Structure & Magnetism of Structure & Magnetism of LaMnLaMn1-1-xxGaGaxxOO33

J. Farrell & G. A. GehringJ. Farrell & G. A. GehringDepartment of Physics and AstronomyDepartment of Physics and Astronomy

University of SheffieldUniversity of Sheffield

ContentsContents

• Why LaMnWhy LaMn1-1-xxGaGaxxOO33??• Theory: postulates and assumptionsTheory: postulates and assumptions• Lattice parametersLattice parameters →→ Orthorhombic strain; cell volumeOrthorhombic strain; cell volume• MagnetisationMagnetisation• ConclusionsConclusions

Why LaMnWhy LaMn1-1-xxGaGaxxOO33??• LaMnOLaMnO33: parent compound of many CMR : parent compound of many CMR

manganites.manganites.• Typically, the MnTypically, the Mn3+3+ is replaced by Mn is replaced by Mn4+4+: : →→ LaLa1-1-xxCaCaxxMnOMnO33, La, La1-1-xxSrSrxxMnOMnO33

• Electron hopping betweenElectron hopping between MnMn3+ 3+ and Mnand Mn4+4+

→→ Double exchangeDouble exchangeSo, any observed effects may be attributed to:So, any observed effects may be attributed to:

• Introduction of MnIntroduction of Mn4+4+

• Removal of MnRemoval of Mn3+3+

LaMnLaMn1-1-xxGaGaxxOO3 3 (LMGO)(LMGO)• To investigate To investigate onlyonly the removal of Mn the removal of Mn3+3+, dope , dope

LaMnOLaMnO33 with “vacancies” with “vacancies”• Try Try GaGa3+3+

• DiamagneticDiamagnetic (unlike Mn (unlike Mn3+3+))• Jahn-Teller inactiveJahn-Teller inactive (unlike Mn (unlike Mn3+3+))• Any disorder will be negligibleAny disorder will be negligible → → rrGa Ga = 76 pm; = 76 pm; rrMn Mn = 78.5 pm= 78.5 pm

Could also try ScCould also try Sc3+ 3+ or Alor Al3+3+ but there is more data but there is more data for LMGO (~ 7 experimental papers)for LMGO (~ 7 experimental papers)

LaMnOLaMnO33 →→ LMGO LMGO

• Long-range, static, Jahn-Teller Long-range, static, Jahn-Teller ordering of the Mnordering of the Mn3+3+ eegg orbitalsorbitals

• Long-range AFM is a Long-range AFM is a direct direct consequenceconsequence of orbital ordering.of orbital ordering.

• GKA predictions:GKA predictions:

Mn O Mn Mn O Mn Mn O Mn

LMGO, LMGO, x < x < 0.5: d0.5: dMM/d/dx > x > 00→ → Orbital flipping; FM evolution along Orbital flipping; FM evolution along zz..

Orbital FlippingOrbital Flipping

• Random Ga-doping causes the Random Ga-doping causes the x x or or y y orbitals to flip into the orbitals to flip into the z z direction.direction.

• Significant Significant elastic elastic energy energy penalty forbids strong overlap.penalty forbids strong overlap.

Khomskii D. I. & Kugel K. I.

PRB 67, 134401

z

Orbital FlippingOrbital Flipping

Forbidden scenario FM Coupling

y

x

z

x

Lattice ParametersLattice Parameters

• Bond lengths from neutron diffraction: Bond lengths from neutron diffraction: Blasco Blasco et al.et al., PRB , PRB 6666, 174431, 174431

• Ga-O = Ga-O = 1.97 1.97 ǺǺ; Mn-O = ; Mn-O = 1.92 Ǻ1.92 Ǻ (compression) (compression)• JT: Mn-O = JT: Mn-O = 1.901.90 and and 2.18 Ǻ2.18 Ǻ (LaMnO (LaMnO33))• Gallium-doping: long-range, static JT is Gallium-doping: long-range, static JT is

suppressed but suppressed but local, static JT persistslocal, static JT persists..• Simulations on Simulations on L = L = 10 cubic lattice with 10 cubic lattice with

periodic boundary conditions.periodic boundary conditions.

Lattice ParametersLattice Parameters

b

a

2/c

• OO´→ O stuctural transition at ´→ O stuctural transition at x ≈ x ≈ 0.550.55• Good agreement with experimental results.Good agreement with experimental results.

Lattice ParametersLattice Parameters

b

a

2/c

Experimental data: Blasco et al., PRB 66, 174431

Lattice ParametersLattice Parameters

b

a

2/c

• OO´→ O structural transition at ´→ O structural transition at x ≈ x ≈ 0.550.55

Blasco et al., PRB 66, 174431

Orthorhombic StrainOrthorhombic Strain

εε = 2 = 2((b – ab – a)/()/(b b + + aa)): Vertruyen : Vertruyen et al.et al., , Cryst. Eng.Cryst. Eng., 5, 5, 299, 299

Cell VolumeCell VolumeV = abcV = abc:: Vertruyen Vertruyen et al.et al., , Cryst. Eng.Cryst. Eng., 5, 5, 299, 299

MagnetisationMagnetisation

• Competition between FM and AFM bonds Competition between FM and AFM bonds may lead to frustration. Suggestions of:may lead to frustration. Suggestions of:• Spin glassSpin glass (Zhou (Zhou et al.et al., PRB , PRB 6363, 184423), 184423)• Spin cantingSpin canting (Blasco (Blasco et al.et al., PRB , PRB 6666, 174431), 174431)• Spin flippingSpin flipping (this work). (this work).

Monte Carlo SimulationsMonte Carlo Simulations• 10000 MCS/S.10000 MCS/S.• JJFM FM = = 9. 6 K9. 6 K, , JJAFM AFM = = - 6.7 K- 6.7 K..• T = T = 5 K5 K; ; B = B = 5.5 T5.5 T applied along easy axis. applied along easy axis.• Spins Spins ↑↑ or or ↓↓ only; no canting. only; no canting.• At large At large xx, assume that , assume that M M evolves due to evolves due to

percolation.percolation.• Isolated Mn contribute negligibly to Isolated Mn contribute negligibly to M.M.• nn Mn couple ferromagnetically (4 nn Mn couple ferromagnetically (4 µµBB each). each).

ResultsResults

• Obvious discrepancy at Obvious discrepancy at x = x = 0 accounts for canting.0 accounts for canting.• Broad plateau is not observed; Broad plateau is not observed; M M peaks at peaks at x = x = 0.5.0.5.• At small At small x, x, ddMM/d/dx x is predicted well.is predicted well.• At large At large x,x, percolation assumption is only qualitatively correct. percolation assumption is only qualitatively correct.

00.5

11.5

22.5

33.5

4

0 0.2 0.4 0.6 0.8 1

x

M (µ

B/M

n)

Vertruyen et al., Cryst. Eng., 5, 299

Simulation

Spin FlippingSpin Flipping• At small At small x, x, Gallium may be placed on Gallium may be placed on ↑↑ or or ↓.↓.

→ → Good estimation of linearity at small Good estimation of linearity at small xx (~ (~ 16 16 µµBB/Ga)/Ga)

+ 12 + 12 µµBB + 20 + 20 µµBB

z

ConclusionsConclusions• LaMnLaMn1-1-xxGaGaxxOO3 3 is an ideal system in which the is an ideal system in which the

disruption of long-range orbital- and magnetic- disruption of long-range orbital- and magnetic- order can be investigated.order can be investigated.

• Orbital flipping (local-JT) correctly describes Orbital flipping (local-JT) correctly describes the evolution of the lattice parameters.the evolution of the lattice parameters.

• The magnetism depends on the orbital orderThe magnetism depends on the orbital order→ → Orbital ordering is paramountOrbital ordering is paramount• Magnetisation successfully described in terms Magnetisation successfully described in terms

of spin-flipping.of spin-flipping.