Curie Weiss law

Curie-Weiss law The molar magnetic susceptibility of a substance may be represented... 

Equation (A2.5.20) is the Curie-Weiss law, and the temperature at which the magnetic susceptibility becomes infinite, is the Curie temperature. Below this temperature the substance shows spontaneous magnetization and is ferromagnetic. Nonnally the Curie temperature lies between 1 and 10 K. However, typical ferromagnetic materials like iron have very much larger values for quantum-mechanical reasons that will not be pursued here. 

The dielectric stiffness can be expressed as a linear temperature dependence based on the Curie-Weiss law at above the Curie point T. 

Perhaps the most convincing argument in favor of intercalant ionization derives from the analogous reaction of graphite with OsFg (B22). The product, formulated as CJOsFs, obeys the Curie-Weiss law, and has a magnetic moment characteristic of OsFs(V) salts. 

At room temperature, osmium hexafluoride yields a blue material of approximate composition CgOsFg (B22). Its magnetic susceptibility obeys the Curie-Weiss law, with a magnetic moment, /lefi = 3.5 BM,... 

The temperature dependence of the molar susceptibility of a paramagnetic substance follows the Curie-Weiss law (if the magnetic field is not too strong) ... 

Above a critical temperature Tc, the Curie temperature, a ferromagnetic material becomes paramagnetic, since thermal motion inhibits the parallel orientation of the magnetic moments. The susceptibility then follows the Curie-Weiss law with a positive value of the Weiss constant, 0 > 0 (Fig. 19.6). 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

Frequently the magnetic behavior of a paramagnetic solid does not follow the Curie law exactly but is rather better fitted by the Curie-Weiss law ... 

Figure 14 shows the result of a Brillouin scattering experiment in the vicinity of Tc [11]. Closed circles and open circles below Tc indicate the modes split from the doubly degenerated ferroelectric soft mode. The closed circles above Tc denote the frequency of the doubly degenerated soft u mode in the paraelectric phase. The results clearly show a softening of the soft mode toward zero frequency at Tc following the Curie-Weiss law. The soft mode remains underdamped even at Tc. Generally, a soft mode is heavily damped in the vicinity of Tc, e.g., as for PbTiOs, which are typical displacive-type... 

Static dielectric measurements [8] show that all crystals in the family exhibit a very large quantum effect of isotope replacement H D on the critical temperature. This effect can be exemphfied by the fact that Tc = 122 K in KDP and Tc = 229 K in KD2PO4 or DKDP. KDP exhibits a weak first-order phase transition, whereas the first-order character of phase transition in DKDP is more pronounced. The effect of isotope replacement is also observed for the saturated (near T = 0 K) spontaneous polarization, Pg, which has the value Ps = 5.0 xC cm in KDP and Ps = 6.2 xC cm in DKDP. As can be expected for a ferroelectric phase transition, a decrease in the temperature toward Tc in the PE phase causes a critical increase in longitudinal dielectric constant (along the c-axis) in KDP and DKDP. This increase follows the Curie-Weiss law. Sc = C/(T - Ti), and an isotope effect is observed not only for the Curie-Weiss temperature, Ti Tc, but also for the Curie constant C (C = 3000 K in KDP and C = 4000 K in DKDP). Isotope effects on the quantities Tc, P, and C were successfully explained within the proton-tunneling model as a consequence of different tunneling frequencies of H and D atoms. However, this model can hardly reproduce the Curie-Weiss law for Sc-... 

Figure 6.39(a) shows the vs. T curve, normalized to the RT value, for a 100 nm thick a-/ -NPNN/glass film obtained from electron paramagnetic resonance (EPR) measurements with the static magnetic field applied perpendicular to the substrate plane. As previously shown in Fig. 3.19, the molecular a -planes are parallel to the substrate s surface. The data points closely follow the Curie-Weiss law = (T — w)/C, where C stands for the Curie constant. In this case w — —0.3 K, indicating that the net intermolecular interactions are weakly anfiferromagnetic. No hint of a transition at low temperature is observed. These results coincide with those derived from SQUID measurements on a single a-p-NPNN crystal (Tamura etal, 2003), where 0.5 < w < 0, which are displayed in Fig. 6.40. 

Figure 6.40. Temperature dependence of x The line denotes the fit to the Curie-Weiss law. Reprinted with permission from Tamura et al, 2003.

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