Spin wave dispersion in the helical spin ordered system...
Transcript of Spin wave dispersion in the helical spin ordered system...
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C. Ulrich1, M. Reehuis1,2, G. Khaliullin1, V. Damljanovic1, Ch. Niedermayer3, A. Ivanov4, K. Schmalzl4, K. Hradil5, A. Schneidewind5, A. Maljuk1, and B. Keimer1
1Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany2Hahn-Meitner-Institut, Berlin, Germany
3Paul-Scherrer-Institut, Villigen, Switzerland4Institut Laue-Langevin, Grenoble, France
5FRM II, Munich, Germany
Spin wave dispersion in the helical spin ordered systemSrFeO3 and CaFeO3
Sydney, 26. 9. 2007
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LaMnO3: Mn3+, 3d4, t2g3eg
1
• insulator• cooperative Jahn-Teller distortion at 800K• commensurate , collinear spin structure
SrFeO3: Fe4+, 3d4, t2g3eg
1
• metal• cubic, no structural transition• incommensurate, helical spin structure
Metallic SrFeO3-δ
metallic conductivityhelical spin arrangement
eg- Orbital
t2g–Orbital
x2-y2 3z2-r2
x2-y2
3z2-r23z2-r2
yz xz xy
yz
xz
xyxy
Jahn-TellerAufspaltung
splittingcubic splitting tetragonal
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Crystal Structures of SrFeO3-δ
Oxygen Vacancy Ordered Phases
SrFeO2.75
orthorhombicCmmm
SrFeO2.875
tetragonalI4mmm
Hodges et al., J. Sol. State Chem. 2000.
cubic SrFeO3.00
ideal cubic perovskite:Pm3m (a = 3.85 Å)no distortion, no rotationof the FeO6 octahedra
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Annealing of CaFeO3
4 GPa hydrostatic pressure
2 hr at 10000 C
Annealing of SrFeO3
5 kbar O2-pressure
24 hr at 9500 C
High pressure single crystal annealing
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Magnetic Phase Transitions in SrFeO3-δ
0 50 100 150 200 250 3000,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
χ (em
u/m
ol)
SrFeO2.77
SrFeO2.81+0.01
SrFeO2.85+0.02
SrFeO3.00+0.04
Temperature (K)
SrFeO2.95+0.03
A. Lebon et al., PRL 92, 37202 (2004).
0 50 100 150 200 250 3000
5
10
15
20
25
30
orthorhombic T
N = 230 K
cubicT
N = 130 K
tetragonalT
N = 75 K
Asy
mm
etry
Temperature (K)
SrFeOx x=3.00 x=2.85 x=2.81 x=2.75
µSR
magnetic phase transitions:
TN1 = 130 K cubicTN2 = 75 K tetragonalTN3 = 230 K orthorhombic
Helical Magnetic Order
-single crystals (floating zone techique)-annealed under 5 kbar oxygen
cubic
tetragonal
orthorhombic
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independentup independentindependentupup
positive MRpositive MR
0T9T0T9T
Magnetoresistance Effects
upward shiftlarge negative MR
downward shiftgiant negative MR
positive MR
A. Lebon et al., PRL 92, 37202 (2004).
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SrFeO3-δ Mössbauer Spectra
SrFeO2.87 110K
30K
SrFeO2.87 110K
30K
SrFeO2.87 110K
30K
cubic SrFeO3.00 tetragonal SrFeO2.875
only Fe4+ present at all temperatures
pure spin rearrangement TN1 = 130 K, TN2 = 65 K ?
magnetic phase transition at 75 K is associated with charge ordering 2 Fe3.5+ => Fe3+ + Fe4+
A. Lebon et al., PRL 92, 37202 (2004).
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Fe3+/Fe4+ Charge Order in SrFeO2.875
Park et al., PRB 1999
different fromFe3+/Fe5+ charge orderin La1/3Sr2/3FeO3, CaFeO3
magnetoresistance around CO transition: similar to Verwey transition in Fe3O4
Gridin et al., PRB 1996
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-0.2 -0.1 0.0 0.1 0.2
15 K
Log.
Int
ensi
ty
(cnt
s / 3
3 se
c)
Qhkl (0,0,1)
140 K
130 K
100 K
60 K
cubic SrFeO3.00
(110)
(001)
0 20 40 60 80 100 120 140 160 1800
5
10
15
20
25
30
Inte
grat
ed In
tens
ity
(cnt
s / 3
3 se
c)
Temperature (K)
0 20 40 60 80 100 120 140 160 1800.095
0.100
0.105
0.110
0.115
0.120
0.125
0.130
Del
ta
δ
Temperature (K)
Elastic Neutron Scattering in cubic SrFeO3.00
helical spinarrangement
TN1 = 130 K magnetic „satellite“ peaks around structural Bragg reflections propagation vector along the [111]-direction µ = 2.48 µB/Fe4+-ionTN2 = 65 K but change in the magnetic correlation length at 65 K weak additional magnetic Bragg peaks at (0, 0, 1/4 )
0 25 50 75 100 125 150 1750
50
100
150
200
250
corr
elat
ion
leng
th
( Å
)
Temperature (K)
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Inelastic Neutron Scattering in cubic SrFeO3.00
cubic SrFeO3.0
Metalnegative magnetoresistance 65 Khelicale spin order TN = 130 Kno charge order
Helix: δ = 0.131.2 – 3.8 meV
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Inelastic Neutron Scattering
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
T = 4 K
7 meV
6 meV
5 meV
4 meV
3 meV
SrFeO2.875
tetragonal
Inte
nsity
(c
nts
/ 100
sec
)
(Qh, Q
K, 1+Q
L)
Tetragonal SrFeO2.875
magnetic Bragg Peaks at δ = 0.2
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Inelastic Neutron Scattering
Cubic CaFeO3.0
magnetic Bragg Peaks at δ = 0.16
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
500
1000
1500
2000
2500
3000
CaFeO3
3 meV
4 meV
5 meV
6 meV
7 meV
8 meV
9 meV
2 meV
Inte
nsity
(c
nts
/ 80
sec)
(QH, Q
K, 1+Q
L)
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Inelastic Neutron Scattering
cubic SrFeO3.0
Metalnegative magnetoresistance 65 Khelicale spin order TN = 130 Kno charge order
Insulatornegative magnetoresistancehelical spin order TN = 75 Kcharge order at TN = 75 K
CaFeO3.0tetragonal SrFeO2.875
Metal-Insulator Transitionno magnetoresistance effecthelical spin order TN = 125 Kcharge disprop. at TN = 290 K
Helix: δ = 0.131.2 – 3.8 meV
Helix: δ = 0.202.2 – 7.8 meV
Helix: δ = 0.162.0 – 6.0 meV
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Strong hybridization of the Fe-eg and O-σ orbitals
M. Mostovoy (PRL 94, 137205 (2005))
t2g
eg
t2g
eg
3d4 3d L5 oxygen p
∆ pd < 0 (- 3 eV)photoemissionBocquet (1992)
charge transfer energy
large negative charge transfer energy ∆pd
for the eg hole, both spin directions are possible
mixing of both states results in a further lowering of the ground state
helical spin arrangement is preferred- 6
- 4
- 2
0
2
Γ Χ Μ R Γ
Ener
gy
(eV
)
Bands for a fictitious FM state
- spin-down dp-holes- spin-up p-holes
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xx x x(U/t)cr U/t
SrFeO3 CaFeO3 LaMnO3
helical AFMT = 130 Kno orbital order
N
helical AFMT = 125 Kcharge orderbelow 290 K
N
A-type AFMT = 140 Korbital order below 780 K
N
InsulatorFMDE
Metal»SE
AFMorbital order
critical
Double Exchange versus Superexchange
cubic SrFeO3.00: - no Jahn-Teller distortion - no orbital order - metallic conductivity of the 3d-Fe4+ electrons enhances the Double Exchange interaction - Superexchange in LaMnO3 and SrFeO3
is comparable
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Model for helical spin arrangement
Let’s consider a cubic crystal with:
J = ij J AFM for the 6 nearest neighbors- J FM for the 12 next nearest neighbors
1
2{
J(q) = [cos(q a) + cos(q a) + cos(q a)] -
- [cos(q a)cos(q a) +
x y z
x y cos(q a)cos(q a) + cos(q a)cos(q a)]y z z x
2J1
N4J2
N
This exchange interaction has a minimum when:
a = cos ( + y + z)Q -1 X J1
4J2
^ ^^
If J < 4J the spin configuration has an incommensurate wavelength with the lattice spacing.
Helical spin arrangement can arise if we have two competing interactions: short range versus long range
1 2
J = Superexchange Fe-O AFM-J = Double Exchange Fe-Fe FM
1
2
P.-G. De Gennes,PR 118, 141 (1960)
J
⇒ Competition between Double Exchange and Superexchange
results in a helical spin structureFe
O
J4J4
J22
J1J1
Fe
O
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Double-exchange / Super-exchange
J = J + J (U, )J = J ( ) (2t/ )2J = J /2
1 DE SE pd
4 1 pd pd
2 4
∆∆ ∆
Fe
O
J4J4
J22
J1J1
Fe
O
Charge fluctuations:
Double-exchange: JDE
Super-exchange: JSE
resulting magnonen-dispersion.Fit of J2 and θ to the experimental data.
excellent aggrement for allother directions in the Brillouin zone.
P.-G. De Gennes, PR 118, 141 (1960)improved model G. Khaliullin (2006)
0.00 0.05 0.10 0.15 0.20 0.25 0.300
2
4
6
8
10
12
Ener
gy
(meV
)
(Qh+1, QK, QL)
cubic SrFeO3 Θ = 47 J2 = 0.34 meV tetra. SrFeO
2.875 Θ = 72 J2 = 0.34 meV
CaFeO3 Θ = 58 J2 = 0.45 meV
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500
5
10
15
20
25
30
35
40
45
50
55
En
ergy
(m
eV)
(Qh+1, QK, QL)
cubic SrFeO3 Θ = 47 J2 = 0.34 meV tetra. SrFeO
2.875 Θ = 72 J2 = 0.34 meV
CaFeO3 Θ = 58 J2 = 0.45 meV
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Double-exchange / Super-exchange
0.00 0.05 0.10 0.15 0.20 0.25 0.300
2
4
6
8
10
12
Ene
rgy
(m
eV)
(Qh+1, QK, QL)
cubic SrFeO3 Θ = 47 J2 = 0.34 meV
tetra. SrFeO2.875
Θ = 72 J2 = 0.34 meV CaFeO
3 Θ = 58 J2 = 0.45 meV
0.0 0.1 0.2 0.3 0.4 0.50
5
10
15
20
25
30
35
40
45
50
55
Ene
rgy
(m
eV)
(Qh+1, QK, QL)
cubic SrFeO3 Θ = 47 J2 = 0.34 meV
tetra. SrFeO2.875 Θ = 72 J2 = 0.34 meV CaFeO3 Θ = 58 J2 = 0.45 meV
Fit to the data of tetragonal SrFeO2.875 and CaFeO3
- extrapolation for cubic SrFeO3
- found high energy branch of tetragonal SrFeO2.875
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Conclusions: SrFeO3-δ
rich electronic phase diagram:
cubic SrFeO3.00
tetragonal SrFeO2.875
-TN1 = 130 K helical spin arrangement no CO, no OO-TN2 = 65 K comensurate spin structure
large magnetoresistance effect no CO, no OO
-TN = 75 K helical spin arrangement charge order 2 Fe3.5+ => Fe3+ + Fe4+
huge negative MR effect
metallic
insulating
tetragonal CaFeO3.0 metal-insulator transition-TN = 125 K helical spin arrangement-TCO = 290 K charge order 2 Fe4+ => Fe3+ + Fe5+
no MR effect
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Conclusions: Ferrates
Charge fluctuations at the borderline of the metal - insulator transition are the reason for the different electronic properties.
Spin structures and magnon dispersion relationsare almost identical in the Ferrates
Interplay between
Double-Exchange and Super-Exchange
Consequence: helicale spin-order
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Outlook: bilayer Sr3Fe2O7
As-grown Sr3Fe2O7-x boule – grown by A. Maljuk
0 50 100 150 200 250 3000.00
0.01
0.02
0.03
0.04
0.05
0.06
mag
netic
sus
cept
ibili
ty, e
mu/
mol
.
Temperature, K.
as-grown Sr3Fe2O7-x crystal, 10 Oe.
T1=78 K
T2=115 K T3=148 K.
annealed Sr3Fe2O7-x crystal, 10 Oe.
Magnetic susceptibility of the Sr3Fe2O7-x crystal.
Ruddlesden-Popper SeriesSrFeO3-x, Sr3Fe2O7-x and Sr2FeO4-x
Sr3Fe2O6.88
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Outlook: bilayer Sr3Fe2O7
0 20 40 60 80 100 120 140 160 180 2000
200
400
600
800
1000
1200
1400
1600
1800
Inte
nsity
(c
nts
/ 12
sec)
Temperature (K)
Int1 Int3
0 20 40 60 80 100 120 140 160 180 2000.7
0.8
0.9
1.0
1.1
1.2
1.3
Pos
ition
(Q
H, 0
, 0 )
Temperature (K)
0.6 0.8 1.0 1.2 1.40
200
400
600
800
1000
1200
1400
1600
1800
2000
1 234 56 78910111213141516171819202122232425262728293031323334353637
3839
404142
43
4445
464748495051525354555657585960616263646566676869707172737475767778798081ABCDEFGH I JKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAK
ALAM
AN
AOAPAQ
AR
ASAT
AUAVAWAXAYAZBABBBCBDBEBFBGBHBIBJBKBLBMBNBOBPBQBRBSBTBUBVBWBXBYBZCACBCCa b cd e f gh i j k l mn opq r s t u vwx y zaaabacadaeafagahaiaj
akalam
anaoap
aq
ar
asatauavawaxayazbabbbcbdbebfbgbhbibjbkblbmbnbobpbqbrbsbtbubvbwbxbybzcacbcc
nuclear
magnetic
magneticSr3Fe2O7
Inte
nsity
(c
nts/
12 s
ec)
(QH, 0, 0 )
Sr3Fe2O6.88
Elastic Neutron Scattering along the a-axis
δ = 0.25
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Outlook: bilayer Sr3Fe2O7
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Group: Prof. B. Keimer
A. Lebon
G. Khaliullin, M. Mostovoy,
A. Maljuk, P. Balock, C.T. Lin
Max-Planck-Institut FKF, Stuttgart, Germany.
Max-Planck-Institut FKF, Stuttgart, Germany.
Max-Planck-Institut FKF, Stuttgart, Germany
Max-Planck-Institut FKF, Stuttgart, Germany.
Magnetoresistance
Mössbauer Spectroscopy
Ellipsometry
P. Adler
A. Boris, C. Bernhard, A.V. Pimenov
Universität Karlsruhe, Germany.
Max-Planck-Institut FKF, Stuttgart, Germany.
.
Theory:
Crystal Growth:
M. Rheinstaedter, W. Schmidt,
D. Reznik,
Institut Laue-Langevin, Grenoble, France.
Laboratoire Léon Brillouin, Saclay, France.
M. Reehuis,
B. Ouladdiaf
Hahn-Meitner-Institut, Berlin, Germany.
Institut Laue-Langevin, Grenoble, France.
Inelastic neutron scattering:
Neutron diffraction:
Ch. Niedermayer, N. Cavadini, Paul-Scherrer Institut, Villigen Switzerland.
Ch. Niedermayer, C. BernhardPaul-Scherrer Institut, Villigen Switzerland.Max-Planck-Institut FKF, Stuttgart, Germany.
Transversal Field µSR
ILL
HMI
LLB
PSI
ILL
PSI
FRM II K. Hradil, A. SchneidewindFRM II, Munich, Germany
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7x104
8x104
9x104
10x104
11x104
12x104
13x104
14x104
0 50 100 150 200 2500
50
100
150
200
250
47x104
48x104
49x104
50x104
51x104
52x104
53x104
54x104
0 50 100 150 200 250 3000
300
600
900
1200
1500
SrFeO2.84 SrFeO2.95
(0, 0, 2)
Inte
nsity
(c
nts
/ 10
sec)
(0.13, 0.13, 1.13)
Inte
nsity
(c
nts
/ 10
sec)
Temperature (K)
(0, 0, 2)
(0.13, 1.13, 0.13)
Temperature (K)
Elastic Neutron Scattering: SrFeO3-δ
- phase mixture: tetragonal/cubic
- magnetic moment: 2.48(2) µB / Fe4+-ion
- evidence for a structural phase transition in the tetragonal phase below 75 K
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0 20 40 60 80 100 120 140
0
20000
40000
60000
80000
100000
120000
140000
160000
pure cubic ?
(111
)
(002
)
(012
) (112
)
(022
)
(011
)
(003
)
(001
)
S3
Inte
nsity
(
cnts
/ 3
.3 s
ec)
2 Theta
y.cubic y.tetra y.ortho 2 K 200 K
0 10 20 30 40 50 600
20
40
60
80
100
120
(0, 0
, 0.7
5)
(0, 0
, 0.2
5)
Inte
nsity
(c
nts
/ 3.3
sec
)
2 Theta
y.cubic y.tetra y.ortho 2 K 200 K
Elastic Neutron Scattering in cubic SrFeO3.00
ratiotetragonal : cubic
sample 1 30 : 70 %sample 2 50 : 50 %sample 3 (cubic) 90 : 10 %
in agreement to the volume fractionsobtained from zero field µSR
tetragonal : cubic
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J = Superexchange Fe-O AFM-J = Double Exchange Fe-Fe FM
1
2
Takeda et al. (JSSC, 1996)
J = 1.2 meVJ = - 0.2 meVJ = - 0.3 meV
1
2
4
{
J4
J2
J1
Fe
O
Model for helical spin arrangement
⇒ Competition between Double Exchange and Superexchange
J1 = Superexchange Fe-O AFM-J2 = Double Exchange Fe-Fe FM
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-0.2 -0.1 0.0 0.1 0.2
15 K
Log.
Int
ensi
ty
(cnt
s / 3
3 se
c)
Qhkl (0,0,1)
140 K
130 K
100 K
60 K
cubic SrFeO3.00
(110)
(001)
Elastic Neutron Scattering in cubic SrFeO3.00
helical spinarrangement
TN1 = 130 K magnetic „satellite“ peaks around structural Bragg reflections propagation vector along the [111]-direction µ = 2.48 µB/Fe4+-ionTN2 = 65 K additional Bragg reflections appear at (0, 0, ¼) doubling of the structural unit cell + antiferromagnetic order ?
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
10
20
30
40
50
60
70
T = 15 K T = 175 K
Inte
nsity
(c
nts
/ 22
sec)
(0, 0, Q l)
0 10 20 30 40 50 60 70 80 90 100 110 120 1300
2
4
6
8
10
12
14
16
18
20
22
24
26
Inte
nsity
(
cnts
/ 3
3 se
c)
Temperature (K)
(0 0 -0.75)
(0,0
, ¼)
(0,0
, ¾)
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The orbital degeneracy in ground state is lifted by: - Jahn-Teller coupling - Superexchange interaction - Spin-orbit coupling
Splitting of the 3d levels
LaMnO3 Mn3+
3d4, t2g3 eg
1
Hund‘s Rules: S = 2
eg- Orbital
t2g–Orbital
x2-y2 3z2-r2
x2-y2
3z2-r23z2-r2
yz xz xy
yz
xz
xyxy
Jahn -TellerAufspaltung
splittingcubic splitting tetragonal