1. Structure & Magnetism of LaMn 1-x Ga x O 3 J. Farrell & G. A. Gehring Department of Physics and Astronomy University of Sheffield

2. Contents Why LaMn 1-x Ga x O 3 ? Why LaMn 1-x Ga x O 3 ? Theory: postulates and assumptions Theory: postulates and assumptions Lattice parameters Lattice parameters → Orthorhombic strain; cell volume → Orthorhombic strain; cell volume Magnetisation Magnetisation Conclusions Conclusions

3. Why LaMn 1-x Ga x O 3 ? LaMnO 3 : parent compound of many CMR manganites. LaMnO 3 : parent compound of many CMR manganites. Typically, the Mn 3+ is replaced by Mn 4+ : Typically, the Mn 3+ is replaced by Mn 4+ : → La 1-x Ca x MnO 3, La 1-x Sr x MnO 3 → La 1-x Ca x MnO 3, La 1-x Sr x MnO 3 Electron hopping between Mn 3+ and Mn 4+ Electron hopping between Mn 3+ and Mn 4+ → Double exchange → Double exchange So, any observed effects may be attributed to: Introduction of Mn 4+ Introduction of Mn 4+ Removal of Mn 3+ Removal of Mn 3+

4. LaMn 1-x Ga x O 3 (LMGO) To investigate only the removal of Mn 3+, dope LaMnO 3 with “vacancies” To investigate only the removal of Mn 3+, dope LaMnO 3 with “vacancies” Try Ga 3+ Try Ga 3+ Diamagnetic (unlike Mn 3+ ) Diamagnetic (unlike Mn 3+ ) Jahn-Teller inactive (unlike Mn 3+ ) Jahn-Teller inactive (unlike Mn 3+ ) Any disorder will be negligible Any disorder will be negligible → r Ga = 76 pm; r Mn = 78.5 pm → r Ga = 76 pm; r Mn = 78.5 pm Could also try Sc 3+ or Al 3+ but there is more data for LMGO (~ 7 experimental papers)

5. LaMnO 3 → LMGO Long-range, static, Jahn-Teller ordering of the Mn 3+ e g orbitals Long-range, static, Jahn-Teller ordering of the Mn 3+ e g orbitals Long-range AFM is a direct consequence of orbital ordering. Long-range AFM is a direct consequence of orbital ordering. GKA predictions: GKA predictions: Mn O Mn Mn O Mn Mn O Mn LMGO, x 0 → Orbital flipping; FM evolution along z.

6. Orbital Flipping Random Ga-doping causes the x or y orbitals to flip into the z direction. Random Ga-doping causes the x or y orbitals to flip into the z direction. Significant elastic energy penalty forbids strong overlap. Significant elastic energy penalty forbids strong overlap. Khomskii D. I. & Kugel K. I. PRB 67, 134401 z

7. Orbital Flipping Forbidden scenarioFM Coupling y x z x

8. Lattice Parameters Bond lengths from neutron diffraction: Blasco et al., PRB 66, 174431 Bond lengths from neutron diffraction: Blasco et al., PRB 66, 174431 Ga-O = 1.97 Ǻ; Mn-O = 1.92 Ǻ (compression) Ga-O = 1.97 Ǻ; Mn-O = 1.92 Ǻ (compression) JT: Mn-O = 1.90 and 2.18 Ǻ (LaMnO 3 ) JT: Mn-O = 1.90 and 2.18 Ǻ (LaMnO 3 ) Gallium-doping: long-range, static JT is suppressed but local, static JT persists. Gallium-doping: long-range, static JT is suppressed but local, static JT persists. Simulations on L = 10 cubic lattice with periodic boundary conditions. Simulations on L = 10 cubic lattice with periodic boundary conditions.

9. Lattice Parameters b a O´→ O stuctural transition at x ≈ 0.55 O´→ O stuctural transition at x ≈ 0.55 Good agreement with experimental results. Good agreement with experimental results.

10. Lattice Parameters b a Experimental data: Blasco et al., PRB 66, 174431

11. Lattice Parameters b a O´→ O structural transition at x ≈ 0.55 O´→ O structural transition at x ≈ 0.55 Blasco et al., PRB 66, 174431

12. Orthorhombic Strain ε = 2(b – a)/(b + a): Vertruyen et al., Cryst. Eng., 5, 299

13. Cell Volume V = abc: Vertruyen et al., Cryst. Eng., 5, 299

14. Magnetisation Competition between FM and AFM bonds may lead to frustration. Suggestions of: Competition between FM and AFM bonds may lead to frustration. Suggestions of: Spin glass (Zhou et al., PRB 63, 184423) Spin glass (Zhou et al., PRB 63, 184423) Spin canting (Blasco et al., PRB 66, 174431) Spin canting (Blasco et al., PRB 66, 174431) Spin flipping (this work). Spin flipping (this work).

15. Monte Carlo Simulations 10000 MCS/S. 10000 MCS/S. J FM = 9. 6 K, J AFM = - 6.7 K. J FM = 9. 6 K, J AFM = - 6.7 K. T = 5 K; B = 5.5 T applied along easy axis. T = 5 K; B = 5.5 T applied along easy axis. Spins ↑ or ↓ only; no canting. Spins ↑ or ↓ only; no canting. At large x, assume that M evolves due to percolation. At large x, assume that M evolves due to percolation. Isolated Mn contribute negligibly to M. Isolated Mn contribute negligibly to M. nn Mn couple ferromagnetically (4 µ B each). nn Mn couple ferromagnetically (4 µ B each).

16. Results Obvious discrepancy at x = 0 accounts for canting. Obvious discrepancy at x = 0 accounts for canting. Broad plateau is not observed; M peaks at x = 0.5. Broad plateau is not observed; M peaks at x = 0.5. At small x, dM/dx is predicted well. At small x, dM/dx is predicted well. At large x, percolation assumption is only qualitatively correct. At large x, percolation assumption is only qualitatively correct. Vertruyen et al., Cryst. Eng., 5, 299 Simulation

17. Spin Flipping At small x, Gallium may be placed on ↑ or ↓. At small x, Gallium may be placed on ↑ or ↓. → Good estimation of linearity at small x (~ 16 µ B /Ga) + 12 µ B + 20 µ B z

18. Conclusions LaMn 1-x Ga x O 3 is an ideal system in which the disruption of long-range orbital- and magnetic- order can be investigated. LaMn 1-x Ga x O 3 is an ideal system in which the disruption of long-range orbital- and magnetic- order can be investigated. Orbital flipping (local-JT) correctly describes the evolution of the lattice parameters. Orbital flipping (local-JT) correctly describes the evolution of the lattice parameters. The magnetism depends on the orbital order The magnetism depends on the orbital order → Orbital ordering is paramount Magnetisation successfully described in terms of spin-flipping. Magnetisation successfully described in terms of spin-flipping.