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 EPR Studies of Quantum Coherent Properties of Rare-Earth Spins Where are we coming from?Where are we coming from? Brief summary of 10 years of EPR studies of molecular magnetsBrief summary of 10 years of EPR studies of molecular magnets Where are we going?Where are we going? Simpler molecular magnets with improved functionalitySimpler molecular magnets with improved functionality EPR studies of a mononuclear rare-earth (Ho 3+ ) moleculeEPR studies of a mononuclear rare-earth (Ho 3+ ) molecule Coherent manipulation of coupled S, L (~J) and I (~F)Coherent manipulation of coupled S, L (~J) and I (~F) Pure speculationPure speculation (or total nonsense?)

Mn(III) Mn(IV) Oxygen S = (8 × 2) – (4 × 3/2) S = 10 S = 3/2 S = 2 The Drosophila of SMMs – Mn 12 S = 10 Simplest effective model: uniaxial anisotropy "up" "down" E  10 E9E9E9E9 E8E8E8E8 E7E7E7E7 E 10 E9E9E9E9 E8E8E8E8 E7E7E7E7 E6E6E6E6 E5E5E5E5 Spin projection - m s E6E6E6E6 E5E5E5E5 Energy E4E4E4E4 E4E4E4E4

"up" "down" E  10 E9E9E9E9 E8E8E8E8 E7E7E7E7 E 10 E9E9E9E9 E8E8E8E8 E7E7E7E7 E6E6E6E6 E5E5E5E5 Spin projection - m s E6E6E6E6 E5E5E5E5 Energy E4E4E4E4 E4E4E4E4 21 discrete m s levels Small barrier - DS 2Small barrier - DS 2 Superparamagnetic at most temperaturesSuperparamagnetic at most temperatures Magnetization blocked at low temperatures (T < 4 K)Magnetization blocked at low temperatures (T < 4 K)  E  E  DS K |D |  0.1  1 K for a typical single molecule magnet Thermal activation Magnetic anisotropy  bistability, hysteresis Simplest effective model: uniaxial anisotropy

Chakov et al., J. Am. Chem. Soc. 128, 6975 (2006). Redler et al, Phys. Rev. B 80, (2009).  o = 2.0 × s U eff = 70 K AC  data for [Mn 12 O 12 (O 2 CCH 2 Br) 16 (H 2 O) 4 ]·Solvent ΄΄  ΄΄

field//z z, S 4 -axis BzBz Magnetic dipole transitions (  m s = ±1 ) - note frequency scale! Obtain the axial terms in the z.f.s. Hamiltonian: Uneven spacing of peaks We can measure transverse terms by rotating field into xy-plane What can we learn from single-crystal HFEPR?

A big problem with large molecules Full calculation for Mn 12 produces matrix of dimension 10 8 × 10 8Full calculation for Mn 12 produces matrix of dimension 10 8 × 10 8 Even after major approximation: dimension is 10 4 × 10 4Even after major approximation: dimension is 10 4 × 10 4 Multiple exchange coupling parameters (J s ); anisotropy (LS- coupling); different oxidation and different symmetry sites.Multiple exchange coupling parameters (J s ); anisotropy (LS- coupling); different oxidation and different symmetry sites. S = 11 S = 9 S = 10 Mn 12 S = 10 Matrix dimension 21 × 21Matrix dimension 21 × 21 J s irrelevant (apparently)!!J s irrelevant (apparently)!! Ignores (10 8 – 21) higher-lying statesIgnores (10 8 – 21) higher-lying states S = 10 But what is the physical origin of parameters obtained from EPR and other experiments – particularly those that cause MQT?

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

Ishikawa et al., Mononuclear Lanthanide Single Molecule Magnets Hund’s rule coupling for Ho 3+ : L = 6, S = 2, J = 8; 5 I 8 Ground state: m J = ±5 Nuclear spin I = 7/2 (100%)

[(tpa Mes )Fe] − 1500 Oe 2.0 K D = cm -1 E = -0.4 cm -1 U = 42 cm -1 τ 0 = 2 x s 1.7 K 6.0 K Mononuclear Transition Metal Single Molecule Magnets Harris, Harmann, Reinhardt, Long

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

Ho 3+ – [Xe]4f 10 Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates [Ln(W 5 O 18 ) 2 ] 9- (Ln III = Tb, Dy, Ho, Er, Tm, and Yb) ~D 4d Hund’s rule coupling for Ho 3+ : L = 6, S = 2, J = 8; 5 I 8 = 5/4 AlDamen et al.,

Ho 3+ – [Xe]4f 10 Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates Hund’s rule coupling for Ho 3+ : L = 6, S = 2, J = 8; 5 I 8 Ground state: m J = ±4 AlDamen et al.,

Ho 3+ – [Xe]4f 10 Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates Hund’s rule coupling for Ho 3+ : L = 6, S = 2, J = 8; 5 I 8 Ground state: m J = ±4 AlDamen et al., Er 3+ and Ho 3+ Exhibit SMM characteristics

High(ish) frequency EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Eight line spectrum due to strong hyperfine coupling to 165 Ho nucleus, I = 7/2 Well behaved EPR: nominally forbidden transitions m J = -4  +4,  m I = 0 B//c

High(ish) frequency EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- B//c Eight line spectrum due to strong hyperfine coupling to 165 Ho nucleus, I = 7/2 Well behaved EPR: nominally forbidden transitions m J = -4  +4,  m I = 0 1K = 21GHz

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

Angle-dependent EPR of [Ho 0.25 Y 0.75 (W 5 O 18 ) 2 ] 9- Very strong g-anisotropy associated with transitions m J = -4  +4 Note: hyperfine interaction also exhibits significant anisotropy

X-band (9GHz) Electron Spin Echo EPR of [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- B//c Recall anisotropic hyperfine interaction Likely neither J or I are good quantum numbers; deal with F = J + I

X-band (9GHz) Electron Spin Echo EPR of [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- x = 0.25 T = 4.8 K Impurity cw EPR 24 ns 120 ns 12 ns 200 ns t Hahn echo sequence T 1 ~ 1  s T 2 ~ 180 ns

X-band (9GHz) Electron Spin Echo EPR of [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- Rabi oscillations also exhibit the same g-anisotropy

Sample: Ho (25%) T = 4.8 K X-band (9GHz) Electron Spin Echo EPR of [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- ESE is T 2 weighted

Source of the additional peaks due to strong to 165 Ho nuclear spin Badly behaved EPR: transitions m J = -4  +4,  m I = 0, ±1 X-band (9GHz) Electron Spin Echo EPR of [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- Schematic: Not an exact Calculation of spectrum

10 % sample 25 % sample E1 E2 E3 E4 P1 P2 P3 Comparing [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- 10% and 25% samples Important to recall: ESE is T 2 weighted

Comparison of T 2 values : PeakT2 (nsec) E P1’ P E P2’ P E P3’ P E PeakT2 (nsec) E1 P1’ P E2 P2’ P E3 P3’ P E4 10 % sample 25 % sample Sequence : Attenuation : 7 dB for 10% sample; 6 dB for 25% sample Comparing [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- 10% and 25% samples

25% [Ho x Y 1-x (W 5 O 18 ) 2 ] 9- : splitting of the main (P) peaks

Lehmann, Gaita-Arino, Coronado, Loss, 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. Why do we care?

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

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

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

Ho 25% sample Peak P1 Peak P3