Transcript Physics of multiferroic hexagonal manganites RMnO 3

Physics of multiferroic
hexagonal manganites
RMnO3
Je-Geun Park
Sungkyunkwan University
KIAS 29 October 2005
Outline
• Introduction
• Part 1: Phonon scattering due to short-ranged spin
fluctuations of YMnO3
• Part 2: Direct evidence of coupling among spin, lattice,
and electric dipole moment for YMnO3 and LuMnO3
• Part 3: Doping and Pressure effects on the magnetic
structure
• Summary
What is multiferroic behavior?
Ferroelectricity
Ferromagnetism
10
M[emu/g]
5
2K
300K
0
-5
-10
-2
-1
0
1
Magnetic Field [T]
Fe3O4
2
PbTiO3
Examples : Ni3B7O13I, BiMnO3, BiFeO3, RMnO3
(R=Ho-Lu, Sc, Y), RMn2O5 (R=Tb,Dy)
Renaissance of Multiferroic
N. A. Spaldin and M. Fiebig
Science (2005)
• Multiple State Memory Device
• Write E / Read M
• Write M / Read E
• Magnetic valve
• Data storage
• Tunable sensors
• Spin transistor
Key Issue : Coupling among P, M, and e
Control of Magnetic Phase by E
HoMnO3
E
T. Lottermoser et al.,
Nature (2004)
(a)
1 kHz
26
Controlling
Polarization by
Magnetic field
3K
e
24
22
20
40
20
0
-20
-40
28 K
+
-
H
3K
0
(c)
+ +
2
4
H (T)
++
6
- b
Pn + c
+
a
8
2
40
2
P (nC/cm )
N. Hur, S.-W. Cheong et
al., Nature (2003)
Pn -
20
0
1
-20
-40
0
1000
2000 3000
Time (sec)
4000
0
H (T)
2
P (nC/cm )
(b)
28 K
A similar demonstration
was presented by
Prof. Tokura’s group for
TbMnO3. see T. Kimura
Nature (2003)
Multiferroic Hexagonal
Manganites RMnO3
Summary of properties of
Hexagonal Manganites
antiferromagnet
ferroelectric
ic ordering
ordering
temperature (K) temperature (K)
a (Å)
c (Å)
ScMnO3
129
~ 900
5.833 11.17
YMnO3
80
914
6.139 11.39
HoMnO3
76
~ 900
6.142 11.42
ErMnO3
80
830
6.112 11.40
TmMnO
86
~ 900
6.092 11.37
YbMnO3
87
983
6.062 11.36
LuMnO3
96
~ 900
6.042 11.37
3
Multiferroic Behavior
Ferroelectric
Antiferromagnetic
Wo-chul Yi et al.Appl. Phys. Lett., (1998)
T.Katsufuji et al., PRB (2001)
AMnO3
Hexagonal structure
O1
Othorhombic structure
O3
O4
O2
Crystal field level of
Orthorhombic manganites
Hexagonal manganites
3z2-r2
x2-y2
eg
3z2-r2
3+
Mn
eg
1.7 eV : IR
5~6 eV : PES
xy x2-y2
t2g
xy
xz ,yz
Jahn-Teller active
t2g
xz yz
Jahn-Teller inactive
J. S. Kang, JGP et al., PRB 71, 092405 (2005)
Origin of FE transition?
antiferromagnet
ferroelectric
ic ordering
ordering
temperature (K) temperature (K)
a (Å)
c (Å)
ScMnO3
129
~ 900
5.833 11.17
YMnO3
80
914
6.139 11.39
HoMnO3
76
~ 900
6.142 11.42
ErMnO3
80
830
6.112 11.40
TmMnO
86
~ 900
6.092 11.37
YbMnO3
87
983
6.062 11.36
LuMnO3
96
~ 900
6.042 11.37
3
Origin of FE transition?
The ferroelectric instability is due
to Y-O displacement, which is
accompanied by MnO5 rotation.
See B. van Aken et al., Nature
Materials (2004)
2D Triangular lattice of Mn moments
Mn O1
O3
O4
O2
Irreducible representations
G1 representation
G3 representation
G2 representation
G4 representation
A. Munoz et al., PRB (2000)
Magnetic structure YMnO3
G1
G1
4
0
G3
a (Å) = 6.1208(1)
b (Å) = 11.4015(2)
V (Å3) = 369.91(1)
a (Å) = 6.1208(1)
b (Å) = 11.4015(2)
V (Å3) = 369.91(1)
Magnetic Moment (mB)
3.30(2)
Magnetic Moment (mB)
3.25(2)
Reliability factors
Rp = 5.79 %
Rwp = 7.93 %
Rmag = 7.88 %
c2 = 2.70
Reliability factors
Rp = 5.83 %
Rwp = 7.98 %
Rmag = 7.35 %
c2 = 2.74
3
Intensity (10 counts)
8
G3
8
4
0
20
60
100
2 (deg.)
140
Junghwan Park, JGP et al.,
Applied Physics A (2002)
Inelastic Neutron Scattering of YMnO3
H  J  [ Six S jx  Siy S jy   Siz S jz ]  D  ( Siz ) 2
i , j 
i
J=3 meV, =0.95,
D=0.03 meV
Junghwan Park, JGP et al.,
Phys.Rev.B (2003)
Spin dynamics of single crystal YMnO3
T. Sato et al.,
Phys.Rev. B (2003)
H    J ij Si  S j  D1  (Siz )2  D2  (Si ni )2
i , j 
i
i
J1=-3.4(2) meV , J2=-2.02(7) meV
J’1-J’2=0.014(2) meV
D1=-0.028(1) meV
D2=0.0007(6) meV
Questions
• What are the effects due to the short-ranged
magnetic fluctuations on their physical
properties?
• How are the magnetic and electric dipole
moments coupled to one another?
• What are doping effects on the magnetic
properties?
Part 1:
Phonon scattering due to shortranged spin fluctuations of YMnO3
Phys. Rev. B 68, 1004426 (2003)
Phys. Rev. Lett. 93, 177202 (2004)
Geometrical frustration
Triangular lattice with AF interaction
Part 1
YMnO3
1/c(mol-Oe/emu)
500
400
CW = - 500 K
300
CW/TN = 6.7
200
100
0
-600 -400 -200
0
200 400 600
Temperature (K)
800 1000
Part 1
1200
300 K
Diffuse scattering seen in
YMnO3 well above TN:
1000
150 K
Intensity (a.u.)
800
110 K
Evidence of short ranged
magnetic correlation, i.e.
spin liquid phase
85 K
600
75 K
72.5 K
HANARO
30MW
70 K
400
40 K
200
10 K
10
20
2 (deg.)
30
Data taken at HANARO,
Korean research reactor
Part 1
80 K Data subtracted off by the 300 K data
200
YMnO3
S(Q)T=80K - S(Q)T=300K
2
I(Q)/F (Q)
100
0
-100
-200
1
2
3
4
-1
Q(Å )
I (Q)
F 2 (Q)
 S
i, j
i
Sj 
sin(Qrij )
Qrij
rij : the distance between nearest neighboring spins
I (Q ) : measured difference curve
F (Q )
: the form factor of Mn3+
E.F. Bertaut et al. Solid State Commun. 5, 279(1967)
Part 1
Fitting of I(Q)/F2(Q) of YMnO3
Sin (Q  r1 ) Sin (Q  r2 ) r  3.54 r  6.13
1
2
S (Q) ~

Q  r1
Q  r2
Junghwan Park, JGP et al.,
Phys.Rev.B (2003)
200
YMnO3
YMnO3
S(Q)T=80K - S(Q)T=300K
100
I(Q)/F (Q)
0
2
2
I(Q)/F (Q)
100
S(Q)T=200K - S(Q)T=300K
0
-100
-100
-200
1
2
3
-1
Q(Å
Å)
4
1
2
3
-1
Q(Å
Å)
4
Part 1
Spin liquid phase
in the paramagnetic phase
Part 1
Additional scattering of acoustic
phonons due to spin liquid phase
Part 1

YMnO3
0.94
B cos 
60
80K
 (Å)
450
400
8
40
6
4
30
70K
350
10
TN
50
2
20
300
50K
0
25
C
20
Phonon-only Fit
Cooperative PM
Phonon Scattering
 (W/Km)
250
200
40K
150
100
15
10
5
0
50
10
15
20
2(deg.)
25
30
I(T)/I(300 K)
500
12
YMnO
0
50
100
150
200
T (K)
P. Sharma, JGP et al., PRL (2004)
Part 2:
Direct evidence of coupling
among spin, lattice, and electric
moments for YMnO3 and LuMnO3
Phys. Rev. B Rapid Comm. 71, 180413 (2005)
Part 2
Moment (mB/Mn-atom)
Temperature dependence
of moment and lattice constants
e
y
ex
plane z=0
plane z=1/2
(105)
(a)
3
2
1
TN
0
6.14
(b)
10000
Г1 magnetic structure
11.403
a-axis
c-axis
2000
6.12
11.391
(c)
3
4000
11.397
372
Volume (Å )
200K
110K
90K
80K
70K
60K
50K
40K
20K
10K
6000
Intensity(a.u.)
(302)
(103)
6.13
371
370
0
(100) (101) (102)
(111)
(104)
0
20
30
40
50
2
60
70
80
100
200
300
Temperature (K)
Junghwan Park, JGP et al.,
Applied Physics A (2002)
c )(Å)
c (Å
8000
(002)
(Å)a (Å )
(202)
(213)
10
G1
G3
Part 2
Temperature dependence of a, c, and volume up to 1200 K
: High temperature neutron diffraction data
HT: P 63/m mc
11.40
11.38
6.18
11.36
6.14
3
Volume (¡Ê )
c (¡Ê)
LT: P 63 cm
a (¡Ê)
6.22
380
375
370
0
400
800
1200
Temperature (K)
J. Park, JGP (unpublished)
Part 2
SIRIUS（High resolution and high intensity powder diffractometer）@ KENS
l
 9  104
l
Part 2
Refinement results : TOF diffractometer SIRIUS at KEK
10K
300K
Y(1)z
0.2773(7)
0.2727(8)
Y(2)z
0.2318(6)
0.2320(7)
Mnx
0.3423(1)
0.3330(1)
O(1)x
0.3007(4)
0.3076(4)
O(1)z
0.1606(7)
0.1625(7)
O(2)x
0.6399(4)
0.6414(4)
O(2)z
0.3339(7)
0.3360(7)
O(3)z
0.4804(8)
0.4754(9)
O(4)z
0.0193(7)
0.0163(8)
Rwp
6.29%
4.19%
Rp
4.89%
3.42%
Part 2
Refinement results
Temperature dependence of atom positions
372.0
0.308
0.163
0.302
O(1) x
0.477
0.161
(a) 0.160
(b)
0.642
O(2)x
0.231
0.336
200
0.332
(e)
0.229
300
0
Temperature(K)
100
200
Temperature(K)
300
Mn x
Y(2) z
Y(1) z
0.340
Y(1) z
100
a (Å)
0.344
6.120
2.12
0.230
0.272
0
11.404
6.128
6.124
(f)
0.232
0.276
Y(2) z
11.408
6.132
0.016
(d)
(c)
0.233
0.274
(a)
11.400
0.332
O(2)z
0.639
0.278
370.4
6.136
Bond length (Å)
0.640
0.334
370.8
11.396
(b)
2.08
2.04
Mn-O1
Mn-O2
Mn-O3
Mn-O4
2.00
1.88
1.84
(c)
0
50
100
150
200
Temperature (K)
250
300
c (Å)
O(2) z
0.018
O(4) z
0.641
O(2) x
O4
O2
371.2
370.0
0.020
0.336
0.270
O3
0.474
O(1)z
0.300
3
Mn O1
Å)
Volume (Å
0.304
O(1) z
O(1) x
0.162
371.6
0.480
O(3) z
0.306
Part 2
KEK YMnO3 results
u
Part 2
u=-a-b
Mn
O4
O3
b
O4
a
Coupling among magnetic moments,
lattice, electric dipole moments
Part 2
Electric dipole moment
ΔP(T)   qi (ri (T) - ri (300K))
Pz
1.5
d(Mn-O3) - d(Mn-O4)
i
Normalized value
mord
Y : 3+
Mn ; 3+
O : 2-
BCS
1.0
0.5
BCS : usual mean field-type
order parameter
0.0
0
50
100
Temperature (K)
150
T 
1  
 TN 
2.9
Seongsu Lee et al., PRB (2005)
Part 3:
Doping and Pressure Effects on
the magnetic properties
Phys. Rev. B 72, 014402 (2005)
JETP 82, 212 (2005)
2D Triangular lattice of Mn moments
Mn O1
O3
O4
O2
Part 3
Doping effects of (Er1-xYx)MnO3
Part 3
Irreducible representations
YMnO3
G1 representation
G3 representation
ErMnO3
G2 representation
G4 representation
Part 3
Magnetic structure of (Er1-xYx )MnO3
Part 3
2D Triangular lattice of Mn moments
Mn O1
O3
O4
O2
Part 3
Part 3
Mn-site doping effects in Y(Mn,X)O3
with X=Zn, Al, and Ru
(a)
3
YMnO3
(002)
Mn moment [mB]
15000
YMn0.9Zn0.1O3
6000
3000
YMn0.1Ru0.9MnO3
2
YMn0.1Zn0.9MnO3
1
(102)
9000
(-101)
(100)
0
0
100
200
YMn0.9Ru0.1O3
Diffuse scattering at 50 [K]
YMn0.9Al0.1O3
0.035
0.045
YMn0.9Zn0.1O30.030
0.040
YMnO3
0
10
300
T [K]
15
0.025
20
25
2 degree
30
Intensity
Intensity [a.u.]
12000
YMn0.1Al0.9MnO3
0.035
YMn0.9Ru0.1O3
0.020
0.030
0.015
YMn0.9Al
O
0.1 3
0.025
YMnO3
0.020
Mixing of G1 and G2 structures
0.010
0.015
0.005
14
16
18
20
22
2
24
26
28
30
Part 3
External Pressure Effects on YMnO3
1. Mixing of magnetic structure Γ1 Γ1+ Γ2: for 2.5 GPa,
μord = 1.52 μB with =60o at 10K:
2. Diffuse scattering enhanced with pressure
T = 295 K
2500
0 GPa
10 K
Intensity, arb. units
800
0 GPa
80 K
2000
b
5 GPa
80 K
400
1500
b
1000
b
5 GPa
3
4
5
6
2.5 GPa
500
0 GPa
0
1500
Intensity, arb. units
T = 10 K
P = 5 GPa
1000
500
P = 0 GPa
0
2
3
4
d-spacing, ?
5
2
3
d-spacing, Å
4
5
Summary
• Spin liquid phase evidenced by the diffuse peaks scatters
acoustic phonons through unusually strong spin-phonon
coupling, which then gives rise to a significant reduction in
thermal conductivity in the paramagnetic phase.
• We have shown that below TN the magnetic moments of
YMnO3 and LuMnO3 are strongly coupled to the lattice
degrees of freedom with further coupling to the
ferroelectric moments. However, an underlying
microscopic mechanism for such a coupling is not clear yet.
• The magnetic ground states of RMnO3 are so subtle that
even a small doping can induce mixing between different
magnetic states.
Acknowledgements
• Seongsu Lee, Misun Kang, Jung Hoon Han, H. Y.
Choi, A. Pirogov: Sungkyunkwan University
• Changhee Lee: KAERI, Korea
• W. Jo: Ewha Womans University, Korea
• S-W. Cheong: Rutgers University, USA
• T. Kamiyama: KEK, Japan
• R. Bewley: ISIS, UK
• Jeongsu Kang: Catholic University, Korea
• D. Kozlenko: Frank Laboratory, Russia