Longitudinal Nuclear Magnetic Relaxation in Ferromagnetic Iron, Cobalt, and Nickel

The longitudinal nuclear relaxation time $T_1$ has been measured in ferromagnetic iron, cobalt, and nickel. A model is presented to account for the measured values. In the Bloch walls, the relaxation is due mainly to domain wall fluctuations. In the domains, the relaxation is due to interaction of the conduction electrons with nuclei via spin waves. The expression for $T_1$ due to this process is $\frac{1}{T_1}=\frac{\left(\frac{\mathrm{kT}}{h}\right){\left(\frac{\omega }{{\omega }_d}\right)}^2{a}^2\Sigma }{\left(32\mathrm{}{\pi }^3{S}^2\right)}$, where $\omega$ is the nuclear resonant frequency, $a$ is the lattice constant, ${\omega }_d$ is the parameter describing the spin wave spectrum $E\left(k\right)=\hslash {\omega }_d{a}^2{k}^2$, $S$ is the average spin per atom, and $\Sigma$ is the area of the Fermi surface per cubic unit cell. If the experimental value of $T_1$ is used in this formula to determine $\Sigma$, then in cobalt, $\Sigma$ will agree closely with the area of a spherical surface containing about one electron per atom. In iron and nickel, $\Sigma$ will be about three times larger.