M. Ueda, T. Yamasaki, and S. Maegawa Kyoto University Magnetic resonance of Fe8 at low temperatures in the transverse field

Contents Molecular magnet Fe8 NMR measurements with longitudinal fields spectrum spin-lattice relaxation rates T 1 -1 observation of QTM NMR measurements with transverse fields spectrum temperature dependence of ZFC spectra spin-lattice relaxation rates T 1 -1 Conclusion We have studied the dynamical behavior in Fe8 and the evidence for the quantum tunneling of magnetization (QTM) were observed through the change of the 1 H-NMR signal. We also studied the feature of NMR spectra by applying the magnetic field perpendicular to the ab plane, which enlarges the tunneling gap  and by applying the RF field with the resonance frequency whose energy corresponds to the modified gap energy. It is expected that the excitation of the cluster spin of S=10 is induced by the RF pulse.

Fe8 [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br8H 2 O Antiferromagnetic interactions J 1 = -147 K, J 2 = -173 K, J 3 = -22 K, J 4 = -50 K Number of spin states : (2s+1) n = 1,679,616 (s=5/2,n=8) Total spin : S = 0 ~ 20 Ground spin state : S = 5/2×6 - 5/2×2 = 10 (Ferrimagnetic) Magnetic interactons between molecules are week Isolated magnetic clusters with S = 10 A molecule Fe8 consists of 8 Fe 3+ ions. Fe 3+ : 3d 5, s = 5/2, l = 0

Spin Hamiltonian H = -DS z 2 +E (S x 2 -S y 2 )+gμ B S H easy axis anisotropy : D = K anisotropy within xy-plane : E = K (by HF-EPR) ・ Double-wells potential ・ Energy barrier due to anisotropy Fe8 : 24.5 K (Mn12:~ 65 K) Relaxation of magnetization above 400 mK : dependent on the temperature--> thermal activation below 400 mK : independent of the temperature, stepwise hysteresis loops -->quantum tunneling Sangregorio et al (1997), Wernsdorfer et al. (1999)

Experiments 1 H-NMR measurement with longitudinal fields spectrum spin-lattice relaxation rates T 1 -1 T = 20mK~300K H = -5T~5T f = 10MHz~230MHz with transverse fields spectrum spin-lattice relaxation rates T 1 -1 T = 150mK~960mK H = 0~6T f = MHz

Temperature dependence of spectra resonance condition ω=γ|H+H N | NMR spectra show structure at low temperatures. Freezing of cluster magnetization Many 1 H sites

Spin lattice relaxation rate, above 400 mK Correlation function(Lascialfari etal. 1998) Life time (Villain etal. 1996) Transition probability due to the spin phonon interaction Then

A = 4 × rad/sec 2 C = 5 × 10 5 Hz/K 3

Recovery of NMR spectra 1) The 1 H spins were saturated by RF pulses with sweeping the field up and down between 0.1 and 1.5 T until no echo signals were observed. 2) Magnetic field was decreased to a certain field Hr. 3) These spectra were observed with increasing the field.

Return field dependence of the echo intensity Stepwise recovery of echo intensities were observed

Field dependence of the energy levels and QTM Landau-Zener : transition probability from m state to m' state  m,m' : tunneling gap, dH/dt : sweep rate The slower sweeping rate dH/dt make the higher transitions probability.

Return field dependence of the echo intensity Stepwise recovery of echo intensities were observed. The recovery is faster with slower sweep rate.

Sweep rate dependence of the recovery of echo intensity assumption : The iron spins which have experienced tunneling at least once contribute to the proton relaxation. the echo intensities I (a) (b) H -10,9 < H r < 0 H -10,8 < H r < H -10,9  -10,10 = 3.52  10 –7 K,  -10,9 = 9.66  10 –7 K

Experiments 1 H-NMR measurement with longitudinal fields spectrum spin-lattice relaxation rates T 1 -1 T = 20mK~300K H = -5T~5T f = 10MHz~230MHz with transverse fields spectrum spin-lattice relaxation rates T 1 -1 T = 150mK~960mK H = 0~6T f = MHz

Field dependence of the tunneling gap Δ Experimental situation and energy levels Experimental situation

1 H NMR spectrum at 960 mK Calculated 1 H spectrum Both the range and structure of the 1 H NMR spectrum are almost explained by the calculation of dipolar fields.

ZFC spectra at 150mK The sign of difference of these two spectra reverse at the field about 4.1T. RF pulses (applied below 3.6T) induce the excitation of the cluster spin. --> The populations of the cluster spins in the ground state and excited state were changed due to this excitation? H = 0 ~ 3.6 T (in this range, there is no 1 H-NMR signal) (a): field was increased with applying the RF field (b): field was increased without applying the RF field H < 4.1 T : (a) < (b) H > 4.1 T : (a) > (b) The signal intensities change. The peak positions do not change.

Temperature dependence of ZFC spectra ・ The signal at a higher magnetic field is independent of the temperature. ・ The signal at a lower magnetic field increases rapidly below 500 mK. ・ The central peak has minimum at the temperature around 500 mK. Temperature dependence of the signal intensity of the peaks marked by arrows. This shows the effect of crossover of thermal and quantum relaxation ?

The recovery of the spin echo intensity The recovery of the spin echo intensity cannot be explained by single exponential function due to the presence of non equivalent protons. T 1 measurement at 960 mK T 1 at 960mK : ~ 10 sec T 1 of several 1 H sites

The recovery of the spin echo intensity until 120 sec T 1 at 150 mK : ~ dozens of seconds over sec T 1 measurement at 150 mK The recovery of the spin echo intensity at 150 mK

Conclusion (1) T 1 above 400mK The spin-lattice relaxation of 1 H spin is dominated by the fluctuation of the Fe8 cluster spin caused by the spin-phonon interaction. (2) Stepwise recovery below 400mK The spin-lattice relaxation of 1 H spins are dominated by the fluctuation of the Fe8 cluster spin caused by QTM. => The intensity of the spectra recovered at every cross field of energy levels. => The quantum tunneling was observed. (3) Spectra and T 1 in the transverse field The RF pulse makes difference of the intensity ratio of spectra. =>This shows the effect of induced excitation of electron spins? Zero field cooling enhances the lower field signal below 500mK. =>This shows the effect of crossover of thermal and quantum relaxations ? Future more detailed experiments are needed.