Introduction to The World's μSR Facilities Basic Techniques of μSR μSR “Toolbox” for QM Examples of μSR in HT c SC Jess H. Brewer CIAR QM Summer School UBC, 7 May 2008 Jess H. Brewer CIAR QM Summer School UBC, 7 May 2008 Visit our Web site!

Where in the World is μSR?

TRIUMF

4.1 MeV   = 2.2  s 500 MeV   = 26 ns Primary Production Target

Pion Decay: Conservation of Linear Momentum: The  + is emitted with momentum equal and opposite to that of the    +   + +  Conservation of Angular Momentum:  + and  have equal and opposite spin. A pion stops in the “skin” of the primary production target. It has zero linear momentum and zero angular momentum. Weak Interaction: Only “left-handed”  are created. Thus the emerging  + has its spin pointing antiparallel to its momentum direction.

Muon Decay Neutrinos have negative helicity, antineutrinos positive. An ultrarelativistic positron behaves like an antineutrino. Thus the positron tends to be emitted along the muon spin when ν e and ν μ go off together (highest energy e + ).

 + Decay Asymmetry Angular distribution of positrons from  + decay. The asymmetry is a = 1/3 when all positron energies are detected with equal probability.

Transverse Field (TF) µ + SR Typical time spectrum (histogram)

Zero Field (ZF)- µ + SR Typical asymmetry spectrum ( B – F ) ────── ( B + F ) B F

Brewer's List of μSR Acronyms Transverse Field Zero Field Longitudinal Field Avoided Level Crossing Resonanc e Muon Spin Echo Muon Spin Resonanc e Fourier Transform µSR

“Themes” in µ + SR Muonium as light Hydrogen (Mu = µ + e - ) (H = p + e - ) ● Mu vs. H atom Chemistry: - gases, liquids & solids - Best test of reaction rate theories. - Study “unobservable” H atom rxns. - Discover new radical species. ● Mu vs. H in Semiconductors: - Until recently, µ + SR → only data on metastable H states in semiconductors! The Muon as a Probe ● Quantum Diffusion: µ + in metals (compare H + ); Mu in nonmetals (compare H). ● Probing Magnetism: unequaled sensitivity - Local fields: electronic structure; ordering - Dynamics: electronic, nuclear spins ● Probing Superconductivity: (esp. H T c SC) - Coexistence of SC & Magnetism - Magnetic Penetration Depth λ - Coherence Length ξ

μSR Toolbox Quantum Materials μSR Toolbox for Quantum Materials ZF-µSRStatic Local Magnetic Fields: ZF-µSR & Static Local Magnetic Fields: Volume fraction of AF/SG order even in powder samples Sensitive to very weak fields (~1 G) T -dependence of B loc  magnetic phase diagram TF-µSRVortex Lattice: TF-µSR & Vortex Lattice: Penetration depth (T,H )  SC phase diagram Coherence length  (T,H ) Pinning, melting etc.

Motion of Muon Spins in Static Local Fields: = Expectation value of a muon's spin direction (a) All muons "see" same field B : for B || S  nothing happens for B  S  Larmor precession:     2    B |   = MHz/T SS (b) All muons "see" same | B | but random direction : 2/3 of S  precesses at   1/3 of S  stays constant

Antiferromagnetism in YBa 2 Cu 3 O ZF S m (0)  c T = 15 K 1 1/3 0 SmSm

● Two muon sites: most at Site 1 ("4 MHz site"), less at Site 2 ("18 MHz site"). ● Changes at 10K and 80K, cause unknown. Antiferromagnetism in YBa 2 Cu 3 O

Magnetism in YBa 2 Cu 3 O 6.35 ZF X T = 4 K /3 0 SmSm

Magnetism in YBa 2 Cu 3 O "3 MHz site" only

Phase Diagram of YBa 2 Cu 3 O x ca. 1990

Motion of Muon Spins in Static Local Fields: = Expectation value of one muon's direction (a) All muons "see" same field B : for B || S  nothing happens for B  S  Larmor precession:     2    B |   = MHz/T SS (b) All muons "see" same | B | but random direction : 2/3 of S  precesses at   1/3 of S  stays constant (c) Local field B random in both magnitude and direction: All do not return to the same orientation at the same time (dephasing)  SS "relaxes" as G zz (t ) [Kubo & Toyabe, 1960's]

ZF-  + SR: Kubo-Toyabe Relaxation due to Nuclear Dipolar Fields "relaxation function" G z z (t ) Hayano, Uemura et al., 1978 (ZF ) LF =

Dynamic Gaussian Kubo- Toyabe Relaxation due to fluctuating local fields

Combined Nuclear Dipolar and Paramagnetic Relaxation MnSi ZF (1984) 150 K 46 K 31 K (Itinerant helimagnet below T c ≈ 29.5 K)

Nuclear Dipolar  "Other" Relaxation 200 1

Nuclear Dipolar  "Other" Relaxation 2002

“Anyon” Search (1990) found similar “dips” in the dipolar relaxation rate around 50K.

wTF-µ + SR:

E × B velocity selector ("DC Separator" or Wien filter) for surface muons: Removes beam positrons Allows TF-µ + SR in high field (otherwise B deflects beam)

Magnetic Field Distribution of a Vortex Lattice NbSe 2 Time (  s) AP x (t), AP y (t) Frequency (MHz) Real Amplitude (  )

HTF-  + SR FFT Lineshapes: Vanadium 1.6 kG 20 mK 2.6 K 1.6 K Fittime Fit in the time domain.

H c ab in the Meissner & Vortex States d-wave

The End

GaAs backing Ag reference Sticky aluminized Mylar 1 cm GaAs backing sample Muon Beam StoppingLuminosity