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Size-selective self-assembly of magnetic Mn nanoclusters on Si(111)
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26.Our calculations show that the Mn atoms on the UFHUC are unfavorable energetically. For example, Mn atom at H2 site on UFHUC is ∼60 meV per atom higher compare to that on FHUC in energy.
29.At finite temperature, the hopping rate (R) can be estimated by R = R0, where R0 is the prefactor, which is about 1013 ∼ 1015, Eb is the energy barrier, kB is the Boltzmann constant, and T is the temperature. With our calculated energy barrier of 0.57, 0.93, and 1.20 eV, the hopping rates are estimated to be 104, 0.07, and 0.00 s−1 at 300 K, and 109, 2 × 105, and 3 × 102 s−1 at 500 K, respectively. Here, the prefactor of 1015 is used.
30.The adsorption energy of the following next Mn atom is defined by (N + 1)*Ead(N + 1) − N*Ead(N), where Ead(N + 1) and Ead(N) are the average adsorption energy of MnN + 1 and MnN clusters, respectively.
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We show by first-principles calculations two types of magnetic magic Mn clusters on the Si(111)-(7 × 7) surface. The first is a small triangular Mn7 cluster stabilized by the solid-centered Mn–Si3 bonds on the top layer, and the second is a large hexagonal Mn13 cluster favored by the confining potential wells of the faulted half unit cells on the Si(111) surface. These two structural models are distinct from that of the planar group-III clusters on Si(111) and produce simulated scanning tunneling microscopy images in reasonable agreement with recent experimental observations. These results offer key insights for understanding the complex energetic landscape on the Si(111)-(7 × 7) surface, which is critical to precisely controlled growth of Mn nanocluster arrays with specific size, magnetic moment, and good uniformity.
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