Quantum control of individual spins in condensed-matter devices is an emerging field with a wide range of applications, from nanospintronics1, 2 to quantum computing3. The electron, possessing spin and orbital degrees of freedom, is conventionally used as the carrier of quantum information in proposed devices4, 5, 6, 7, 8, 9. However, electrons couple strongly to the environment, and so have very short relaxation and coherence times. It is therefore extremely difficult to achieve quantum coherence and stable entanglement of electron spins. Alternative concepts propose nuclear spins as the building blocks for quantum computing10, because such spins are extremely well isolated from the environment and less prone to decoherence. However, weak coupling comes at a price: it remains challenging to address and manipulate individual nuclear spins11, 12, 13, 14. Here we show that the nuclear spin of an individual metal atom embedded in a single-molecule magnet can be read out electronically. The observed long lifetimes (tens of seconds) and relaxation characteristics of nuclear spin at the single-atom scale open the way to a completely new world of devices in which quantum logic may be implemented.
Figures at a glance
Figure 1: Geometry of the molecular spin transistor and magnetization reversal processes. 
a, Three-dimensional extrapolation of a scanning-electron-microscope image showing the most favourable structure of the single-molecule-based transistor. A schematic zoom into the nano gap shows the molecular structure of the TbPc2 SMM and its easy axis. The charge state of the ligand read-out dot can be controlled by the gate voltage, Vg, and the voltage difference between the electrodes is controlled through the drain-source voltage, Vds. b, Zeeman diagram presenting the energy, E, of the two ground states, Jz = ±6, as a function of the magnetic field (B). The two ground states are each split into four different sub-states owing to the hyperfine coupling with the nuclear spin of I = 3/2. Coloured lines denote the Iz components of the nuclear spin states: purple, −3/2; blue, −1/2; green, 1/2; and red, 3/2. Two processes are responsible for the magnetization reversal. In small magnetic fields, QTM can occur at the avoided energy-level crossings with the same Iz but opposite Jz, indicated by the black circles. In higher fields, a direct relaxation process can lead to the reversal of J.
Figure 2: Conductance characteristics and electronic read-out procedure. 
a, Stability diagram of the Pc read-out quantum dot exhibiting the differential conductance, dI/dV, in units of the quantum of conductance, G0, as a function of gate voltage, Vg, and bias voltage, Vds, at 0.1 K. b, dI/dV measurements for a given working point (Vg = −0.9 V; Vds = 0 V) as function of the magnetic field, B. The arrows indicate the field-sweep direction. Abrupt jumps in the differential conductance, attributed to the switching of the Tb3+ magnetic moment, are visible for all traces of B, showing a clear hysteresis in the dI/dV characteristics. c, Histogram of switching field obtained for 11,000 field sweeps showing four preferential field values that are assigned to QTM events. d, Normalized hysteresis loop of a single TbPc2 SMM obtained by integration of 1,000 field sweeps and performed for trace and retrace on a larger magnetic-field range than in c. The four arrows on the trace curve show the four preferential field values associated to QTM (red, −40 mT; green, −14 mT; blue, 14 mT; purple, 40 mT).
Figure 3: Transition matrix of the QTM events as a function of the waiting time. 
The switching fields of the Tb3+ magnetic moment of subsequent field sweeps are plotted in two-dimensional histograms for three waiting times, tw: a, tw = 0 s; b, tw = 20 s; and c, tw = 50 s. The two axes correspond to the trace and retrace field sweeps, Bt and Br, respectively. Two successive measurements with the same nuclear spin states are situated on the diagonal of the matrix, whereas the off-diagonal positions correspond to nuclear spin-state changes of ΔmI = ±1, ±2 and ±3. The predominance of diagonal terms up to tw = 20 s indicates the long level lifetime of the nuclear spin states. For tw = 50 s, the diagonal terms vanish owing to nuclear spin-flip processes. Furthermore, the high amplitude of the bottom-right (Bt = Br = 40 mT) matrix element accounts for the relaxation of the nuclear spin towards a thermal equilibrium.
Figure 4: Spin-flip dynamics and nuclear spin-state occupancy of the Tb3+ nuclear spin states. 
Evolution of the nuclear spin-state occupancy as a function of the waiting time, tw, for two different working points: a, gate voltage Vg = −0.9 V; and b, Vg = −0.1 V (both at bias voltage Vds = 0 V). The measurements clearly show that the populations evolve towards different thermal equilibriums. c, Spin dynamics for a fixed waiting time of 10 s, as a function of temperature, T. With increasing temperature, the population of the different spin states evolves towards equal occupancy.
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