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This article has been retracted as it is found to contain a substantial amount of material, without referencing, from the paper “Ground State Tunnel Splitting in Mn12 Acetate, undergraduate Senior Honors Thesis (Amherst College),” Micheal Foss-Feig, 2006.

View the full Retraction here.


  1. Y. Yousefi and K. K. Muminov, โ€œQuadrupole excitation in tunnel splitting oscillation in nanoparticle,โ€ Advances in Condensed Matter Physics, vol. 2012, Article ID 530765, 4 pages, 2012.
Advances in Condensed Matter Physics
Volume 2012, Article ID 530765, 4 pages
Research Article

Quadrupole Excitation in Tunnel Splitting Oscillation in Nanoparticle ๐Œ ๐ง 1 2

Physical-Technical Institute Named after S.U.Umarov, Academy of Sciences of Republic of Tajikistan, Aini Ave 299/1, Dushanbe, Tajikistan

Received 25 January 2012; Revised 14 March 2012; Accepted 14 March 2012

Academic Editor: Rosa Lukaszew

Copyright © 2012 Yousef Yousefi and Khikmat Kh. Muminov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyze the interference between tunneling paths that occur for a spin system with special Hamiltonian both for dipole and quadrupole excitations. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting for both excitations is modulated, with zeros occurring periodically and the number of quenching points for quadrupole excitation decreasing. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.