the electronic density of each layer. Canting starts Novel “canted CE” state at n~1 Standard CE Mainly G-AF but CE influenced Standard CE but at 90o from previous layer

Orbital order also modified by proximity to other orders. Tendency to enhance 3z2-r2 component. Not equal X2-y2 3z2-r2 develops