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Spin structure and dynamics in the half-doped cobaltate La 1.5 Sr 0.5 CoO 4. Igor A. Zaliznyak Brookhaven National Laboratory. Collaboration J. Tranquada BNL G. Gu BNL R. Erwin NIST CNR S.-H. Lee NIST CNR Y. Moritomo CIRSE Nagoya Univ. Outline. - PowerPoint PPT Presentation
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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
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).