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arXiv:2505.10523 · The Journal of Physical Chemistry Letters

Magnetic Deflection of High-Spin Sodium Dimers Formed on Helium Nanodroplets

Thomas H. Villers, Benjamin S. Kamerin, Vitaly V. Kresin

Published Apr 29, 2025• 2 citations
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Abstract

Spectroscopic data on alkali-atom dimers residing on the surface of liquid helium nanodroplets have revealed that they are detected primarily in the weakly bound, metastable, spin-triplet state. Here, by measuring the magnetic Stern-Gerlach deflection of a sodium-doped nanodroplet beam, we transparently demonstrate the abundance of high-magnetic-moment dimers. Their electron spins thermalize with the cryogenic superfluid droplets and become fully oriented by the external magnetic field.

DOI
10.1021/acs.jpclett.5c00861

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•Jul 1, 2010•0 citations
Spectroscopic data on alkali-atom dimers residing on the surface of liquid helium nanodroplets have revealed that they are detected primarily in the weakly bound, metastable, spin-triplet state. Here, by measuring the magnetic Stern-Gerlach deflection of a sodium-doped nanodroplet beam, we transparently demonstrate the abundance of high-magnetic-moment dimers. Their electron spins thermalize with the cryogenic superfluid droplets and become fully oriented by the external magnetic field.
The pickup of alkali atoms by helium nanodroplets is unusual in that these atoms are not wetted and enveloped by the liquid, but reside in weakly binding surface dimples. As a result, it has been suggested that the alkali clusters which assemble on droplet surfaces must exist in spin-polarized states with a low condensation energy. We consider the size distribution statistics which would be exhibited by the alkali agglomerates in such a case, and show that it would be very different from the conventional Poisson shape. A careful measurement of the variation of the intensities of droplet-grown alkali clusters with size and/or vapor pressure in the pickup region may be able to test the giant-spin hypothesis.
The population ratio of Zeeman sublevels of atoms on the surface of superfluid helium droplets (T=0.37 K) has been measured. Laser induced fluorescence spectra of K atoms are measured in the presence of a moderately strong magnetic field (2.9 kG). The relative difference between the two states of circular polarization of the exciting laser is used to determine the electron spin polarization of the ensemble. Equal fluorescence levels indicate that the two spin sublevels of the ground-state K atom are equipopulated, within 1%. Thermalization to 0.37 K would give a population ratio of 0.35. We deduce that the rate of spin relaxation induced by the droplet must be <520/s. For the K2 triplet dimer we find instead full thermalization of the spin.
Helium nanodroplet isolation has been applied to agglomerate alkali clusters at temperatures of 380 mK. The very weak binding to the surface of the droplets allows a selection of only weakly bound, high-spin states. Here we show that larger clusters of alkali atoms in high-spin states can be formed. The lack of strong bonds from pairing electrons makes these systems nonmetallic, van der Waals-like complexes of metal atoms. We find that sodium and potassium readily form such clusters containing up to 25 atoms. In contrast, this process is suppressed for rubidium and cesium. Apparently, for these heavy alkalis, larger high-spin aggregates are not stable and depolarize spontaneously upon cluster formation.
Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense femtosecond laser pulse leading to fragmentation into a pair of Rb+{\mathrm{Rb}}^{+}Rb+ ions. We show that the kinetic energy of the Rb+{\mathrm{Rb}}^{+}Rb+ fragment ions can be used to identify dimers formed in either the XXX $^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ ground state or in the lowest-lying triplet state, $a\text{ }^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$. From the experiment, we estimate the abundance ratio of dimers in the aaa and XXX states as a function of the mean droplet size and find values between $4\ensuremath{\mathbin:}1$ and $5\ensuremath{\mathbin:}1$. Our technique applies generally to dimers and trimers of alkali atoms, here also demonstrated for Li2{\mathrm{Li}}_{2}Li2​, Na2{\mathrm{Na}}_{2}Na2​, and K2{\mathrm{K}}_{2}K2​, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.
The study of small clusters is intended to fill the knowledge gap between single atoms and bulk material. He nanodroplets are an ideal matrix for preparing and investigating clusters in a superfluid environment. Alkali-metal atoms are only bound very weakly to their surface by van der Waals forces. Due to the formation process, high-spin states of alkali-metal clusters on He nanodroplets are favorably observed, which is in contrast to the abundance in other preparation processes. Until now, the prevailing opinion was that stable clusters of the heavy alkali-metal atoms, rubidium (Rb) and cesium (Cs) on He nanodroplets, are limited to 5 and 3 atoms, respectively (Schulz et al., Phys. Rev. Lett. 2004, 92, 13401). Here, we present stable complexes of Rb(n)⁺ and Cs(n)⁺ consisting of up to n = 30 atoms, with the detection of large alkali-metal clusters being strongly enhanced by one-photon ionization. Our results also suggest that we monitored both high-spin and low-spin state clusters created on nanodroplets. The van der Waals bound high-spin alkali-metal clusters should show strong magnetic behavior, while low-spin states are predicted to exhibit metallic characteristics. Alkali-metal clusters prepared in these two configurations appear to be ideal candidates for investigating nanosized particles with ferromagnetic or metallic properties.
Spectroscopy of doped helium nanodroplets has become, in recent years, a popular tool for the study of bothfinite size samples of the helium quantum fluid and molecules isolated in this sub Kelvin environment. Whilemany dopants migrate to the center of the droplet, alkali (Ak) atoms in their ground electronic state, becauseof their so weak interaction with He, remain at the surface, the latter being in this way slightly distortedexhibiting a dimple. However, when in their first excited states, Ak atoms are forming exciplexes. These areanisotropic with the central atom surrounded by a ring of He atoms located in the nodal plane of the valenceelectron pz orbital. Structural properties, obtained by DMC and PIMC, are presented here for some Ak -Hen exciplexes.Ak2 dimers in helium environment have also gained interest in this last decade, in connexion with the generationof ultracold molecules. When attached to helium droplets, Ak atoms can float on the surface andform molecules in cold collisions. DMC and PIMC methods are used to compute energetics and structuralinformations for Rb2 in helium. In particular, the orientation of the dimer relative to the droplet surface isexamined.