F. Branzoli ¶ , P. Carretta ¶ , M. Filibian ¶ , S. Klytaksaya ‡ and M. Ruben ‡

1. Low energy excitations in the neutral [LnPc2]0 single molecule magnets from μSR and NMR F. Branzoli¶, P. Carretta¶, M. Filibian¶ , S. Klytaksaya‡ and M. Ruben‡ ¶Department of Physics "A.Volta", University of Pavia-CNISM,Via Bassi 6, I-27100, Pavia (Italy) ‡Institute of Nanotechnology, Forschungszentrum, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)

2. [LnPc2 ]0 SMM: • New class of Single Molecule Magnets (SMM) [1]; • Highest magnetic anisotropy ever achieved in a molecular magnet [2]; • Slow relaxation and quantum tunneling of magnetization; • Energy separation ∆ between the double degenerate ground state and the first excited levels of several hundreds of kelvin; • Correlation time(τc) for the spin fluctuations reaching several µs at liquid nitrogen temperatures ; • Applications: • - molecular spintronic devices [3] • - logic units in quantum computers [4] • - contrast agents [5]. Fig. 1: Schematic rapresentation of the TbPc2 molecule. On the left, the energy level succession of Tb3+ ion ground multiplet.

3. Muon polarizations Pμ(t) • The time decay of the muon polarization Pµ(t) shows a different behaviour for temperatures above and below T* ≈ 90 K for [TbPc2]0 and T* ≈ 60 K for [DyPc2]0 : • T > T* → high frequency regime: • with β≈ 0.5 and A ≈ 20 %. • T < T* → onset of very low-frequency fluctuations:only the long tail of a static Kubo-Toyabe function can be detected due to the too fast initial decay of Pµ(t): with α(H) the field dependent initial asymmetry. Fig 2: Time evolution of the muon polarization in [TbPc2]0 sample normalized to its value for t  0 at six selected temperatures.

4. Spin-lattice relaxation rates 1/T1 from 1H NMR [6] • [TbPc2]0 and [DyPc2]0 NMR relaxation rates: • The linewidth at half intensity increases from about 37 kHz at 202 K to a few MHz at 19 K  evidence of the slowing down of the spin dynamics; • T > 130 K→ 1/T1 progressively increases on cooling; • T < 40 K→ 1/T1slowly decreaseson cooling. • 140 K ≥ T ≥ 40 K→ the observation of the signal is prevented by the too short relaxation time. • The small peak in 1/T1 for [YPc2]-TBA+ sample should be ascribed to the TBA+ molecular motions. In fact, the Y3+ ion is non magnetic and no high intensity peak is expected. Fig. 3: T dipendence of 1H NMR 1/T1 in [TbPc2]0 (black diamond), [DyPc2]0 (green squares)and [YPc2]-TBA+ (blue circles)for H = 1 T.

5. Spin-lattice relaxation rates λ from μSR [6] • [TbPc2]0 and [DyPc2]0μSR relaxation rates: • Peak at Tm≈ 90 K for [TbPc2]0 and Tm≈ 60 K for [DyPc2]0 , in agreement with NMR findings. • The intensity of the peak is observed to scale with the inverse of the field intensity  the frequency of the fluctuations is close to Larmor frequency ωL at T = Tm. Fig. 4: T dependence of the muon longitudinal relaxation rate in [TbPc2]0 and [DyPc2]0 for H = 1000 Gauss (black and green circles) and for H = 6000 Gauss (blue squares).

6. Estimating the correlation time of [LnPc2 ]0 SMM • The life-time τm can be expressed in terms of the transition probabilities between m, m ± 1 levels: • Owing to spin-phonon scattering processes each CF level is characterized by a finite life-time τmwhich yields a lorentian broadening with C the spin-phonon coupling constant. The µSR (1H NMR) spin-lattice relaxation rate λ (or 1/T1) can be written as [7]: • If ∆ >> T over all the the explored T range, Eq. (3) can be simplified in the form: with with <∆h2┴> the mean-square amplitude of the hyperfine field fluctuations and Emthe eigenvalues of the CF levels.

7. Estimating the correlation time of [LnPc2 ]0 SMM • [TyPc2]0 correlation time: • T > 50 K → high T activated regime: it describes spin fluctuations among m = ± 6 and m = ± 5 levels. • T < 50 K → low T regime: the constant correlation time signals tunneling processes among m = +6 and m = -6 levels. • The sum of the fluctuation rates associated with each process gives: Energy barrier:∆ ≈ 880 K Spin-phonon coupling constant:C ≈ 3000 Hz/K3 Tunneling rate:(1/τc)tunn≈ 11 ms-1 Fig. 5: T dependence of the correlation time for the spin fluctuations in [TbPc2]0 and [DyPc2]0 (for T > T*), derived from λ data reported in Fig. 4 on the basis of Eq. (5). The solid lines are the best fits according to Eq. (7). • [DyPc2]0 correlation time: • T > 40 K  high T activated regime: • ∆ ≈ 610 K and C ≈ 1780 Hz/K3. • T < 40 K  Eq. (3) should be resorted: the two lowest doublets are separated by an energy barrier in the tens of K range. The high energy barrier extimated corresponds to the one between the first and the second excited doublets.

8. Spin susceptibility • The analysis of the static uniform spin susceptibility allows to determine the low energy level structure of the Dy3+ ion spin multiplet J = 15/2. • The lowest energy splittings which allow to better reproduce the experimental data for χT are: • - ∆1 = 115 K; • - ∆2 = 547 K; • - ∆3 = 57 K. • These values are larger than the ones deduced for [DyPc2]- on the basis of crystal field calculations [8]. • The muon relaxation rate behaviour can be correctly modelled with Eq. (3) by considering the first four CF levels and by using three different spin-phonon constants C1  0 Hz/K3, C2 ≈ 2400 Hz/K3and C3 ≈ 3100 Hz/K3,associated with the four lowest transitions. Fig.6: T dependence of χT in [DyPc2]0 for H = 1000 gauss (open circles) and calculated curve (line).

9. References: [1]Ishikawa N., Sugita M., Ishikawa T., Koshihara S. and Kaizu Y.,J. Phys. Chem. B, 108, 11265 (2004). [2] Branzoli F., Carretta P., Filibian M., Zoppellaro G., Graf M. J., Galan-Mascaros J. R., Fhur O., Brink S. and Ruben M.,J. Am. Chem. Soc.,131, 4387 (2009). [3]Bogani L. and Wernsdorfer W.,Nat. Mater., 7, 179 (2008). [4]Leuenberg M. and Loss D.,Nature, 410, 789 (2001). [5]Cage B., Russek S. E., Shoemaker R., Barker A. J., Stoldt C., Ramachandaran V. and Dalan N.,Polyhedron, 26, 2413 (2007). [6]Branzoli F., Carretta P. and Filibian M.,Phys. Rev. B,79, 220404(R) (2009). [7]Lascialfari A., Jang Z. H., Borsa F., Carretta P. and Gatteschi D.,Phys. Rev. Lett., 81, 3773 (1998). [8]Ishikawa N., Tomochika I. and Kaizu Y.,J. Phys. Chem. A, 106, 9543 (2002).