Thermal and quantum fluctuations and thedisruption of orbital/magnetic order in KCuF3
S. L. Cooper U. of Illinois
Dept. of Physics and Materials Research Lab
Shi Yuan (UIUC) James Lee (UIUC)
Growth, characterization, and Raman studies of KCuF3
Collaborators:X-ray studies of KCuF3
Peter Abbamonte(UIUC)
Paul Goldbart(UIUC)
Siddhartha Lal(UIUC)
Dept. of Energy, Division of Materials Sciences, Grant DEFG02-07ER46453
Support:
6 32g gt e
Standard View: KCuF3 is a relatively simple ‘model’ spin-1/2 orbital-ordering material
Simple perovskite structure with one hole in the d-band:
Cu
F
C FE
eg
t2g
Energy Cu2+ (d9)
CuF6octahedra
J-Tdistortion
eg
2zd 2 2x y
d
EJT
2 2x zd
2 2y zd
Orbital order in KCuF3: Kugel-Khomskii (KK) orbital order*
*Kugel, Khomskii, Sov. Phys. Usp. 25 (1982)
Ja
Jc
• cubic-to-tetragonal “orbital-ordering” transition at Too ~ 800 K
Standard KK view of KCuF3:
Tennant et al. PRB (1995)
TN
Problems with the standard view of KCuF3: Suppressed magnetic ordering temperature
Suppressed antiferromagnetic ordering temperature suggests magnetic frustration
TN = 40 K ~ (1/20)Too
A-type antiferromagnetic order
Jc ~ 200 K
Jab ~ 2 K
Jc ~ 100 Jab ! (Satija et al. PRB (1980))
• large superexchange anisotropy, |Jc|/Ja~100
1D antiferromagnetic chains
Problems with the standard view of KCuF3: Unexplained superexchange anisotropy
Nature Materials (2005)
Neutron scattering: spin fluctuations in KCuF3exhibit 1D quantum critical scaling down to TN!
• Crystallography indicates KCuF3 has a tetragonal structure But, other measurements (e.g., anomalous electron spin resonance (ESR) linewidth) indicate a static Dzyaloshinsky-Moriya (DM) vector consistent with orthorhombic symmetry
(Eremin et al. PRL (2008))
Suggests dynamical fluctuations of orthorhombic domains, but nature of fluctuations is unknown!
Problems with the standard view of KCuF3: Unexplained structural anomalies
To explore these puzzles, we grew KCuF3single crystals for Raman and X-ray studies
• aqueous solution precipitation method
• large (4 4 4 mm3) single crystals
(004)FWHM=0.2166o
x-ray diffraction measurements:
• The value of in-plane lattice parameter, a=b=8.25Å, is consistent with reference value
Shi Yuan (UIUC)
Inelastic light (Raman) scattering phonon spectrum of KCuF3
Eg
KCuF3
B1g
Eg
50 100 150 200 250 300
Inte
nsity
(arb
. uni
ts)
Energy (cm-1)
90K
• Raman spectrum of phonons similar to that observed at low temperatures in previous studies
The 370 cm-1 A1g phonon in KCuF3 exhibits a conventional temperature dependence
350 400
Inte
nsity
(arb
. uni
ts)
Energy Shift (cm-1)
KCuF3
270 K
3 K
110 K
0 50 100 150 200 250 300
372
374
376
378
Temperature (K)
Freq
uenc
y (c
m-1
)
246810121416182022
Linewidth (cm
-1)
TN
KCuF3
• Temperature-dependence of A1gmode frequency typical of that expected from anharmonic effects
A1g- symmetry
65 70 75 80 85 90 95 100
Inte
nsity
(arb
. uni
ts)
Energy Shift (cm-1)
270 K
3 K
110 K
B1g-symmetry
KCuF3
0 50 100 150 200 250 30072747678808284
0
2
4
6
8
10
Temperature (K)Fr
eque
ncy
(cm
-1)
Linewidth (cm
-1)TNB1g-mode
KCuF3
The 72 cm-1 B1g phonon in KCuF3 exhibits ‘mode softening’ with decreasing temperature
• Temperature-dependent softening of B1g mode frequency indicates thermally driven structural fluctuations well below Too!
50 100 150 200 250 300
Inte
nsity
(arb
. uni
ts)
Energy (cm-1)
3K20K
40K90K
150K
210K
Eg B1g Eg
Two-step stabilization of orbital order in KCuF3: Fluctuational regime halted by structural transition just above TN
• KCuF3 is characterized by structural (and spin) fluctuations down to a tetragonal-to-orthorhombic structural transition at 50 K, which appears to help stabilize orbital/magnetic order
What’s responsible for structural fluctuations in KCuF3? X-ray evidence for rotations of CuF6 octahedra
James Lee(Abbamonte group, UIUC)
• (105) Bragg reflections not allowed by Kugel-Khomskii orbital ordering, but ARE consistent with GdFeO3-type rotations of CuF6 octahedra
Raman and x-ray results suggest these GdFeO3fluctuations persist down to 50 K, then “lock-in” just prior to the Neel transition into a “glassy” configuration
Sidebands suggest many equivalent configurations of octahedral distortions
(105) reflection
Peter Abbamonte(UIUC)
KCuF3
Phonon softening via “molecular fluctuations”:Critical dynamics of pseudospin-phonon coupling*
Phonon KE Phonon PE Pseudospin-Pseudospin coupling
Pseudospin-Phonon coupling
Phonon Response Function:
*Yamada, Takatera, Huber, J. Phys. Soc. Japan (1974)Related models discussed for:• Displacive phase transitions (Halperin and Varma, PRB (1976))
• Dynamics of Jahn-Teller transitions (Pytte, PRB (1971))
• Dynamics of ferroelectrics (Silverman, PRL (1970))
Critical dynamics of pseudospin-phonon coupling:Fast relaxation of pseudospins (CuF6 configurations)
Yamada, Takatera, Huber, J. Phys. Soc. Japan (1974)
• Significant phonon mode softening for fast molecular (pseudospin) relaxation
mol = 10ph
0.1 0.2 0.3 0.4 0.5 0.6
0
10
20
30
40
50
(T-Tc)/TcTemperature
0.4
0.6
0.8
Cen
tral p
eak
inte
nsity
f=10
mol = 10ph
Phonon ‘sees’ time-averaged octahedral configuration, which changes with decreasing temperature
Critical dynamics of pseudospin-phonon coupling:Slow relaxation of pseudospins (CuF6 configurations)
Yamada, Takatera, Huber, J. Phys. Soc. Japan (1974)*
• Slow molecular fluctuations give a broad central peak, no significant phonon mode softening mol ph
0.1 0.2 0.3 0.4 0.5 0.6
0
10
20
30
40
50
f =0.1
Cen
tral p
eak
inte
nsity
(T-Tc)/TcTemperature
0.0
0.6
1.2
1.8
mol = ph
Central peak reflects Debye relaxation of octahedral (pseudospin) fluctuations
PHydrostatic pressure reduces octahedral tilts and favors lower octahedral volume
Pressure-tuned “quantum” (T~0) octahedral fluctuations in KCuF3
250 m
ruby sample
gasket
ruby chipsample
gasket
diamond anvil
scattered photonincident photonOptical pressure cell
(e.g., Hucker, Tranquada, et al., PRL (2010) for (La,Ba)CuO4 and Steffens et al., PRB (2008) for Ca2RuO4)
Pressure
thermally fluctuating
CuF6 KCuF3
T
quantum fluctuating CuF6?
QCP?
orbital ordered, frozen CuF6
Energy Shift (cm-1)
0
1.3
4.5
7.3
P(kbar)
260 270
Inte
nsity
T=3K
0 3 6 9 12
255
260
265
270
Pressure (kbar)
Ene
rgy
Shi
ft (c
m-1
)
Sample 1 Sample 2 Sample 3 Sample 4
T=3K
Reversing the low temperature structural phase transition with pressure in KCuF3
P Pressure-tuned orthorhombic-to-tetragonal structural transition in KCuF3 at T = 3 K
KCuF3
Energy Shift (cm-1)
0
6
23
35
50
P(kbar)
T=3K
Inte
nsity
(arb
.uni
t)
80 120 160 200
T = 3K
Pressure-induced central peak in KCuF3:Slow quantum fluctuations of CuF6 octahedra
0 3 6 9 12
255
260
265
270
Pressure (kbar)
Ene
rgy
Shi
ft (c
m-1
)
Sample 1 Sample 2 Sample 3 Sample 4
0 10 20 30 40 500
3
6
9
12
I(P)/I
(0)
Sample 1 Sample 2 Sample 3
Pressure (kbar)
T = 3K
KCuF3 Pressure-induced ‘simple relaxational’ response in KCuF3 at T = 3 K; ~ 10 meV
Critical dynamics of pseudospin-phonon coupling:Slow relaxation of pseudospins (CuF6 configurations)
Yamada, Takatera, Huber, J. Phys. Soc. Japan (1974)*
• Slow molecular fluctuations give a broad central peak, no significant phonon mode softening mol ph
0.1 0.2 0.3 0.4 0.5 0.6
0
10
20
30
40
50
f =0.1
Cen
tral p
eak
inte
nsity
(T-Tc)/TcTemperature
0.0
0.6
1.2
1.8
mol = ph
Central peak reflects Debye relaxation of octahedral (pseudospin) fluctuations
0 3 6 9 12
255
260
265
270
Pressure (kbar)
Ene
rgy
Shi
ft (c
m-1
)
Sample 1 Sample 2 Sample 3 Sample 4
0 10 20 30 40 500
3
6
9
12
I(P)/I
(0)
Sample 1 Sample 2 Sample 3
Pressure (kbar)
Energy Shift (cm-1)
0
6
23
35
50
P(kbar)
T=3K
Inte
nsity
(arb
.uni
t)
80 120 160 200
Pressure-tuned central peak development in KCuF3:Slow quantum fluctuations of CuF6 octahedra
T = 3K
40kBT
Central peak results from slow fluctuations (~10 meV = 40kBT) of CuF6 octahedra characteristic fluctuation rate >> kBT, suggesting zero-point fluctuations
T = 3K
KCuF3
Energy Shift (cm-1)
0
6
23
35
50
P(kbar)
T=3K
Inte
nsity
(arb
.uni
t)
80 120 160 200
Pressure-tuned central peak development in KCuF3:Slow quantum fluctuations of CuF6 octahedra
40kBT
Temperature-independence of central peak also supports quantum fluctuation interpretation (>T regime)
80 120 160 200
Inte
nsity
(arb
. uni
t)
45K 35K 25K 15K 3K
P=42.3kbar
Energy Shift (cm-1)
T = 3K
KCuF3
Aronson et al., Phys. Rev. Lett. (1995)
Helton et al., Phys. Rev. Lett. (2010)
Similarity to quantum spin fluctuations observed in various magnetic materials using neutron scattering
0 3 6 9 12 15 18Pressure (kbar)
0
20
40
60
80
Tempe
rature (K
)
100
120
Frozen CuF6tilts
Fast thermal CuF6 fluctuations
21
mol >> ph
E
1 2
Slow quantum CuF6 fluctuationsmol ph
E
1 2
1 2
Summary of fluctuational behavior observed in KCuF3
How do octahedral fluctuations frustrate magnetic/orbital order in KCuF3?
Siddhartha Lal Paul Goldbart
Model by Lal and Goldbart supplements the KK model with a direct, orbital exchange term.*
Adding this term creates a near degeneracy of orbital/spin states that dynamically frustrates the spin subsystem
1MO2MO
E
*J.C.T. Lee, S. Lal, S. Yuan, et al., submitted to Nature Physics (2011)
~ 3 K << kBT
thermal/quantum fluctuations disrupt in-plane magnetic order
Summary: Thermal and quantum fluctuations of CuF6 octahedra in KCuF3
• KCuF3 exhibits phonon mode softening due to thermal fluctuations of the CuF6 octahedra down to a structural transition near 50 K, just above TN
• A model of pseudospin-phonon coupling in both fast and slow octahedral fluctuation regimes explains both the temperature- and pressure-dependent spectra
• Adding a direct orbital exchange term to the KK model generates nearly degenerate orbital/spin states that should be susceptible to thermal fluctuations, frustrating magnetic/orbital order down to low temperatures
• Pressure-dependent measurements show evidence for a pressure-tuned quantum phase transition to a regime characterized by quantum fluctuations of CuF6 octahedra
0
6
23
35
50
P(kbar)
T=3K
Inte
nsity
(arb
.uni
t)