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Stephen Hill, Saiti Datta and Sanhita Ghosh, NHMFL and Florida State University

EPR Studies of Quantum Coherent Properties of Rare-Earth Spins. Stephen Hill, Saiti Datta and Sanhita Ghosh, NHMFL and Florida State University. In collaboration with: Enrique del Barco, U. Central Florida; Fernando Luis, U. Zaragoza, Spain;

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Stephen Hill, Saiti Datta and Sanhita Ghosh, NHMFL and Florida State University

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  1. EPR Studies of Quantum Coherent Properties of Rare-Earth Spins Stephen Hill, Saiti Datta and Sanhita Ghosh,NHMFL and Florida State University In collaboration with: Enrique del Barco, U. Central Florida; Fernando Luis, U. Zaragoza, Spain; Eugenio Coronado and Salvador Cardona-Serra, U. Valencia, Spain • Where are we coming from? • Brief summary of 10 years of EPR studies of molecular magnets • Where are we going? • Simpler molecular magnets with improved functionality • EPR studies of a mononuclear rare-earth (Ho3+) molecule • Coherent manipulation of coupled S, L (~J) and I (~F) • Pure speculation (or total nonsense?)

  2. The Drosophila of SMMs – Mn12 Simplest effective model: uniaxial anisotropy Spin projection - ms S = 2 Energy E-4 E4 S = 3/2 E-5 E5 E-6 E6 E-7 "up" E7 E-8 E8 "down" E-9 E9 S = (8 × 2) – (4 × 3/2) S = 10 E-10 E10 Mn(III) Mn(IV) Oxygen S = 10

  3. Magnetic anisotropy  bistability, hysteresis Spin projection - ms Simplest effective model: uniaxial anisotropy Energy E-4 E4 E-5 E5 E-6 E6 E-7 E7 • Small barrier - DS2 • Superparamagnetic at most temperatures • Magnetization blocked at low temperatures (T < 4 K) E-8 E8 DE  DS2 10-100 K E-9 E9 "up" "down" |D | 0.1 - 1 K for a typical single molecule magnet E-10 E10 21 discrete ms levels Thermal activation

  4. AC c data for [Mn12O12(O2CCH2Br)16(H2O)4]·Solvent to = 2.0 × 10-9 s Ueff = 70 K c΄΄ c΄ Chakov et al., J. Am. Chem. Soc. 128, 6975 (2006). Redler et al, Phys. Rev. B 80, 094408 (2009). c΄΄

  5. What can we learn from single-crystal HFEPR? Uneven spacing of peaks • Obtain the axial terms in the z.f.s. Hamiltonian: • Magnetic dipole transitions (Dms = ±1) - note frequency scale! We can measure transverse terms by rotating field into xy-plane field//z z, S4-axis Bz

  6. Matrix dimension 21 × 21 • Js irrelevant (apparently)!! • Ignores (108 – 21) higher-lying states S = 10 S = 10 S = 10 A big problem with large molecules Mn12 S = 11 S = 9 • Full calculation for Mn12 produces matrix of dimension 108× 108 • Even after major approximation: dimension is 104 × 104 • Multiple exchange coupling parameters (Js); anisotropy (LS-coupling); different oxidation and different symmetry sites. But what is the physical origin of parameters obtained from EPR and other experiments – particularly those that cause MQT?

  7. S4 symmetry MnIII Centrosymmetric (2S + 1)6 = 15625 (2S + 1)4 = 81 (2S + 1)3 = 125 To answer this.... ..study simpler molecules Ueff = 45K Ueff = 75K Ni4: E.-C. Yang et al., Inorg. Chem. 44, 3836 (2005); A. Wilson et al., PRB 74, R140403 (2006). Mn3: P. Feng et al., Inorg. Chem. 46, 8126 (2008); T. Stamatatos et al., JACS 129, 9484 (2007). Mn6: C. Milios et al., JACS 129, 12505 (2007); R. Inglis et al., Dalton 2009, 3403 (2009).

  8. Mononuclear Lanthanide Single Molecule Magnets Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8 Ground state: mJ = ±5 Nuclear spin I = 7/2 (100%) Ishikawa et al.,

  9. Mononuclear Transition Metal Single Molecule Magnets [(tpaMes)Fe]− D = -39.6 cm-1 E = -0.4 cm-1 Harris, Harmann, Reinhardt, Long 1.7 K 1500 Oe 2.0 K 6.0 K U = 42 cm-1 τ0 = 2 x 10-9 s

  10. Coherent Quantum Dynamics in CaWO4:0.05% Er3+ Rabi m m Hund’s rule coupling for Er3+: L = 6, S = 3/2, J = 15/2; 4I15/2 Nuclear spin I = 0, 7/2 (70%, 30%) Bertaina et al., PRL 103, 226402 (2009). Bertaina et al., Nat. Nanotech. 2, 39 (2007).

  11. Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates [Ln(W5O18)2]9- (LnIII = Tb, Dy, Ho, Er, Tm, and Yb) ~D4d Ho3+ – [Xe]4f10 Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8 AlDamen et al., = 5/4

  12. Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates Ho3+ – [Xe]4f10 Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8 AlDamen et al., Ground state: mJ = ±4

  13. Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates Ho3+ – [Xe]4f10 Er3+ and Ho3+ Exhibit SMM characteristics Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8 AlDamen et al., Ground state: mJ = ±4

  14. High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9- B//c Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2 Well behaved EPR: nominally forbidden transitions mJ = -4  +4, DmI = 0

  15. High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9- 1K = 21GHz B//c Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2 Well behaved EPR: nominally forbidden transitions mJ = -4  +4, DmI = 0

  16. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  17. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  18. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  19. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  20. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  21. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  22. Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9- Very strong g-anisotropy associated with transitions mJ = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

  23. X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9- B//c Recall anisotropic hyperfine interaction Likely neither J or I are good quantum numbers; deal with F = J + I

  24. X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9- x = 0.25 T = 4.8 K Impurity cw EPR T1 ~ 1 ms T2 ~ 180 ns Hahn echo sequence t 200 ns 24 ns 120 ns 12 ns

  25. X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9- Rabi oscillations also exhibit the same g-anisotropy

  26. X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9- ESE is T2 weighted Sample: Ho (25%) T = 4.8 K

  27. X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9- Schematic: Not an exact Calculation of spectrum Badly behaved EPR: transitions mJ = -4  +4, DmI = 0, ±1 Source of the additional peaks due to strong to 165Ho nuclear spin

  28. Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples 10 % sample 25 % sample E4 E1 E2 E3 P3 P2 P1 Important to recall: ESE is T2 weighted

  29. Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples Comparison of T2 values : 10 % sample 25 % sample Sequence : 12-120-24 Attenuation : 7 dB for 10% sample; 6 dB for 25% sample

  30. 25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks

  31. 25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks

  32. 25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks

  33. Why do we care? • Coherent nutation of the ground-state magnetic moment deriving from crystal-field effects acting on ~J = ~L + ~S (and ~J + ~I) is not yet well understood. • For Ho, the hyperfine coupling is strong, i.e. the nuclear spin is coherently coupled to the electron spin during nutation. • A magnetic moment much larger than 1/2 allows spin manipulations in low driving field-vectors (amplitude and direction). • Rare-earth polyoxometallates are stable outside of a crystal, and may be scalable and addressable on surfaces, e.g. via an STM. Lehmann, Gaita-Arino, Coronado, Loss,

  34. Variation of t2 versus temperature (4.8K – 9K) at 3 fields (A=0deg): Data was taken at 10K too, but those plots show huge errors in fitting

  35. Variation of t1 versus temperature (4.8K – 10K) at 1875G (A=0deg): T1 measurements were also done at 645G and 1260G, but those are not included in this plot since they do not show the expected variation : some of the plots have significantly large error, I will try to improve the fitting if possible and check if they show better results

  36. Ho 10% sample Peak E1 Peak P1 Peak E3 Peak P3

  37. Ho 25% sample Peak P1 Peak P3

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