Transcript x - Angelfire

Theory of Orbital-Ordering in LaGa1-xMnxO3
Jason Farrell
1. Introduction
4. Interplay of Spin- and Orbital-Ordering
7. Theoretical Approach
•LaGaxMn1-xO3 is an example of a manganese oxide known as a manganite.
• Coupling between spins in neighbouring Mn orbitals is determined by the amount
of orbital overlap → Pauli Exclusion Principle.
• Finite cubic lattice (of Mn and Ga) with periodic boundary conditions.
•The electronic properties of manganites are not adequately described by simple
semiconductor theory or the free electron model.
•Manganites are strongly correlated systems:
• Large orbital overlap: antiferromagnetic ↑↓ spin coupling.
Begin with LaGaO3 and dope with Mn3+:
• Less orbital overlap: ferromagnetic ↑↑ spin coupling.
•Electron-electron interactions are important.
• Theory: ferromagnetic spin exchange along the Mn-O-Mn axes.
• Also have to consider the intermediate O2- neighbours.
•Electron-phonon coupling is also crucial.
(a)
• Period of rotation of these axes is faster than spin relaxation time.
(b)
(c)
→ Isotropic ferromagnetic coupling between nearest-neighbour Mn spins.
→ 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.
Mn
O
Mn
Mn
O
Mn
Mn
O
Mn
Try a percolation approach:
• As Mn content increases, ferromagnetic Mn clusters will form.
• Extended treatment considers virtual interorbital electron hopping: the
Goodenough-Kanamori-Anderson (GKA) rules.
• At higher Mn content, larger clusters will form.
• Gives the same result; also gives each exchange constant.
• At a critical Mn fraction, the percolation threshold, xc, a ‘supercluster’ will
extend over the entire lattice.
→ Possible use in magnetic devices; technological importance.
BUT: LaGaxMn1-xO3 (Mn3+ only; no CMR) has not been extensively studied.
• Spin-only Mn3+ magnetic moment = 4 µB; CF-quenching of orbital moment.
5. Physics of LaMnO3
→ Determine the magnetisation per Mn3+ as a function of doping:
Magnetisation of LaGa1-xMnxO3
@ T = 5 K; applied B = 5 Tesla
•Based upon the perovskite crystal structure:
2. General Physics of Manganites
• Ion of interest is Mn3+.
act coherently throughout the entire crystal.
• Neutral Mn: [Ar]3d7 electronic configuration.
→ Mn3+ has valence configuration of 3d4.
• Free ion: 5 (= 2l +1; l = 2) d levels are wholly degenerate.
• Ion is spherical.
•This cooperative, static, Jahn-Teller effect is
M (µB/Mn)
•Jahn-Teller effect associated with each Mn3+
responsible for the long-range orbital ordering.
• Long and short Mn-O bonds in the basal plane → a pseudo-cubic crystal.
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.
x
Polycrystalline experimental data: Vertruyen B. et al., Cryst. Eng., 5 (2002) 299
20 x 20 x 20 percolation simulation
• Excellent agreement at small x: evidence for magnetic percolation.
• As x → xc (= 0.311 for a simple cubic lattice) simple approach fails.
orbitals
spins
• 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.
• This is expected: percolation is a critical phenomenon.
Change in orbital-ordering also leads to change in the crystal dimensions:
• Hypothesis: upon introducing a Ga3+ ion, neighbouring x and y Mn3+ orbitals in
the above/below planes flip into z direction.
Orthorhombic Strain in
LaMn1-xGaxO3 @ T = 5 K
• Long-range orbital order is more robust: destroyed above TJT ~ 750 K.
20 x 20 x 20 Simulation
→ Structural transition to cubic phase.
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.
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?
Supervisor: Professor Gillian Gehring
2(b-a)/(b+a)
eg
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t2g
• On-site Coulomb repulsion U (4 eV) is greater than electron bandwidth W (1 eV)
→LaMnO3 is a Mott-Hubbard insulator.
Experimental Data: Vertruyen B. et al., Cryst. Eng., 5 (2002) 299
x
• Good qualitative agreement: the orbital-flipping hypothesis is correct.
→ Crystal c-axis evolution (not shown) is also predicted correctly.
→ True understanding of how Ga-doping perturbs the long-range JT order.
Future Work: investigate the behaviour of the high-x (Mn-rich) magnetisation.