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

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

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

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

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)

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

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

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

e+ m+ e+ detector U incoming muon counter sample detector time D 2.5 e+ detector D U 1.7

e+ m+ e+ detector U incoming muon counter sample detector time D 2.5 e+ detector D U 1.7 D 1.2

e+ m+ e+ detector U incoming muon counter sample detector time D 2.5 e+ detector D U 1.7 D 1.2 D 9.0 + 106-107 more…

asy(t) = A0 Gz(t) (+ baseline) Histograms for opposing counters asy(t) = A0 Gz(t) (+ baseline) a Total asymmetry ~0.2-0.3 Muon spin polarization function 135.5 MHz/T Represents muons in a uniform field

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]+

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

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

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

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

(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

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

Ca2RuO4 AF insulator, moment 1.3B Competition between A- and B- type ordering TN  110-150K Ca doping induces Mott transition Decreased bandwidth Increased on-site Coulomb repulsion → Increased U/W Ru-Ru in-plane dist > Sr2RuO4 RuO6 flattening, tilting

Ca2-xSrxRuO4 M-I transition near x=0.2 (I-II) Near x=0.5: (II-III) Susceptibility @ 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 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 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.

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

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 ~ 50-100 G Dilution fridge 15mK < T < 10K He gas-flow cryo 1.7K < T < 300K

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

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

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

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

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

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

LF temp scans: map out dynamics

Comparison of ZF & LF field estimates tanh(H/Ho) 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)O4 Past: Sr2RuO4 p-wave SC Tc  1.5K, TRSB magnetic fluctuations Sr2Ru1-yTiyO4 y  0.002 suppresses SC neutrons: incommensurate AF y = 0.09 Ca2RuO4 AF insulator TN  100-150K 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