Giant electron-spin $g$ factors in a ferromagnetic nanoparticle

We utilize single-electron tunneling spectroscopy to measure the discrete energy levels in a nanometer-scale cobalt particle at $T=60$ mK, and find effective single-electron spin $g$ factors $\approx 7.3$. These large $g$ factors do not result from the typical orbital contribution to $g$ factors, since the orbital angular momentum is quenched. Instead, they are due to nontrivial many-body excitations. A kink in the plot of conductance vs voltage and magnetic field is a signature of degenerate total spin on the particle. Spin-orbit interactions cause the new particle eigenstates to have “spin” that is an admixture of pure spin states. Fluctuations in the discrete energy level spacing allow for the total change in “spin” on the particle during a single-electron tunneling event to be $\Delta S^{\prime }=3/2$, leading to a $g$ factor of around 6.

Figure 1

(a) Circuit diagram of tunneling through particle. (b) Energy level diagram for tunneling process. (c) $I$-$V$ curve displaying Coulomb blockade and discrete single-electron tunneling steps.

Figure 2

Experimental data of differential conductance vs magnetic field and bias voltage. The dotted lines follow the conductance peak behavior for two different spin transitions. The slope of the red dotted lines [(a) and (b)] yield a $g$ factor of $\approx 7.3$, while the green dotted lines (c) correspond to a $g$ factor $\approx 0.6$.

Figure 3

(a) Electron-in-a-box levels for minority and majority electrons. The black dots signify occupied levels. (b) Stability diagram for $N$- and ($N+1$)-electron particles. The spin value in each region denotes the ground state spin for the given magnetic field range. There is a degeneracy in ground state spin at $B=B_d$ and $B=B_d^{\prime }$ for the $N$- and ($N+1$)-electron cases respectively.

Figure 4

Possible spin transitions upon the tunneling event of a single electron onto the particle. The lengths of the arrows represent the energy change of the particle upon such a transition. (a) Case where $B_d^{\prime }<B_d$ $({\delta }_m>U/2)$. (b) Case where $B_d^{\prime }>B_d$ $({\delta }_m<U/2)$. (c), (d) Kink in energy curve as a function of $B$ for the two cases considered in (a) and (b).

Figure 5

Sample fabrication process. The cobalt particles are shown in red between the two tunneling barriers (blue) and the conducting Al electrodes (yellow).

Figure 6

TEM image of Co nanoparticles (dark) on amorphous Al${}_2$O${}_3$ background (light).

Figure 7

Low magnetic field data $<1.5$ T.