68 research outputs found
Spin tunnelling in mesoscopic systems
We study spin tunnelling in molecular magnets as an instance of a mesoscopic
phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel
splitting between various pairs of Zeeman levels in this molecule oscillates as
a function of applied magnetic field, vanishing completely at special points in
the space of magnetic fields, known as diabolical points. This phenomena is
explained in terms of two approaches, one based on spin-coherent-state path
integrals, and the other on a generalization of the phase integral (or WKB)
method to difference equations. Explicit formulas for the diabolical points are
obtained for a model Hamiltonian.Comment: 13 pages, 5 figures, uses Pramana style files; conference proceedings
articl
Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity
It is shown that crystals of molecular nanomagnets exhibit enhanced magnetic
relaxation when placed inside a resonant cavity. Strong dependence of the
magnetization curve on the geometry of the cavity has been observed, providing
evidence of the coherent microwave radiation by the crystals. A similar
dependence has been found for a crystal placed between Fabry-Perot
superconducting mirrors. These observations open the possibility of building a
nanomagnetic microwave laser pumped by the magnetic field
Low-Temperature Quantum Relaxation in a System of Magnetic Nanomolecules
We argue that to explain recent resonant tunneling experiments on crystals of
Mn and Fe, particularly in the low-T limit, one must invoke dynamic
nuclear spin and dipolar interactions. We show the low-, short-time
relaxation will then have a form, where depends on the
nuclear , on the tunneling matrix element between the two
lowest levels, and on the initial distribution of internal fields in the
sample, which depends very strongly on sample shape. The results are directly
applicable to the system. We also give some results for the long-time
relaxation.Comment: 4 pages, 3 PostScript figures, LaTe
Quantum tunneling of two coupled single-molecular magnets
Two single-molecule magnets are coupled antiferromagnetically to form a
supramolecule dimer. We study the coupling effect and tunneling process by
means of the numerical exact diagonalization method, and apply them to the
recently synthesized supramoleculer dimer [Mn4]2 The model parameters are
calculated for the dimer based on the tunneling process. The absence of
tunneling at zero field and sweeping rate effect on the step height in the
hysterisis loops are understood very well in this theory.Comment: 4 pages including 3 figure and 1 tabl
Resonant Magnetization Tunneling in Mn12 Acetate: The Absence of Inhomogeneous Hyperfine Broadening
We present the results of a detailed study of the
thermally-assisted-resonant-tunneling relaxation rate of Mn12 acetate as a
function of an external, longitudinal magnetic field and find that the data can
be fit extremely well to a Lorentzian function. No hint of inhomogeneous
broadening is found, even though some is expected from the Mn nuclear hyperfine
interaction. This inconsistency implies that the tunneling mechanism cannot be
described simply in terms of a random hyperfine field.Comment: Some minor revisions, title changed, updated figures, two added
notes, one added reference. RevTeX, 4 pages, 3 postscript figures. Submitted
to Rapid Communication
Convolution of multifractals and the local magnetization in a random field Ising chain
The local magnetization in the one-dimensional random-field Ising model is
essentially the sum of two effective fields with multifractal probability
measure. The probability measure of the local magnetization is thus the
convolution of two multifractals. In this paper we prove relations between the
multifractal properties of two measures and the multifractal properties of
their convolution. The pointwise dimension at the boundary of the support of
the convolution is the sum of the pointwise dimensions at the boundary of the
support of the convoluted measures and the generalized box dimensions of the
convolution are bounded from above by the sum of the generalized box dimensions
of the convoluted measures. The generalized box dimensions of the convolution
of Cantor sets with weights can be calculated analytically for certain
parameter ranges and illustrate effects we also encounter in the case of the
measure of the local magnetization. Returning to the study of this measure we
apply the general inequalities and present numerical approximations of the
D_q-spectrum. For the first time we are able to obtain results on multifractal
properties of a physical quantity in the one-dimensional random-field Ising
model which in principle could be measured experimentally. The numerically
generated probability densities for the local magnetization show impressively
the gradual transition from a monomodal to a bimodal distribution for growing
random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the
introduction and the conclusions, some typos were corrected, 24 pages,
LaTeX2e, 9 figure
Orbits and phase transitions in the multifractal spectrum
We consider the one dimensional classical Ising model in a symmetric
dichotomous random field. The problem is reduced to a random iterated function
system for an effective field. The D_q-spectrum of the invariant measure of
this effective field exhibits a sharp drop of all D_q with q < 0 at some
critical strength of the random field. We introduce the concept of orbits which
naturally group the points of the support of the invariant measure. We then
show that the pointwise dimension at all points of an orbit has the same value
and calculate it for a class of periodic orbits and their so-called offshoots
as well as for generic orbits in the non-overlapping case. The sharp drop in
the D_q-spectrum is analytically explained by a drastic change of the scaling
properties of the measure near the points of a certain periodic orbit at a
critical strength of the random field which is explicitly given. A similar
drastic change near the points of a special family of periodic orbits explains
a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a
decisive role in this mechanism is played by a specific offshoot. We
furthermore give rigorous upper and/or lower bounds on all D_q in a wide
parameter range. In most cases the numerically obtained D_q coincide with
either the upper or the lower bound. The results in this paper are relevant for
the understanding of random iterated function systems in the case of moderate
overlap in which periodic orbits with weak singularity can play a decisive
role.Comment: The article has been completely rewritten; the title has changed; a
section about the typical pointwise dimension as well as several references
and remarks about more general systems have been added; to appear in J. Phys.
A; 25 pages, 11 figures, LaTeX2
Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others
The dynamical theory of thermally activated resonant magnetization tunneling
in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is
developed.The observed slow dynamics of the system is described by master
equations for the populations of spin levels.The latter are obtained by the
adiabatic elimination of fast degrees of freedom from the density matrix
equation with the help of the perturbation theory developed earlier for the
tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There
exists a temperature range (thermally activated tunneling) where the escape
rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias
field due to tunneling at the top of the barrier. At lower temperatures this
regime crosses over to the non-Arrhenius law (thermally assisted tunneling).
The transition between the two regimes can be first or second order, depending
on the transverse field, which can be tested in experiments. In both regimes
the resonant maxima of the rate occur when spin levels in the two potential
wells match at certain field values. In the thermally activated regime at low
dissipation each resonance has a multitower self-similar structure with
progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure
- …