Molecular field constant

Our spectroscopic study of the (ErxYi.x)2BaNiOs system (0.1wave functions, and g-factors of the Er3+ ion practically do not depend on x. It is physically reasonable to assume that the molecular-field constant X of the Er-Ni interaction also does not depend on x. In this case, Eqs. (2) and (3) are valid for an arbitrary x and the ordered magnetic moments of the Er and Ni magnetic subsystems can be extracted from the experimentally measured ground-state splittings. 

In 1907 Weiss suggested that the magnetic field //, seen by an individual dipole in a solid was the macroscopic internal field //modified by the presence of dipoles in the neighbourhood of the individual. This idea was expressed by H = H+wM, (c.f. Eq. (2.84)) where w is known as the molecular field constant . Under this assumption Eq. (9.22) is modified to... 

Al mard (5) has applied the method to the ferrimagnetic garnets, where the ionic distributions are known. He includes, to first order, the temperature dependence of the molecular field constants, n = no(l + yT), that was first formulated by N6el (472). The coefficient 7 10 4 is proportional to the coefficient of thermal ex-... 

Fig. 28. Paramagnetic susceptibilities of (a) yttrium and (b) gadolinium ferrogarnets. Solid lines are theoretical curves based on molecular field model and empirically determined molecular field constants. Dashed lines are experimental curves indicating effects of short-range order in the neighborhood of the Curie temperature. (After A16onard (5).)...

In our preliminary communication an error was made in estimating the molecular field constant. 

It is important to mention that from the analysis of the elastic and dielectric measurements and of the A and B molecular field constants the relative contribution of the acoustical and optical vibrations to the structural ordering could be estimated. 

Fig. 28. Variation of the Curie temperature through the series of R2Fe]4B compounds [after Sinnema et al. (1984), bottom part]. The top part shows the variation of the molecular-field constant nRFe [full circles, after Belorizky et al. (1987)] and the variation of the absolute values of the exchange constant /Rf e (full triangles). The middle part is discussed in more detail in the main text.

For a general introduction to the field of NMR in magnetically ordered compounds with non-S state lanthanide ions, we refer the reader to Taylor (1971) or McCausland and Mackenzie (1980), where the interplay of the exchange and crystal-field interactions has been analysed. Generally, for cubic systems like RAI2 at least a three-parameter mean-field model is adopted, based on a single-ion Hamiltonian comprising a crystal field of cubic symmetry [CEF parameters W, x Barnes (1979)] and an isotropic molecular field constant (A) ... 

The main magnetoelastic effects, such as magnetostriction and alterations of sound velocity in a magnetic field, may be described by considering only those terms in the corresponding series expansion of the free energy, which are linear and quadratic in the deformation parameters Uap, Wa(A). It should be noted that the function / depends on the deformation parameters both explicitly, through He-], and implicitly, because of the dependence of molecular field constants on the lattice structure ... 

A peculiarity of the two-particle mechanism of magnetoelastic coupling in dipolar ferromagnets should be noted here - the molecular field constants Aq and their derivatives along the components of the deformation tensor, A (see eq. 110), in the ferromagnetic phase at Ho=0 are different from Aq and A > in the paramagnetic phase, due to the development of a specific domain structure with the zero demagnetizing field at r < 7c. 

R =g/U )h/ r o(AgoP Korringa ratio X molecular field constant... 

Here y is the gyromagnetic ratio for both local moments and conduction electrons, and A is the molecular field constant determined by 7(0). The term containing the field H is the dynamic term . A clear experimental proof of this term has been provided in the systems Yb(Eu ) and Yb/Ca(Eu +) (Schmidt 1972, Schmidt et al. 1972). In controversial form Davidov and Shaltiel (1968) and Male and Taylor (1975) discussed the possibility to observe dynamic effects in the system LaNi5(Gd). 

Compound Experimental Crystal field parameters Molecular field constant T n(K) Calculated tilting angle (°)... 

K = adiabatic compressibility Ap = molecular-field constant Aq = quadrupolar parameter /tb = Bohr magneton X = magnetic susceptibility >l/ =4f eigenfunction belonging to the m-fold level F ... 

A amplitude of sonnd wave rr> rm molecular field constants... 

R-TM and R-R interactions, is the molecular field constant in the d-electron system (it is proportional to /eff), and Xdo(T ) is the magnetic susc tibility of d-electrons without exchange interactions. 

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