Isotropic magnets

Fig. 2. The two principle modes of observable magnetostriction for an isotropic magnetic substance.

The isotropic magnetic properties computed for TEMPO (4 in Figure 2.1) by different methods and basis sets are compared in Table 2.1 with the corresponding experimental values. 

In the case of isotropic magnetic particles, that is, TJ = -p(e H), both linear and cubic dynamic susceptibilities may be obtained analytically. To show this, we first transform Eq. (4.90) into an infinite set of differential recurrence relations ... 

The case of finite magnetic rigidity of the particles is addressed in Section V the theory becomes much more complicated and, hence, cumbersome in form. Meanwhile, the case of magnetically hard particles suspended in a fluid is formally very close to the case of isotropic magnetic particles in a solid matrix. That is why we present it here. 

In general a ferromagnetic material does not show isotropic magnetization behavior (Ch. 3). Experimentally certain directions can be found, which favor magnetization (easy axes) and others which do not (hard axes). This leads to a new energy term. 

This form of Vn(R) has the advantage of generality and converges well for the lower part of the potential function. It is clear from the form of equation (7.171) that if Xn(R) has only a weak dependence on R, the corresponding parameter in the effective Hamiltonian will not depend strongly on the vibrational quantum number either. For example, the isotropic magnetic hyperftne interaction samples the electronic wave... 

Both Eqs. (1) and (2) are valid for isotropic magnetic moments, which is not always valid for the electron magnetic moment. 

Figure 8. Absorption profiles for a copper complex dissolved in a disordered liquid. Molecular reorientation in this intermediate region of motion is isotropic. Magnetic parameters are the same as in Fig. 7.

Second-order phase transitions also show up via the critical slowing down of the critical fluctuations (Hohenberg and Halperin, 1977). In structural phase transitions, one speaks about soft phonon modes (Blinc and Zeks, 1974 Bruce and Cowley, 1981) in isotropic magnets, magnon modes soften as T approaches Tc from below near the critical point of mixtures the interdiffusion is slowed down etc. This critical behavior of the dynamics of fluctuations is characterized by a dynamic critical exponent z one expects that some characteristic time r exists which diverges as T - TCl... 

The dipolar magnetic interaction may roughly be estimated from the metal-metal distance assuming isotropic magnetic moments, we obtain Dd= — g2ujj/r3 = — 0.04 K. 

A further fabrication method, known as mechanical alloying leads to an amorphous material by ballmilling of the elements in a closed container, followed by heat treatment to homogenise and crystallise the compound (Cahn, 1990). Usually, this method results in isotropic magnets. 

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