Coherent spin rotation in the presence of a phonon-bottleneck effect

Abstract

PACS 75.45.+j -Macroscopic quantum phenomena in magnetic systems PACS 75.50.Xx -Molecular magnets PACS 75.10.Jm -Quantized spin modelsAbstract. -A characteristic of spin reversal in the presence of phonon-bottleneck is the deviation of the magnetization cycle from a reversible function into an opened hysterezis cycle. In recent experiments on molecular magnets (e.g. V15 and Ru2), the zero-field level repulsion was sufficiently large to ensure an otherwise adiabatic passage through zero-field and the magnetization curves can be described by using only a phonon-bottleneck model. Here, we generalize the phonon-bottleneck model into a model able to blend the non-adiabatic dynamics of spins with the presence of a nonequilibrium phonon bath. In this simple phenomenological model, Bloch equations are written in the eigenbasis of the effective spin Hamiltonian, considered to be a two-level system at low temperatures. The relaxation term is given by the phonon-bottleneck mechanism. To the expense of calculus time, the method can be generalized to multi-level systems, where the notion of Bloch sphere does not apply but the density matrix formalism is still applicable. Introduction. -Molecular magnets [1] or less complex systems containing diluted spins [2] have been explored intensively in the recent years for their potential application in information technology. In addition, despite their macroscopic dimensions, crystals containing magnetic molecules show measurable manifestations of fundamental quantum mechanical phenomena at large scale. This is due only to the fact that the magnetic molecules are relatively well separated from each other and their quantum properties are amplified by the large number contained in a tiny monocrystal. Consequently, they show remarkable phenomena, like Quantum Tunneling of the Magnetization (QTM) measured first [3] in spin S = 10 systems (Mn 12 , Fe 8 ) and Berry Phase quantum interference [4] (Fe 8 ). This large spin molecular magnets show significant anisotropy barriers protruded by tunneling channels which are generated by a transverse magnetic field or anisotropy terms. A sweeping longitudinal field (that is, parallel with the main spin quantification axis) will force the spin to sequentially visit the tunneling channels and obey the Landau-Zener tunneling mechanism each time. Consequently, distinct jumps are generated in the hys-

Spin transition in Gd3N@C80, detected by low-temperature on-chip SQUID technique

“…By aligning the magnetic field with high precision in the plane of a Nb SQUID, the on-chip SQUID technique employed here extends the observation of quantum magnetic phenomena into a higher magnetic field range. Therefore, this improved technique is very promising in gathering more information about effects such as spin state transitions and entanglements, the anisotropy-induced tunneling gap 10 , phonon bottleneck effects 11,12 and others.…”

On-chip SQUID measurements in the presence of high magnetic fields

“…Sensitive magnetization measurements in sweeping magnetic fields have been performed by means of superconducting quantum interference devices (SQUIDs) [1], Hall probe magnetometers [10] or Electron Paramagnetic Resonance (EPR) [11] spectroscopy. Such techniques are highly desirable to gather more information about effects such as the anisotropy-induced tunneling gap [12], spin states entanglements, phonon bottleneck effects [13,14] and others.SQUID devices are well established as highly sensitive magnetic flux detectors for low temperature applications. A commercial SQUID fabricated with Nb-AlO x -Nb Josephson junctions is usually magnetically shielded and coupled to the sample through a pick-up coil [15].…”

“…Sensitive magnetization measurements in sweeping magnetic fields have been performed by means of superconducting quantum interference devices (SQUIDs) [1], Hall probe magnetometers [10] or Electron Paramagnetic Resonance (EPR) [11] spectroscopy. Such techniques are highly desirable to gather more information about effects such as the anisotropy-induced tunneling gap [12], spin states entanglements, phonon bottleneck effects [13,14] and others.…”

Mesoscopic systems: classical irreversibility and quantum coherence

“…the expectation value solutions of (4.5) are given by S z (∞) ) = 1 − 2P LZ = 2 exp[−p(D/h) 2 /gc] − 1 and S x (∞) = S y (∞) = 0. Such Bloch equations can be used to blend the nonadiabatic dynamics of spins with the presence of a non-equilibrium phonon bath, by using an effective Hamiltonian and a relaxation term given by a phononbottleneck mechanism [17]. Note that eliminating the transverse spin components in equation (4.5) gives d 2 S z (t) /dt 2 = c 2 t S z dt − (D 2 + c 2 t 2 ) S z , the solution of which must also be S z (∞) = 1 − 2P LZ when time goes from −∞ to +∞.…”