1. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 1 Polarized inelastic neutron scattering in the CMR manganite La 0.70 Ca 0.30 MnO 3 *Center for Neutron Scattering, Oak Ridge National Laboratory + Spallation Neutron Source, Oak Ridge National laboratory ++ Institut Laue Langevin, Grenoble, France PINS workshop, BNL April 6-7, 2006 J. A. Fernandez-Baca*, Mark Hagen +, Jiri Kulda ++

2. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 2 Polarized inelastic neutron scattering in the CMR manganite La 0.70 Ca 0.30 MnO 3 OUTLINE  Motivation: LCMO30: Softening and damping of spin waves near the zone boundary.  The magnon-phonon interaction  Experimental  polarized neutron setup (half polarized and full polarization)  magnons and phonons in LCMO  Unpolarized measurements  Results and discussion  Summary

3. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 3 COLOSSAL MAGNETORESISTANCE MANGANITES Cubic perovskite La/Ca in A site Substitution of Ca 2+ for La 3+ leads to mixed Mn 3+ /Mn 4+. La 1-x Ca x MnO 3 Double exchange

4. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 4 Spin-wave excitations – Double exchange (DE) t  electron hoping J H  Hund coupling between localized t 2g electrons (S=3/2) and e g electrons. In the strong coupling limit (J H >>t) the spin wave spectrum is approximately the same as that for a Heisenberg FM with nn interactions. Furukawa J. Phys. Soc. Jpn. (1996) D  J  T C Heisenberg model

5. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 5 Spin waves in CMR manganites Ln 1-x A x MnO 3 near x=0.30 Pr 0.63 Sr 0.37 MnO 3 Hwang et al. PRL (1998) Nd 0.30 Sr 0.30 MnO 3 Fernandez-Baca et al, PRL (1998) La 0.70 Ca 0.30 MnO 3 Dai et al., PRB (2000) Similar dispersion throughout the Brillouin zone SW “softening” & broadening at the Brillouin zone boundary

6. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 6 Spin waves in CMR manganites Ln 1-x A x MnO 3 near x=0.30 Proposed explanations Peculiar ground state (not globally FM) (Zang et al J. Phys. Cond Matt (1999) Purely magnetic DE (Solovyev and Terakura, PRL 82, 2959 (1999)) Charge and orbital fluctuations (Khaliullin, PRB 71, 3494 (2000)) Disorder (Motome and Furukawa) Magnon-phonon interaction (Dai, PRB 61, 9553(2000))

7. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 7 Spin waves in CMR manganites Ln 1-x A x MnO 3 near x=0.30 Proposed explanations Peculiar ground state (not globally FM) (Zang et al J. Phys. Cond Matt (1999) Purely magnetic DE (Solovyev and Terakura, PRL 82, 2959 (1999)) Charge and orbital fluctuations (Khaliullin, PRB 71, 3494 (2000)) Disorder (Motome and Furukawa) Magnon-phonon interaction (Dai, PRB 61, 9553(2000)) Predicts broadening and softening

8. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 8 Magnon- Phonon Interactions (S. Lovesey, “Theory of Neutron Scattering from Condensed Matter systems,” sect. 9.8)  Linked to significant magnetoelastic interactions  Magnon-phonon hybridization: Lattice vibrations may modulate the orbital properties. The modulation is transmitted to the spin by the spin-orbit interaction, which is not strong in 3d ions.  More common in 4f ions but observed in FeF 2 (Rainford) and FeCl 2 (Ziebeck 1976).

9. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 9 Magnon- Phonon Interactions (S. Lovesey, “Theory of Neutron Scattering from Condensed Matter systems,” sect. 9.8)  Linked to significant magnetoelastic interactions  Magnon-phonon hybridization: Lattice vibrations may modulate the orbital properties. The modulation is transmitted to the spin by the spin-orbit interaction, which is not strong in 3d ions.  More common in 4f ions but observed in FeF 2 (Rainford) and FeCl 2 (Ziebeck 1976).

10. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 10 Magnon-phonon hybridization  Tb-10% Ho. Möller (1968)  When magnon and phonon branches “cross”, excitations are mixed.  An energy gap appears.  No magnon broadening expected

11. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 11 Magnon- Phonon Interactions (S. Lovesey, “Theory of Neutron Scattering from Condensed Matter systems,” sect. 9.8)  Linked to significant magnetoelastic interactions  Modulation of the exchange interaction: Lattice vibrations modulate can modulate J.  Two-ion coupling of lattice vibrations and spins. Magnon damping. (Lovesey)

12. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 12 Magnon- Phonon Interactions (S. Lovesey, “Theory of Neutron Scattering from Condensed Matter systems,” sect. 9.8)  Linked to significant magnetoelastic interactions  Modulation of the exchange interaction: Lattice vibrations modulate can modulate J.  Two-ion coupling of lattice vibrations and spins. Magnon damping. (Lovesey) Furukawa (J. Phys. Soc. Japan (1999)) k k-q q A magnon with k and  q decays into A phonon with q and  q and A magnon with k-q and  k-q

13. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 13 Magnon- Phonon Interactions (S. Lovesey, “Theory of Neutron Scattering from Condensed Matter systems,” sect. 9.8)  Linked to significant magnetoelastic interactions  Modulation of the exchange interaction: Lattice vibrations modulate can modulate J.  Two-ion coupling of lattice vibrations and spins. Magnon damping. (Lovesey) Furukawa (J. Phys. Soc. Japan (1999)) k k-q q A magnon with k and  q decays into A phonon with q and  q and A magnon with k-q and  k-q Damping when phonon and magnon branches “cross” Softening occurs

14. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 14 Institut Laue Langevin High Flux Reactor neutron source IN20 3-Axis Polarized neutrons

15. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 15 Magnons and phonons in LCMO  To separate magnons and phonons need polarized neutrons  Need to understand the phonon behavior  Polarized and unpolarized inelastic scattering experiments  Polarized neutrons:  IN20 at ILL  Half polarization and full polarization  Unpolarized neutrons: HB3 at HFIR

16. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 16 Full polarization analysis Triple Axis Spectrometer Define incident wavevector/energy Define final wavevector/energy Measure wavevector/energy change Neutron wavevector/energy change = sample (phonon/magnon) wavevector/energy Polarized neutrons Define incident/final neutron spin (polarization) Measure change in neutron spin = change in sample ang. momentum Magnon ang. mom. = 1 Phonon ang. mom. = 0 Heusler (111) – only reflects one neutron polarization

17. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 17 Horizontally focussed Heusler monochromator Vertically focussed PG (002) analyser PG Filter Soller Mezei flipper Helmholtz coil Half polarization: Holden-Stirling Method Holden-Stirling method (J. Phys. F 7, 1901, (1977)) Ferromagnet - saturate the magnetisation Measure with Q parallel M and P both parallel and antiparallel P-parallel = 0 x magnetic P-antiparallel = 4 x magnetic Nuclear (phonon) scattering is independent of P Take the difference to separate magnetic and nuclear Advantage --- don’t need a polarising analyser, use HOPG and have higher count rate

18. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 18 Half polarization: Holden-Stirling Method Holden-Stirling method (J. Phys. F 7, 1901, (1977)) Ferromagnet - saturate the magnetisation Measure with Q parallel M and P both parallel and antiparallel P-parallel = 0 x magnetic P-antiparallel = 4 x magnetic Nuclear (phonon) scattering is independent of P Take the difference to separate magnetic and nuclear Advantage --- don’t need a polarising analyser, use HOPG and have higher count rate P-parallel Nuclear P-antiparallel Nuclear + 4x Magnetic P-antiparallel - P-parallel = 4x Magnetic

19. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 19 Does the subtraction work?? Ferromagnet isn’t saturated Beam isn’t fully polarized Is it the same as fully polarized? Corrections for stray field in Mezei flipper? Fully polarized: Circles = (+, -), Squares = (-, +) Holden-Stirling (squares) Fully polarized (circles) Scale factor of 7.5 for analyzers [+background estimate from (-,+)]

20. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 20 [H,H,0] [0,0,L] M (0,0,2) (0,0,1) (1,1,0) Q q q Q M q Q Q q Polarized Neutron Measurements Magnetized along (001) Applied 2T field horizontal Heusler(111) → HOPG(002) Fixed E F =14.68 or 34.83meV Heusler(111) → Heusler(111) Fixed E F =34.83meV Magnetized along (-110) Applied 2T field vertical Heusler(111 ) → Heusler(111) Magnetized along (110) Applied 2T field horizontal Si(111) → Heusler(111) Fixed E F =34.83meV

21. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 21 Spin waves in LCMO30 MagneticNuclear

22. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 22 Spin waves in LCMO30

23. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 23 Spin waves in LCMO30

24. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 24 Spin waves in LCMO30 Linewidths

25. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 25 [H,H,0] [0,0,L] (0,0,2) (0,0,1) (1,1,0) Q q q Q eTeT eLeL (2,2,0) q eTeT Q Q q eLeL eTeT Measuring Longitudinal and Transverse Phonons Eigenvectors Longintudinal e L parallel to q Transverse e T perpendicular to q

26. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 26 Transverse phonon measurements – TA & TO 1 HB3 triple axis spectrometer at HFIR reactor, ORNL HOPG(002) – HOPG(002), fixed E F = 35meV [H,H,0] [0,0,L] (0,0,2) (0,0,1) (1,1,0)(2,2,0) q eTeT Q (3,3,0) q eTeT Large Q – magnetic form factor ~ 0 Transverse modes only.

27. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 27 (3,3,0) Zone TA modes have weak structure factor TO 1 is broad and ~ dispersionless over whole zone TO 1 – Optic Mode

28. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 28

29. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 29 Phonons in LCMO30 Recent experiment at HFIR Flat TO mode at E=20meV Strongly damped (FWHM =13meV) ·“External” mode not a MnO 6 mode but external vibration of La/Ca against MnO 6 octahedra

30. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 30 Phonons in LCMO30 Recent experiment at HFIR Flat TO mode at E=20meV Strongly damped (FWHM =13meV) LSMO Reichardt and Braden, Physica B (1999)

31. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 31 Spin waves in LCMO30 ·This TO is a “external” mode not a MnO6 mode but external vibration of La/Ca against MnO6 octahedra

32. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 32 Spin waves in LCMO30 Broadening occurs when SW branch “crosses” the phonon band

33. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 33 Magnon dispersion along [110]

34. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 34 Spin waves in LCMO30 Significant difference between the polarized and unpolarized measurements Unpolarized measurements do not separate both contributions (PSMO)

35. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 35 Spin waves in LCMO30 Magnon-phonon interaction expected to produce softening Magnitude of softening difficult to predict Fit to SW dispersion needs several neighbor coupling Fits not satisfactory up to order four (J1 and J4)

36. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 36 Summary  Half-polarized, full-polarized and unpolarized experiments to study the role of the phonons in the SW dispersion of LCMO30.  Half-polarized measurements essential to separate magnon and phonon contributions.  Holden Stirling method (horizontal H) very useful provided magnetic saturation is achieved.  SW broadening near zone boundary likely due to magnon-phonon interaction.  Magnitude of SW softening due to magnon- phonon interaction difficult to quantify.  Observed softening likely due to other origins.

37. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 37 Recent results on Sm 0.55 Sr 0.45 MnO 3 Endoh et al. Phys. Rev. Lett 94, 17206 (2005) Zone boundary magnons below the acustic phonon Fit with J1 and J4 J4 attributed to (3z 2 -r 2 ) orbital fluctuations

38. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 38 New experimental results In all cases there is a remarkable similarity of low energy spin waves Softening at zone boundary increases with doping