associated magnetic excitations in Hg1201 (Yuan Li talk)

Using polarized neutron diffraction over the last 6 years: LLB-Saclay, ILL-Grenoble

Magnetic order in the pseudogap state of high-Tc cuprates (examples in 4 different families: YBCO, Hg1201, LSCO, Bi2212)

Do we have a broken symmetry below T* ?

Philippe Bourges Laboratoire Léon Brillouin, CEA-Saclay

Orbital-like Order in Several Families of Cuprates

La2-xSrxCuO4

• K. Conder, E. Pomjakushina, N. Christensen (Riso), J. Mesot (PSI, Switzerland)

• Yuan Li (MPI), G. Yu, M. Chan (University Minnesota) •M. Greven (University Minnesota,USA) •P. Steffens (ILL-Grenoble) HgBa2CuO4+x

• X Chaud (CRETA, Grenoble), LP Regnault (CEA Grenoble) •H.A. Mook (Oak Ridge, USA) YBa2Cu3O6+x

• V. Balédent (PHD), B. Fauqué, S. Pailhès, Y. Sidis (Laboratoire Léon Brillouin - Saclay) (Y,Ca)Ba2Cu3O6+x • D. Haug, C.T. Lin, V.Hinkov (MPI Stuttgart)

Collaborators :

1) Motivation: Loop-current order 2) Neutron scattering 3) Long range magnetic Q=0 AF order in YBCO and Hg1201 4) Preliminary result in Bi2212 5) Short range magnetic order in LSCO 6) Updated phase diagram in YBCO and Implications

Outline:

Hidden order parameter: Spin Density Wave, Charge DW, more Exotic: Circulating current, D-Density Wave,… Electronic Liquid Crystal

Role of the related fluctuations in the SC pairing mechanism?

Quantum critical point?

Broken symmetry?

Order parameter?

Pseudo gap: Hidden Ordered State

C.M. Varma, PRB 73, 155113 (2006)

Cu

Phase ordonnée

O

supra

- Yields a sizeable magnetic moment of 0.1 µB

Kaminski et al. Nature 416, 610 (2002).


Dichroic signal in ARPES in BiSrCaCuO

Circulating currents: phase ΘII - Respects Translation Symmetry (q = 0 transition) - Breaks Time-Reversal symmetry

2 current loops circulating clockwise and anticlockwise => producing Orbital moments

4 possible domains

Toroidal moment

In each unit cell:

• 3-band Hubbard model: Cu(dx2−y2), O(2px), O(2py)

Circulating Currents:

2 type of Domains at 90°

In k-space: Q=(H,K)

vecteur vector d'onde Wave

nuclear

NSF

SF

magnetic

Orbital moments (⊥ ⊥ CuO2 plane) measurable with neutron diffraction

Ising-type

C.M. Varma, PRB (1997)(2006)

Q=0 Orbital AF

Circulating currents

Intensité intensity

In k-space: Q=(H,K)

Orbital moments (2D Ising)

S. Chakravarty PRB (2001)

CC-phases NMR Silent Probe

measurable with neutrons

C.M. Varma, PRB (1997)(2006)

Charge currents: DDW and Circulating currents

Spin

Orbital

Polarized neutron cross sections

* Magnetic Scattering

•Nuclear Scattering Non spin flip:

Neutron polarization: p=(I--I+)/(I-+I+) ~ 96%

Flipping ratio: R=NSF/SF=I-/I+ (R ~ 50)

H=10 G, P//H

Polarizing mirror

Polarized monochromatic neutron beam : 4F1-LLB

h

OD

(twinning: 10L=01L)

A systematic study on 8 different samples (different origin, twinned [t] or detwinned [d])

YBa2Cu3O6+x

Underdoped YBa2Cu3O6.6 H.Mook’s sample (Tc=63 K) [t]

UD89 (x=0.85 ,Tc=89K) [t]

OD75 (x=1, Tc=75 K) [t]

Y0.85Ca0.15Ba2Cu3O6+x

UD68 (x=0.75 ,Tc=75K) [t]

UD64 (x=0.6 , Tc=64 K) [d]

UD 61(x=0.6 , Tc=61 K) [t]

UD54 (x=0.5, Tc=54 K) [t]

UD35 (x=0.45, Tc=35 K) [d]

n =0.19 picture Very consistent hole doping

UD

Generic phase diagram

on (Y,Ca)Ba2Cu3O6+x

Polarized neutron scattering experiments

temperature

N.B. L=1, weak nuclear Bragg peak

For Q=(0,1,1): |FN|2/ |FM|2 =400

R: flipping ratio

(per triangle)

m~0.1 mB

No effect on Q=(002) (open symbols)

Tmag

B. Fauqué et al, PRL 96 197001 (2006)

Polarized neutron results in YBCO: P//Q, Q=(0,1,1)

Weak or zero structure factor for Q=(2,0,1)

Angle (M,c*) ~ 45 deg

Polarization analysis:

For Q=(1,0,1):

YBCO6.6 : H.A. Mook et al, PRB 020506(R) (2008).

(H,0,0)

(ξ>50 Å)

• L-scan Long range order

(1,0,1)

0 0.4

20

40

60

80

100

0.6

0.8

Magnetic

1.2

(1 0 L)

1

Nuclear Peak

1.4

0

0.4

0.8

1.2

1.6

1.6

70 K - 300 K

SF HF P//Q (101)

YBCO: Long range magnetic order

H.A. Mook et al, PRB 020506(R) (2008).

(0,0,L)

- Resonant ultrasound spectroscopy Arkady Shekhter

B. Leridon et al EPL, 87, 17011, (2009)

- Uniform magnetic susceptibility

J. Xia, et al, PRL, 100, 127002 (2008)

B. Fauqué et al, PRL 96 197001 (2006) H.A. Mook et al, PRB 78 020506 (2008)

color map: [ρ ρab(T)-ρ ρab(300K)]/T

Other reports of a phase transition at T*: - Polar Kerr effect

T. Ito et al PRL 70 (1993) 3995

Resistivity in YBCO

Phase diagram: Magnetic order at Tmag ~T*

T. Ito et al PRL 70 (1993) 3995

A single scaling factor with |M|2 for all doping

Comparison with resistivity

• Cu-O octaedra

• Tetragonal • 1 CuO2 Plane

Breakthrough in single crystal synthesis in Hg1201: mass ~ 1 g, M. Greven (Stanford/Univ Minnesota) Zhao et al., Adv. Materials, 18, 3243 (2006).

• Orthorhombic • 2 CuO2 Planes • distorded CuO2 planes • Cu-O pyramids

From YBa2Cu3O6+x to HgBa2CuO4+x

R> 90

m ~ 0.2 µB

Q=(1,0,1) P//Q

Yuan Li et al, Nature 455,372 (2008).

Polarized neutron results in Hg1201

Comparison Resistivity ∆ρ

Q=0 AF Magnetic order at Tmag ~T*

Tmag-> 0 at p=0.19, expected end point of the pseudo-gap phase NMR, Entropy, resistivity, ARPES…. Tallon and Loram, Physica C (2001,2004)
Quantum Critical Point

B. Fauqué et al, PRL 96 197001 (2006) H.A. Mook et al, PRB 78 020506 (2008) Y. Li et al, Nature 455 372 (2008)

"Universal" phase diagram: from YBa2Cu3O6+x to HgBa2CuO4+x


Angle (M,c*) ~ 45° .... Origin ?

C. Weber et al, PRL 102, 017005 (2009).

Chandra Varma Spin moment on O sites (should have been detected by NMR.....) talk Quantum Monte-Carlo calculations

or

or even


Orbital or spin magnetic moments ?

Stanescu, Philipps PRB 69, 245104 (2002).

- Intra unit cell magnetism (2 antiparallel moments) electronic nematicity by STM in Bi2212 M.J. Lawler et al Nature 2010 - Cu spins alone cannot account for this magnetic phase. Seamus Davis - One needs to reconsider the role of oxygens talk -Effective 1 band model
3 bands Hubbard model

Q=0 AFM, What are the implications ?

L=3

Tc=83K

Bragg peaks at (10L) for L odd (Tetragonal notations) 45 deg to the inc modulation

Annealed with p(O2)=0.05 atm at 450°C

S. de Almeida F. Giovanelli I. Laffez University of Tours (France)

Large single crystal growth

Preliminary results in Bi2Sr2CaCu2O8+δ

In te n s ity (M n = 3 1 0 4 )

300

350

400

450

500

50

150

200

Temperature (K)

100

Q=(1 0 3)

SF NSF x 1/45.5

250

300

0

AF

0.05

0.1

mag

SC

T

0.25

Bi-2212

0.2

doping

0.15

pseudogap

T*

0.3

A. Kaminski et al, PRL, 90 207003 (2003)

0

50

100

150

200

250

300

350

resistivity in thin films

Q=0 AF Magnetic order in Bi-2212

Temperature (K)

Incommensurate AF fluctuations (Spin density wave) Fingerprint of dynamical stripes Static stripe phase for Nd co-doping or with Ba

µSR, NMR,…

Tranquada et al, Nature 1995, 2004 Lattice invariance and fourfold symmetry broken

•

•

Mitrovic et al, PRB 78 014504 (2008)

bond centered charge stripes

LSCO case: Charge inhomogeneities: Stripes

3 Samples (7 g) (from PSI, E. Pomjakushina) co-aligned with x=0.085, Tc=22 K. Tetragonal notations
Orbital-like moments at Q=(10L)

Inc

H//Q

(M< 0.02 µB)

No Long Range ordered moment in LSCO

R-1 =R0-1 +M2/NSF

For

Q=(1,0,1)

(R-1=SF/NSF)

Inverse Flipping Ratio : R-1

Bourges and Sidis, arXiv: 1101.1786

YBCO6.6 from Fauqué et al, 2006

Search for Static Q=0 AF order in La1.915Sr0.085CuO4

ξ110 ~ 11 Å

No signal in NSF channel

Spin-flip H//Q

• • •

2D : Around Q=(1,0,L) any L

(H,0,0)

•

(1,0,1)

V. Balédent et al, PRL 105, 027004 (2010)

ξ100 ~ 8 Å

ξ=2/∆ ∆q

Along 100

In plane Correlations length:

Along 110

2D Short range magnetic correlations La1.915Sr0.085CuO4 (0,0,L)

Temperature dependence

• Q-Integrated intensity (as Bragg scattering in YBCO6.6) 1.2 mbarns
Local moment ~ 0.1 µB

• I(H//Q)=I(H//z)+I(H//y) • I(H//z) ~ I(H//y)
isotropic moments or angle (M,c*) ~ 45 deg

• Tmag ~ 120 K for 8.5%
Lower than generally expected T*

Polarisation analysis

Polarization analysis and T-dependence : La1.915Sr0.085CuO4

below Tmag ~120K

intensity

Upturn of IC

AF order and IC fluctuations

interplay between the Q=0

Unpolarized neutron E= 4 meV (2T-LLB) Incommensurate magnetic fluctuations at Qinc=(1/2±δ δ,1/2,0)

Tmag=120K

V. Balédent et al,PRL 105, 027004 (2010)

Temperature dependence of Q=0 AF order

AF domains

with circulating currents

2-leg charge ladder

For x=0.085 ~ 1/12

Mixte phase ?

ξ(100)

ξ(110)

no phase coherence

V. Suchaneck et al., PRL, 105, 037207 (2010).

Zn induces low energy incommensurate spin excitations near (π,π) π,π)

V. Balédent et al., PRB 83, 104504 (2011).

Same Tmag but weaker intensity

Swiss cheese model

1/Flipping Ratio=R-1=SF/NSF = R0-1 +M2/NSF

Zn known not to change T* (NMR Knigh shift, Alloul et al, 1993)

Zn(2%)-YBa2Cu3O6.6 : Tc = 30 K

⇒ Electronic nematic liquid state (ELC)

Q=0 AF

R-1=SF/NSF = R0-1 +M2/NSF

(D. Haug, MPI Stuttgart)

TC =35K, Hole doping= 0.085

Hinkov et al., Science 319, 597 (2008).

Detwinned YBa2Cu3O6.45

Q=(100)

Q=0 AF order develops close to Tmag ~150K ~ Tnematic

IN YBCO6.45

It is generally assumed that T* increases (No compelling evidence that this is correct for T* above Room Temperature )

whereas

Near 9% Tmag decreases with doping

V. Baledent et al., PRB 83, 104504 (2011).

Comparaison Q=0 AF Bragg peak intensity in YBCO

Q=0 AF order

Anisotropic Nerst effect in YBCO R. Daou et al Nature (2010)

QO

V. Baledent et al., PRB 83, 104504 (2011).

No QO

YBCO: Updated Phase diagram

⇒ There are associated specific magnetic excitations (next talk, Yuan Li)

⇒ Hidden order parameter of the pseudogap phase having the symmetry proposed for the loop current order (talk Chandra Varma)

Bourges and Sidis, arXiv: 1101.1786

• Technique: Polarized neutron diffraction • Result: Magnetic order in the pseudogap state of high-Tc cuprates in 4 different families: YBCO, Hg1201, LSCO,Bi2212 • Implication: There is a broken symmetry below T* which does not break the translation symmetry but breaks Time reversal symmetry

Conclusions: