The geometric phase of Zn- and T-symmetric nanomagnets as a classification toolkit

Abstract

We derive the general form of the non-trivial geometric phase resulting from the unique combination of point group and time reversal symmetries. This phase arises e.g. when a magnetic adatom is adsorbed on a non-magnetic Cn crystal surface, where n denotes the fold of the principal axis. The energetic ordering and the relevant quantum numbers of the eigenstates are entirely determined by this quantity. Moreover, this phase allows to conveniently predict the protection mechanism of any prepared state, shedding light onto a large number of experiments and allowing a classification scheme. Owing to its robustness this geometric phase also has great relevance for a large number of applications in quantum computing, where topologically protected states bearing long relaxation times are highly desired.

Electron-assisted magnetization tunneling in single spin systems

“…As has already been reported 10,17,18 , two inherent symmetries of H CF play an important role for the properties of the atom wavefunction: the rotational symmetry and the time-inversion symmetry.…”

“…The Hamiltonian H CF is due to the electrostatic interactions and thus H CF has to commute with the time reversal operator T (see [17][18][19] ). T is antiunitary, i.e.…”

“…Rotational symmetry: In C q symmetry, the environment of the magnetic atom is invariant under a rotation by 2π/q, and so H CF also commutes with the rotation operator R 2π/q (see [17][18][19] ). Therefore, we can choose the eigenstates of the system to be eigenstates of both H CF and R 2π/q .…”

“…18 derived under the assumption T + J = −J T + becomes invalid. Through these mistakes the final classification scheme 18 gives wrong results in almost one half of the cases: for half-integer J all doublets in 3-, 4-and 6-fold symmetric environments are listed as protected. A direct calculation shows that this is untrue.…”

“…During the preparation of this manuscript several other theoretical works analysing magnetic stability have been published [16][17][18] . This work, however, allows stability analysis without restricting the ground state spin or the magnetic field direction.…”