Nonlinear response of permanent dipoles in a uniaxial potential to alternating fields

It is shown how the existing theory of the dynamic Kerr effect and nonlinear dielectric relaxation based on the noninertial Brownian rotation of noninteracting rigid dipolar particles may be generalized to take into account interparticle interactions using the Maier-Saupe mean field potential. The results (available in simple closed form) suggest that the frequency dependent nonlinear response provides a method of measuring the Kramers escape rate (or in the analogous problem of magnetic relaxation of fine single domain ferromagnetic particles, the superparamagnetic relaxation time).

Figure 1

$-\mathrm{Im}\left[{\chi }_{2n-1}\left(\omega \right)\right]$ vs $\omega {\tau }_D$ [solid lines, Eqs. (3, 7) for $n=1$,3,5]; ${\chi }_{2n-1}\omega {\tau }_{2n-1}$ (dotted lines); and ${\chi }_{2n-1}{\left(\omega {\tau }_{2n-1}^{eff}\right)}^{-1}$ (dashed lines). Symbols, Eq. (9)

Figure 2

Exact $\mathrm{Re}\left[F_0^{\left(2\right)}\left(\omega \right)\right]∕{\xi }^2$ [Eq. (12), solid lines] and approximate [Eq. (16), symbols] solutions.

Figure 3

Exact $\mathrm{Re}\left[F_2^{\left(2\right)}\left(\omega \right)\right]∕{\xi }^2$ [Eq. (12), solid lines] and approximate [Eq. (16), symbols] solutions.