1 NMR1. NMR

2. Pnictides

J. BobroffLaboratoire de Physique des Solides, Orsay, France

CEA ( t LLB)CEA (neutrons LLB)

S h t S l ilSynchrotron Soleil

Le LPS

Université d’OrsayPolytechnique

Nuclear Magnetic ResonanceNuclear Magnetic Resonance

NMR Nobel Prices

Bloch & Purcell, Nobel Physique 1952

Zeeman, Nobel Physique 1902

Rabi, Nobel Physique 1944 Nobel Physique 1952Nobel Physique 1902 Nobel Physique 1944

Lauterbur & Mansfeld, Nobel Medecine 2003

Ernst, Nobel Chimie 1991

Wuthrich, Nobel Chimie 2002

First NMR signal in a solid and a liquid

MRI

Chemistry NMR

14 Tesla 23 Tesla

A nuclear spin I in a magnetic field H0 A nuclear spin I in a magnetic field H0

Zeeman Effect 0 0.noyauhf zH M H H I

-5/2

.

.

.5/2

-3/2-1/2o

-I E = ħ H0

resonance

1/23/2m

=I t

0= h

5/2

.

= /2 H0..

= /2 H0

How do we measure the resonance ?the resonance ?

1 put the nuclear spin 1. put the nuclear spin in a static field

2. put a transverse zoscillating field :

at the resonance, it

H0will rotate the spin

3. stop the transverse fi ld d field and measure Hoscillating

Why doing NMR ?

Zeeman : = /2 H0

in matter : = /2 Hlocal

= H0 = /2 Hloc

Difference between Hlocal and H0 : information about the viscinity of the nucleus

NMR is a local probe

because coupling between nuclear spin Iand its neighboring is very short rangeg g y g

frequency

NMR of oxygen in a cuprate

Nb of nucleiBa

H0

Y

CuO2

Y

Cu O

Local field or frequency or shift~ Hlocallocal

YBa2Cu3O7

What can you measure ?

The electron : • Orbitals• Magnetic susceptibility in different positions• Inhomogeneities

Dynamics of electrons:• correlations• Gap and symetries in superconductors• Magnetic transitions

Local fields :• magnetic ordersmagnetic orders• charge orders• vortex• spin liquids

…

The NMR shifts

Nb of nuclei 0totalK

0

total

reference0=H0

)1(,, ii

ib

zyxi KK )1(2 spinorb KK

gyromagnetic ratio depends on the nucleus

orbital or chemical shift

spin shift

Orbital Shift

used in chemistry to characterize orbitals

ligasoline

Shift orbitalShift orbital

Spin Shift Kspin

s

IHloc=H0+aH0H0

I

0

measures uniform magnetic susceptibility

AK 1

close to the nucleus

electronen

hfspin AK 2

hyperfine coupling

Kspin measures

High Tc superconductor Cuprate YBa2Cu3O6+x

KK

Alloul et al PRL (1989)

T

Alloul et al., PRL (1989)

Why not measure i tibilit i t d ?macroscopic susceptibility instead ?

Kspin measures intrinsic ff d b i inot affected by impurity

1,0

VolborthiteVolborthite

magnetic impurity

0,6

0,8

n % RMN

Squid

Volborthitespin liquid

0,4ne

shi

ft in Squid

0 0

0,2

lin

intrinsic behavior

0 50 100 150 200 250 3000,0

Temperature (K)

Mendels et al., PRL (2000)

Kspin measures at different locations of the cell

Bi2212 Oxygen NMR

at different locations of the cell

Trokiner et al., PRB (1991)

different susceptibilities pso different dopings for each planeplane

Kspin measures a histogram of , not a sum:

spin chain with non magnetic impurities

access to local variations

Ni Ni Ni Ni Ni Ni Ni Zn Ni Ni Ni Ni Ni

p g p

Y B Ni Z O

0 6

0.8

1.0 Y2 Ba Ni98% Zn2% O5 T = 200 K

s arb

itrai

res)

0.2

0.4

0.6

ensit

é (u

nité

s pur

Zn 2%

14580 14600 14620 14640 146600.0

0.2

(kHz)

Inte

Tedoldi et al., PRL 99; Das et al.PRB 04

Nb of nuclei

Zn 2%

champ local

<SZ>

Zn Ni

Alloul, Bobroff, Gabay, Hirschfeld, RMP 2009Alloul, Bobroff, Gabay, Hirschfeld, RMP 2009

Kspin measures inhomogeneities

STM

RMN

YB C O7YBaCuO

intensité

RMN

YBaCuO7YBaCuO6.6

Bi2212

0 05 0 1 0 15 0 2Cren et al., PRL 2000

P t l N t 2001 0.05 0.1 0.15 0.2dopage

JB et al., PRL 02

Pan et al., Nature 2001McElroy et al. Science 2005

dynamicsdynamics

Relaxation times in NMR

z

H T1 H0

T

T1

transverse relaxation T2 MdM

T2

transverse relaxation T2 energy is conserved YX

YXYX HMTM

dtdM

,2

,,

ZZmequilibriuZ HMT

MMdt

dM

longitudinal relaxation T1 exchange with the network Tdt 1

g

longitudinal relaxation T1

due to fluctuations of local magnetic field at RMN

1

dttiBtBT RMNLL exp)0()(~1

1

n

nt

qB

B qqAgk

TT

),()(11 "

222

1

nqBg1

examples of T1

spin-gap systemmetal Magnetic Orderspin-gap system

TAeT

1Korringa

Law

2

21

41

nBk

TKT

metal Magnetic Order

T1

1/T1

Law1 eTKT

1/T1T1/T1

TTT

TCT

BCS superconductor unconventional superconductor

T TC

1/T

gap + Hebel-Slichter Peak

1/T

power law + no Peak

1/T1 1/T1

TTC

TTC

L l fi ld i NMRLocal fields in NMR

ti d magnetic orders, charge orders,

tvortex…

Example : AF order in pnictides

Fe

Fe

Kitagawa, JPSJ 08

Effect of a charge ordersensitivity to charge through electric field gradiants (NQR)

Ch D it W i Rb M O

sensitivity to charge through electric field gradiants (NQR)

Charge Density Wave in Rb0.30MoO3

Butaud et al., PRL 1985

vortex in superconductor

champ local

YBaCuO7

L RMN d l t d L T1 i l l iti La RMN donne la carte de champs associée aux vortex

Mitrovic et al., Nature (2001)

Le T1 varie selon la position par rapport au vortex

SSummary

NMR allows to measure…

Using the spectrum position and shape: • type of orbitals (Korb)yp ( orb)• spin susceptibility at various positions (Kspin)• magnetic orderings or freezings, order parameters…g g g , p• charge orders, vortex…• inhomogeneitiesinhomogeneities

Using dynamics:Using dynamics:• dynamical susceptibilities ’’(q,)• correlations spin fluctuations• correlations, spin fluctuations• gaps, magnetic excitations• superconducting symetries and gaps• superconducting symetries and gaps

NMR study of superconductivity and magnetism in pnictidesand magnetism in pnictides

Y. Laplace, J. BobroffLaboratoire de Physique des Solides, Orsay

D. Colson, F. Rullier-Albenque, A. ForgetSPEC CEA Gif S Y ttSPEC, CEA Gif Sur Yvette

Nature of

SDW

Ba(Fe1-xCox)2As2

Nature of magnetism ?

BaSDW

SCFe

As

SC

x = dopagex(Co) %0.15

Coexistence ?

what is doping really doing ?

SDW

Ba(Fe1-xCox)2As2

SDW

SCSC

x = dopagex(Co) %0.15

Coexistence ?

An old question…

CupratesHigh Tc

d t

Organic SC Heavy fermions

« Métal »

superconductors

AF SC

doping pressure

Lefebvre 2000

Pagliuso 2001

x in CeRh1-xIrxIn5

2000 2001

YesNot yet settled,Depends on families Yesy ,rather segregated

Lee, PRL 2005

Depends on families rather nano-segregated (stripes)

Miller, PRB 2009 Lee, PRL 2005Miller, PRB 2009Sanna, PRL 2004 Mito et al., PRL 2003

A key question for the determination of the superconducting gap symmetrysuperconducting gap symmetry

PRB 2009

PRB 2009PRB 2009

PRB 2010

A true atomic coexistence is only compatible with a s+- gap symmetry

Two possible situations

T l l i S iTrue local coexistence Segregation

SupraMagnetic

SUPERCONDUCTOR

Need a local probe :RMN, SR, Mossbauer...

• SmOFeAs : segregationDrew et al, Nat. Mat. 08

• Ba1-xKxFe2As2 : segregation

,

Takeshita et al. JPSJ;Aczel et al. PRB 08; Goko PRL 08; Goko PRL 08; Fukazawa et al.,JPSJ 09;Julien et al. EuroPhys.Lett.09

Fukazawa JPSJ 09

Ba(Fe1-xCox)2As2

SDW

SC

x = dopage

Ba(Fe0.94Co0.06)2As2

0

S)c

(MK

S v

olum

ic

-1

0 10 20T (K)

Superconducting fraction : 90 - 100%

75As RMN x=6% : spectrums

400 2000

21 K

8 K 200 1000

a

b(G

)

// c (G 21 K 25 K

29 K 27 K

0 10 20 30 40 50 600 0

G)

36 K

29 K

30 K

0 10 20 30 40 50 60 T (K)

-0.05 0.00H-H0 (Tesla)

Homogeneous magnetic broadening :100% magnetic fraction below 31Kg

Coexistence in Ba(Fe0.94Co0.06)2As2

100% magneticbelow 31K200

400

1000

2000

a

b(G

)

//

below 31K

12000 0

1000

c (G

)

100% superconduct. below 21K2 600

900

NM

R cavi1 K

-1)

below 21K

Dynamically, the same Fe300

600 ity detuning1/T 1T

(s

-1

atoms display magnetismand superconductivity

0 -300

0g (kH

z)

T t i i t

0 10 20 30 40 50 60Temperature (K)

True atomic coexistence

Nature of

SDW

Ba(Fe1-xCox)2As2Nature of magnetism ?

SDW

SCSC

x = dopagex(Co) %0.15

Nature of the magnetism

undoped BaFe2As2: commensurate AF

Co6% : incommensurate AF

Kitagawa, JPSJ 08

b T=23K

H//c

Co6% : incommensurate AFand very small moment

H//ab

Incommensurability

b T 23Kb T=23K

H//c

H//ab

l,0,21 Incommensurate order

0.6

rapport calculéH//ab / H//c

0.4

H//c

ppSimulated ratio

0.2 rapport expérimentalExperimental ratio

0.00 0.25 0.50 0.75 1.00

H perp c

//ab

~ 0.04

Non doped x=0% doped x=6%No doped 0% doped 6%

TN=31KTN=135K TN 31Kmoment < 0.1 B

incommensurate SDW

TN 135Kmoment ~ 0.9 B

commensurate AF order

Incommensurability recently confirmed by neutronsconfirmed by neutrons

Pratt et al. Phys. Rev. Lett. 106, 257001 (2011)

Phase diagram from NMR/Mossbauer

moment amplitude

1 .0(NMR/Mossbauer)

AF commensurate

0 .5

.

SDW incommensurate

coexistenceincom. SDW &

0 .0

Superconductivity

0 .00 0 .05 0 .10 0 .15C o dop ingCo Doping

How can magnetism and superconductivity

A consequence of the multi(5) band character

coexist together ?

• A consequence of the multi(5)-band character of the Fermi Surface ?

M ld i i t f ti d i i t bilitM could originate from a nesting driven instabilitySC could gap different Fermi sheets

Singh & al., PRL 08

•Competition/Coexistence over different parts of the Fermi Surface seems possible even in a two band Fermi Surface seems possible even in a two band model

I thi d l i t i ibl l if th In this model, coexistence is possible only if the magnetic state is incommensurate.

--> COMPATIBLE WITH OUR MEASUREMENTS

Vorontsov & al., PRB 09

SDW

Ba(Fe1-xCox)2As2

SDW

SCSC

x = dopagex(Co) %0.15

what is doping really doing ?

160 160

100

120

140

e (K

) Ba(Fe1-xCox)2As2100

120

140

re (K

) Ba(Fe1-xRux)2As2

40

60

80

Tem

pera

ture

SDW 0.15 40

60

80

Tem

pera

tur

SDW

0 2 4 6 8 10 12 14 16 18 200

20

T

Co doping content (%)

SC0 10 20 30 40 50 60 70

0

20T

Ru doping content (%)

SC

x(Co) %Increase both the number of holes & electrons , VFermi increases, correlation

simple rigid band fillingelectron doping

decrease by a factor 3Brouet et al., 2011

p g

Co vs Ru doping

NMR shift vs substitution in the normal state :in the normal state :

0,45

0,50

0,55

0,60

B F R A d i l

Ba1-2xK2xFe2As2 : dopage en trous

0 20

0,25

0,30

0,35

0,40 Ba(Fe1-xRux)2As2 : dopage isovalent

K (%

)0 00

0,05

0,10

0,15

0,20

Ba(Fe1-xCox)2As2 : dopage en électrons

-5 0 5 10 15 20 25 30 35 40 45 50 550,00

Taux de substitution x par atome de Fe (%)

Co = electron doping Ru = chemical pressure (isovalent doping)Ru = chemical pressure (isovalent doping)

Co doping homogeneous bothfrom macroscopic and local probesp p

superconducting transition

150

T-0 5

0.0

x=6%

Susc

eptib

ility

100

TN

5 10 15 20 25-1.0

0.5

Nor

mal

ized

magnetic transition

5 10 15 20 25Temperature (K)

50 TC1.0

units

)

magnetic transition

0 2 4 6 80

Co doping x (%)0.0

0.5

MR*T

(arb

.u x=6%

Co doping x (%)0 20 40 60 80

Temperature (K)

INM

Ru doping homogeneous from macroscopic probesfrom macroscopic probes

transport & neutrons

Rullier-Albenque et al., PRB 2010 Kim et al. PRB 2011

Ru doping homogeneous from X-ray

90

0010

000

Ru sample homogeneous sample with

0070

0080

00

g sample with macroscopic segregation

000

5000

600

2000

3000

4

X-ray : 002 line

010

00

12.4 13 14 1512.4 13 14 15

Ru doping not homogeneous from NMR

But...not homogeneous from NMR

1.0 Ru 80%

Ru 50%1.0

0 6

0.8Ru 35%

Co 2%fract

ion

0 6

0.8

Co 2%fract

ion

0.4

0.6 Co 2%

mag

netic

Co 6%

0.4

0.6 Co 2%

mag

netic

Co 6%

0.2

R 15%

Ru 25%

Par

am

0.2Par

am

0 50 100 1500.0

Ru 15%

0 50 100 1500.0

Temperature (K)Temperature (K)

How to reconcile NMR inhomogeneit & NMR inhomogeneity &

macroscopic homogeneity ?

if Ru effect effect is homogeneous

100

120

140

160

e (K

) Ba(Fe1-xRux)2As2

nsit

y

40

60

80

Tem

pera

ture

SDW

NM

R In

ten

0 10 20 30 40 50 60 700

20T

Ru doping content (%)

SCTN

T

N

160

if Ru effect is averaged but on a nanoscale

100

120

140

160

ure

(K) Ba(Fe1-xRux)2As2

tens

ity

20

40

60

80

Tem

pera

tu

SC

SDW

NM

R In

t

0 10 20 30 40 50 60 700

Ru doping content (%)

SC T

Ru 20%

140

160

B (F R ) A

Ru 20%

60

80

100

120

erat

ure

(K) Ba(Fe1-xRux)2As2

0 10 20 30 40 50 60 700

20

40

60

Tem

pe

SC

SDW

0 10 20 30 40 50 60 70

Ru doping content (%)

nten

sity

T

NM

R In

T

Ru 20%Ru 20%

140

160

B (F R ) A

60

80

100

120

erat

ure

(K) Ba(Fe1-xRux)2As2

0 10 20 30 40 50 60 700

20

40

60

Tem

pe

SC

SDW

0 10 20 30 40 50 60 70

Ru doping content (%)

nten

sity

T

NM

R In

T

Ru 20%140

160

B (F R ) A

60

80

100

120

erat

ure

(K) Ba(Fe1-xRux)2As2

0 10 20 30 40 50 60 700

20

40

60

Tem

pe

SC

SDW

0 10 20 30 40 50 60 70

Ru doping content (%)

sity

NM

R In

ten

T

N

T

2*2

simulation versus experiment

0.8

1.0

Frac

tion

2*2 3*3 4*4 5*5 7*71010te

nsit

y

0.4

0.6

Mag

netic

F 1010 20*20 Infinity*Infinity expN

MR

Int

0.0

0.2

Froz

en MT

0 20 40 60 80 100

Ru substitution (%)

Local averaging of Ru effect Local averaging of Ru effect over 5*5 cell units

Reconcile macro and local

NMR start of the transition

140 Tonset seen by NMR T @ 0.5* Wipeout NMR line

the transition

100

120

K)

Tn resistivitypercolation treshold (50%)

60

80

00er

atur

e (K

resistitivity

20

40

60

Tem

pe

y

0 20 40 60 80 1000

20

Ru substitution (%)

Co doping Ru dopingsummary

Ba(Fe1-xCox)2As2

p g

RandomCo distribution :

RandomRu distribution :

l d l l Local chemical pressure Electron delocalization Local chemical pressure averaged over 1 nm

Homogeneous electronic state

Inhomogeneouselectronic state

Homogeneous low temperature low temperature phases Inhomogeneous

low temperature phases on 1 nm scale