Weiss temperature

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. 

The above statements apply to an assembly of independent spins. Deviation from proportionality, if any is observed, suggests the presence of cooperative magnetic phenomena, i.e. ferro-, antiferro-, ferri-, meta-, micto-magnetism, and so on. The magnetic susceptibility at above the spinordering temperature (Tq) can be usually fitted by the Curie-Weiss expression (18) with the Weiss temperature 0 > 0 for the sample with dominant... 

Magnetic susceptibihty measurements [256] on Cu VCo VZn/Al LDHs indicate that the Cmie-Weiss law is obeyed with a Weiss temperature close to zero, indicating the lack of magnetic interactions between paramagnetic ions and thus a random distribution in the lattice. It has been proposed, however, that the catalytic activity of Mg Al LDHs n = 2,3) containing interlayer carbonate anions in the oxyethylation of 1-dodecanol with ethylene oxide can be correlated with the distance between AP" cations in ordered lattices [250]. 

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-... 

Experimentally, one thus expects that a triplet paramagnet (5=1) should display Pgff = 2.83pg, a quintet (5 = 2) 4.90 pg, and so on. A mixture of two states of different spin should have a value intermediate between the two values. For two such states in equilibrium, the energy gap can be calculated from the value of % and the Weiss temperature 0 in the Curie-Weiss law (Eq. 5.) ... 

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...

Recently, the discovery of short range ferromagnetic interactions (SRFM) (Weiss temperature, 0 IK from l/% vs T, magnetization saturation curves corresponding to S = 2, rather than S = 1/2) in crystals of 1(2) was reported(7, ). 

Here, the Weiss temperature 9 is a function of the exchange energies /ex that can be obtained from a high-temperature series expansion ... 

It is important to observe the applicability limits of the Curie-Weiss law and the implied physical meaning of the Weiss temperature It can only be applied to magnetic materials containing spin-only magnetic centers, and it only applies to magnetically condensed systems (as opposed to magnetically dilute systems) at sufficiently high temperatures fer>/ex). 

NdRu4Sbi2 is metallic and undergoes some type of magnetic transition near 1.3 K. The magnetic susceptibility follows a Curie-Weiss law above 50 K with an effective moment of 3.45/u.b and a Weiss temperature of -28 K. Crystal fields likely effect the susceptibility and magnetic interactions for temperatures below 50 K. Low temperature heat capacity data confirm the bulk nature of the magnetic transition (Takeda and Ishikawa, 2000b). 

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