Nave perspective on transition metal oxide physics

1
Naïve perspective ontransition metal oxide
physics

• C.C. Joseph Wang
• B. Sahu
• W.C. Lee
• A.H. MacDonald

2
Outline

• Complexity in Bulk states
• Heterostructure

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Structure of cubic perovskites(ABO_3)
B
A
O
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Simplest Transition Metal Oxide

• LaAlO3(Band Insulator, non-magnetic, cubic)
• LaTiO3(Mott Insulator, anti-ferromagnetic(G),
  orthorhombic)
• SrTiO3(Band Insulator, Ferroelectric(?), cubic)
• Isolated atom ground state configurations
• LaXe6s25d1? 3 valence electrons
• SrKr5s2 ? 2 valence electrons
• TiAr4s23d2 ? 4 valence electrons
• AlNe3s23p1? 3 valence electrons
• OHe2s22p4 ? 6 valence electrons

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Electronic structure of LaAlO_3-local density
approximation? my first DFT calculation
Experimental gap5.6 ev, LDA gap3.5ev Error due
to inclusion of self-energy
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Why RTiO_3 ?

• More close to the Hubbard Model with 3d electron
  (half filling)
• Complexity
• Rich magnetic orders
• JT distortion AND GdFeO3 distortion
• Interplay of various order (spin, orbital,
  electron interactions, lattice distortion)

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GdFeO_3 type distortion due to covalency
between A and O
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Energy level of 3d electron andorbital order
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Low energy physics

• t_2g levels are most relevant to light
• transition metals (Ti, V,Cr,..)
• e_g levels are most relevant
• to heavy transition metals
• (Cu,Ni)
• If t_2g and e_g are partial
• filled, the degeneracy will be lifted
• by other effect such as Jahn-Teller effect

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Magnetic order for RTiO_3

• Theory based on degenerate t_2g orbitals
  predicts FM
• (J. Phys. Soc. Jpn. 71, 2039 (2002))
• Theory based on GdFeO_3 type distortion
  Crystal field due to
• R is crucial to determine the correct magnetic
  order for RLa,Pr, Nd, Sm (P.R.L. 91, 167203)
  

Our DFT bulk calculation with U shows the
following energetic Order G-type(
-15164.06421528 ev) lt A-type(-15164.0320918  ev)
ltC-type( 15164.03132880 ev) lt ferro-magnetic(
.16246031E03 ev) for LaTiO3 without relaxation
of the lattice to optimal structure
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Well-defined TMO Heterostructure

• Author H.Y. Hwang et al. Nature 419, P378 (2002)
• Demonstrate experimentally the possibility to
  grow
• well-defined superlattice between
  LaTiO3(Polar)/SrTiO3
• with conduction along layer growth direction

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Why such a Heterostructure?
N-TYPE CONDUCTOR

• Electronic Reconstruction
• Atomic Reconstruction

P-TYPE Insulator
Nature material, 5, p204(2006)
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Magnetic effects at the interfacebetween
nonmagnetic oxides

• LaAlO3(Polar)/SrTiO3(cond-mat 070328)
• Induction of localized magnetic moment at the Ti
  interface sites
• Versatile system to study interplay
• between localized magnetic moment and
  conducting electrons
• on the sheet

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Theoretical work

• Explanation of conducting behavior
• for a MI/BI and map out phase diagram as a
  function of layer number n and t/U based on
  multi-band Hubbard model with mean field
  approximation

It would be interesting to suggest the right
material to work in the light yellow region and
study the competition of different orders
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Conduction between MIMI (Orbital order is not
discussed ) by W.C. and Allan
AFM
FM
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What could be understood?

• The interplay of different orders in the
  interface with realistic consideration in the
  primitive system I mentioned.
• Propose new interface system with different
  essential physics in the bulk,
• especially the bulk systems with good
  understanding.
• New Many-body physics in the interface

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Advantage of first principle calculation

• Derive or justifying effective Hamiltonian for
  each compound
• Predict better ground states with
• different orders
• Allow us to treat the interface more reliablely

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Why LDAU?

• LDA estimates exchange-correlation interaction
  based on uniform electron gas(Not right for
  HIGHLY localized orbitals in TMO)

-E_dc
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Work to do

• Interplay of orders on the interface with more
  realistic considerations
• Construct the effective Hamiltonian of 2DEG in
  the interface
• Many-body physics in the 2DEG
• Is there something new in the interface?