Quantum tunneling of the magnetization in a single molecule magnet has been studied in experiments that combine microwave spectroscopy with high sensitivity magnetic measurements. By monitoring spin-state populations in the presence of microwave radiation, the energy splittings between low lying superpositions of high-spin states of SMM Ni₄ (S = 4) have been measured. Absorption linewidths give an upper bound on the rate of decoherence. Pulsed microwave experiments provide a measure of energy relaxation time, which is found to increase with frequency..

Experimental conditions

1. Longitudinal field sweep (H_L // z-axis):
A longitudinal magnetic field is swept across resonance k = 0 to invert the population of high-spin levels. Longitudinal fields change the weight of the quantum superposition coefficients and allow a better understanding of the quantum properties of SMMs.

2. High transverse fields (H_T = 2-4 T):
High transverse fields are used to increase the quantum splitting, , between symmetric and antisymmetric states and allow studies in a range of frequencies where quantum tunneling is expected to be coherent.

3. Low temperature (T = 0.4 K):
At the temperatures used in our experiments only the lowest lying spin levels, m = 4, are thermally populated. Moreover, for the transverse fields used, the thermal energy is much smaller than the tunnel splitting energy, k_BT<<hf.

4. High mw frequencies (f = 20-50 GHz):
High microwave frequencies are used to induce transitions (PITs) between symmetric and antisymmetric states. The mw frequency used in our experiments is higher than the decoherence frequency of this system, f > f_D.

5. Pulsed-radiation for dynamical studies:
The ability to apply pulses of mw radiation allows studies of the dynamics of the magnetization in the presence of radiation in SMMs and provide the first results on spin-lattice relaxation phenomena in these systems.

Lowest lying levels of SMM Ni₄

This is a scheme of the instrumentation used in this experiment. Description of each equipment can be found in laboratory.

A high frequency switch is used to pulse the CW microwave signal generated by the Vector Network Analyzer. The switch is controlled by a TTL pattern generated by a Pattern generator.
The pulsed microwave signal is conducted through a semirigid coaxial line down to the sample. A superconducting loop is placed at the end of the coaxial line and used to convert the microwave signal into ac magnetic field at the position of the sample. The sample is placed inside a ³He cryostat. A vector superconducting magnet is used to apply magnetic fields at arbitrary directions with respect to the axes of the Ni₄ single crystal.

This figure shows the behavior of the lowest lying levels (Sz=+4 and-4) as a function of the longitudinal field. A transverse field is used to generate a tunnel splitting, D, between symmetric and antisymmetric superpositions.

These states can be described in terms of “classical” up and down levels.

A high sensitivity micro-Hall effect magnetometer is used to measure the magnetization of a millimeter-sized single crystal (pyramidal shape) of Ni₄ that is placed with one of its faces parallel to the plane of the Hall-sensor. The z-axis, which is parallel to the axis of the pyramid, is misaligned with respect to the plane of the sensor by 20 degrees. The Hall device responds to the average magnetic field perpendicular to the plane of the sensor, which for the sample shape and placement, is mainly due to the z-component of sample magnetization.

The figure shows magnetization curves recorded in the presence of continuous-wave (CW) radiation at 39.8 GHz while transverse fields from 2.4 to 3.6 T were applied. Peaks and dips are observed at opposite  polarities of the longitudinal field demonstrating PITs between magnetic states of the molecules with opposite spin-projections. At PITs the sample temperature increases by less than 0.01 K  (measured with a thermometer placed close to the sample), showing that these features are not due to sample heating T ~1 K would be necessary to explain the observed changes).

decoherence time

(M-Meq)/Meq for different powers with cw 39.4 GHz radiation applied to the sample. The longitudinal field was swept at 1.6x10^-4 T/s and H_T=3.2 T. The curves are offset for clarity. The green line is a fit to the sum of three Lorentzian functions. The red lines are the Lorentzian functions corresponding to dip A (solid) with t2=0:26 ns and dips B1 and B2 (dashed), for Psource=2.5 dBm. (b),(c) show the dependence of the amplitude and half width of PIT A as a function of the source power, respectively.

From the width of the peaks we can determine a lower bound for the decoherence time, t_f > 0.5 ns.