621 research outputs found
Hysteresis loops and adiabatic Landau-Zener-St\"uckelberg transitions in the magnetic molecule V
We have observed hysteresis loops and abrupt magnetization steps in the
magnetic molecule V, where each molecule comprises a pair of identical spin
triangles, in the temperature range 1-5 K for external magnetic fields with
sweep rates of several Tesla/ms executing a variety of closed cycles. The
hysteresis loops are accurately reproduced using a generalization of the Bloch
equation based on direct one-phonon transitions between the instantaneous
Zeeman-split levels of the ground state (an doublet) of each spin
triangle. The magnetization steps occur for and they are explained
in terms of adiabatic Landau-Zener-St\"{u}ckelberg transitions between the
lowest magnetic energy levels as modified by inter-triangle anisotropic
exchange of order 0.4 K.Comment: 4 pages, 3 figure
Continuous families of isospectral Heisenberg spin systems and the limits of inference from measurements
We investigate classes of quantum Heisenberg spin systems which have
different coupling constants but the same energy spectrum and hence the same
thermodynamical properties. To this end we define various types of
isospectrality and establish conditions for their occurence. The triangle and
the tetrahedron whose vertices are occupied by spins 1/2 are investigated in
some detail. The problem is also of practical interest since isospectrality
presents an obstacle to the experimental determination of the coupling
constants of small interacting spin systems such as magnetic molecules
Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30
We derive the low temperature properties of the molecular magnet Mo72Fe30,
where 30 Fe(3+) paramagnetic ions occupy the sites of an icosidodecahedron and
interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange.
The key idea of our model (J.S. & M.L.) is that the low-lying excitations form
a sequence of rotational bands, i.e., for each such band the excitation
energies depend quadratically on the total spin quantum number. For
temperatures below 50 mK we predict that the magnetisation is described by a
staircase with 75 equidistant steps as the magnetic field is increased up to a
critical value and saturated for higher fields. For higher temperatures thermal
broadening effects wash out the staircase and yield a linear ramp below the
critical field, and this has been confirmed by our measurements (R.M.). We
demonstrate that the lowest two rotational bands are separated by an energy gap
of 0.7 meV, and this could be tested by EPR and inelastic neutron scattering
measurements. We also predict the occurrence of resonances at temperatures
below 0.1 K in the proton NMR spin-lattice relaxation rate associated with
level crossings. As rotational bands characterize the spectra of many magnetic
molecules our method opens a new road towards a description of their
low-temperature behaviour which is not otherwise accessible.Comment: 7 pages, 6 figures, accepted for Europhysics Letter
Classical Heisenberg model of magnetic molecular ring clusters: Accurate approximants for correlation functions and susceptibility
The article of record as published may be found at https://doi.org/10.1063/1.476144We show that the measured magnetic susceptibility of molecular ring clusters can be accurately reproduced, for all but low temperatures T, by a classical Heisenberg model of N identical spins S on a ring that interact with isotropic nearest-neighbor interactions. While exact expressions for the two-spin correlation function, C{sub N}(n,T), and the zero-field magnetic susceptibility, {chi}{sub N}(T), are known for the classical Heisenberg ring, their evaluation involves summing infinite series of modified spherical Bessel functions. By contrast, the formula C{sub N}(n,T)=(u{sup n}+u{sup N{minus}n})/(1+u{sup N}), where u(K)=cothK{minus}K{sup {minus}1} is the Langevin function and K=JS(S+1)/(k{sub B}T) is the nearest-neighbor dimensionless coupling constant, provides an excellent approximation if N{ge}6 for the regime {vert_bar}K{vert_bar}{lt}3. This choice of approximant combines the expected exponential decay of correlations for increasing yet small values of n, with the cyclic boundary condition for a finite ring, C{sub N}(n,T)=C{sub N}(N{minus}n,T). By way of illustration, we show that, for T{gt}50K, the associated approximant for the susceptibility derived from the approximate correlation function is virtually indistinguishable from both the exact theoretical susceptibility and the experimental data for the {open_quotes}ferric wheel{close_quotes} molecular cluster ([Fe(OCH{sub 3}){sub 2}(O{sub 2}CCH{sub 2}Cl)]{sub 10}), which contains N=10 interacting Fe{sup 3+} ions, each of spin S=5/2, that are symmetrically positioned in a nearly planar ring. {copyright} {ital 1998 American Institute of Physics.
Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann
O. Waldmann has shown that some spin systems, which fulfill the condition of
a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal
energies are rather poorly approximated by a quadratic dependence on the total
spin quantum number. We comment on this observation and provide the new
argument that, under certain conditions, the approximating parabolas appear as
natural bounds of the spectrum generated by spin coherent states.Comment: 2 pages, accepted for Europhysics Letter
Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron
The observation of hysteresis effects in single molecule magnets like
Mn-acetate has initiated ideas of future applications in storage
technology. The appearance of a hysteresis loop in such compounds is an outcome
of their magnetic anisotropy. In this Letter we report that magnetic hysteresis
occurs in a spin system without any anisotropy, specifically, where spins
mounted on the vertices of an icosahedron are coupled by antiferromagnetic
isotropic nearest-neighbor Heisenberg interaction giving rise to geometric
frustration. At T=0 this system undergoes a first order metamagnetic phase
transition at a critical field \Bcrit between two distinct families of ground
state configurations. The metastable phase of the system is characterized by a
temperature and field dependent survival probability distribution.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings
Accurate results are obtained for the low temperature magnetization versus
magnetic field of Heisenberg spin rings consisting of an even number N of
intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor
antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte
Carlo method. A straightforward analysis of this data, in particular the values
of the level-crossing fields, provides accurate results for the lowest energy
eigenvalue E(N,S,s) for each value of the total spin quantum number S. In
particular, the results are substantially more accurate than those provided by
the rotational band approximation. For s <= 5/2, data are presented for all
even N <= 20, which are particularly relevant for experiments on finite
magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s)
on s can be described by a scaling relation, and this relation is shown to hold
well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s
<= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the
energy gap between the ground state and the first excited state approaches zero
proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2.
Finally, we demonstrate the usefulness of our present results for E(N,S,s) by
examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate
estimate of the exchange constant for this system than has been obtained
heretofore.Comment: Submitted to Physical Review B, 10 pages, 10 figure
Bounding and approximating parabolas for the spectrum of Heisenberg spin systems
We prove that for a wide class of quantum spin systems with isotropic
Heisenberg coupling the energy eigenvalues which belong to a total spin quantum
number S have upper and lower bounds depending at most quadratically on S. The
only assumption adopted is that the mean coupling strength of any spin w.r.t.
its neighbours is constant for all N spins. The coefficients of the bounding
parabolas are given in terms of special eigenvalues of the N times N coupling
matrix which are usually easily evaluated. In addition we show that the
bounding parabolas, if properly shifted, provide very good approximations of
the true boundaries of the spectrum. We present numerical examples of
frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter
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