Temperature Curie—Weiss

The temperature dependence of the molar magnetic susceptibility (x) of an assembly of paramagnetic spins without interaction is characterized by the Curie behavior with x = C/T where C = /Vy2( 2.S (.S + l)/3k. It is a very common situation in the organometallic chemistry of radical species when the spin density is essentially localized on the metal atom. Since, in most cases, this atom is surrounded by various innocent ligands, intermolecular interactions are very weak and in most cases are reflected by a small contribution described by a Curie-Weiss behavior, with x = C/(T 0) where 0 is the Curie-Weiss temperature. A positive value for 0 reflects ferromagnetic interactions while a negative value — the most common situation — reflects an antiferromagnetic interaction. 

We have described above the evolution of the magnetic properties of the [Cp2M (dmit)]AsFg salts upon isomorphous Mo/W substitution. Another possibility offered by this attractive series is the isomorphous substitution of the counter ion, that is PFg- vs AsF6 vs Sbl- fi. Electrocrystallization experiments conducted with [Cp2Mo(dmit)] and the three different electrolytes afforded an isomorphous series, with a smooth evolution of the unit cell parameters with the anion size [32], This cell expansion with the anion size leads to decreased intermolecular interactions between the [Cp2Mo(dmit)]+ radical cation, as clearly seen in Table 2 from the decreased Curie-Weiss temperatures and Neel temperatures (associated with the transition they all exhibit to an AF ground state). 

A three-dimensional set of intermolecular interactions is further confirmed by the observation of a transition to an antiferromagnetic ground state in both radical complexes, at a Neel temperatures of 8 (Mo) and 4.5 K (W), in accordance with the difference of Curie-Weiss temperatures between both complexes. Note also the spin-flop field in the antiferromagnetic state, found at 5.5 kG in [Cp M(dmit)2] and at 8 kG in [Cp W(dmit)2] , a consequence of the stronger spin orbit coupling in the latter. 

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-... 

Fig. 18. Temperature dependence of the Hall coefficient h and resistivity p of a 1.3-ftm thick film of In, Mn As with x = 0.013. Rh can be modeled over a wide range of temperatures as Rq + cpx/Po, which is shown by the solid line assuming c = 5.6. The susceptibility x (depicted by the dashed line) is calculated assuming the Curie-Weiss law with x = 0.013, Mn spin S = 5/2, and the Curie-Weiss temperature 6 = 3.8 K...

FIGURE 17 The experimental values ( ) and calculated values of the Curie-Weiss temperature 0 scaled with the de Gennes factor ( ) and gj/x /(/ + 1) (A) which are then normalized to the experimental value of TbB44Si2- Data for RB44Si2 with R = Tb, Dy, Ho, Er, Tm, Yb were obtained for FZ grown crystals while Gd data was obtained for arc melted GdB44Si2 polycrystalline samples (Mori, 2006a). 

From fits of the high temperature (150 K < T < 250 K) magnetic susceptibilities of RAIB14 (Tb, Dy, Ho, Er), relatively large Curie-Weiss temperatures of 0 10 K were determined by Korsukova et al. (1989). However, the existence of magnetic transitions were not reported. An anomaly is that the Tb phase is reported to have 0 = 10 K, which indicates ferromagnetic interaction. 

Because BLT is ferroelectric, above its Curie temperature s = C/(T — 6) (see Eq. (2.90)), where C is the Curie constant and 6 is the Curie-Weiss temperature. Therefore... 

Tob effective Curie-Weiss temperature due to distribution of barrier energies... 

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