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Soviet Journal of Low Temperature Physics

Impurity-spin relaxation in a one-dimensional X-Y model

О. Б. Заславский, V. M. Tsukernik

Published Oct 1, 1980• 0 citations
Publisher

Abstract

The time evolution of the impurity spin projection in an X-Y chain on the direction of the external magnetic field is considered for a stepwise change in the field acting on the impurity. The mode of relaxation is substantially dependent on the presence of discrete impurity levels in the system, and also on the closeness of these to the edge of the continuum. Low-temperature and high-temperature cases are considered.

DOI
10.1063/10.0030161

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The time evolution of the impurity spin projection in an X-Y chain on the direction of the external magnetic field is considered for a stepwise change in the field acting on the impurity. The mode of relaxation is substantially dependent on the presence of discrete impurity levels in the system, and also on the closeness of these to the edge of the continuum. Low-temperature and high-temperature cases are considered.
A semiinfinite X-Y chain is considered with an impurity at the end which interacts with a transverse magnetic field. It is shown that by using a unitary transformation that includes a nonlinear canonical transformation of Fermi operators, such a system will reduce to the model of an ideal Fermi gas. The evolution of the impurity spin with time is investigated for a jump-like change in the transverse field. It is shown that the nature of the relaxation depends on the presence of a discrete level and its closeness to the edge of the continuous spectrum. The switching on and switching off of the field are analyzed. The evolution of the total spin in time is considered for an Ising chain on which a transverse circularly polarized field acts.
A Mori-Lee theoretic study of spin relaxation in the neighborhood of a magnetic impurity in the s=1/2 nearest-neighbor (NN) Heisenberg chain at high temperatures is presented. Our calculations suggest that in the limit of zero impurity coupling, the spectral function for the ``surface spin'' is consistent with a set of discrete frequencies given approximately by wn{\mathit{w}}_{\mathit{n}}wn​\ensuremath{\approxeq}[n(w0{\mathit{w}}_{0}w0​+1/4)-1/4] against a shallow continuum background, where w0{\mathit{w}}_{0}w0​\ensuremath{\approxeq}3J/4 with 2J being the coupling between NN spins. The frequencies broaden as the impurity coupling is increased to the NN coupling.
The exact energy spectrum in a longitudinal magnetic field is found for an infinite XY chain (s=1∕2) with an impurity fragment. It is shown that, in addition to a continuum band and a discrete set of levels, the existence of from one to four bound states, localized at the boundaries of the impurity fragment with the main chain, is possible. The critical behavior of the local static thermodynamic characteristics and time dependence of the longitudinal dynamic correlation functions for different temperatures are studied. It is shown that local thermodynamic characteristics of the model can be influenced significantly by both the discrete levels and the bound states.
The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-1/21/21/2 XYXYXY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's ggg factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.
We study by Monte Carlo simulations a magnetic impurity coupled antiferromagnetically to a one-dimensional quantum spin model. The impurity susceptibility and the spin-correlation function are calculated. By defining and evaluating an energy scale from the inverse of the impurity susceptibility at zero temperature, we find a scaling relation for the impurity susceptibility in agreement with the prediction of the conformal field theory. We analyze the problem by mapping the spin model onto the resonant-level model, and interpret the energy scale as the resonant-level width. The spin-correlation function between the impurity spin and the spins in the chain is found to extend over long range at low temperatures. We show that the system can be considered as a model of an insulator with heavy-fermion behavior.