Nonclassical dipoles in cold niobium clusters

Electric deflections of niobium clusters in molecular beams show that they have permanent electric dipole moments at cryogenic temperatures but not higher temperatures, indicating that they are ferroelectric. Detailed analysis shows that the deflections cannot be explained in terms of a rotating classical dipole, as claimed by Andersen et al.. The shapes of the deflected beam profiles and their field and temperature dependence indicates that the clusters can exist in two states, one with a dipole and the other without. Cluster with dipoles occupy lower energy states. Excitations from the lower states to the higher states can be induced by low fluence laser excitation. This causes the dipole to vanish.

Figure 1

(Color online) Representative beam profiles of Nb clusters at $T=20\mathrm{K}$ and $V=20\mathrm{kV}$, where $V$ is the voltage applied to deflection plates that generate the inhomogeneous electric filed $E$. The zero field profile represents the collimation function, which depends only on the geometry of the apparatus.

Figure 2

(Color online) Beam profiles of ${\mathrm{Nb}}_{14}$ at $T=50\mathrm{K}$ and several electric fields. For each profile we can distinguish a main peak and a tail. (b) The deflections of the main peaks and the tails. The dotted lines are guides to the eyes. The main peaks are deflected quadratically. The deflections are consistent with a polarizability of about $5{\mathrm{\AA }}^3$ per atom. The tails are deflected linearly. The maximum deflections are determined from the location of the baseline intercept and correcting for the natural beam width. The dipole moment of ${\mathrm{Nb}}_{14}$ is about 2 Debye.

Figure 3

(Color online) Beam profiles of ${\mathrm{Nb}}_{18}$ at several temperatures. At low temperature, the beam profiles are very asymmetric at $V=20\mathrm{kV}$. As the temperature increases, the asymmetry becomes less. At $T=300\mathrm{K}$, the deflected beam profile shows only a rigid shift.

Figure 4

(Color online) Calculated beam profiles for ${\mathrm{TiC}}_{60}$ at $T=85\mathrm{K}$, $v=920\mathrm{m}∕\mathrm{s}$. Lines are calculated by using the CDM by the authors; symbols are calculated by Dugourd et al.

Figure 5

(Color online) Beam profiles of ${\mathrm{Nb}}_{18}$ at $T=20\mathrm{K}$ and $v=313\mathrm{m}∕\mathrm{s}$ and (a) $V=20\mathrm{kV}$, (b) $V=5\mathrm{kV}$. $P_{on}$ and $P_{off}$ are the experimental beam profiles with electric field on and off respectively and ${P_{on}}^{CDM}$ are the profiles with electric field on, calculated by classical dipole model. The calculation uses $\mu =1.3$ Debye, which is found from the extension of the tail [see Fig. 2b]. $P_{on}^{TC}$ are the profiles with electric field on, calculated by assuming two components, one is polarizable and the other is a dipole moment fixed to the cluster. From the calculation of $P_{on}^{TC}$ of ${\mathrm{Nb}}_{18}$ we find 50% is in the polarizable component both at $5\mathrm{kV}$ and at $20\mathrm{kV}$, demonstrating that population of the two components is not field dependent.

Figure 6

(Color online) Beam profiles of ${\mathrm{Nb}}_{18}$ at $T=300\mathrm{K}$ and $V=20\mathrm{kV}$. $P_{on}$ and $P_{off}$ are the experimental beam profiles and ${P_{on}}^{CDM}$ are the profiles calculated by classical dipole model. (a) using He carrier gas $(v=965\mathrm{m}∕\mathrm{s})$; (b) using Ar carrier gas $(v=435\mathrm{m}∕\mathrm{s})$.

Figure 7

(Color online) Experimental beam profiles of ${\mathrm{Nb}}_{28}$ at $T=20\mathrm{K}$ and $V=20\mathrm{kV}$. $P_{off}$ is the profile with no electric field, $P_{on}$ is the profile with electric field on, and ${P_{on}}^{Laser}$ is the profile with electric field on, after the cluster beam is illuminated with a $500\mathrm{nm}$ laser light pulse. Note that laser heating extinguishes the dipole.