A Straight Forward Method to Read the Nuclear Qudit of $4f$ Single-Molecule Magnets : $^{163}$DyPc$_2$

Abstract

Nuclear spins in $4f$ single-molecule magnets (SMMs) are promising qubits or qudits candidates for quantum information processing due to their relative isolation and reduced susceptibility to environmental disturbances, while hyperfine coupling with the $4f$ moments enables readout and control. So far, the nuclear spin states of individual TbPc$_2$ SMMs have been detected in transport measurements via the spin-cascade effect, in which transitions of the Tb$^{3+}$ magnetic moment coupled to the unpaired ligand electron manifest as conductance jumps in spin-polarized transport. The ligand electron also gives rise to a Kondo effect through its interaction with the metallic contacts. By sweeping a magnetic field along the easy axis of the Tb$^{3+}$ moment, the system is tuned to avoided crossings of the hyperfine levels, such that the magnetic field at which the conductance jumps occur indicates the nuclear spin state. Here, we present a method to read the nuclear spin of $^{163}$DyPc$_2$ ($I=5/2$) using millikelvin spin-polarized scanning tunneling microscopy without the need for magnetic-field sweeps. Instead, hyperfine interactions modify the statistics of the telegraph noise generated by reversals of the Dy$^{3+}$ moment, thereby revealing the nuclear spin state. We observe nuclear spin relaxation times $T_1$ in excess of minutes at \SI{35}{mK}. Furthermore, we drive nuclear spin transitions using a radio-frequency field and detect the resulting nuclear magnetic resonance directly in the tunneling current, as the conductance near the split Kondo peaks depends on the nuclear spin state.

Figures (10)

• Figure 1: Readout principle based on the spin cascade. (a) Schematic side view of a $^{163}$DyPc$_2$ molecule measured by a spin-polarized tip, together with an STM topography of a DyPc$_2$ molecule on Au (111) (1V, 20pA). The spin-polarized STM tip (tip magnetization indicated by a red arrow) senses the ligand spin (blue arrow), which is exchange-coupled to the Dy$^{3+}$ total angular momentum (purple arrow); this, in turn, is hyperfine-coupled to the nuclear spin (green arrow). (b) Scheme of the resulting spin cascade, illustrating the electronic, exchange, and hyperfine couplings. (c) STM measurement principle. Energy splitting of the ligand spin states and the resulting spin-polarized differential conductance spectra for two orientations of Dy$^{3+}$ momentum.
• Figure 2: (a) Experimental magnetization data (left) and Zeeman diagram (right) for $^{164}$DyPc$_2$ with $I = 0$. The red line is calculated with $T=200mK$ which agrees with $T_\mathrm{eff}=206mK$ of the experimental data. (b) We observed a change in spin polarization as a jump in the z-signal (middle), as well as in $dI/dU$ spectroscopy measurements with the split Kondo peak, both before ($t=0s$) and after the jump ($t=250s$). An asymmetry change was observed, which corresponds to a spin flip. (c) Simulated magnetization curves (top) and Zeeman graph for $^{163}$DyPc$_2$ with nuclear spin of $I=5/2$ (bottom). The different shades of green represent the values for $I_z$ and the two different slopes the momenta $J_z$.
• Figure 3: Z-position changes of the tip represent conductance height changes at Kondo peak (a) Expected differential conductivity with 30% spin polarization for different quantum states (b) Time trace of the tip z-position on top of a $^{164}$DyPc$_2$ molecule. The signal shows colored sections that differ in their behavior. (c)-(e) Zoomed in plots for the colored sections with population and jump height.
• Figure 4: Manipulation with RF signal (a) Zoomed in Zeeman graph with frequencies of dipole and quadrupole direct transitions. (b) Measured difference in current for dipole transitions.
• Figure 5: The configuration comprises an STM tip positioned above the sample and controlled by Nanonis electronics. For RF measurements, an RF antenna is coupled to the cryostat, thereby enabling cooling to dilution temperatures. The antenna is connected to the UHV chamber through a feedthrough and a 6dB attenuator. The RF signal is generated by an external source and demodulated within the Nanonis system.