거대자기저항 효과 물질과 다강체 물질에서의
결맞음 포논에 관한 연구
The Study of Coherent Optical and Acoustic Phonons in
Correlated Electron Materials (CMR, Multiferroic)
박사학위 청구논문 심사
2010년 5월 7일
장경진
KAIST
한국과학기술원 물리학과 초고속양자광학연구실
Ultrafast Quantum Optics Lab.
Content
Ultrafast dynamics of lattice motion
depend on phases !
Ultrafast dynamics?
- experimental tools
Lattice motion?
- coherent optical phonon
- coherent acoustic phonon
Phases?
- hole-doped manganite
(La2/8Pr3/8Ca3/8MnO3)
KAIST
- hexagonal manganites
(LuMnO3, YMnO3)
Ultrafast Quantum Optics Lab.
Pump-probe method
 Need two short pulses
- powerful pump pulse and weaker probe pulse
 Two optical path lengths are different in order to make time delay.
KAIST
- two types of delay generation (shaker and mechanical delay)
 The photo-induced changes in reflectivity or transmission are
measured.
Ultrafast Quantum Optics Lab.
Experimental setup
KAIST
Realization of pump-probe method
1. 20-fs pulse duration : enough to measure sub-picosecond dynamics
2. 400 kHz repetition rate : higher energy per pulse (tens nJ order)
(for 80 MHz repetition rate, a few nJ order)
3. Raster scanning shaker : eliminate high frequency parts so data is clean
4. Cryostat : from 10 K to 300 K filled with liquid He
Ultrafast Quantum Optics Lab.
What is observed?
Jang, Lim, Ahn, et al.,
PRB, under review
KAIST
Coherent oscillations in differential reflectance are measured
as function of probe delay.
Ultrafast Quantum Optics Lab.
Coherent optical phonon generation
Impulsive
Stimulated
Raman
Scattering
- sin-like
- transparent
KAIST
- optic phonon in Si
Riffe et al., PRB 76, 085207(2007)
- coherent Eg phonons of Bi
Ishioka et al., J. Appl. Phys. 100,
093501 (2006)
Displacive
Excitation of
Coherent
Phonon
- cos-like
- opaque
- A1 or A1g modes in Bi, Sb, Te, Ti2O3
Zeiger et al., PRB 45, 768 (1992)
- A1g mode of Bi, associated with the
Peierls distortion
Zijlstra et al., PRB 74, 220301 (2006)
Optical phonons in results are generated by DECP !
Ultrafast Quantum Optics Lab.
Coherent acoustic phonon generation
Strained
Pulse
propagation
- sin-like
- propagating coherent acoustic phonon
in InxGa1-xN/GaN heterostructure
: Liu et al., PRB 72, 195335 (2005)
KAIST
Acoustic phonons in results are generated by strained pulse propagation !
Ultrafast Quantum Optics Lab.
Optical phonon : DECP
DECP (Displacive Excitation of Coherent Phonon)
dn (t )
  P (t )   n (t )
dt
 2Q
t
2
n(t) : the electron density
in excitation band
P(t) : laser power density
β : electronic decay constant
   [Q   n(t )]  2
2
0
n(t)
Q
t
ω0 : mode freq, γ : damping constant of mode
2
2
 t
0
0
R(t ) 
 

 t 
  A B 2
e

B
e
cos

t

sin

t



2
2
2
R




2





2




0
0


  02   2
KAIST
R (t )
R
 A1e   t cos(t   )  B1e   t
and
 0
Ultrafast Quantum Optics Lab.
Acoustic Phonon :
Strained pulse propagation
1.
The strained layer which is
generated by pump pulse at
surface moves through sample at
velocity of vs.
2.
The interference of reflected probe
pulse at the surface and at z
shows an oscillatory behavior.
 n   n  i
 2 E ( z, t )  pr
2

[
n


n
(
z
,
t
)]
E ( z, t )  0
0
2
2
z
c
2
KAIST
R
( , t ) 
R
r0  r  r0
2
r0
2
2
 pr
t



sin  2   
c
 T

T 
 probe
2 n0 vs
 0
Liu et al., PRB 72, 195335 (2005)
Ultrafast Quantum Optics Lab.
Ultrafast dynamics of lattice motion
depend on phases !
Ultrafast dynamics?
- experimental tools
Lattice motion?
- coherent optical phonon
- coherent acoustic phonon
Phases?
- hole-doped manganite
(La2/8Pr3/8Ca3/8MnO3)
KAIST
- hexagonal manganites
(LuMnO3, YMnO3)
Ultrafast Quantum Optics Lab.
Hole doped manganite : La1-xCaxMnO3
 Parent material, LaMnO3, is antiferromagnetic charge transfer insulator
 With Ca doping, d-orbital configuration is changed.
 various phases as functions of doping rate and temperature
KAIST
Hole doped manganite meets the temperature-dependent phase study !
Ultrafast Quantum Optics Lab.
Phases of La5/8-yPryCa3/8MnO3
20K (III)
Charge-disordered domain
(ferromagnetic metallic)
Charge-ordered domain
III
II
I
M. Uehara et al., Nature 399, 560 (1999)
17K (III)
I : paramagnetic insulator
II : short-range ferromagnetic metal
short-range charge-ordering phase
KAIST
III : long-range FM and CO phases
120K (II)
Different two
phases coexist
below TCO !
Ultrafast Quantum Optics Lab.
Two coherent optical phonons
Oscillation amplitudes by FT of oscillating part
R(t )
 A1e1t cos(1t  1 )  A2 e  2t cos(2t  2 )
R
 A3e 3t cos(3t  3 )  Be  t  D
KAIST
 A 5.15-THz component is about 10 times smaller
than a 2.43-THz component.
 From the low temperature Raman study on
charge-ordering Bi1-xCaxMnO3, this fast mode
(5.15 THz) is inferred the Mn vibration.
Optical phonons (inferred the Mn ion vibration) are generated
at low temperature !
Ultrafast Quantum Optics Lab.
CO phase relation
The relation of 2.43 THz optical phonon and CO phase
1t
Ae
cos(1t  1 )
1
I : PI
II : s-r CO and FM
III : l-r FM and CO
Jang et al., PRB, under review
KAIST
 The optical mode requires a CO phase (unequal Mn-O distance).
 The metallic phase(equal Mn-O distance) doesn’t have optical mode generation.
Optical phonon is related to the charge-ordering phase !
Ultrafast Quantum Optics Lab.
Coherent acoustic phonon
KAIST
 The temperature dependence of acoustic phonon is opposite to that of
optical phonon.
 Below TCO, the amplitude of acoustic mode decreases.
Acoustic phonon is not generated as the charge ordering is formed !
Ultrafast Quantum Optics Lab.
 Lattice motion related charge-ordering phase in La2/8Pr3/8Ca3/8MnO3.
 Spin-lattice coupling in LuMnO3.
KAIST
 Phonon related iso-structural transition in hexagonal manganites.
La2/8Pr3/8Ca3/8MnO3
LuMnO3
YMnO3
Optical phonon
(DECP)
2.4 THz & 5.1 THz
3.6 THz
X
Acoustic phonon
(strained pulse
propagation)
34 GHz
47 GHz
31 GHz
phonon-CO phase
coupling
Ultrafast Quantum Optics Lab.
Why multiferroic material?
Multiferroic is good material to study of coupling between
spin and lattice by optical measurement !
KAIST
Eerenstein et al., Nature 442, 759 (2003)
Multiferroic
- materials that possess two or all three of the so-called
‘ferroic’ properties (ferroelectricity, ferromagnetism, ferroelasticity)
Ultrafast Quantum Optics Lab.
Hexagonal manganites : (Y or Lu)MnO3
S. Lee et al., Nature 451 (2008)
KAIST




Hexagonal structure
Ferroelectric ordering at high temperature ~ 900 K along c-axis
Antiferromagnetic transition near 80 or 90 K.
Mn ions consist ideal triangle structure in the ab-plane above TN,
while Mn ions move toward or far away O3 ion below TN.
No structural phase transition at TN.
Isostructural transition through magnetic ordering !
Ultrafast Quantum Optics Lab.
Our essential insight
vs
Do we obtain remarkable
result near TN?
KAIST
D. Lim et al., APL 83, 4800 (2003)
Our experiment
Previous work
Our experiment
No optical phonon
optical phonon ?
Acoustic phonons at all temperatures
Change near TN ?
Ultrafast Quantum Optics Lab.
Results of LuMnO3
Two coherent phonons are observed and
disappeared in magnetic ordered phase !
KAIST
Jang et al., NJP 12, 023017 (2010)
 Coherent optical phonon ~ 280 fs period
 Coherent acoustic phonon ~ 21 ps period
Ultrafast Quantum Optics Lab.
Coherent optical phonon in LuMnO3
3.63 THz optical phonon at room temperature
Lu1
Lu2
S.-T. Lou et al., PRB 79, 214301 (2009)
KAIST
 3.63 THz optical phonon is result of an A1-symmetry LO phonon (3.61 THz).
 Lu1 and Lu2 atoms are distinguished by ferroelectric transition.
Coherent optical phonon involves motions of Lu atoms along the c-axis
in opposite direction !
Ultrafast Quantum Optics Lab.
Coherent acoustic phonon in LuMnO3
 The mode hardens as temperature is lowered to ~160 K.
 Weakly softening behavior below ~160 K down to 90 K.
KAIST
The acoustic phonon is strongly coupled to spin fluctuations
above and below TN !
Ultrafast Quantum Optics Lab.
Temperature dependence of phonons
Jang et al.,
NJP 12, 023017 (2010)
 Indicate the coupling of coherent phonons with the AFM ordering transition.
 Similar disappearance of phonon is found at the structural transitions in other
materials.
 By neutron scattering, isostructural phase transition (Mn ions move) at TN.
KAIST
Spin-phonon coupling with iso-structural transition !
Ultrafast Quantum Optics Lab.
Our experimental achievement
Jang et al., NJP 12, 023017 (2010)
KAIST
Do we obtain remarkable
result near TN?
Previous work
Our experiment
System
Amplifier system
Cavity dumper system
Optical phonon
No
Observed
Temperature dependence
No change
Exist only above TN
Ultrafast Quantum Optics Lab.
 Lattice motion related charge-ordering phase in La2/8Pr3/8Ca3/8MnO3.
 Spin-lattice coupling in LuMnO3.
KAIST
 Phonon related iso-structural transition in hexagonal manganites.
La2/8Pr3/8Ca3/8MnO3
LuMnO3
YMnO3
Optical phonon
(DECP)
2.4 THz & 5.1 THz
3.6 THz
X
Acoustic phonon
(strained pulse
propagation)
phonon-CO phase
coupling
spin-lattice
coupling
34 GHz
47 GHz
31 GHz
Ultrafast Quantum Optics Lab.
General behavior of hexagonal manganites?
S. Lee et al., Nature 451 (2008)
KAIST
For YMnO3, Mn ions move opposite to that of LuMnO3 as magnetic
ordering occurs.
Spin-phonon coupling is general behavior of hexagonal manganites ?
Ultrafast Quantum Optics Lab.
Result of YMnO3
1. Coherent acoustic phonon (period ~32 ps) above TN
KAIST
2. Below TN, other frequency mode is observed in the
magnetic ordering phase.
Similar behavior in other hexagonal manganite !
Ultrafast Quantum Optics Lab.
Comparison between hexagonal manganites
Same behavior in LuMnO3 and YMnO3 !
KAIST
Jang et al., NJP 12, 023017 (2010)
Jang et al., in preparation
 Used pump pulse energy is near resonant d-d transition.
 Acoustic phonons are strongly coupled to spin fluctuation above
and below TN.
Ultrafast Quantum Optics Lab.
 Lattice motion related charge-ordering phase in La2/8Pr3/8Ca3/8MnO3.
 Spin-lattice coupling in LuMnO3.
KAIST
 Phonon related iso-structural transition in hexagonal manganites.
La2/8Pr3/8Ca3/8MnO3
LuMnO3
YMnO3
Optical phonon
(DECP)
2.4 THz & 5.1 THz
3.6 THz
X
Acoustic phonon
(strained pulse
propagation)
phonon-CO phase
coupling
spin-lattice
coupling
34 GHz
47 GHz
31 GHz
iso-structural
transition
Ultrafast Quantum Optics Lab.
Conclusion
 Lattice motion related charge-ordering phase in La2/8Pr3/8Ca3/8MnO3.
 Spin-lattice coupling in LuMnO3.
KAIST
 Phonon related iso-structural transition in hexagonal manganites.
La2/8Pr3/8Ca3/8MnO3
LuMnO3
YMnO3
Optical phonon
(DECP)
2.4 THz & 5.1 THz
3.6 THz
X
Acoustic phonon
(strained pulse
propagation)
phonon-CO phase
coupling
spin-lattice
coupling
34 GHz
47 GHz
31 GHz
iso-structural
transition
Ultrafast Quantum Optics Lab.
KAIST
Ultrafast Quantum Optics Lab.
KAIST
Ultrafast Quantum Optics Lab.
Time-scale of phonon
KAIST
Coherent phonons (solid state lattice vibration)
Time scale < 10-12 sec
Ultrafast Quantum Optics Lab.
Phonons in solid
10-15
Energy transfer
to the electrons
10-13
Optical
phonons
10-12
10-11
Acoustic
phonons
time (s)
Equilibrium poisitions
of atoms
KAIST
Acoustic vibration:
The two atoms on the
unit cell vibrate along
the same direction
Optical vibration:
The two atoms on the
unit cell vibrate in
opposing motion
Ultrafast Quantum Optics Lab.
Optical phonon : ISRS
• ISRS (Impulsive Stimulated Raman Scattering)
(not used in our experiment)
 2Q
Q
1    2
2
 2
 0 Q  N 
 EL
2
t
t
2   Q 0
  
 Q
 Q 0
where polarizability   0  
driving force : 1 N    EL2
2   Q 0
Q( z  0, t  0)
KAIST
 Q0e (t  zn / c ) sin[0 (t  zn / c)]
Ultrafast Quantum Optics Lab.
Complement

n(t )   pump  g (t   )e  d
0
02 pump
Q(t )  2
0   2  2


0
g (t   ){e
 
e

(cos  


sin  )}d

n(t )   pump  g (t   )e  d
0
02 pump
Q(t )  2
0   2  2
KAIST
where  


0
g (t   ){e
 
e

(cos  


sin  )}d
02   2 ,      
2

R(t )
0
 Ae  t  B 2
R
0   2  2
   t  t 


e

e
c
o
s

t

s
i
n

t







Ultrafast Quantum Optics Lab.
Optical phonon : DECP
2
2
 t
0
0
R(t ) 
 

 t 
  A B 2
e

B
e
cos

t

sin

t



2
2
2
R




2





2




0
0


 β is large
- oscillatory term is depressed due to 02 / 02   2  2
- rapid return of the quasi-equilibrium displacement to zero
- sin-like oscillation is not negligible (phase shift from cosine)
02
A1  B 2
0   2  2
R (t )
KAIST
R
02
B1  A  B 2
0   2  2
   

  
  tan 1 
 D  A1e  t cos(t   )  B1e   t
Ultrafast Quantum Optics Lab.
Fit by DECP (LPCMO)
예심
    1.0012
 
 Ae
 t
B
2
0
    2
2
R
2
0
R
KAIST

 D  Ae
Sb
0.009
Bi
-0.0174
Te
0.0351
Ti2O3
0.0425
 0.065

R(t )
  15.4902
e

 t
 t
e
t

cos t 
 

cos(t   )  Be
sin t



t
R
Ultrafast Quantum Optics Lab.
Complement
 n   n  i
r  r0  r1  r2  O( n2 )
r1  ei 2k z n
r2  ei 2k ( z d ) n
KAIST
R
( , t ) 
R
r0  r  r0
2
r0
2
2
 sin(k d )  n sin(2k z  k d )   cos(2k z  k d ) 
probe
R
t

c


(, t )   n sin(k d ) sin  2    where T 

R
nCs 2nCs
 T

Ultrafast Quantum Optics Lab.
Complement
KAIST
Ferromagnetic metal
- Colossal Magnetoresistance
Charge-ordering insulator
- Anti-ferromagnetic insulator
Ultrafast Quantum Optics Lab.
Complement
20K (I)
In LPCMO, there coexist
ferromagnetic metallic (FM) phase and
charge-ordering insulating (CO) phase.
Charge-disordered domain
(ferromagnetic metallic)
Charge-ordered domain
KAIST
17K (I)
Fs study of phase-separated manganite,
there is a strong opportunity to
optically control the competing ground
states between metallic and insulating
phases.
120K(II)
Ultrafast Quantum Optics Lab.
Coherent optical phonon
R / R
KAIST
lose coherence
get random in 1~10 ps
(dephasing)
The dephasing is caused by coupling with electron and phonon,
and by scattering by crystalline impurities and defects.
Ultrafast Quantum Optics Lab.
Electronic decay of DECP
KAIST
R (t )
R
 Ae
 t
 B e
 t
e
 t
cos(t   ) 
Ultrafast Quantum Optics Lab.
Phonon decay of DECP
KAIST
R (t )
R
 Ae
 t
 B e
 t
e
 t
cos(t   ) 
Ultrafast Quantum Optics Lab.
Cosine-like DECP
2

R(t )
t
 t
0

 Ae  t  B 2
e

e
cos(t   ) 
2

R
0    2
KAIST
R
R
 D

Ai e
it
cos( i t   i )  Be
t
i 1, 2 ,3
Ultrafast Quantum Optics Lab.
Damping amplitudes of phonons
1t
Ae
1
A2e 2t
KAIST
In the CO phase, the different charges on the Mn3+ and Mn4+ sites
cause out-of-phase Mn vibrations have a nonzero net charge
fluctuation that couples to the polarizability. (Mn3+-O-Mn4+)
Ultrafast Quantum Optics Lab.
Complement
KAIST
Non-oscillatory relaxations
Ultrafast Quantum Optics Lab.
Complement
KAIST
• Two absorption bands in s(w) in Bi1-xCaxMnO3 : Liu et al.,
PRL 81, 4684 (1998).
• Two IR bands in s(w) in La1/8Sr7/8MnO3 :Jung et al., PRB
59, 3793 (1999).
• Electron Microscopy of Co domains La5/8-yPryCa3/8MnO3 :
Uehara et al,. Nature 399, 560 (1999).
• Two absorption bands in s(w) in La5/8-yPryCa3/8MnO3 : Lee
et al., PRB 65, 115118 (2002).
• Coherent phonons in La1-xCaxMnO3 : Lim et al,. PRB 71,
134403 (2005).
• Raman scattering study of LaxPryCa1-x-yMnO3 : Kim et al.,
PRB 77, 134411 (2008).
Dearth of femtosecond study
Ultrafast Quantum Optics Lab.
KAIST
Complement
Amelitchev et al., PRB 63, 104430 (2001)
Ultrafast Quantum Optics Lab.
KAIST
Fast oscillation
 3.63 THz coherent optical phonon
 optical phonon maintain till to 10 ps
 below 90K, no optical phonon
Slow oscillation
 47 GHz coherent acoustic phonon
 below 90 K, acoustic phonon is
disappeared.
Ultrafast Quantum Optics Lab.
Optical phonon
KAIST
 Similar with the lowest optical
phonon mode (3.57 THz) reported by
Souchkov et al.*
*Souchkov
et al., PRL 91, 027203 (2003)
Acoustic phonon
 Weakly softening behavior below
~160 K down to 90 K.
 The acoustic phonon is strongly
coupled to spin fluctuations above and
below TN.
Ultrafast Quantum Optics Lab.
KAIST
Complement
Ultrafast Quantum Optics Lab.
Fast & slow oscillations
R
R
 A1e
 A2 e
KAIST
 Be
  1t
 2t
 t /
cos(1t  1 )
cos(2t  2 )
C
Ultrafast Quantum Optics Lab.
Dephasing and relaxation times
KAIST
 The excited electrons relax faster than nuclei.
 For acoustic dephasing time, the skin depth is considered.



 Another time scale is the absorption time constant, abs
4 vs
Ultrafast Quantum Optics Lab.
KAIST
Complement
Ultrafast Quantum Optics Lab.