Magnetic field dependence of spin-lattice relaxation in three iron group salts

An extension is proposed to the iron group of the Orbach-Huang theory outlined for the relaxation field dependence in rare-earth salts. The general equation $T_1^{-1\mathrm{}}=T_{10}^{-1\mathrm{}}\frac{(H^2+\frac{1}{2}{\mu }^{\prime }{H}_{\mathrm{dip}}^2+\mu H_n^2)}{(H^2+\frac{1}{2}{H}_{\mathrm{dip}}^2+H_n^2)}$ remains valid, but new expressions are given for ${\mu }^{\prime }$ and $T_{10}^{-1\mathrm{}}$ (if exchange predominates ${\mu }_1^{\prime }$ and $H_{\mathrm{exch}}$ replace ${\mu }^{\prime }$ and $H_{\mathrm{dip}}$). They are used to compute the coefficients in three salts selected as permitting calculation in CrK alum, CuK double sulfate, and FeK alum. The internal field is typically dipolar in the first and the third while it is due to exchange in the second; furthermore, the third ion is in a $S$ state. The parameters at 77 K have also been measured at frequencies of 0.2, 0.7, 4 and from 8.2 to 12.4 GHz by the resonant modulation method, investigating the field dependence of $T_1$. The agreement between theory and experiment is good in iron alum, in spite of complex calculations in this salt. It is excellent in copper double sulfate and rather moderate in chromium alum. There is a careful discussion of all the assumptions used in computation. To determine $T_{10}$, the temperature dependence of $T_1$ has also been measured, $T$ ranging from 50 to 150 K. Calculation and experiment are in good agreement, adopting for the upper limit of the $I_8$ Van Vleck integral a value close to the Debye temperature in chromium alum, but higher by a factor 1.6 in copper double sulfate and 2 in iron alum.