Due to the quantum evolution of molecular magnetic moments, the magnetic state of nanomagnets can suffer spontaneous changes. This process can be completely quenched by environment-induced decoherence. However, we show that for typical small supported atomic objects, the substrate-induced decoherence does change the magnetic-moment evolution but does not quell it. To be specific and to compare with experiment, we analyze the spontaneous switching between two equivalent magnetization states of atomic structures formed by Fe on Cu2N/Cu (1 0 0), measured by Loth et al (2012 Science 335 196-9). Due to the substrate-induced decoherence, the Rabi oscillations proper to quantum tunneling between magnetic states are replaced by an irreversible decay of long characteristic times leading to the observed stochastic magnetization switching. We show that the corresponding switching rates are small, rapidly decreasing with system's size, with a 1/T thermal behavior and in good agreement with experiments. Quantum tunneling is recovered as the switching mechanism at extremely low temperatures below the μK range for a six-Fe-atom system and exponentially lower for larger atomic systems. The unexpected conclusion of this work is that experiments could detect the switching of these supported atomic systems because their magnetization evolution is somewhere between complete decoherence-induced stability and unobservably fast quantum-tunneling switching.
Due to the quantum evolution of molecular magnetic moments, the magnetic state of nanomagnets can suffer spontaneous changes. This process can be completely quenched by environment-induced decoherence. However, we show that for typical small supported atomic objects, the substrate-induced decoherence does change the magnetic-moment evolution but does not quell it. To be specific and to compare with experiment, we analyze the spontaneous switching between two equivalent magnetization states of atomic structures formed by Fe on Cu2N/Cu (1 0 0), measured by Loth et al (2012 Science 335 196-9). Due to the substrate-induced decoherence, the Rabi oscillations proper to quantum tunneling between magnetic states are replaced by an irreversible decay of long characteristic times leading to the observed stochastic magnetization switching. We show that the corresponding switching rates are small, rapidly decreasing with system's size, with a 1/T thermal behavior and in good agreement with experiments. Quantum tunneling is recovered as the switching mechanism at extremely low temperatures below the μK range for a six-Fe-atom system and exponentially lower for larger atomic systems. The unexpected conclusion of this work is that experiments could detect the switching of these supported atomic systems because their magnetization evolution is somewhere between complete decoherence-induced stability and unobservably fast quantum-tunneling switching.
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like relaxation of S(z) with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.
Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow-field region in which both phonon- and nuclear-spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the Fe-8 nanomolecule, for Ni particles, and for Ho ions in ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.$ The reduction in the decoherence, compared to low field rates, can exceed six orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.
Single molecule magnets are novel mesoscopic materials exhibiting both classical and quantum properties. Revealing the decoherence and entanglement mechanisms in these systems is crucial for the applications in quantum information technologies. In this thesis, quantum tunneling of magnetization is studied in single molecule magnet dimer [Mn4]2. Motivated by the recent experiments demanding the modification of the current theories, phonon mediated spin bath decoherence model is proposed. In the first part of the thesis, the magnetization of the [Mn4]2 dimer under external magnetic field is investigated. Alternative entangled spin states involved in quantum tunnelings are identified by means of the exact solution of the Schrödinger equation and the Landau-Zener-Stückelberg method. Later, a decoherence model is introduced in which the interaction between the single molecule magnet (central spin) and spin bath is mediated by phonons in a coherent state or thermal distribution. It is observed that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times for coherent states and low temperature thermal distribution. In the former case, if the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. Possible effects of the temperature on spin bath contribution to decoherence is discussed. Then, the effect of entangled environment on decoherence is analyzed. Entanglement within environment is shown to reduce the decoherence of central spin. Also, the entanglement dynamics of the central bipartite spin system is studied. Classification of the Bell states is examined for common spin bath, and separate spin baths. Last part of the thesis is the analysis of dephasing in entangled qutrits (three level quantum systems) under the classical noise, and quantum decoherence. Density matrix formalism is shown to give equivalent results for both cases. For common and separate baths, robust and fragile Bell-like qutrit states were determined, and Horodecki's bound entangled state is shown to be more robust to decoherence in the latter case.
The time evolution of low energy spin states of a single molecular magnet in a local electric field is investigated. The decoherence of the driven single molecular magnet weakly coupled to a thermal bosonic environment is analyzed by the second-order time-convolutionless non-Markovian master equation. If the characteristic time of the system is much smaller than the correlation time of the environment, the analytical expression of the reduced density matrix of the system is obtained. The non-Markovian dynamics of the spin states at low temperatures is induced by the memory effects in the decay rates. The non-Markovian oscillation of the Bloch vector is presented. The quantum decoherence can be effectively restrained with the help of the reasonable manipulation of the environment spectral density function and local electric field. The influence of the dissipation on the pointer states are investigated by the von Neumann entropy. The pointer states can be selected by the environment.
This thesis is about the tunneling dynamics of the Fe8 molecule in the presence of an environment. Although a lot of progress has been made experimentally to determine among many things the extremely small tunnel splitting energies of this macromolecule, the question of how the environment affects the molecule has still not been properly understood. It is the purpose of this thesis to put forward a coherent model for the decoherence processes that affect the Fe8 molecule. The decoherence allows us to treat the Fe8 molecules as classical objects and we can write down rate equations that determine the relaxation dynamics of the entire Fe8 solid. The theoretical predictions are in very good agreement with Monte-Carlo simulations of spherical samples. We believe that the model developed can be generalized to different geometries and also improvised to tackle the different experimental protocols that have been undertaken on these macroscopic molecules.