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Register a new userEquilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2
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It has long been believed that equilibrium random-field Ising model (RFIM) critical scattering studies are not feasible in dilute antiferromagnets close to and below Tc(H) because of severe non-equilibrium effects. The high magnetic concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide equilibrium behavior. We have employed scaling techniques to extract the universal equilibrium scattering line shape, critical exponents nu = 0.87 +- 0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.
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The high magnetic concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2 does not exhibit the severe critical scattering hysteresis at low temperatures observed in all lower concentration samples studied. The system therefore provides equilibrium neutron scattering line shapes suitable for determining random-field Ising model critical behavior.
Critical scattering analyses for dilute antiferromagnets are made difficult by the lack of predicted theoretical line shapes beyond mean-field models. Nevertheless, with the use of some general scaling assumptions we have developed a procedure by which we can analyze the equilibrium critical scattering in these systems for H=0, the random-exchange Ising model, and, more importantly, for H>0, the random-field Ising model. Our new fitting approach, as opposed to the more conventional techniques, allows us to obtain the universal critical behavior exponents and amplitude ratios as well as the critical line shapes. We discuss the technique as applied to Fe(0.93)Zn(0.07)F2. The general technique, however, should be applicable to other problems where the scattering line shapes are not well understood but scaling is expected to hold.
The specific heat critical behavior is measured and analyzed for a single crystal of the random-field Ising system Fe(0.93)Zn(0.07)F2 using pulsed heat and optical birefringence techniques. This high magnetic concentration sample does not exhibit the severe scattering hysteresis at low temperature seen in lower concentration samples and its behavior is therefore that of an equilibrium random-field Ising model system. The equivalence of the behavior observed with pulsed heat techniques and optical birefringence is established. The critical peak appears to be a symmetric, logarithmic divergence, in disagreement with random-field model computer simulations. The random-field specific heat scaling function is determined.
The critical exponent beta =0.17(1) for the three-dimensional random-field Ising model (RFIM) order parameter upon zero-field cooling (ZFC) has been determined using extinction-free magnetic x-ray scattering techniques for Fe(0.85)Zn(0.15)F2. This result is consistent with other exponents determined for the RFIM in that Rushbrooke scaling is satisfied. Nevertheless, there is poor agreement with equilibrium computer simulations, and the ZFC results do not agree with field-cooling (FC) results. We present details of hysteresis in Bragg scattering amplitudes and line shapes that help elucidate the effects of thermal cycling in the RFIM, as realized in dilute antiferromagnets in an applied field. We show that the ZFC critical-like behavior is consistent with a second-order phase transitions, albeit quasi-stationary rather than truly equilibrium in nature, as evident from the large thermal hysteresis observed near the transition.
The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy temperature Tg approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable frequency dependence in earlier zero-field ac susceptibility measurements on this sample. These results indicate that long-range order coexists with short-range nonequilibrium clusters in this highly diluted magnet.
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