(Sr,Ca)(Ru,Ti)O Revealed by SR

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The Magnetic Phase Diagram of
(Sr,Ca)
2
(Ru,Ti)O
4

Revealed by
m
SR

Jeremy P. Carlo

jeremy.carlo@nrc.gc.ca

June 2, 2010

Columbia University


Canadian Neutron Beam Centre,

National Research Council

Outline


Overview


Correlated electron materials


Magnetic order


Superconductors


The
m
SR method


Local probe of magnetism


(Sr,Ca)
2
RuO
4

& Sr
2
(Ru,Ti)O
4


Superconductivity


Magnetic Phase Diagram


Overview


Relation between magnetic order & superconductivity


BCS: Cooper pairs: electron
-
phonon interaction


High
-
T
c
: magnetic fluctuations more important



“Canonical” cuprate



phase diagram:



Parent compound: AF



Magnetic order close to



SC dome

Overview


Ongoing questions:


Behavior of different families of unconventional SCs?



Cuprates

Heavy
fermion

SCs

Organic SCs


Sr
2
RuO
4


Fe
pnictides


etc.


How do magnetism / magnetic fluctuations relate?


“Normal” state behavior, M
-
I / structural links?



Holy Grail:


What is the comprehensive theory

of unconventional superconductivity?



Present Study


The
m
SR method


Production of muons


Protons extracted from cyclotron/synchrotron


p

+
low Z production target


+

+
stuff



+


m
+

+

m


parity violation: beam is
spin polarized


separate out positrons, etc.


collimate / steer beam to sample



Polarized muon sources:


TRIUMF, Vancouver BC


PSI, Switzerland


ISIS, UK
(pulsed)


KEK, Japan
(pulsed)



Muon beam


Positive muons
m
+


Can rotate


polarization


Insert muons


one at a time


Come to rest


Interstitial sites


Near anions


Along bonds


Continuous
-
beam
m
SR

Decay Asymmetry

Muon spin


at decay

e

= E / E
max

normalized e
+

energy

Detection:

m
+


e
+

+

m

+

e

e
+

e+ detector U

sample

m
+

e+ detector D

detector

time

D 2.5

incoming

muon counter

e
+

e+ detector U

sample

m
+

e+ detector D

detector

time

D 2.5

U 1.7

incoming

muon counter

e
+

e+ detector U

sample

m
+

e+ detector D

detector

time

D 2.5

U 1.7

D 1.2

incoming

muon counter

e
+

e+ detector U

sample

m
+

e+ detector D

detector

time

D 2.5

U 1.7

D 1.2

D 9.0

incoming

muon counter

+ 10
6
-
10
7

more…

Represents

muons in a

uniform field

135.5 MHz/T

Histograms for
opposing counters

asy(t) = A
0

G
z
(t)

(+ baseline)

Total asymmetry


~0.2
-
0.3

Muon spin

polarization

function

a

Field configurations


ZF
-
m

:


m
+

sees: field due to nearby moments


Spontaneous ordering?


Precession


Rapid relaxation




vs. out
-
of
-
plane doping

vs. in
-
plane doping

T
-
dependence

(in
-
plane doping)

T
-
dependence

(out
-
of
-
plane doping)

NbO
6

La

(CuCl
)LaNb
2
O
7

[CuCl]
+



Example

Field configurations




LF
-
m

:


m
+

sees: skewed


local field distribution



Static order


Decoupling if
H
appl

~
B
int


Dynamic order


No decoupling


Drift of “1/3 tail”








H



楮楴楡氠浵潮m獰楮

Example

Field configurations


wTF
-
m

:


Calibration of baseline (
a
), total asymmetry (A
0
)


m
+

sees:


(mostly) applied field (paramagnetic state),


appl. + internal fields (ordered state)







H



楮楴楡氠浵潮m獰楮

Determine ordered,


PM fractions

Example

Field configurations






(strong)
TF
-
m

:


Order induced by applied field


Metamagnetism, etc.



Vortex lattice in Type
-
II SC


Rlx



<

B
2
>


1/

2


n
s
/m
*




= penetration depth


n
s
/m
*

= superfluid density



Polyxtal samples:


distribution broadened


~ Gaussian

=> Gaussian rlx



=> 1/

2




=> sf. density




H



楮楴楡氠浵潮⁳m楮

J. E. Sonier, 1998 & 2007

Sr
n
+1
Ru
n
O
3
n
+1


Ruddlesden
-
Popper series


n
=

: SrRuO
3

(113)


perovskite

structure


Ferromagnetic,
T
c



165K


n
=3: Sr
4
Ru
3
O
10

(4
-
3
-
10)


multi
-
layered structure


FM,
T
c



105K


n
=2: Sr
3
Ru
2
O
7


(327)


quantum
metamagnetism


FM, AF fluctuations


mag. ordering w/
Mn


n
=1: Sr
2
RuO
4


(214)


Unconventional SC
T
c



1.5K




Spin
-
triplet pairing, p
-
wave


isostructural

to LBCO, LSCO

RuO
6
6

Sr

(Sr,Ca)RuO
3

= ‘113’


n=



3
-
D structure


Ca/Sr substitution


Sr
x
Ca
1
-
x
RuO
3



isoelectronic doping


FM suppressed
x



0.25


Phase separation, QPT

Sr
2
RuO
4

= ‘214’


n=1


SC state (Maeno
et al.

1994)


T
c

up to 1.5 K


NMR: Spin
-
triplet pairing


TRSB


(Luke
et al.

1996)


distinguish between p
-
wave states


Incommensurate spin fluctuations



q ≈ (

0.6

/a,

0.6

/a, 0)


Normal state: 2
-
D Fermi liquid



Doping:


“Out
-
of
-
plane:” Ca on Sr site: Sr
x
Ca
2
-
x
RuO
4



“In
-
plane:” Ti on Ru site: Sr
2
Ru
1
-
y
Ti
y
O
4




Small doping on either site suppresses SC



Maeno et al. 1994

Fermi surface:

MacKenzie & Maeno, 2003

Luke et al. 1996

Ca
2
RuO
4


AF insulator, moment

1.3
m
B


Competition between A
-

and B
-

type ordering



T
N


110
-
150K


Ca doping induces Mott transition


Decreased bandwidth


Increased on
-
site Coulomb repulsion


→ Increased U/W


Ru
-
Ru in
-
plane


dist > Sr
2
RuO
4


RuO
6

flattening, tilting

Ca
2
-
x
Sr
x
RuO
4

M
-
I transition near
x
=0.2
(I
-
II)

Near
x
=0.5:
(II
-
III)

Sharp increase in susceptibility

Correlations more FM
-
ish

Low susc @ higher
x


Old Picture: Ordering at low
x

only


Antiferro. near
x
=0


Susc. peak near
x
=0.5


Paramagnetic at higher
x


SC at
x
=2


m
SR:

Rapid relaxation observed 0.2 ≤
x

≤ 1.6

Peaks near
x



0.5, 1.5

Ordered ground state throughout!


Nakatsuji & Maeno, 2000.

Susceptibility @ 2K:

Nakatsuji & Maeno, 2003.

Sr
2
Ru
1
-
y
Ti
y
O
4


y
=0: SC Sr
2
RuO
4




<0.2% Ti doping suppresses T
c




>2.5% doping induces magnetic ground state


neutrons:
Braden et al.

(2002)


Incommensurate AF in
y
=0.09


q



(0.3, 0.3, q
z
)


m
SR: rapid relaxation


with increasing
y
.

from MacKenzie et al. 2003

Experiments


Samples


(Ca
2
-
x
Sr
x
)
2
RuO
4

x

= 0.0, 0.2, 0.3, 0.5, 0.57, 0.65,







0.9, 1.0, 1.4, 1.5, 1.6, 1.8, 1.95


Sr
2
(Ru
1
-
y
Ti
y
)O
4

y

= 0.01, 0.03, 0.05, 0.09


single xtals from Kyoto U. (Maeno et al. or







Tsukuba (Yoshida et al.


ZF
-

& LF
-
m
SR: M20 (LAMPF) and/or M15 (DR)

DC Susceptibility: ZFC, FC, H ~ 50
-
100 G

He gas
-
flow cryo

1.7K < T < 300K

Dilution fridge

15mK < T < 10K

Ca
2
RuO
4


m
SR spectra:


Sum of 2 frequencies

Ca
2
RuO
4

ZF
-
m


ZF
-
m
SR

Temperature Scans

(Ca,Sr) system

ZF
-
m
SR Temperature Scans

(Ru,Ti) system






dynamic

+
static




d

a
s


“root
-
exponential”
“Lorentzian Kubo
-
Toyabe”





Uemura “spin glass” function (
Uemura, 1985
):


a
s

= a

Q


d

= 4a
2
(1
-
Q)/


Edwards
-
Anderson
order parameter

Field
width

Fluctuation
rate


ZF Relaxation vs. Temp: Magnetic ordering!

Define:
Rlx

= sqrt (

d
2
+
a
s
2

)

Fit to:
Rlx
(
T
) = R [ 1


(
T
/
To
)
g

]

all

Ti
only

Ca
only

zoom


LF @ base temp: decoupling → static order

Static ordering at base temp!

Fit to tanh(
H
/
Ho
)


LF temp scans: map out dynamics


Comparison of ZF & LF field estimates

R [ 1


(T/To)
g

]

Adapted from Braden et al. (2002)


Neutrons: Braden


Muons: present study

DC Susceptibility

Curie
-
Weiss:

more

AF

Old view
:

New View
:

Summary: (Sr,Ca)
2
(Ru,Ti)O
4

Past:

Sr
2
RuO
4

p
-
wave SC



T
c



1.5K, TRSB




magnetic fluctuations

Sr
2
Ru
1
-
y
Ti
y
O4


y


0.002 suppresses SC


neutrons: incommensurate AF y = 0.09

Ca
2
RuO
4

AF insulator



T
N



100
-
150K

Sr
2
-
x
Ca
x
RuO4



M
-
I transition x



0.2



susceptibility peak x



0.5






New:


Sr
2
-
x
Ca
x
RuO
4



muons : magnetic order over almost entire range



x

= 0: commensurate AF, gone by
x

= 0.2


peaks x


0.5 (FM
-
ish?), 1.5 (more AF)


incommensurate AF / SDW ?


need long
-
range magnetic probe!


Sr
2
Ru
1
-
y
Ti
y
O
4



muons: rapid relaxation y ≥ 0.03



susc: large negative

w

→ AF