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)