# Presentation: 530813

## Polarized inelastic neutron scattering in the CMR manganite La0.70Ca0.30MnO3

**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++

## Polarized inelastic neutron scattering in the CMR manganite La0.70Ca0.30MnO3

**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**

## COLOSSAL MAGNETORESISTANCE MANGANITES

- Cubic perovskite
- La/Ca in A site
- Substitution of Ca2+ for La3+
-  leads to  mixed Mn3+ /Mn4+.

**La****1-x****Ca****x****MnO****3**

**Double exchange**

## Spin-wave excitations – Double exchange (DE)

*t*  electron hoping

*J**H*  Hund coupling between localized t2g electrons (*S*=3/2) and eg 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

## Spin waves in CMR manganites Ln1-xAxMnO3 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

## Spin waves in CMR manganites Ln1-xAxMnO3 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))

## Spin waves in CMR manganites Ln1-xAxMnO3 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**

## 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).**

## 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).**

## 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

## 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)

## 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**

## 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

## Institut Laue Langevin

- High Flux Reactor neutron source

## 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

## 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

## Half polarization: Holden-Stirling Method

_**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

## 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

## 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 (-,+)]**

## Polarized Neutron Measurements

_**Polarized Neutron Measurements**_

## Spin waves in LCMO30

**Magnetic**

**Nuclear**

## Spin waves in LCMO30

## Spin waves in LCMO30

## Spin waves in LCMO30

_**Linewidths**_

## Measuring Longitudinal and Transverse Phonons

_**Measuring Longitudinal and Transverse Phonons**_

_**Eigenvectors**_
**Longintudinal**
_**e**_**L**** parallel to **_**q**_
_**Transverse**_
_**e**_**T**** perpendicular to **_**q**_

## Transverse phonon measurements – TA & TO1

**Transverse phonon measurements – TA & TO****1**
- HB3 triple axis spectrometer at HFIR reactor, ORNLHOPG(002) – HOPG(002), fixed EF= 35meV

## TO1 – Optic Mode

**(3,3,0) Zone**
**TA modes have weak****structure factor**
**TO****1**** is broad and ~****dispersionless over****whole zone**

**TO****1**** – Optic Mode**

## Slide 28

## 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**

## Phonons in LCMO30

_**Recent experiment at HFIR**_
- Flat TO mode at E=20meV
- Strongly damped
- (FWHM =13meV)

- LSMO
- Reichardt and Braden, Physica B (1999)

## Spin waves in LCMO30

**This TO is a “external” mode not a MnO6 mode but external vibration of La/Ca against MnO6 octahedra**

## Spin waves in LCMO30

- Broadening occurs when SW branch “crosses” the phonon band

## Magnon dispersion along [110]

_**Magnon dispersion **__**along [110]**_

## Spin waves in LCMO30

- Significant difference between the polarized and unpolarized  measurements
- Unpolarized measurements do not separate both contributions (PSMO)

## 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)

## 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.**

## Recent results on Sm0.55Sr0.45MnO3

- Endoh et al. Phys. Rev. Lett 94, 17206 (2005)

- Zone boundary magnons below the acustic phonon
- Fit with J1 and J4
- J4 attributed to (3z2-r2) orbital fluctuations

##  New experimental results

- In all cases there is a remarkable similarity of low energy spin waves
- Softening at zone boundary increases with doping