Gd-Based Single-Ion Magnets with Tunable Magnetic Anisotropy: Molecular Design of Spin Qubits

We report ac susceptibility and continuous wave and pulsed EPR experiments performed on ${\mathrm{GdW}}_{10}$ and ${\mathrm{GdW}}_{30}$ polyoxometalate clusters, in which a ${\mathrm{Gd}}^{3+}$ ion is coordinated to different polyoxometalate moieties. Despite the isotropic character of gadolinium as a free ion, these molecules show slow magnetic relaxation at very low temperatures, characteristic of single molecule magnets. For $T\lesssim 200\mathrm{mK}$, the spin-lattice relaxation becomes dominated by pure quantum tunneling events, with rates that agree quantitatively with those predicted by the Prokof’ev and Stamp model [Phys. Rev. Lett. 80, 5794 (1998)]. The sign of the magnetic anisotropy, the energy level splittings, and the tunneling rates strongly depend on the molecular structure. We argue that ${\mathrm{GdW}}_{30}$ molecules are also promising spin qubits with a coherence figure of merit $Q_{\mathrm{M}}\gtrsim 50$.

Figure 1

(a) ${\mathrm{GdW}}_{10}$ molecule (left) and three-dimensional plot of the probability for its spin to point along any direction of space, calculated at $T=0.5\mathrm{K}$ (right). (b) Energy levels of ${\mathrm{GdW}}_{10}$ for ${\mu }_0{H}_z=10\mathrm{mT}$. (c) ${\mathrm{GdW}}_{30}$ molecule (left) and the corresponding probability plot at $T=0.5\mathrm{K}$ (right). (d) Energy levels of ${\mathrm{GdW}}_{30}$ for ${\mu }_0{H}_y=10\mathrm{mT}$.

Figure 2

Top: real component of the ac magnetic susceptibility (${\chi }^{\prime }$) measured at different frequencies on ${\mathrm{GdW}}_{10}$ (a) and ${\mathrm{GdW}}_{30}$ (b). The equilibrium susceptibility ${\chi }_T$ is obtained as the low frequency limit of ${\chi }^{\prime }$. Solid lines show ${\chi }_T$ calculated for noninteracting spins. Bottom: (c) imaginary part of the ac magnetic susceptibility measured at different temperatures on ${\mathrm{GdW}}_{10}$ and ${\mathrm{GdW}}_{30}$ (scatter) fitted to Cole-Cole laws (solid lines); (d) relaxation rates of ${\mathrm{GdW}}_{10}$ and ${\mathrm{GdW}}_{30}$ obtained from the Cole-Cole fits. Horizontal lines show the spin tunneling rates $\Gamma$ that follow from Eq. (2).

Figure 3

Powder EPR absorption spectra of ${\mathrm{GdW}}_{10}$ (a) and ${\mathrm{GdW}}_{30}$ (b) at $T=10\mathrm{K}$ and $f=25\mathrm{GHz}$. Black solid lines, experimental data; red dotted lines, fits based on Eq. (1).

Figure 4

Main panel: echo-detected $\mathrm{X}$-band EPR spectrum measured on a powdered sample of ${\mathrm{Gd}}_{0.001}{\mathrm{Y}}_{0.999}{\mathrm{W}}_{30}$ at $T=6\mathrm{K}$ using a two-pulses Hahn echo sequence with a $\pi /2$ pulse length of 16 ns and an interpulse delay of 180 ns. Inset: relaxation times $T_1$ (solid symbols) and $T_2$ (open symbols) of three ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{W}}_{30}$ samples measured at $T=6\mathrm{K}$ and for two magnetic fields, ${\mu }_{0}H=100\mathrm{mT}$ (dots) and ${\mu }_{0}H=347\mathrm{mT}$ (stars).