| Abstract | The theory of spin-spin relaxation in a solid lattice containing two groups of spin has been developed for a large assembly of spins. The situation treated is that of a strong steady magnetic field much larger than the total internal interaction field. On the large field is superposed for a limited length of time a small step field or an oscillatory field under conditions of relaxation absorption or emission. The Hamiltonian of the isolated spin system contains the dipolar, exchange, and Stark or quadrupolar types of interaction for each of the spin groups, in addition to the intergroup dipolar, or hyperfine for the electronic-nuclear spin system. The Hamiltonian is divided into secular and nonsecular parts. The relaxation functions of the system are expressed in the form of infinite integral aeries in the nonsecular Hamiltonian. The principal diagonal parts of the commutators are retained and the integral series is changed into two integrodifferential equations similar to the one obtained by Caspers for the one spin group system. These integro-differential equations are of a coupled first order type involving a 2 x 2 relaxation time matrix. A substitution increasing the order of the differential equation by one, diagonalizes the relaxation time matrix and the two principal relaxation times characteristic of the two-group system are obtained. The method is independent of representation. In order to make a specific application of the theory, a Gaussian shape was chosen for the frequency distribution function. The calculations for the ammonium cupric tutton salt check with those of Caspers if his values of the internal fields are used in the special case of one spin group in the lattice. When the two-group theory is used to take account of the strong hyperfine internal field, a negligible effect is obtained. In either case a discrepancy is observed. When this special one-group theory is applied to the ammonium manganic tutton salt with the additional Stark internal field a discrepancy is obtained. The causes believed to be responsible for the discrepancy are discussed. Due to the lack of paramagnetic measurements on a two-group system. a hypothetical example is worked out assuming that some of the magnetic momenta are due to the presence of a dopant in the sample. The result is that a doping of 1% or less with the four-valent manganese ions suffices to lower the calculated relaxation time to a value much closer to the one extrapolated from measurement. A functional dependence on the concentration of the doping ions is also obtained. The example of nuclear spin-spin relaxation in the lithium fluoride system gives a discrepancy similar to that of the paramagnetic systems. This has to do with the relative roughness of the approximation. In all the examples an NaCl face-centered cubic structure is used and the [100] crystal orientation employed. Since LiF has this simple structure while the tutton salts do not, an improvement was expected. The relaxation time is found to be anisotropic, that is, a function of the crystal orientation with respect to the external fields. Its dependence on the external field is that of a positive exponential in the square of the field. The different coupled spin systems to which the formalism on two spin groups in a solid lattice applies are discussed. |
