Logarithmic Corrections in the Magnetic Equation of State for LiTbF4

Abstract

Using SQUID (superconducting quantum interference device) detection, the field and temperature dependence of the magnetization m has been measured close to the critical point of this uniaxial dipolar-coupled ferromagnet. It is shown for the first time that the Landau expansion of the field h holds if m is scaled by [liiidm/dh)/^] 1^* while other equations (of Ising, mean field) yield less agreement and unrealistic parameters. The expansion coefficients of the present analysis can explain in detail formerly measured zero-field properties.The critical-point singularities of uniaxial ferromagnets and ferroelectrics are expected to behave rather exceptionally in that they should not obey the conventional power-law forms, but the mean-field (MF) laws enhanced by logarithmic factors, which are due to dipolar anisotropic critical fluctuations 1 ' 2 X(r)ccx(r)\lnr\ l/S .(1)X denotes the MF relation of the quantity X, e.g., order parameter, susceptibility, specific heat, or correlation length, while r measures the distance from the critical point. Equation (1) corresponds to exact solutions of the renormalization group available at the marginal dimension d = d* and, therefore, experimental checks for the logarithmic corrections on dipolar Ising systems, where d* = 3, are of relevance for the modern theory of phase transitions. 2 In fact, a considerable number of data from an uniaxial ferromagnets, GdCl 3 , 3 LiTbF 4 , 4 " 6 DyEtS0 4 , 7 and TbF 3 , 8 proved to be consistent with Eq. (1), but in all cases pure power laws also provided equivalently good fits.In the present work, we analyze our data for the magnetic equation of state of LiTbF 4 , striving for a check of the full equation as derived in the original theory 1 for the order parameter in dipolar Ising systems m=m|lnr| 1/3 .(Here m follows from the Landau expansion of the field with* = T/T C -1, and r, except for a scale factor Xo, i* s given by the inverse of the isothermal susceptibility x = (dm/dh) t°.r and B represent the critical amplitudes of the susceptibility (t>0) and magnetization (t<0) at h = 0, respectively. In contrast to the previous investigations mentioned above, where special lines in the h-i plane were sampled by varying either the temperature at h = 0 or the field at T = T C , our measurements encompass quasicontinuously the critical region of the h-t plane aiming at a more stringent test of the theory. Binder, Meissner, and Mais, 9 analyzing the equation of state for ferroelectric triglycine sulfate (TGS) in a small region near the critical isochore (t > 0, h -*0; setting r=t) stressed the value of this method by pointing out that the third-order term in Eq. (2a) should sense the relevance of the logarithmic correction much better than the linear one investigated hitherto. The isothermal magnetizations shown in Fig. 1 normalized to saturation have been measured by means of a SQUID (superconducting quantum interference device) magnetometer on a single crystal (3 mm diam). Experimentally, the temperature of the sample was varied while the magneti...

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