Experimental observation and theoretical analysis of spontaneous magnetic moment of Rb atom clusters
Authors: Di Shu-Hong , Zhang Yang , Yang Hui-Jing , San Xing-Yuan , Liu Hui-Yuan , Zhang Su-Heng , Li Fan-Lin , Tai Jun-Jun , Zhou Chun-Li ,   Institute of Physics Science & Technology, Tangshan Normal University, Tangshan 063000, China,   State Key Laboratory of Disastrous Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China,   Institute of Physics Science & Technology, Hebei University, Baoding 071002, China,   Department of Chemistry, Tangshan Normal University, Tangshan 063000, China
Published: June 2021

For the magnetism of alkali metal clusters, it is difficult to determine the number of atoms and the magnetic moment of isolated atoms cluster. In this paper, we investigate the magnetic moment of single atomic molecule <sup>87</sup>Rb<sub>1</sub> and 14 kinds of cluster particles (<sup>87</sup>Rb)<inline-formula><tex-math id="Z-20210617162030">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162030.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162030.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="Z-20210617161856">\begin{document}$n' $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161856.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161856.png"/></alternatives></inline-formula>= 2, 3, 4, ···, 15) in a saturated rubidium vapor sample at about 328 K, by using optical magnetic resonance spectroscopy. The experimental results show that there is a relationship <i>f</i><inline-formula><tex-math id="Z-20210617161925">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161925.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161925.png"/></alternatives></inline-formula> = <i>f</i> */<inline-formula><tex-math id="Z-20210617161921">\begin{document}$n' $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161921.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161921.png"/></alternatives></inline-formula> between the resonant frequencies <i>f</i><inline-formula><tex-math id="Z-20210617161939">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161939.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161939.png"/></alternatives></inline-formula> of 14 kinds of cluster particles (<sup>87</sup>Rb)<inline-formula><tex-math id="Z-20210617161944">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161944.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161944.png"/></alternatives></inline-formula> and the resonant frequencies <i>f</i> * of <sup>87</sup>Rb<sub>1</sub>. The magnetic moment and their resonance amplitudes show two different relationships with the <inline-formula><tex-math id="Z-20210617162058">\begin{document}${n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162058.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162058.png"/></alternatives></inline-formula> odevity. When the particles have an odd number of 5s electrons, they must have spontaneous magnetic moment, and the value of magnetic moment increases with <i>n</i> and decreases inverse proportionally with the combined angular momentum <i>F</i> of the cluster particles. The amplitude obtained from resonance spectrum complies with the variation law of magnetic moment value. On the other hand, for the cluster particles with <i>n</i> being even number, the magnetic moment value becomes 0 and the amplitude is also 0 in the most cases, except for the cluster particles <sup>87</sup>Rb<sub>2</sub> with <i>n</i> = 2 i.e. two 5s electrons, which is caused by the Jahn-Teller effect of the linear molecules, and the magnetic moment value is consistent with the calculation results of the odd number particles. When <i>n</i> > 2, the coupling effect between the magnetic moments of the Rb cluster shows a long-range ordered antiferromagnetic property with the increase of the number of 5s valence electrons <i>n</i>. The electron configuration and molecular state of the ground state and the lowest excited state of 14 kinds of 2—15 atoms cluster particles <sup>87</sup>Rb<i><sub>n</sub></i>, as well as the stability of each molecular state and the possibility of visible Zeeman effect are obtained by using the molecular orbital-state theory analysis and constructing the <sup>87</sup>Rb<sub><i>n</i>–1</sub> + <sup>87</sup>Rb<i><sub>n</sub></i> atomic cluster model. Furthermore, based on the magnetic moment of diatomic molecules ruler, it is found that when <i>n</i> = <inline-formula><tex-math id="Z-20210617162122">\begin{document}${n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162122.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617162122.png"/></alternatives></inline-formula>, the magnetic moment of (<sup>87</sup>Rb)<inline-formula><tex-math id="Z-20210617161959">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161959.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161959.png"/></alternatives></inline-formula> and <sup>87</sup>Rb<i><sub>n</sub></i> are in strict consistency (the average relative error is only 0.6765%), confirming the corresponding relationship between (<sup>87</sup>Rb)<inline-formula><tex-math id="Z-20210617161951">\begin{document}${}_{n'} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161951.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20210031_Z-20210617161951.png"/></alternatives></inline-formula> and <sup>87</sup>Rb<i><sub>n</sub></i>. This research will be of great value in the magnetic research of cluster particles.