Experimental characterization of the Ising model in disordered antiferromagnets

The current status of experiments on the d = 2 and d = 3 random-exchange and random-field Ising models, as realized in dilute anisotropic antiferromagnets, is discussed. Two areas of current investigation are emphasized. For d = 3, the large random field limit is investigated and equilibrium critical behavior is characterized at high magnetic concentrations.

Authorship

D. P. Belanger

University of California, Department of Physics , Santa Cruz, , United StatesUniversity of CaliforniaUnited StatesSanta Cruz, , United StatesUniversity of California, Department of Physics , Santa Cruz, , United States

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Figures | Tables

Figures (7)
Tables (4)

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Figure 1.
A comparison of the logarithm of the scaling functions f(q/k) versus q/k for different models (See Eq. 1).The pure cases are from approximate expressions from numerical studies [9, 10].The REIM and RFIM are determined from the experiments. Note that the corrections to the MF equation are largest below the transition and are very significant for the pure d = 2 and random-field d = 3 cases.

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Figure 2.
C_m vs. T for Fe_0.93Zn_0.07F₂ at H = 7 T as determined using the birefringence technique. The inset shows the FC data. There appears to be a tiny hysteresis very close to the transition, perhaps a consequence of random-field activated dynamics.

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Figure 3.
C_m vs. T from Monte Carlo simulations modeled after the Fe_0.8Zn_0.2F₂ system. The simularity with the data is striking, though not all Monte Carlo simulations yield a sharp peak in C_m.

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Figure 4.
The H - T phase diagram for Fe_xZn_1-xF₂ measured in pulsed magnetic fields. The concentrations for the alphabetic labels are given in Fig.5.

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Figure 5.
Low temperature spin flips and phase boundary for Fe_xZn_1-xF₂ as a function of x. Note that the phase boundary behavior is quite different for x < x_e and x > x_e.

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Figure 6.
The H - T phase diagram for x = 0.56 showing the upper equilibrium boundary,the phase boundary and a lower equilibrium boundary.

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Figure 7. Monte Carlo simulation data for the staggered magnetization versus T for magnetic concentrations 0.5, 0.6, 0.7 and 0.8. The ZFC and FC procedures exhibit hysteresis for the lower concentrations, which only gets worse for slower runs or larger lattices. No hysteresis is observed for the higher concentrations.

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Table 1. Asymptotic forms for commonly measured static critical behaviors. The superscript + (-) on the amplitudes signifies T > Tc(T < Tc). The exponent values and the amplitude ratios are universal quantities that depend only on the general properties of the system.

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Table 2.
The pure d = 2 and d = 3. Ising static critical exponents obtained from experiments, theory and Monte Carlo simulations.

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Table 3.
The d = 2 and d = 3 REIM Ising critical exponents obtained from experiments, simulations theory.

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Table 4.
The d = 3 RFIM Ising static critical exponents obtained from experiments,simulations and theory.

Figure 1. A comparison of the logarithm of the scaling functions f(q/k) versus q/k for different models (See Eq. 1).The pure cases are from approximate expressions from numerical studies [9, 10].The REIM and RFIM are determined from the experiments. Note that the corrections to the MF equation are largest below the transition and are very significant for the pure d = 2 and random-field d = 3 cases.

Figure 2. C_m vs. T for Fe_0.93Zn_0.07F₂ at H = 7 T as determined using the birefringence technique. The inset shows the FC data. There appears to be a tiny hysteresis very close to the transition, perhaps a consequence of random-field activated dynamics.

Figure 3. C_m vs. T from Monte Carlo simulations modeled after the Fe_0.8Zn_0.2F₂ system. The simularity with the data is striking, though not all Monte Carlo simulations yield a sharp peak in C_m.

Figure 4. The H - T phase diagram for Fe_xZn_1-xF₂ measured in pulsed magnetic fields. The concentrations for the alphabetic labels are given in Fig.5.

Figure 5. Low temperature spin flips and phase boundary for Fe_xZn_1-xF₂ as a function of x. Note that the phase boundary behavior is quite different for x < x_e and x > x_e.

Figure 6. The H - T phase diagram for x = 0.56 showing the upper equilibrium boundary,the phase boundary and a lower equilibrium boundary.

Table 1. Asymptotic forms for commonly measured static critical behaviors. The superscript + (-) on the amplitudes signifies T > T_c(T < T_c). The exponent values and the amplitude ratios are universal quantities that depend only on the general properties of the system.

Table 2. The pure d = 2 and d = 3. Ising static critical exponents obtained from experiments, theory and Monte Carlo simulations.

Table 3. The d = 2 and d = 3 REIM Ising critical exponents obtained from experiments, simulations theory.

Table 4. The d = 3 RFIM Ising static critical exponents obtained from experiments,simulations and theory.

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Experimental characterization of the Ising model in disordered antiferromagnets

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