Theory of Orbital-Ordering in LaGa1-xMnxO3 Jason Farrell

1
Theory of Orbital-Ordering in LaGa1-xMnxO3
Jason Farrell

• 1. Introduction
• LaGaxMn1-xO3 is an example of a manganese oxide
  known as a manganite.
• The electronic properties of manganites are not
  adequately described by simple semiconductor
  theory or the free electron model.
• Manganites are strongly correlated systems
• Electron-electron interactions are important.
• Electron-phonon coupling is also crucial.
• ? Magnetisation is influenced by electronic and
  lattice effects.
• La1-xCaxMnO3 (Mn3 and Mn4) and similar
  mixed-valence manganites are extensively
  researched.
• These may exhibit colossal magnetoresistance
  (CMR).
• ? Very large change in resistance as a magnetic
  field is applied.
• ? Possible use in magnetic devices technological
  importance.
• BUT LaGaxMn1-xO3 (Mn3 only no CMR) has not
  been extensively studied.

• 4. Interplay of Spin- and Orbital-Ordering
• Coupling between spins in neighbouring Mn
  orbitals is determined by the amount of orbital
  overlap ? Pauli Exclusion Principle.
• Large orbital overlap antiferromagnetic ?? spin
  coupling.
• Less orbital overlap ferromagnetic ?? spin
  coupling.
• Also have to consider the intermediate O2-
  neighbours.
• Extended treatment considers virtual
  interorbital electron hopping the
  Goodenough-Kanamori-Anderson (GKA) rules.
• Gives the same result also gives each exchange
  constant.

• 7. Theoretical Approach
• Finite cubic lattice (of Mn and Ga) with
  periodic boundary conditions.
• Spin-only Mn3 magnetic moment 4 µB
  CF-quenching of orbital moment.
• Begin with LaGaO3 and dope with Mn3
• Theory ferromagnetic spin exchange along the
  Mn-O-Mn axes.
• Period of rotation of these axes is faster than
  spin relaxation time.
• ? Isotropic ferromagnetic coupling between
  nearest-neighbour Mn spins.
• Try a percolation approach
• As Mn content increases, ferromagnetic Mn
  clusters will form.
• At higher Mn content, larger clusters will form.
• At a critical Mn fraction, the percolation
  threshold, xc, a supercluster will extend over
  the entire lattice.
• ? Determine the magnetisation per Mn3 as a
  function of doping

(a)
(b)
(c)
Mn O Mn
Mn O Mn
Mn O Mn

• 5. Physics of LaMnO3
• Based upon the perovskite crystal structure
• Jahn-Teller effect associated with each Mn3
• act coherently throughout the entire crystal.
• This cooperative, static, Jahn-Teller effect is
• responsible for the long-range orbital ordering.
• Long and short Mn-O bonds in the basal plane ? a
  pseudo-cubic crystal.
• The spin-ordering is a consequence of the
  orbital ordering (Section 4).
• ? A-type spin ordering spins coupled
  ferromagnetically in the xy plane
  antiferromagnetic coupling along z.
• Long-range magnetic order is (thermally)
  destroyed above TN 140 K.
• Long-range orbital order is more robust
  destroyed above TJT 750 K.
• ? Structural transition to cubic phase.
• On-site Coulomb repulsion U (4 eV) is greater
  than electron bandwidth W (1 eV) ?LaMnO3 is a
  Mott-Hubbard insulator.

Magnetisation of LaGa1-xMnxO3
_at_ T 5 K applied B 5 Tesla

• 2. General Physics of Manganites
• Ion of interest is Mn3.
• Neutral Mn Ar3d7 electronic configuration.
• ? Mn3 has valence configuration of 3d4.
• Free ion 5 ( 2l 1 l 2) d levels are wholly
  degenerate.
• Ion is spherical.
• Place ion into cubic crystal environment with six
  Oxygen O2- neighbours
• Electrostatic field due to the neighbours the
  crystal field.
• Stark Effect electric-field acting on ion.
• Some of the 5-fold degeneracy is lifted.
• Cubic crystal less symmetric than a spherical
  ion.
• ? d orbitals split into two bands eg and t2g.
• t2g are localised the eg orbitals are important
  in bonding.
• On-site Hund exchange, JH, dominates over the
  crystal field splitting ?CF.
• ? 4 spins are always parallel a high-spin ion.

M (µB/Mn)
x
Polycrystalline experimental data Vertruyen B.
et al., Cryst. Eng., 5 (2002) 299
20 x 20 x 20 percolation simulation
orbitals
spins
Orthorhombic Strain in
LaMn1-xGaxO3 _at_ T 5 K
20 x 20 x 20 Simulation
2(b-a)/(ba)
Experimental Data Vertruyen B. et al., Cryst.
Eng., 5 (2002) 299
t2g
eg

hello

• 6. Gallium Doping
• Randomly replace some of the Mn3 with Ga3 to
  give LaMn1-xGaxO3.
• Ga3 has a full d shell (10 electrons)
• ? Ion is diamagnetic (no magnetic moment)
• ? Not a Jahn-Teller ion GaO6 octahedra, unlike
  MnO6, are not JT-distorted.
• How does such Gallium-doping affect the orbital
  ordering and hence the magnetic and structural
  properties of the material?

• 3. The Jahn-Teller Effect
• Despite crystal field splitting, some degeneracy
  remains.
• Fundamental Q.M. theory the Jahn-Teller effect.
• Lift as much of the ground state degeneracy as
  possible
• ? Further splitting of the d orbitals
• Orbitals with lower energy preferential
  occupation
• ? JTE introduces orbital ordering.
• Lift degeneracy ? reduce symmetry.
• Strong electron-lattice coupling.
• ? Jahn-Teller effect distorts the ideal cubic
  lattice.

x

• Supervisor Professor Gillian Gehring