Neutron and X-ray Scattering Studies ofSpin, Charge and Orbital Order in TM Oxides

Andrew BoothroydDepartment of Physics, Oxford University

magnetization

resistivity

100

102

104

106

108

1010

0 50 100 150 200 250 300

La5/3Sr1/3NiO4

Res

ista

nce

(Ohm

)

Temperature (K)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0 50 100 150 200 250 300

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

H = 500 OeLa1.67Sr0.33NiO4

0 5 10 15 20

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

FC

ZFC

H = 50 Oe

× 10–3

0.50

0.49

0.48

La5/3Sr1/3NiO4

Transition Metal Oxide Research in Oxford Physics Department

Sample Preparation lab.

Single CrystalsDr Prabhakaran

Neutron ScatteringDr BoothroydDr ColdeaProf Cowley

Muon-spin RotationDr Blundell

X-ray scatteringDr Hatton (Durham)Prof Cowley

Characterization•Magnetization•Transport etc

Crystal growth — floating-zone method

Image furnace (Clarendon Laboratory)

Oxford single crystals of TM oxides

La5/3Sr1/3NiO4

La0.7Sr0.3MnO3

CoNb2O6

La3/2Sr1/2CoO4

Na0.7CoO2

Neutron scattering studies of stripe-ordered nickelates

D. Prabhakaran Oxford University

Paul Freeman

Mechthild Enderle Institut Laue-Langevin

Jiri Kulda

Arno Hiess

Louis-Pierre Regnault CEA, Grenoble,

Felix Altorfer Paul-Scherrer Institut, Switzerland

Christof Niedermayer

Chris Frost ISIS

Hyungje Woo Brookhaven National Lab/ISIS

Kenji Nakajima University of Tokyo

John Tranquada Brookhaven National Lab

collaborators

Outline

Overview of stripe phenomena in La2–xSrxNiO4

What can be learned by neutron diffraction ?

Interesting aspects of magnetic ordering

Interesting features in magnetic excitation spectra

Stripe order in La2–xSrxNiO4

L a (S r)

O

N i/C u

T (K

)

1 0 0

3 0 0

T C O

0

2 0 0

0 .10 0 .2 0 .3 0 .4 0 .5

S r c on ten t, x

L a S r N iO2 – 4x x

T N

‘g lassy’

T S

antiferro-magnetic

insula tor

charge stripeordered

spin-chargestripe ordered

insula tor

T S

x = 0

x = 1/4 x = 1/3 x = 1/2

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5

Hatton et al

Yoshizawa et alInco

mm

ensu

rabi

lity,

Sr doping, x

La2–xSrxNiO4

= x

(Tranquada et al, Cheong et al, Yoshizawa et al)

ideal stripe structures

Neutron Diffraction

Q k i

k f

Braggn = 2d sin

LaueQ =

(1) Scattering from nuclei

Q

Q = ki - kf

Applications:

• Crystal structure refinement

• Structural distortions (e.g. charge order)

Neutron diffraction

(2) Scattering from magnetic moments

V(r) = –n.B(r)

Neutrons scatter from component of magnetization perpendicular to Q

Q

m

m

No!

Yes!

Applications:

• Spin arrangements in ordered phases

• Magnetic form factors

Polarized neutron scattering

x

y

z

QP

1. P || Q

SF: Myy + Mzz

NSF: N

x

y

z

PQ

x

y

z

Q

P

2. P Q (in plane)

3. P Q (vertical)

SF: Mzz

NSF: N + Myy

SF: Myy

NSF: N + Mzz

Magnetic field defines polarization axis, P

Incident neutrons Scattered

neutrons

Spin-flip (SF)

Non-spin-flip (NSF)

Advantages of polarized neutron scatteringfor studying complex order

0

500

1000

1500

2000

2500

3000

0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37

SFNSF

neut

ron

coun

ts /

7 se

c

h (r.l.u.)

(h, h, 5)T = 14 K

kf = 2.662 Å–1

P || Q

static: charge vs magnetic order

dynamic: spin fluctuations vs phonons

1. Distinguishing magnetic and non-magnetic scattering

2. Separating different magnetic components

static: determining moment directions

dynamic: identifying anisotropy gaps and anisotropic fluctuations

La5/3Sr1/3NiO4

real space

Spin & charge order in La3/2Sr1/2NiO4

600

700

800

900

1000

1100

1200

1300

1400

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7

Inte

nsity

(cou

nts/

M1=

2000

0)

h (r.l.u.)

T 190 K

(1.5, 1.5, 1.15)

0

100

200

300

400

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7

SFNSF

Inte

nsity

(cou

nts/

M1=

2500

0)

h (r.l.u.)

(1.5, 1.5, 1.15)

T = 10 K

P || Q

0

500

1000

1500

2000

0.15 0.2 0.25 0.3 0.35

SFNSF

Inte

nsity

(cou

nts/

M1=

2500

0)

h (r.l.u.)

(h, h, 3)T = 10 K

P || Q

170 K < T < 460 K

‘checkerboard’ charge ordering

N i 2 +

N i 3 +

charge order magnetic orderT < 170 K spin & charge ordering

Not simple checkerboard pattern

Freeman et al, Phys. Rev. B 66 (2002) 212405

Kajimoto et al, Phys. Rev. B 67 (2003) 14511Half-doping:

• Correlation length 35 Å

T (K

)

1 0 0

3 0 0

T C O

0

2 0 0

0 .10 0 .2 0 .3 0 .4 0 .5

S r con ten t, x

L a S r N iO2 – 4x x

T N

‘glassy’

T S

antiferro-ma gnetic

insula tor

charge stripeordered

sp in-chargestripe ordere d

insula tor

T S

Models for spin-charge order in La3/2Sr1/2NiO4

Possible diagonal stripe pattern:

• Charge peaks at Qco = (½, ½) and ), 4/9

• Magnetic peaks at Qm = (½, ½) ± )

x x x x x x x x x x x x x x x x x x x x

x

N i sp in2+

O 2 – ion

h o le

ch e ck e rb o a rd

in co m m en su ra tes trip e

x x x x x x x x x x x x x x x x xx x x

Spin reorientations

1.1

1.15

1.2

1.25

1.3

1.35

1.4

0 20 40 60 80 100

Mag

netiz

atio

n (E

MU

per

mol

)

Temperature (K)

H = 500 OeH ll ab

FC

ZFC

TSR

TSO

30

40

50

60

70

80

90

0 20 40 60 80

Ang

le

from

stri

pe d

irect

ion

(deg

)

Temperature (K)

La2–xSrxNiO4

x = 0.37

x = 0.5

La3/2Sr1/2NiO4

La1.63Sr0.37NiO4

0.9

1

1.1

1.2

1.3

1.4

1.5

0 50 100 150 200 250 300 350

Mag

netiz

atio

n (E

MU

/ mol

)

Temperature (K)

H = 500 OeH ll ab

TSR

TSO TCO

FC

ZFC1.25

1.30

1.35

1.40

0 10 20 30 40 50

Mag

netiz

atio

n (e

mu/

mol

)

Temperature (K)

H = 500 OeH ll ab

TSR

FC

ZFC

Similar results for La5/3Sr1/3NiO4 reported by Lee et al, Phys. Rev. B 63 (2001) 60405(R)[TSR = 50 K, = 13 deg]

Overview of spin dynamics in La2–xSrxNiO4

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1

Dispersion || (h, h, 0)

Ene

rgy

(meV

)

h (r.l.u.)

real space

e.g. La5/3Sr1/3NiO4

Spin waves Gap-like features 2 components

Low energy quasi-1D spin fluctuation in La5/3Sr1/3NiO4

Diffuse inelastic scatteringScans along line A

Ni3+ ions (probably) carry spin S = ½ Consistent with quasi-1D AFM chains

0 0.1 0.2 0.3 0.4

neut

ron

coun

ts /m

onito

r=80

0,00

0

(r.l.u.)

2.5 meV

4 meV

6 meV

8 meV

2

4

6

8

× 103

(a)

0.1 0.15 0.2 0.25 0.3 0.35 0.40

2

4

6

8

10

12

(r.l.u.)

Energy (m

eV)

(0.08+, 1.08–, 0)

(b)

Scans along line B

Soft X-ray scattering studies of manganates

Peter Hatton University of Durham

Philip Spencer

Stuart Wilkins Institute of Transuranium Elements,Karlsruhe, and

European Synchrotron Radiation Facility, Grenoble

D. Prabhakaran Oxford University

Steve Collins Daresbury Laboratory

Mark Roper

collaborators

X-ray Scattering

Non-resonant scattering

• X-rays can probe charge density (Thomson) – very strong!

• X-rays also scatter from spin and orbital moments – very weak!

Resonant scattering

Strong enhancements at atomic absorption edges

• Resonant scattering from spin and orbital moments

• Element specific

• Higher-order ‘anomalous’ scattering processes observable

Examples of X-ray resonant magnetic scattering

Antiferromagnetic order in PrBa2Cu3O6+x

J.P. Hill et al, Phys. Rev. B 61 (2000) 1251

Cu K edge Pr LII edge

J.P. Hill et al, Phys. Rev. B 58 (1998) 11211

X-ray resonant scattering from Mn

1s

4p

EA = 6.55 keV

= 1.9 Å

K edge resonance

2p

3dEA = 0.65 keV = 19 Å

L edge resonance

Soft X-rays

Long period structures only

• Probes 3d orbitals directly• Very large resonant enhancements• Long wavelengths

Indirect probe of 3d magnetism

Daresbury Laboratory

• 2 GeV Machine

• 5U1 – Soft X-ray Undulator

• Good Sample Environment

• Awful Food

Soft X-ray scattering at 5U1, SRS

Air absorption at 650 eV is severe!

Soft X-ray resonant scattering from La2–2xSr1+2xMn2O7 (x = 0.45)

630 635 640 645 650 655 6600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Nor

mal

ised

Inte

nsity

[arb

.uni

ts]

Photon Energy [eV]

LIII

LII

T = 83 K

• Charge order between 120 K and 220 K• Antiferromagnetic order below 170 K

(001) AFM Bragg peak

80 100 120 140 160 180 200 2200

5

10

15

20

25

30

35

40

(0, 0, 1) AFM

Inte

grat

edIn

tens

ity[a

rb.u

nits

]

Temperature [K]

0

5

10

15

20

25

30

35

40(1.5, 0.5, 0) CO

Inte

grat

edIn

tens

ity[a

rb.u

nits

]

S.B. Wilkins et al Phys. Rev. Lett. 90 (2003) 187201

Orbital ordering in La0.5Sr1.5MnO4

Spin, charge and orbital order below 240 K;Jahn-Teller distortion very small

AFM order

Soft X-ray scattering & theory

(Castelton & Altarelli, Phys. Rev. B 62 (2000) 1033)

Theoretical predictions

No Jahn-Tellerdistortion

Strong JTdistortion

(¼, ¼, 0)

Soft X-ray resonant scatteringAt the orbital ordering Bragg peak

(S.B. Wilkins et al, to appear in Phys. Rev Lett.)

Conclusion: scattering is due to combined orbital ordering and cooperative Jahn-Teller distortions

Conclusions

• Spin and charge order – La3/2Sr1/2NiO4 not checkerboard!• Spin reorientations occur• Evidence for coupling of spin excitations to charge stripes• AFM spin correlations on the charge stripes

Neutron scattering studies of stripe-ordered nickelates

Soft X-ray studies of spin-charge-orbital ordered manganates

• Large resonant enhancements at L edge• Can probe ordering of 3d orbitals directly• Limited to ordering phenomena with period d > 10 Å• Jahn-Teller mechanism important in driving orbital order