1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. Magnetic fields rotate the direction of polarization

7. 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, (2003)

8. 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

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

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

11. 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.

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

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

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

15. 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

16. 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, (2006); Mostovoy et al.
HDM= g
Tokura et al.

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

18. Next challenge: doped multiferroicsFM C G CE T x W ? PM
T: temperature
W: Bandwidth
R1-xAxMnO3

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

20. 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?

21. 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.

22. ========================

23. 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)

24. 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?

25. 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.

26. 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

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

28. SMO/LMO/SMO/LMO MC, DMRG, Poisson equation, one orbital, large W
I. Gonzalez et al., JPCM
20, (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, (2007); PRB 78, (2008).

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

30. 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.

31. 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

32. 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

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