The Positive Muon as a Condensed Matter Probe

1. The Positive Muon as a Condensed Matter Probe Francis Pratt ISIS Facility, Rutherford Appleton Laboratory, UK

2. Introduction • The muon and its properties • The range of mSR techniques • Molecular Magnetism • Critical behaviour in a layered magnet • Spin fluctuations in a highly ideal 1DHAF • Molecular Superconductors • Stability of the vortex lattice • Universal scaling of the electrodynamic response • Dynamical Processes in Polymers • Charge mobility in polymers • Polymer surface dynamics

3. Familiar Particles and Muons

4. Familiar Particles and Muons

5. Familiar Particles and Muons A positive muon behaves like an unstable light isotope of hydrogen

6. Primary International Facilities for mSR ISIS PSI TRIUMF JPARC Continuous sources Pulsed sources

7. Producing Muons at ISIS 50 m

8. View of the ISIS Experimental Hall

9. The mSR Sequence of Events 1) Pions produced from proton beam striking carbon target e.g. p + p  p + n + p+ p + n  n + n + p+ • Pion decay:p+ m++nm (lifetime 26 ns) the muons are 100% spin polarised 3) Muon implantation into sample of interest • Muons experience their local environment: spin precession and relaxation • Muon decay:m+ e++ne+nm (lifetime 2.2 ms) we detect the asymmetric positron emission

10. Nature of the Muon Probe States • Paramagnetic states • Muonium (Mu = m+e); the muon analogue of the neutral hydrogen atom • … highly reactive in many molecular systems, leading to the formation of molecular radicals, e.g. • Diamagnetic states • Bare interstitial m+ • Chemically bonded closed shell states, e.g.

11. Formation of Muon Probe States Ionisation energy loss to below 35 keV m+ (MeV) m+ Radiolytic e-

12. Formation of Muon Probe States Charge exchange cycle e- capture Ionisation energy loss to below 35 keV m+ (MeV) m+13.5 eVMu e- loss Radiolytic e-

13. Formation of Muon Probe States Charge exchange cycle Thermal Mu PARAMAGNETIC e- capture Ionisation energy loss to below 35 keV m+ (MeV) m+13.5 eVMu e- loss Radiolytic e- Thermal m+ DIAMAGNETIC

14. Formation of Muon Probe States Charge exchange cycle Thermal Mu PARAMAGNETIC e- capture Ionisation energy loss to below 35 keV m+ (MeV) m+13.5 eVMu e- loss Chemical reaction Radiolytic e- Thermal m+ DIAMAGNETIC Mu Radical PARAMAGNETIC

15. Formation of Muon Probe States Charge exchange cycle Thermal Mu PARAMAGNETIC e- capture Ionisation energy loss to below 35 keV m+ (MeV) m+13.5 eVMu e- loss Chemical reaction Delayed Mu formation Radiolytic e- Ionization/ reaction Thermal m+ DIAMAGNETIC Mu Radical PARAMAGNETIC

16. Positron Emission and Detection W(q) = 1+ a cos q

17. Positron Emission and Detection W(q) = 1+ a cos q LF/ZF Sm B F

18. Positron Emission and Detection W(q) = 1+ a cos q LF/ZF TF U Sm Sm B F B F D

19. Muon Instruments at ISIS

20. mSRRRR… • Muon Spin Rotation • Muon Spin Relaxation • Muon Spin Resonance • Muon Spin Repolarisation

21. Muon Spin Rotation

22. Energy Levels

23. Energy Levels Single frequency wD wD/2p = 13.55 kHz/G

24. Energy Levels

25. Energy Levels Pair of frequencies A = w1 + w2

26. Energy Levels

27. Energy Levels Still one pair of frequencies at high B A = w1 + w2

28. TF Muon Spin Rotation Spectoscopy of Muoniated Molecular Radicals 2kG TF TTF Singly occupied molecular orbital of muoniated radical Magn. Res. Chem. 38, S27 (2000)

29. Muon Spin Relaxation

30. RF Resonance • B swept to match a level splitting with the RF frequency also • 90⁰ pulse techniques • Spin echoes • Spin Decoupling

31. Paramagnetic/Diamagnetic State Conversion measured with RF Polybutadiene above and below the Glass Transition T>Tg D → P T<Tg T<Tg P → D

32. Level Crossing Resonance DM=1 mLCR Resonances classified in terms of M = me + mm + mp DM = 1 muon spin flip: B0 = Am / 2gm (needs anisotropy) DM = 0 muon-proton spin flip-flop: B0 = (Am- Ak ) / 2(gm- gk) (to first order)

33. Quadrupolar Level Crossing Resonance 14N quadrupolar mLCR in TTF-TCNQ T>TCDW T<TCDW 14N m+ Quadrupolar splitting depends on electric field gradient at the nucleus

34. Repolarisation of Mu • Progressive quenching of the muon spin from its dipolar and hyperfine couplings • Useful for orientationally disordered systems with residual anisotropy

35. Repolarisation of Mu Quenching of the superhyperfine coupling to nuclear spins Sensitive to total number of spins e.g. protonation/deprotonation studies

36. Molecular Magnetism

37. Critical Fluctuations in a Co Glycerolate Layered Magnet Co (S=3/2) Mohamed Kurmoo, University of Strasbourg

38. Critical Exponents Measured with mSR Local susceptibility: c (T - TN ) -g Relaxation rate: l | T -TN | -w Magnetic order: M  (TN - T) b

39. Comparison with Established Universality Classes Scaling relations: a = 2 – 2b – gn = (2b + g)/d h = 2 – g/n Dynamic exponent: z = d(2b + w)/(2b + g) = 1.25(6) (c.f. z=d/2=1.5 for 3D AF)

40. Quantum Critical Fluctuations in a Highly Ideal Heisenberg Antiferromagnetic Chain Structure of DEOCC-TCNQF4 viewed along the chain axis Molecular radical providing the S=1/2 Heisenberg spins Cyanine dye molecule providing the bulky diamagnetic spacers

41. Just How Ideal is DEOCC-TCNQF4? Zero field muon spin relaxation for DEOCC-TCNQF4 at 20 mK and 1 K. Comparison of DEOCC-TCNQF4 with other benchmark 1DHAF magnets. J = 110 K but no LRMO down to 20 mK ! i.e. TN / J < 2 x 10-4

42. T-dependent Relaxation from Spinons T dependent mSR relaxation rate l at 3 mT with contributions from q=p/a and q=0. The 1DHAF spin excitation spectrum contributing to l.

43. Anisotropic Spin Diffusion The B dependence of l at 1 K. The dotted line illustrates the behaviour expected for ballistic spin transport. The solid line is a fit to an anisotropic spin diffusion model. The form of the spin correlation function S(t) that is consistent with the data. Crossover between 1D and 3D diffusion takes place for time scales longer than ~10 ns.

44. Summary of 1DHAF Magnetic Parameters TN (mK) |J'| (mK) J (K) TN/J (10-2) |J'/J| (10-3) Experiment <20 2.2 110 <0.018 0.020 Estimate 7 <7 0.006 <0.06 Sr2CuO3 5.4 K 2 K 2200 0.25 0.93 CuPzN 107 46 10.3 1.0 4.4 KCuF3 39 K 21 K 406 9.6 52 DEOCC-TCNQF4 looks like the best example of the 1D Heisenberg Antiferromagnet yet discovered PRL 96, 247203 (2006)

45. Molecular Superconductors

46. Measuring Properties of Type II Superconductors H < Hc1 : Meissner state Surface measurement: l Abrikosov Vortex Lattice Hc1 < H < Hc2 : Vortex state Bulk measurement: l, x saddles RMS Width: Brms or s Lineshape: b = (Bave - Bpk) / Brms (skewness) cores minima

47. Muon Spin Rotation Spectrum

48. Melting/Decoupling of the Vortex Lattice in the Organic Superconductor ET2Cu(SCN)2 3D Flux Lattice Decoupled 2D Layers