1 nmr1. nmr - centro de supercomputación de...
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1 NMR1. NMR
2. Pnictides
J. BobroffLaboratoire de Physique des Solides, Orsay, France
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CEA ( t LLB)CEA (neutrons LLB)
S h t S l ilSynchrotron Soleil
Le LPS
Université d’OrsayPolytechnique
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Nuclear Magnetic ResonanceNuclear Magnetic Resonance
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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
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First NMR signal in a solid and a liquid
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MRI
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Chemistry NMR
14 Tesla 23 Tesla
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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
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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
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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
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NMR is a local probe
because coupling between nuclear spin Iand its neighboring is very short rangeg g y g
frequency
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NMR of oxygen in a cuprate
Nb of nucleiBa
H0
Y
CuO2
Y
Cu O
Local field or frequency or shift~ Hlocallocal
YBa2Cu3O7
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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
…
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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
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Orbital Shift
used in chemistry to characterize orbitals
ligasoline
Shift orbitalShift orbital
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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
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Kspin measures
High Tc superconductor Cuprate YBa2Cu3O6+x
KK
Alloul et al PRL (1989)
T
Alloul et al., PRL (1989)
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Why not measure i tibilit i t d ?macroscopic susceptibility instead ?
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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)
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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
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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
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Nb of nuclei
Zn 2%
champ local
<SZ>
Zn Ni
Alloul, Bobroff, Gabay, Hirschfeld, RMP 2009Alloul, Bobroff, Gabay, Hirschfeld, RMP 2009
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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
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dynamicsdynamics
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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
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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
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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
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L l fi ld i NMRLocal fields in NMR
ti d magnetic orders, charge orders,
tvortex…
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Example : AF order in pnictides
Fe
Fe
Kitagawa, JPSJ 08
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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
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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
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SSummary
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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
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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
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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 ?
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SDW
Ba(Fe1-xCox)2As2
SDW
SCSC
x = dopagex(Co) %0.15
Coexistence ?
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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
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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
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Two possible situations
T l l i S iTrue local coexistence Segregation
SupraMagnetic
SUPERCONDUCTOR
Need a local probe :RMN, SR, Mossbauer...
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• 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
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Ba(Fe1-xCox)2As2
SDW
SC
x = dopage
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Ba(Fe0.94Co0.06)2As2
0
S)c
(MK
S v
olum
ic
-1
0 10 20T (K)
Superconducting fraction : 90 - 100%
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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
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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
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Nature of
SDW
Ba(Fe1-xCox)2As2Nature of magnetism ?
SDW
SCSC
x = dopagex(Co) %0.15
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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
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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
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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)
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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
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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
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SDW
Ba(Fe1-xCox)2As2
SDW
SCSC
x = dopagex(Co) %0.15
what is doping really doing ?
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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
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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)
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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
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Ru doping homogeneous from macroscopic probesfrom macroscopic probes
transport & neutrons
Rullier-Albenque et al., PRB 2010 Kim et al. PRB 2011
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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
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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)
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How to reconcile NMR inhomogeneit & NMR inhomogeneity &
macroscopic homogeneity ?
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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
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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
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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
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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
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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
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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 (%)
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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