arXiv subjects
Publications and source records attributed to P. C. E. Stamp.
Comment on the paper: "Magnetization Process of Single Molecule Magnets at Low Temperatures" of J.F.Fernandez and J.J.Alonso (PRL 91, 047202 (2003)).
We discuss how the crossovers in models like spin-boson model are changed by adding the coupling of the central spin to localised modes- the latter modelled as a 'spin bath'. These modes contain most of the environmental entropy and energy at low T in solid-state systems. We find that the low T crossover between oscillator bath and spin bath dominated decoherence, occurring as one reduces the energy scale of the central spin, is characterised by very low decoherence- we show how this works out in practise in magnetic insulators. We then reconsider the standard quantum-classical crossover in the dynamics of a tunneling system, including both spin and oscillator baths. It is found that the general effect of the spin bath is to broaden the crossover in temperature between the quantum and classical activated regimes. The example of tunneling nanomagnets is used to illustrate this.
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 $LiHo_xY_{1-z}F_4$. The reduction in the decoherence, compared to low field rates, can exceed 6 orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.
The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a 'hole' to appear in the distribution of internal fields in the system. The form of this hole, and its time evolution, are studied using Monte Carlo simulations. It is shown that the line-shape of the tunneling hole in a weakly polarised sample must have a Lorentzian lineshape- the short-time half-width $ξ_o$ in all experiments done so far should be $\sim E_0$, the half-width of the nuclear spin multiplet. After a time $τ_o$, the single molecule tunneling relaxation time, the hole width begins to increase rapidly. In initially polarised samples the disintegration of resonant tunneling surfaces is found to be very fast.
In a recent letter Alonso et al. (Phys. Rev. Lett. 87, 097205 (2001)) present Monte Carlo simulations for interacting dipoles. Short-time relaxation was caused by a simple noise field, acting uniformly over an "energy window" of small width (to simulate the fluctuating nuclear spin bias). However, the physics of the tunneling relaxation of an ensemble of tunneling nanomagnets or magnetic molecules (as well as of the "tunneling hole" formation) is different and here we discuss this point.
We briefly review the oscillator and spin bath models of quantum environments, which can be used to describe the low-energy dynamics of open quantum systems. We then use them to discuss both the mechanisms causing decoherence at low $T$, and the dynamics of this decoherence. This is done first for a central 2-level system coupled to these environments- the results can be applied to the dynamics of quantum nanomagnets and superconducting SQUIDs, where large-scale tunneling of magnetisation and flux take place. Decoherence in these systems is caused principally by coupling to electrons and nuclear spins, the spin bath couplings are particularly dangerous at low $T$. These models are also generalised to discuss quantum measurements in which the measured system, the measuring apparatus, and the environment are treated quantum mechanically. The results can be used to calculate the dynamics of coupled SQUIDs and/or nanomagnets, in which one acts as a measuring apparatus and the other exhibits large-scale quantum superpositions. The same model can be used to describe coupled qubits.
We investigate the motion of a domain wall in the presence of a dynamical hyperfine field. At temperature T high compared to the hyperfine coupling, the nuclear spins create a spatially random potential landscape, with dynamics dictated by the nuclear relaxation time $T_2$. The distribution of the domain wall relaxation times (both in the thermal and quantum regimes) can show a long tail, characteristic of stochastic processes where rare events are important. Here, these are due to occasional strong fluctuations in the nuclear spin polarisation.
The low-energy behaviour of 2 coupled nanomagnets or 2 coupled SQUIDs, interacting with their environment, can be described by the model of a ``Pair or Interacting Spins Coupled to an Environmental Sea'' (PISCES). These physical systems can then be used for a measurement operation in which system, apparatus and environment are all treated quantum mechanically. We design a ``Bell/Coleman-Hepp'' measuring system, and show that in principle one may design a situation in which quantum interference between system and apparatus can upset the usual measurement operation.
We calculate the magnetisation relaxation in the short-time regime for an ensemble of nanomagnets in the presence of a low-frequency external AC biasing field, at temperatures lower than the magnetic anisotropy energy of the individual nanomagnets. It is then found that the relaxation is strongly affected by AC fields with amplitude larger than that of the $T_2$ fluctuations in the nuclear field. This will allow experimental probing of the nuclear spin relaxation mechanism.
Recent theory and experiment in crystals of molecular magnets suggest that fundamental tests of the decoherence mechanisms of macroscopic quantum phenomena may be feasible in these systems (which are almost ideal quantum spin glasses). We review the results, and suggest new experiments.
The low-energy physics of systems coupled to their surroundings is understood by truncating to effective Hamiltonians; these tend to reduce to a few canonical forms, involving coupling to "baths" of oscillators or spins. The method for doing this is demonstrated using examples from magnetism, superconductivity, and measurement theory, as is the way one then solves for the low-energy dynamics. Finally, detailed application is given to the exciting recent Quantum relaxation and tunneling work in naomagnets.
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion, in the parameter $omega_c/μ$. We show that in two dimensions this expansion breaks down, and derive a new expression, exact in the limit where rainbow graphs dominate the self-energy. Application of our results to the fractional quantum Hall effect near half-filling shows very strong deviations from Lifshitz-Kosevich behaviour. We expect that such deviations will be important in any strongly-interacting 2-dimensional electronic system.
We solve for the dynamics of a pair of spins, coupled to each other and also to an environmental sea of oscillators. The environment mediates an indirect interaction between the spins, causing both mutual coherence effects and dissipation. This model describes a wide variety of physical systems, ranging from 2 coupled microscopic systems (eg., magnetic impurities, bromophores, etc), to 2 coupled macroscopic quantum systems. We obtain analytic results for 3 regimes, viz., (i) The locked regime, where the 2 spins lock together; (ii) The correlated relaxation regime (mutually correlated incoherent relaxation); and (iii) The mutual coherence regime, with correlated damped oscillations. These results cover most of the parameter space of the system.
We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules interacting with a surrounding spin environment, such as nuclear spins. We describe a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then verify the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a microscopic spin, using exact diagonalisation techniques.
We consider the quantum dynamics of a magnetic domain wall at low temperatures, where dissipative couplings to magnons and electrons are very small. The wall motion is then determined by its coupling to phonons and nuclear spins, and any pinning potentials. In the absence of nuclear spins there is a dominant superOhmic 1-phonon coupling to the wall velocity, plus a strongly T-dependent Ohmic coupling to pairs of phonons. There is also a T-independent Ohmic coupling between single phonons and the wall chirality, which suppresses ``chirality tunneling''. We calculate the effect of these couplings on the T-dependent tunneling rate of a wall out of a pinning potential. Nuclear spins have a very strong and hitherto unsuspected influence on domain wall dynamics, coming from a hyperfine-mediated coupling to the domain wall position. For $k_B T \gg ω_{0}$ this coupling yields a spatially random potential, fluctuating at a rate governed by the nuclear $T_2$. When $k_B T \ll ω_{0}$, the hyperfine potential fluctuates around a linear binding potential. The wall dynamics is influenced by the fluctuations of this potential, ie., by the nuclear spin dynamics. Wall tunneling can occur when fluctuations open an occasional ``tunneling window''. This changes the crossover to tunneling and also causes a slow "wandering", in time, of the energy levels associated with domain wall motion inside the pinning potential. This effect is fairly weak in $Ni$- and $Fe$- based magnets, and we give an approximate treatment of its effect on the tunneling dynamics, as well as a discussion of the relationship to recent domain wall tunneling experiments.
We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy and the first excited states. The electron-phonon problem is treated for both Debye and Einstein phonons. In the case of composite fermions, it is found that the singular Landau level structure strongly affects the renormalised gap in the intermediate coupling regime, which is relevant to experiments on the fractional quantum Hall effect. We compare our findings with measurements of the gap in fractional Hall states with filling fraction nu near nu=1/2.
We calculate the self-energy of fermions in Landau level n, in a finite field. Two cases are considered, in which fermions couple either to gauge fluctuations (as in the composite fermion gauge theory) or to phonons, as an example of a Fermi liquid. Perturbative calculations of the composite fermion spectrum show an unphysical suppression of the quasiparticle spectral weight at the composite fermion levels. We argue that this problem might be resolved by a non-perturbative calculation; alternatively, the system might be unstable.
We consider here the problem of a "central spin", with spin quantum number $S \gg 1$, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with nuclear spins and with any surrounding paramagnetic electronic spins. It has also been used to describe $Si:P$ near the metal-insulator transition, and quantum spin glasses. In this paper we consider the possible coherent motion of the central spin. We reduce the model to an effective low-energy Hamiltonian, and then calculate the correlation function using instanton methods. The general solution is given for the unbiased case, for all relevant values of the couplings. Under certain conditions, nuclear spin diffusion also plays a role. The results are then used to calculate the spectral absorption for 2 experimental systems, viz., $TbFe_3$ grains, and ferritin molecules. Our results have general implications for the observation of mesoscopic and macroscopic quantum coherence, and for the foundations of quantum mechanics. They show that a spin environment usually has a very destructive effect on coherence, which cannot be understood using the conventional "oscillator bath" models of quantum environments.