Curie paramagnets

No explicit temperature dependence is included in the equations for R m and Rim, except for cases where Curie spin relaxation is the dominant term (Section 3.6). In the latter case, Curie paramagnetism has a T x dependence and therefore relaxation depends on T 2. The effect of temperature on linewidths determined by Curie relaxation is dramatic also because of the xr dependence on temperature, as shown in Eq. (3.8). All the correlation times modulating the electron-nucleus coupling, either contact or dipolar, are generally temperature dependent, although in different ways, and their variation will therefore be reflected in the values of Rim and Rim-... 

The Curie paramagnets [e.g., octahedral Fe(III) complexes] are rather rare, and the temperature dependence of the magnetic susceptibility requires more parameters, depending on the actual spacing of the low-lying energy levels. Let us enumerate the MPs associated with the SH formalism ... 

Zeeman term appropriate to the Curie paramagnet.) The MPs gx, gy, gz, D, and E are understood as constants that characterize the sample under study. 

Fig. 9 Magnetization curves for various ZFS systems modeled as a powder average at T = 4.2 K top panel D/k = -5 (solid), - 10 (long dashed), - 15 (medium dashed),- 20 K (short dashed) bottom panel D/k = + 5 (solid), + 10 (long dashed), + 15 (medium dashed), + 20 K (short dashed) Brillouin function for a Curie paramagnet - dot-dashed...

Level-1. The Hamiltonian contains only the isotropic Zeeman term, and this is appropriate for an isotropic Curie paramagnet. The energy levels and the magnetic susceptibility are simple functions like xmoi = fig). 

Fig. 13 Effective magnetic moment for octahedral dl complexes like Ti(III) solid - k = 1 long dashed -k = 0.7 short dashed - k = 0.4 dot-dashed - k = 0 (a Curie paramagnet with spin-only contribution). Right the calculated energy levels (not to scale, values in cm 1)...

Spin-only Hamiltonian is appropriate a perfect Curie paramagnet for S = 3/2, x =/(g) Meflfis constant down to low temperatures. 

The magnetic functions are modeled in Fig. 53. Above some temperature (50 K in the present case) the system behaves like a Curie paramagnet with a small TIP. Below this limit it reflects the thermal population of the mentioned five multiplets and shows features of the ZFS system. However, a simple ZFS modeling (level-2) is not permitted since there are ten magnetic levels in play and not five members of the S = 2 manifold. 

For systems comprising magnetic centers that are both exchange coupled and affected by ligand field effects (i.e., non-Curie paramagnetic centers), the susceptibility (above an ordering temperature) can be approximated by molecular field models. 

Fig. 3 Example comparisons of X versus T behavior for a ferromagnet (left) and a sample with antiferromagnetic exchange (right) to theoretical Curie paramagnet behavior.

In contrast, TDAE-C70 does not show magnetic order. The ESR and magnetization properties of TDAE>-C6o and TDAE-C70 were compared by Th,naka et aL, who reproduced the magnetic transition in TDAE-Ceo) but found only Curie paramagnetism in TDAE-C7o.[Ta92a] It is not yet known whether this difference is due to the difference in the electronic structure of Ceo vs. C70, or if TDAEI-C70 adopts some different crystal structure. 

For Curie paramagnets analytic functions were derived the Brillouin function and its classical analogue, the Langevin function. 

For Curie paramagnets non-linear behaviour is observed at low temperature and high fields, i.e. when the linear approximation to the Brillouin function is violated. 

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