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  SR 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

5. A positive muon behaves like an unstable light isotope of hydrogen

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

7. Producing Muons at ISIS 50 m

8. View of the ISIS Experimental Hall

9. The  SR Sequence of Events 1)Pions produced from proton beam striking carbon target e.g.p + p  p + n +  + p + n  n + n +  + 2)Pion decay:  +   + +  (lifetime 26 ns) the muons are 100% spin polarised 3)Muon implantation into sample of interest 4)Muons experience their local environment: spin precession and relaxation 5)Muon decay:  +  e + + e +  (lifetime 2.2  s) we detect the asymmetric positron emission

10. Nature of the Muon Probe States Paramagnetic states Muonium (Mu =  +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 1)Bare interstitial  + 2)Chemically bonded closed shell states, e.g.

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

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

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

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

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

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

17. Positron Emission and Detection W(  ) = 1+ a cos  SS BF LF/ZF

18. Positron Emission and Detection W(  ) = 1+ a cos  SS BF LF/ZF SS BF TF U D

19. Muon Instruments at ISIS

20.  SRRRR… Muon Spin Rotation Muon Spin Relaxation Muon Spin Resonance Muon Spin Repolarisation

21. Muon Spin Rotation

22. Energy Levels

23. Single frequency  D  D /2  = 13.55 kHz/G

24. Energy Levels

25. Pair of frequencies A =  1 +  2

26. Energy Levels

27. Still one pair of frequencies at high B A =  1 +  2

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

29. Muon Spin Relaxation

30. RF Resonance B swept to match a level splitting with the RF frequency also 90 ⁰ pulse techniques Spin echoes Spin Decoupling

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

32. Level Crossing Resonance Resonances classified in terms of M = m e + m  + m p  M = 1 muon spin flip: B 0 = A  / 2   (needs anisotropy)  M = 0muon-proton spin flip-flop: B 0 = (A   A k ) / 2(    k  (to first order)  M=1  LCR

33. Quadrupolar Level Crossing Resonance 14 N quadrupolar  LCR in TTF-TCNQ T>T CDW T<T CDW 14 N ++ 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 Mohamed Kurmoo, University of Strasbourg Co (S=3/2)

38. Critical Exponents Measured with  SR Magnetic order: M  (T N - T)  Relaxation rate:   | T -T N | -w Local susceptibility:   (T - T N ) 

39. Comparison with Established Universality Classes Scaling relations:  = 2 – 2  –  = (2  +  )/d  = 2 –  / Dynamic exponent: z = d(2  + w)/(2  +  ) = 1.25(6) (c.f. z=d/2=1.5 for 3D AF)

40. Quantum Critical Fluctuations in a Highly Ideal Heisenberg Antiferromagnetic Chain Molecular radical providing the S=1/2 Heisenberg spins Cyanine dye molecule providing the bulky diamagnetic spacers Structure of DEOCC-TCNQF 4 viewed along the chain axis

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

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

43. Anisotropic Spin Diffusion The B dependence of 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. T N (mK)|J'| (mK) J (K) T N /J (10 -2 )|J'/J| (10 -3 ) Experiment <202.2 110 <0.018 0.020 Estimate 7 <7 0.006 <0.06 Sr 2 CuO 3 5.4 K 2 K 22000.25 0.93 CuPzN 107 46 10.31.0 4.4 KCuF 3 39 K21 K 406 9.6 52 DEOCC-TCNQF 4 looks like the best example of the 1D Heisenberg Antiferromagnet yet discovered Summary of 1DHAF Magnetic Parameters PRL 96, 247203 (2006)

45. Molecular Superconductors

46. Measuring Properties of Type II Superconductors H < H c1 : Meissner state Surface measurement: H c1 < H < H c2 : Vortex state Bulk measurement:  cores minima saddles RMS Width: B rms or  Lineshape:  = (B ave - B pk ) / B rms (skewness) Abrikosov Vortex Lattice

47. Muon Spin Rotation Spectrum

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

61. Overall Vortex Phase Diagrams d8-ETSCN h8-ETSCN

62. Scaling Properties in the Electrodynamic Response of Molecular Superconductors Famous ‘Uemura Plot’ for cuprates and other superconductors T c   (  SR relaxation rate) Equivalently: T c  n s /m* T c   s (superfluid strength) T c  1/ 2 ( is penetration depth) What about molecular superconductors? n/m* is small and doesn’t vary much, so they should sit in one small region of the plot

63.  s across the range of Molecular Superconductors

64. Uemura Plot for the Molecular Superconductors Molecular systems have their own empirical scaling law: T c follows 1/ 3 rather than 1/ 2 ⇒ T c  (n s /m b ) 3/2

65. Key: 1.  -BETS 2 GaCl 4 2. TMTSF 2 ClO 4 3.  -ET 2 NH 4 Hg(SCN) 4 4.  -ET 2 IBr 2 5. -BETS 2 GaCl 4 6.  -ET 2 Cu(NCS) 2 7. K 3 C 60 8. Rb 3 C 60 Closer look at Superconducting Parameters vs Conductivity 2D 1D 2D 3D 1D, 2D & 3D systems SC properties correlate with highest  direction Note the completely opposite  s -  0 scaling between molecular and cuprate superconductors  0 - 1.05  0 - 0.77  0 + 0.75 PRL 94, 097006 (2005)

66. Is there a single controlling parameter? The simplicity of the scaling suggests a single dominant control parameter U/W is a likely candidate for molecular systems, which are generally rather close to a Mott insulator phase Real pressure as well as ‘chemical pressure’ can be used to tune U/W Increasing pressure decreases U/W, increases  0 and decreases T c and  s, following the trends expected from the scaling curves

67. Dynamical Mean-Field Theory for Calculating effect of U/W on  s Loss of quasiparticle spectral weight is expected as the Mott-Hubbard transition is approached

68. Superfluid Strength vs U/W Powell and McKenzie PRL94, 047004 (2005) RVB Feldbacher et al, PRL93, 136405 (2004) DMFT Merino and McKenzie PRB61, 7996 (2000) DMFT sZsZ Experimental picture

69. Dynamical Processes in Polymers

70. Conducting Polymers Muon both generates a polaron and probes its motion, e.g. for PPV:

71. Diffusion and the Risch-Kehr Model Stochastic model describing muon relaxation due to intermittent hyperfine coupling with a diffusing polaron The relaxation function takes the form: with the relaxation parameter  following a 1/B law at high field: (Risch-Kehr function)

72. Polyaniline Data are well fitted by the Risch-Kehr function

73. Polyaniline 1/B law predicted by RK model is seen for  at higher B Cutoff at low B reflects interchain hopping

74. Polyaniline Effect of ring librational modes at higher temperatures

75. Two types of PPV polymer with different side chains Similar on-chain behaviour

76. Interchain Diffusion Rate D  Inter-chain behaviour highly dependent on sidegroups

77. Slow Muons Normal (4 MeV) muons penetrate ~1-2 mm 10-15% stopping width, so thinnest sample is ~100  m, (a bit less with flypast mode) For studying nanoscale structures and phenomena need muons with energies in the region of keV rather than MeV Two methods for producing slow muons : 1)Degrading the energy in a cold moderator layer (PSI) 2)Laser ionization of thermal muonium (RIKEN-RAL)

78. Surface and Interface Dynamics in Polymers Supported polystyrene films (overlaid data from 6 groups using various different techniques) Forrest and Dalnoki-Veress, Adv. Coll. Int. Sci. 94, 167 (2001) Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer

79. Calculated Range for Muons in Polystyrene using TRIM.SP Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer

80. Polystyrene Film Sample used for LEM Study Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer M w = 62,600, M w /M n =1.04 1 mm thick by 50 mm diameter copper substrate Film prepared by spin-coating from a 15% solution of PS in cyclohexanone Film thickness of 0.46  m was estimated from ellipsometry PRB 72, R121401 (2005)

81. Measured ZF Relaxation in PS Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer

82. Measured Relaxation in the Bulk Polymer Fast fluctuation regime: Indirect coupling to segmental dynamics: WLF law for segmental dynamics: Model

83. Depth Scan at T q Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer d ~ 35 nm at T q

84. Size of the Surface Dynamical Region Surface melting model: d(T) follows from linear dispersion of surface capillary waves Herminghaus et al PRL 93, 017801 (2004)

85. Size of the Surface Dynamical Region Surface melting model: d(T) follows from linear dispersion of surface capillary waves Herminghaus et al PRL 93, 017801 (2004) Glassy polymer Molten layer Substrate Glassy polymer Molten layer Substrate Molten layer Substrate T1T1 T2T2 T3T3 T1T1 T2T2 T3T3

86. Summary Flexible local magnetic probe Magnetism, superconductivity and various dynamical phenomena Also applications in semiconductors and using the muon as a hydrogen analogue Single crystal samples not essential Overlap and complementarity with other techniques such as neutron scattering

87. Acknowledgements  SRSteve BlundellOxford Molecular MagnetsMohamed KurmooStrasbourg Seishi TakagiKyushu Molecular SuperconductorsNaoki ToyotaTohoku & Takahiko Sasaki Steve LeeSt. Andrews PolymersAndy MonkmanDurham Andrew HolmesCambridge Hazel AssenderOxford Slow MuonsElvezio MorenzoniPSI

89. Introduction to Muon Techniques For a short review see: S.J. Blundell, Contemp. Phys. 40, 175 (1999)

90. The muon thermalises as  + or as muonium (Mu).  + will combine with a TCNQF 4 - to form a muoniated radical state with hyperfine parameters A and D (below). A and D can be independently measured using muonium level-crossing-resonance (LCR) spectroscopy of neutral TCNQF 4 (right). Muon Probe States in DEOCC-TCNQF 4 ++ Mu

91. Anisotropic spin diffusion parameters derived from the B dependence of The on-chain spin diffusion rate. The interchain diffusion rate and anisotropy (inset).

92. ‘Homes Plot’ bringing in Conductivity just above T c Key: 1.  -BETS 2 GaCl 4 2. TMTSF 2 ClO 4 3.  -ET 2 NH 4 Hg(SCN) 4 4.  -ET 2 IBr 2 5. -BETS 2 GaCl 4 6.  -ET 2 Cu(NCS) 2 7. K 3 C 60 8. Rb 3 C 60 Homes scaling law  s   0 T c doesn’t apply to molecular superconductors

93. RK Relaxation in DB-PPV DB-PPV

94. Intrachain Mobility Taking d~7Å and the Einstein relation  = eD/k B T gives  ~ 0.05 cm 2 V -1 s -1 at 300 K for both PPV samples This is comparable with local mobility values measured in pulse radiolysis time-resolved microwave measurements: e.g.  e ~ 0.5 cm 2 V -1 s -1 at 300 K Other techniques, e.g. time of flight, give mobility values several orders of magnitude smaller

95. Depth Resolution: Fluorescence Labelling Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer Ellison and Torkelson Nature Materials 2,695 (2003)

96. Muoniated Radicals in PS A ~ 500 MHz D ~ 10-15 MHz TF LF Physica B 326,34 (2003)

97. Coupling to Polymer Dynamics Segmental diffusion Local phenyl rotation

98. Depth Resolution: Implanted Positrons Surface Layer Model Substrate Bulk polymer Surface layer Thin film properties dominated by higher mobility surface layer Jean et al PRB 56, R8459 (1997)