Van Vleck temperature-independent

Many of the Th nitrides are more or less stable at elevated temperatures, electrically and thermally insulating, and have an extremely weak (Van Vleck) temperature-independent paramagnetism. The face-centered cubic (fee) mononitride, ThN, is an important exception. It is metallic. It has a weak temperature-independent (Pauli) paramagnetism. Subsequent comparison of the electronic properties will show many simularities between ThN and metallic Th. An appreciable metallic bonding is also indicated by anomalously large interatomic distances in ThN. 

Another additive term in the magnetic susceptibility arises from the temperature-independent core diamagnetism of all the ions in a solid. For YBa2Cu307 the core diamagnetism is approximately -2 x 10 7 based on a calculation using Pascal s constants (9). This small negative contribution serves to reduce the total susceptibility. A third possible contribution arises from Van Vleck paramagnetism (10) caused by excited states in the atoms of the... 

While the singlet ground state will be unaffected by an external magnetic field, the S 1 state will become Zeeman split into the Ms =—1,0, 1 sublevels. Thus, the energies of the four possible 15, Ms) states are known (10, 0)) = Jex (ll, + 1)) = —g/rB77 (ll, 0)) = 0 (ll, —1))= I /ab//. When these four expressions are introduced into the Van Vleck equation, the Bleaney-Bowers equation7 is obtained. This equation describes the temperature dependence of the susceptibility (for the zero-field limit), independent of the sign of Jcx ... 

The diamagnetic term for molecules is given by equation 12, just as in the case of atoms, except that the r for the electrons may be considerably greater in molecules than in atoms. Van Vleck (628) has emphasized that temperature-independent susceptibilities cannot be accounted for by equation 12 alone since contributions of the type expressed by equation 55 are always present and may even be of sufficient magnitude to give a net positive, temperature-independent susceptibility from field-induced atomic moments. 

Here A% and Aorb are the hyperfme field due to spin and orbital angular momentum, Xs and Xvv are the spin and Van Vleck susceptibility, respectively, and pe is the Bohr magneton. In a heavy fermion system, where 4/ or 5/ electrons play principal roles, the state is specified by j = l +. 7, so that Ks is associated with the ground state (not purely due to spin and temperature dependent in general). AVv is induced from the transition between the ground state and the excited state, and is temperature independent. Each of As and Aorb includes the spin and orbital hyperfme fields. 

It is assumed that the measured magnetic susceptibility has already been corrected for the underlying diamagnetism (usually using the set of Pascal constants) and also for the temperature-independent paramagnetic (van Vleck) term (its mononuclear estimate being multiplied by the number of magnetic centres). 

Here ps is the Bohr magneton, p is the effective number of Bohr magnetons, and ks is Boltzman s constant. Thus a plot of 1 // versus temperature is a straight line with an intercept at zero. Other contributions to the susceptibility of an isolated molecule include core diamagnetism and Van Vleck paramagnetism, both of which are small and temperature independent (231). 

At low temperatures, when only the ground state of the lanthanide ion in the crystal field is populated, the total magnetic moment of the ion is the sum of the induced (Van Vleck) moment and the intrinsic moment (the latter differs from zero only in the degenerate state). The contributions to the magnetostriction and the elastic constants due to changes in the intrinsic magnetic moment of the lanthanide ion with lattice strain can be written explicitly when considering the effective spin Hamiltonian. The latter contains a smaller number of independent parameters (constants of spin-phonon interaction) than the Hamiltonian of the electron-deformation interaction (18) and is more suitable in the description of experimental data. 

Shaltiel et al. (1964a) noticed that Sm produces a positive g-shift for the Gd resonance in Pdo.96Gdo.02Smo.02> opposite to what is expected from a simple model. They pointed to the fact that the temperature-independent van-Vleck part of the susceptibility should produce an additional positive shift. Malik and Vijayaraghavan (1975) confirmed these results and provided more detailed information. They found that the distance between the H5/2 ground state and the H7/2 first excited state of Sm " " is so small that the van-Vleck terms contribute appreciably and as a consequence the z-component of the lanthanide spin changes sign. 

Our search of all the magnetization measurements which are presently available, leads us to regret that they are often incomplete. Susceptibility measurements at elevated temperature are rare, yet they would reveal readily whether Jq-J mixing occurs, i.e. whether at high temperature the Van Vleck theory has to be applied. Very often susceptibility values below the Neel temperature are not given or plotted. Yet, they would allow us to draw important conclusions. For isotropic exchange in cubic samples the susceptibility must become temperature independent below TJm. Any upturn of the inverse susceptibility below in cubic samples means necessarily that... 

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