Spin structure and dynamics in the half-doped cobaltate La 1.5 Sr 0.5 CoO 4

ACNS 2004

Spin structure and dynamics in the half-Spin structure and dynamics in the half-doped cobaltate Ladoped cobaltate La1.51.5SrSr0.50.5CoOCoO44

CollaborationCollaboration

• J. Tranquada BNL• G. Gu BNL• R. Erwin NIST CNR• S.-H. Lee NIST CNR• Y. Moritomo CIRSE Nagoya Univ.

Igor A. ZaliznyakIgor A. Zaliznyak

Brookhaven National LaboratoryBrookhaven National Laboratory

ACNS 2004

OutlineOutline

• Crystal structure of La1.5Sr0.5CoO4 and electronic properties of Co2+/Co3+ ions in it

• Charge and spin order at half-doping– neutron-scattering signatures of charge and spin order– sample dependence of the short-range order

• Spin-freezing transition: critical slowing down of the spin dynamics

• Low-energy excitations in La1.5Sr0.5CoO4 – magnons– RIP:optic phonon, magnetic continuum?

• Summary

ACNS 2004

Crystal structure of the layered perovskite Crystal structure of the layered perovskite cobaltate around half-dopingcobaltate around half-doping

LaLa1.51.5SrSr0.50.5CoOCoO44 always (at all T)remains in “high-temperature tetragonal” (HTT) phase

Space group I4/mmm, lattice spacings aa≈≈3.833.83 Ǻ, cc≈≈12.512.5 Ǻ

Perfect “checkerboard” superstructure corresponds to a twice larger unit cell

2aax 2aaxcc, with space group F4/mmm.

ACNS 2004

LaLa1.51.5SrSr0.50.5CoOCoO44: bulk properties.: bulk properties.

Resistivity: activation behavior,Ea ~ 6000 K

Susceptibilivity: anisotropic, spin-glass-like behavior

T~30 KT~30 K

Moritomo et al (1997)

J~250-450 KJ~250-450 KD~400-900 KD~400-900 K

ACNS 2004

Charge and orbital order at half-dopingCharge and orbital order at half-doping

Possible checkerboard fillings of the eegg levels on a square lattice

In-plane “zig-zag” (3x2-r2) / (3y2-r2)

Out of plane (3z2-r2)

In-plane (x2-y2)

ACNS 2004

Electronic structure of CoElectronic structure of Co2+2+/Co/Co3+3+ ions in ions in LaLa1.51.5SrSr0.50.5CoOCoO44

CoCo2+2+ (3d7)

S=3/2

eg

t2g

CoCo3+3+ (3d6)

S=0 S=1 S=2

eg

t2g

ACNS 2004

Charge order in Charge order in LaLa1.51.5SrSr0.50.5CoOCoO44: neutron : neutron

diffuse elastic scatteringdiffuse elastic scattering

Short-range “charge glass” order, I. Zaliznyak, et. al., PRL (2000), PRB (2001)

cc = 0.62(6)cc abab= 3.5(3)a a 2

Al(1

11)

Al(2

00)

c

c

c

c

c

c

c

c

c c

ACNS 2004

Spin-entropy driven melting of the charge order in Spin-entropy driven melting of the charge order in LaLa1.51.5SrSr0.50.5CoOCoO44: neutron diffuse elastic scattering: neutron diffuse elastic scattering

Melting of the short-range “charge glass” order, I. Zaliznyak, et. al., PRB (2001)

CoCo2+2+ CoCo3+3+

z

x

x=0.011(1) lu, x=0.011(1) lu, z=0.0068(4) luz=0.0068(4) lu

ACNS 2004

Charge order and a spin systemCharge order and a spin system

CoCo2+2+ form a square-lattice AFM with almost critical frustration, JJ11~2J~2J22

JJ11

JJ22

CoCo2+2+

S=3/2 2D2D

CoCo3+3+

S=1or

S=2 S z = 0

S z = ±1DD

Strong single-ion anisotropy D~500 KD~500 K quenches CoCo3+3+ spin at low T

S z = ±1/2

S z = ±3/2

ACNS 2004

-2 0 2 4 6l (rlu)

0

200

400

600

800

1000

Neu

tron

cou

nts

mon

itor

=5.

0e+05

Spin order in Spin order in LaLa1.51.5SrSr0.50.5CoOCoO44: magnetic elastic : magnetic elastic

neutron scattering neutron scattering

-0.5 0.0 0.5 1.0 1.5 2.0h (r lu )

0

200

400

600

800

1000

Neu

tron

cou

nts

mon

itor

=5.

0e+

05

1122

33

44

55

66CoCo2+2+

““CoCo3+3+””

88

77

Q=(0.258(1),0,1)Q=(0.258(1),0,1), in I4/mmm abab=14.5(5)a a 2

cc=0.85(5)cc

mm

mm

mm

mm

Q = (h,h,1)

T=10K

Q = (0.258,0.258,l)

T=6K

E

μ

m

μ

mrN

dEdΩ

Ed

B

Bm

el

,1

12

1

12

022

coscosh

sinh

2

coscosh

sinh

2

,

aQq

q

aq

qq

Q

Lattice-Lorentzian scattering functionI. A. Zaliznyak and S.-H. Lee in “Modern Techniques for Characterizing Magnetic Materials”, ed. Y. Zhu (Kluwer)

ACNS 2004

Magnetic elastic scattering from the frozen Magnetic elastic scattering from the frozen spin structure in spin structure in LaLa1.51.5SrSr0.50.5CoOCoO44..

Lattice-Lorentzian scattering from a damped spin spiral in

the a-ba-b plane gives perfect fit to the measured intensity

Intensity map, calculatedfrom the fit

Al(

111)

Al(

200)

Al(

111)

Al(

200)

T=6 KT=6 K

ACNS 2004

Universal or sample-dependent?Universal or sample-dependent?

Sample #1, by

Y. Moritomo, m≈0.5g

Sample #2, by

G. Gu, m≈6g

ACNS 2004

Charge-order scattering from big new Charge-order scattering from big new sample #2sample #2

abab= 3.4(6)a a 2cc = 0.2cc(fixed)

Al(1

11)A

l(200)

x=0.011(1) lu, x=0.011(1) lu, z=0.0068(4) lu, z=0.0068(4) lu,

zzLa/SrLa/Sr=0.0010(1) lu=0.0010(1) lu

ACNS 2004

2500

2000

1500

1000

500

0

Inte

nsity

(co

unts

in 2

8 s)

0.0 0 .5 1 .0 1 .5h(rlu)

400

300

200

100

0

sam ple #2 = 0.255(1)

Al (

111)

Al (

200)

(a)

Al (

220)

sam ple #1 = 0.258(1)

(b)

,Q = ( ,3)

Magnetic scattering from two samplesMagnetic scattering from two samplesT=8K

T (K)

Q = (0.256,0.256,1)

abab=14.5(5)a a 2

abab=23.0(5)a a 2

ACNS 2004

Melting of the frozen spin order.Melting of the frozen spin order.

abab15 a a 2

cc0.9cc

abab8 a a 2

cc0.5cc

abab4 a a 2

cc0.2cc

6K6K

38K38K

50K50K

BT2&BT4, Ef=14.7 meV, 60’-20’-20’-100’.

ACNS 2004

Temperature evolution of the magnetic Temperature evolution of the magnetic scattering: raw data.scattering: raw data.

BT2&BT4, Ef=14.7 meV, 60’-20’-20’-100’. SPINS, Ef=3.7 meV, 40’-60’-60’-240’.

~40K?~40K?

~30K?~30K?

~40K?~40K?

~30K?~30K?

Where is the spin-ordering transition?

ACNS 2004

Slowing down of the spin fluctuations: is Slowing down of the spin fluctuations: is there a criticality?there a criticality?

EE~(T-T~(T-Tcc))

EE~T~T EE~ ~ 00+T+T

EE~ ~ 00+(T-T+(T-Tcc))

Although the critical behavior EE~(T-T~(T-Tcc)), =3.0(3)=3.0(3) is not ruled out, log(log(EE)) is surprisingly linear in log(T):log(T): EE~T~T with ~8 ~8 (!?).

log(log(EE)~log(T) )~log(T) ?? log(log(EE)~log(T) )~log(T) ??

ACNS 2004

Spin dynamics: acoustic magnonsSpin dynamics: acoustic magnons

ACNS 2004

RIP: scattering at higher energy: phonon, RIP: scattering at higher energy: phonon, magnetic continuum?magnetic continuum?

E (m eV )

0

5

10

15

20

Inte

nsit

y (c

ts/m

in)

0 10 20 30

(0.5,0.5,5)

(1.5,1.5,1)

phonon magnetic continuum?

0 100 200 300

5

10

15

Inte

nsi

ty (c

ts/m

in)

0

T (K )

E = 25 m eVQ = (0 ,0 ,5 )

ACNS 2004

RIP, dynamics in RIP, dynamics in LaLa1.51.5SrSr0.50.5CoOCoO44: acoustic : acoustic

magnons, optic phonon, magnetic continuum?magnons, optic phonon, magnetic continuum?

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30

h (rlu)

T = 5 K = (h,h,3)Q

v s in(2 (h - ) = 21.2(5), v = 0.244(1)

E (

meV

)

m agnetic scattering

phonon

ACNS 2004

SummarySummary

• A short-range checkerboard charge order yields a peculiar spin system in La1.5Sr0.5CoO4

• A short-range, incommensurate spin order results from the frustration and the lattice distortion– the incommensurability and the correlation length are slightly

sample dependent

• Static spin ordering: a spin-freezing transition at Ts ≈ 30 K– relaxation rate vanishes– correlation length saturates

• Dynamics at low E is dominated by a well-defined, strong band of acoustic magnons– crosses an optic phonon at 15 meV – interaction?

• Continuum magnetic scattering at 20 meV < E < 30 meV?

ACNS 2004

Exchange modulation by superlattice Exchange modulation by superlattice distortiondistortion

Heisenberg spin Hamiltonian

Superlattice distortion

Modulated-exchange Hamiltonian

(eg)

++

==

ACNS 2004

Spin-spiral ground state better adapts to Spin-spiral ground state better adapts to distortiondistortion

Harmonics at nQc are generated in spin distribution,

As a result, the MF ground state energy of a spin spiral is lowered

To the leading order,

In the presence of a superlattice distortion in the crystal antiferromagnetism may loose to a competing near-by spiral state

I. A. Zaliznyak, Phys. Rev. B (2003).