Theory of Orbital-Ordering in LaGa 1- x Mn x O 3 Jason Farrell

1. 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 correlatedsystems: • 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 percolationapproach: • 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: • Excellent agreement at small x: evidence for magnetic percolation. • As x → xc(= 0.311 for a simple cubic lattice) simple approach fails. • 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. • 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. Theory of Orbital-Ordering in LaGa1-xMnxO3 Jason Farrell (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 effectis • 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 @ T = 5 K; applied B = 5 Tesla • 2. General Physics of Manganites • Ion of interest is Mn3+. • 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. • Place ion into cubic crystal environment with six Oxygen O2- neighbours: • Electrostatic field due to the neighbours; thecrystal 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: egand t2g. • t2gare 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 Supervisor: Professor Gillian Gehring 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 @ T = 5 K 20 x 20 x 20 Simulation 2(b-a)/(b+a) 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