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Russian Physics Journal

The Effect of Nonmagnetic Impurities on Phase-Transition Kinetics and Correlation Effects in a Quasi-1D Ising Nanomagnetic

E. V. Shabunina, D.V. Spirin, А. А. Попов, V. N. Udodov, А. И. Потекаев

Published May 1, 2013• 0 citations
Publisher
DOI
10.1007/s11182-013-9982-y

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Izvestiya of Altai State University•Jan 1, 2017•1 citation
In recent decades, one-dimensional (quasi-one-dimensional) Ising magnetic compounds have been synthesized, on which new promising materials are based. Here, percolation effects are considered in the model of a one-dimensional Ising magnet of finite nanometer size with boundary conditions “dangling ends”. The model takes into account the interaction with an external magnetic field, nearest-site interaction of nodes, interaction of second and third neighbors, as well as four-particle interactions. To model the phase transition, the Metropolis algorithm was used. Two options for the localization of a nonmagnetic impurity are considered: with mobile impurities and with fixed impurities (frozen impurities). For mobile impurities, the Metropolis algorithm contains the possibility of moving non-magnetic nodes along the chain. In the second variant, when the initial configurations are formed, nonmagnetic impurities in the magnet take random constant equiprobable positions. It is shown that the presence of non-magnetic nodes leads to a weakening of the correlation inside the chain and the magnet breaks up into several parts unconnected by magnetic interaction. The fraction of nonmagnetic atoms, in which the magnet is divided into two non-correlating parts, is an analogue to the percolation threshold in the percolation site problem. The percolation radius corresponds to the farthest nonzero interaction. The paper shows the existence of a relationship between the percolation threshold and the dependences of the relaxation time of the ferromagnet — antiferromagnet phase transition and the dynamic critical exponent Z on the fraction of nonmagnetic impurities in the model of a one-dimensional Ising magnet with fixed (frozen) nonmagnetic impurities. In the case of mobile nonmagnetic impurities, the absence of a clear connection between the percolation threshold and the dependences of the relaxation time and the dynamic critical exponent is shown.
We study the effects of nonmagnetic impurities in a spin Bose-metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Sheng et al., arXiv:0902.4210). This phase is a quasi-one-dimensional (quasi-1D) descendant of a two-dimensional (2D) spin liquid with spinon Fermi sea and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local-energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The spin Bose metal has dominant correlations at characteristic incommensurate wave vectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually increases as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. 75, 934 (1995)]. We calculate the corresponding power-law exponents for the textures as a function of one Luttinger parameter of the SBM theory.
The paper presents the results of computer simulation of the generalized Ising model of a quasi-onedimensional nanomagnet by the Monte Carlo method. The simulation is performed for antiferromagnetferromagnet phase transition with periodic boundary conditions. The dynamic scaling ratio Y = v* z and the static scaling relation dv = 2 – α have been verified for the Ising nanomagnet using values of the critical temperature, as well as values of the critical exponents. Temperature dependences of the kinetic critical index and the product of the dynamic critical index Y(T) on the correlation length index of the v* z(T) are constructed for a linear system (cluster) of finite size. The influence of interaction energy of the second, third neighbors, and four-particle interaction on the fulfillment of dynamic and static scaling hypotheses is described. Parameters are found for the dynamic scaling ratio near the critical region to be within the errors. It is shown that the static scaling hypothesis within the framework of the one-dimensional Ising magnet model near the critical region is violated for any type of interaction. However, the relation v + α = 2 is satisfied within the errors for some temperatures. The obtained results are compared with the values for the Ising model with the «dangling ends» boundary conditions.DOI 10.14258/izvasu(2017)4-04