1. Canadian Neutron Beam Centre, National Research Council
The Magnetic Phase Diagram of (Sr,Ca)2(Ru,Ti)O4 Revealed by mSR
Jeremy P. Carlo
Columbia University
Canadian Neutron Beam Centre,
National Research Council
June 2, 2010

2. Outline Overview The SR method (Sr,Ca)2RuO4 & Sr2(Ru,Ti)O4
Correlated electron materials
Magnetic order
Superconductors
The SR method
Local probe of magnetism
(Sr,Ca)2RuO4 & Sr2(Ru,Ti)O4
Superconductivity
Magnetic Phase Diagram

3. Overview Relation between magnetic order & superconductivity
BCS: Cooper pairs: electron-phonon interaction
High-Tc: magnetic fluctuations more important
“Canonical” cuprate phase diagram:
Parent compound: AF
Magnetic order close to SC dome

5. Overview Ongoing questions:
Behavior of different families of unconventional SCs?
Cuprates Heavy fermion SCs Organic SCs
Sr2RuO4 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

6. The SR method Production of muons
Protons extracted from cyclotron/synchrotron
p + low Z production target → + + stuff
+ → + + 
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)

8. Continuous-beam SR Muon beam Positive muons +
Can rotate polarization
Insert muons one at a time
Come to rest
Interstitial sites
Near anions
Along bonds

9. e = E / Emax normalized e+ energy
Decay Asymmetry
Muon spin
at decay
Detection:
+ → e+ + + e
e = E / Emax normalized e+ energy

10. e+ m+ e+ detector U incoming muon counter sample detector time D 2.5
e+ detector D

11. e+ m+ e+ detector U incoming muon counter sample detector time D 2.5
e+ detector D U

12. e+ m+ e+ detector U incoming muon counter sample detector time D 2.5
e+ detector D U D

13. e+ m+ e+ detector U incoming muon counter sample detector time D 2.5
e+ detector D U D D
more…

14. asy(t) = A0 Gz(t) (+ baseline)
Histograms for opposing counters
asy(t) = A0 Gz(t) (+ baseline) a
Total asymmetry ~
Muon spin
polarization
function
135.5 MHz/T
Represents
muons in a
uniform field

15. Field configurations ZF-SR:  sees: field due to nearby moments
Spontaneous ordering?
Precession
Rapid relaxation
T-dependence
(in-plane doping)
vs. out-of-plane doping
T-dependence
(out-of-plane doping)
vs. in-plane doping
Example
(CuCl)LaNb2O7 La
NbO6
[CuCl]+

16. Field configurations LF-SR: Decoupling if Happl ~ Bint Example
 sees: skewed local field distribution
Static order
Decoupling if Happl ~ Bint
Dynamic order
No decoupling
Drift of “1/3 tail”
H  initial muon spin

17. Field configurations wTF-SR:
Calibration of baseline (a), total asymmetry (A0)
 sees:
(mostly) applied field (paramagnetic state),
appl. + internal fields (ordered state)
H  initial muon spin
Determine ordered,
PM fractions
Example

18. Field configurations (strong) TF-SR: Order induced by applied field
Metamagnetism, etc.
Vortex lattice in Type-II SC
Rlx  √<B2>  1/2  ns /m*
 = penetration depth
ns /m* = superfluid density
Polyxtal samples: distribution broadened ~ Gaussian
=> Gaussian rlx
=> 1/2
=> sf. density
H  initial muon spin
J. E. Sonier, 1998 & 2007

19. Srn+1RunO3n+1 Ruddlesden-Popper series n=: SrRuO3 (113)
perovskite structure
Ferromagnetic, Tc  165K
n=3: Sr4Ru3O10 (4-3-10)
multi-layered structure
FM, Tc  105K
n=2: Sr3Ru2O7 (327)
quantum metamagnetism
FM, AF fluctuations
mag. ordering w/ Mn
n=1: Sr2RuO4 (214)
Unconventional SC Tc  1.5K
Spin-triplet pairing, p-wave
isostructural to LBCO, LSCO Sr

20. (Sr,Ca)RuO3 = ‘113’ Past Work: n= 3-D structure Ca/Sr substitution
SrxCa1-xRuO3
isoelectronic doping
FM suppressed x  0.25
Phase separation, QPT

21. Sr2RuO4 = ‘214’ n=1 SC state (Maeno et al. 1994) Tc up to 1.5 K
MacKenzie & Maeno, 2003
Fermi surface:
n=1
SC state (Maeno et al. 1994)
Tc 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: SrxCa2-xRuO4
“In-plane:” Ti on Ru site: Sr2Ru1-yTiyO4
Small doping on either site suppresses SC
Luke et al. 1996

22. Ca2RuO4 AF insulator, moment 1.3B
Competition between A- and B- type ordering
TN  K
Ca doping induces Mott transition
Decreased bandwidth
Increased on-site Coulomb repulsion
→ Increased U/W
Ru-Ru in-plane dist > Sr2RuO4
RuO6 flattening, tilting

23. Ca2-xSrxRuO4 M-I transition near x=0.2 (I-II) Near x=0.5: (II-III)
2K:
M-I transition near x=0.2 (I-II)
Near x=0.5: (II-III)
Sharp increase in susceptibility
Correlations more FM-ish
Low 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
SR:
Rapid relaxation observed 0.2 ≤ x ≤ 1.6
Peaks near x  0.5, 1.5
Ordered ground state throughout!
Nakatsuji & Maeno, 2000.
Nakatsuji & Maeno, 2003.

24. Sr2Ru1-yTiyO4 y=0: SC Sr2RuO4 <0.2% Ti doping suppresses Tc
>2.5% doping induces magnetic ground state
neutrons: Braden et al. (2002)
Incommensurate AF in y=0.09
q  (0.3, 0.3, qz)
SR: rapid relaxation with increasing y.
from MacKenzie et al. 2003

25. Experiments
Samples (Ca2-xSrx)2RuO4 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 Sr2(Ru1-yTiy)O4 y = 0.01, 0.03, 0.05, 0.09 single xtals from Kyoto U. (Maeno et al. or Tsukuba (Yoshida et al. ZF- & LF-mSR: M20 (LAMPF) and/or M15 (DR) DC Susceptibility: ZFC, FC, H ~ G
Dilution fridge
15mK < T < 10K
He gas-flow cryo
1.7K < T < 300K

26. Ca2RuO4
Ca2RuO4 ZF-SR
SR spectra:
Sum of 2 frequencies

27. ZF-SR
Temperature Scans
(Ca,Sr) system

28. ZF-SR Temperature Scans
(Ru,Ti) system

29. Edwards-Anderson order parameter
Uemura “spin glass” function (Uemura, 1985):
dynamic static
d as
“root-exponential” “Lorentzian Kubo-Toyabe”
Field width
as = a √Q
ld = 4a2(1-Q)/n
Fluctuation rate

30. ZF Relaxation vs. Temp: Magnetic ordering!
Define: Rlx = sqrt ( d2 + as2 )
Fit to: Rlx(T) = R [ 1 – (T/To)g ]
zoom
all
Ti only
Ca only

31. LF @ base temp: decoupling → static order
Fit to tanh(H/Ho)
Static ordering at base temp!

32. LF temp scans: map out dynamics

33. Comparison of ZF & LF field estimates
tanh(H/Ho)
R [ 1 – (T/To)g ]

35. Adapted from Braden et al. (2002)
Neutrons: Braden
Muons: present study

36. DC Susceptibility
Curie-Weiss:
more AF

37. Old view:
New View:

38. Summary: (Sr,Ca)2(Ru,Ti)O4
Past:
Sr2RuO4 p-wave SC
Tc  1.5K, TRSB
magnetic fluctuations
Sr2Ru1-yTiyO4
y  suppresses SC
neutrons: incommensurate AF y = 0.09
Ca2RuO4 AF insulator
TN  K
Sr2-xCaxRuO4
M-I transition x  0.2
susceptibility peak x  0.5
New:
Sr2-xCaxRuO4
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!
Sr2Ru1-yTiyO4
muons: rapid relaxation y ≥ 0.03
susc: large negative w → AF