Low-field susceptibility of classical Heisenberg chains with arbitrary and different nearest-neighbour exchange

Cregg, P J and Svedlindh, Peter and Garcia-Palacios, J L and Murphy, Kieran (2008) Low-field susceptibility of classical Heisenberg chains with arbitrary and different nearest-neighbour exchange. Journal of Physics: Condensed matter. ISSN 09538984 (In Press)

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Abstract

Interest in molecular magnets continues to grow, o®ering a link between the atomic and nanoscale properties. The classical Heisenberg model has been effective in modelling exchange interactions in such systems. In this, the magnetization and susceptibility are calculated through the partition function, where the Hamiltonian contains both Zeeman and exchange energy. For an ensemble of N spins, this requires integrals in 2N dimensions. For two, three and four spin nearest neighbour chains these integrals reduce to sums of known functions. For the case of the three and four spin chains, the sums are equivalent to results of Joyce. Expanding these sums, the effect of the exchange on the linear susceptibility appears as Langevin functions with exchange term arguments. These expressions are generalised here to describe an N spin nearest neighbour chain, where the exchange between each pair of nearest neighbours is different and arbitrary. For a common exchange constant, this reduces to the result of Fisher. The high temperature expansion of the Langevin functions for the different exchange constants, leads to agreement with the appropriate high temperature quantum formula of Schmidt et al., when the spin number is large. Simulations are presented for open linear chains of three, four and five spins with up to four different exchange constants, illustrating how the exchange constants can be retrieved successfully.

Item Type: Article
Departments or Groups: Materials Characterisation and Processing Group
Divisions: School of Science > Department of Computing, Maths and Physics
School of Engineering > Department of Engineering Technology
Depositing User: P.J. Cregg
Date Deposited: 12 May 2008 11:28
Last Modified: 22 Aug 2016 10:25
URI: http://repository.wit.ie/id/eprint/909

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