Nuclear Magnetic Relaxation in Antiferromagnetics, II

Theory of nuclear magnetic relaxation in antiferromagnetics treated in the preceding paper for non-magnetic ·ions is extended to the case of magnetic ions. Strong hyperfine interactions and quadru pole interactions are the distinctive feature of the problem. The line width and the relaxation rate are calculated by using the spin wave approximation at low temperatures and the model of Gaussian random modulation at high temperatures. Order estimations of T 1 and T 2 are made for several substances, which predict that the nuclear resonance will be difficult to detect above the Curie point because of the broadening due to the hyper fine interaction, while the resonance will become detectable at sufficiently low temperatures where the low frequency components of the local field spectra decrease remarkably. The effects of the quadrupole interaction are also discussed. In the preceding paper>, referred to below as I, the writer has presented a theoretical treatment of the nuclear magnetic relaxation of non-magnetic atoms in antiferromagnetic substances. The predominant relaxation mechanism in that case is provided by magnetic dipolar field coming from electron spins modulated by exchange interaction. The relaxation time of protons in CuC12 • 2H20 calculated by using the spin wave approximation agreed well with the experiment both in the order of magnitude and in the nature of temperature dependence. On the other hand, for fluorine re&onance in MnF2, the same mechanism has proved to be insufficient for explaining the reported absence of the resonance, and this compelled the present author to expect a hyperfine interaction between F nuclei and the unbalanced valence electron spins on F ions. This anticipated unbalance of spins was considered to result from the existence of a partial covalency in the crystal and the asymmetric arrangement of Mn + + ions around each p- ion in MnF2• In the present article, we shall extend our consideration to the nuclei which belong to the magnetic ions. In this case a nucleus is subjected to a very strong magnetic field due to the hyperfine interaction which is 102-103 times as large as the dipolar field from different magnetic ions, and its order of magnitude is 105-106 gauss. We expect, therefore, high resonance frequencies, broad line widths, and short relaxation times, and in some cases even the impo~sibility of observing the resonance. However, there is an effect of exchange narrowing which favours the observation of the resonance. Though the fluctuating local magnetic field is very large, its effect on nuclei is much diminished by a very ra.pid modulation due to the exchange interaction. Among the frequency spectra