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Ordering and phase transitions in ising systems with competing short range and dipolar interactions

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Zeitschrift für Physik B Condensed Matter

Abstract

As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ 2/a 3. ForJa 3/µ 2<−1.3384 the ground-state is antiferromagnetic, while for −1.3384<Ja 3/µ 2<0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa 3/µ 2=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa 3/µ 2>0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa 3/µ 2 where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero.

The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa 3/µ 2 of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.

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Author notes

  1. R. Kretschmer & K. Binder

    Present address: Institut für Festkörperforschung, Kernforschungsanlage Jülich, Postfach 1913, D-5170, Jülich 1, Germany

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  1. Theoretische Physik, Universität, Saarbrücken, W-Germany

    R. Kretschmer & K. Binder

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Supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 130 “Ferroelektrika”

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Kretschmer, R., Binder, K. Ordering and phase transitions in ising systems with competing short range and dipolar interactions. Z Physik B 34, 375–392 (1979). https://doi.org/10.1007/BF01325203

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