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.

Quantum point contact due to Fermi-level pinning and doping profiles in semiconductor nanocolumns

We show that nanoscale doping profiles inside a nanocolumn in combination with Fermi-level pinning at the surface give rise to the formation of a saddle-point in the potential profile. Consequently, the lateral confinement inside the channel varies along the transport direction, yielding an embedded quantum point contact. An analytical estimation of the quantization energies will be given

Glauber dynamics in a single-chain magnet: From theory to real systems

The Glauber dynamics is studied in a single-chain magnet. As predicted, a single relaxation mode of the magnetization is found. Above 2.7 K, the thermally activated relaxation time is mainly governed by the effect of magnetic correlations and the energy barrier experienced by each magnetic unit. This result is in perfect agreement with independent thermodynamical measurements. Below 2.7 K, a crossover towards a relaxation regime is observed that is interpreted as the manifestation of finite-size effects. The temperature dependences of the relaxation time and of the magnetic susceptibility reveal the importance of the boundary conditions.Comment: Submitted to PRL 10 May 2003. Submitted to PRB 12 December 2003; published 15 April 200

Depletion lengths in semiconductor nanostructures

The discrepancy between W(R) and Wp becomes significant when the dimensions of the structure becomes comparable to the depletion length, as can occur in nanostructure devices