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Soviet Journal of Low Temperature Physics

Low-lying impurity states in quasi-one-dimensional magnetic systems

E. V. Ezerskaya, V. M. Tsukernik

Published Dec 1, 1986• 0 citations
Publisher

Abstract

The effect of impurities on the spectrum of one-magnon excitations of two quasi-one-dimensional spin systems—a double XY chain with an impurity atom and an analogous chain with an impurity link, in which two identical impurity atoms occupy neighboring nodes on different XY chains—is studied. The conditions for the existence of impurity levels and their number are determined for the system with one impurity, and for the system with an impurity link the explicit expressions for the energy and wave functions of localized states are also determined.

DOI
10.1063/10.0031620

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The effect of impurities on the spectrum of one-magnon excitations of two quasi-one-dimensional spin systems—a double XY chain with an impurity atom and an analogous chain with an impurity link, in which two identical impurity atoms occupy neighboring nodes on different XY chains—is studied. The conditions for the existence of impurity levels and their number are determined for the system with one impurity, and for the system with an impurity link the explicit expressions for the energy and wave functions of localized states are also determined.
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The ground state for S 0 =1 and the low-lying excited states including localized states for S 0 =1/2 of a linear Heisenberg ferromagnet of spin 1/2 containing an antiferromagnetic impurity spin are calculated, where S 0 is a magnitude of the impurity spin. In these cases they belong to the subspace spanned by the two spin deviation kets. The two magnon states are solved. The method is based on the excitation from the rigorous one magnon localized state. The wave functions and the averages of the Z component of each spin are calculated. Numerical calculations for a ring consisting of twelve spins are performed. The results are in good agreement with analytical results for the ground state energy and localized levels.
We study the energy spectrum of a dual spin chain with an XY interaction among nearest neighbors. This model is applicable in particular to the description of the magnetic properties of the compound Cu(NO3)2 · 2.5H2O. We obtain exact expressions for the energy and wave functions of the one- and two- magnon states. Analysis of the stationary states with a large number of excitations is carried out in terms of perturbation theory under the condition that the exchange interaction J1 between the members of a spin pair significantly exceeds the interaction between pairs, J2. For small ratios J2/J1 the curves of the thermodynamic functions obtained as functions of magnetic field indicate the presence of two critical fields at low temperatures (T≪J2), in agreement with the experimental data.
The one dimensional XY model of spin 1/2 is discussed by transforming the spin operators to the Fermi operators. This method can be applied to the XY model with an impurity spin. In that case a pair of localized exciton (or a kind of magnon) levels are obtained. The energy of states can be determined by distributing the excitons over two sets of exciton levels which depend on whether the number of excitons is even or odd. The energy levels of states are calculated by the computer for small rings of 4, 6 and 8 spins. The results can be perfectly understood by the theory.
Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.