Temperature Dependence of Paramagnetic Resonance Lines

Changes in the position and shape of paramagnetic absorption lines of ${\mathrm{Nd}}^{3+}$ in neodymium ethyl sulfate, ${\mathrm{Ni}}^{2+}$ in nickel fluosilicate, and ${\mathrm{Cu}}^{2+}$ in copper potassium sulfate have been observed at 30 kMc/sec in the temperature range from 0.4 to 4.2°K. The observed shifts are compared to first and second line moments calculated from spin-spin interactions when the average populations of the spin levels are weighted by the proper Boltzmann factors. In this manner it is possible to determine the magnitude and sign of the exchange interaction ${\mathcal{H}}_{\mathrm{ij}}=A{\mathrm{S}}_i·{\mathrm{S}}_j$ between spins. We find a ferromagnetic interaction $A=-(3.9\mathrm{}\pm 0.4)\times {10}^{-18\mathrm{}}$ erg between nearest-neighbor ${\mathrm{Ni}}^{2+}$ ions in NiSi${\mathrm{F}}_6$·6${\mathrm{H}}_2$O with no evidence of anisotropic exchange. Nearest-neighbor spins at similar lattice positions in ${\mathrm{K}}_2$Cu${\left(\mathrm{S}{\mathrm{O}}_4\right)}_2$·6${\mathrm{H}}_2$O appear to be coupled by an exchange interaction of approximately $A=-9\mathrm{}\times {10}^{-18\mathrm{}}$ erg, while the exchange between the two neighboring dissimilar ${\mathrm{Cu}}^{2+}$ ions in the unit cell is $A=-1.4\mathrm{}\times {10}^{-18\mathrm{}}$ erg. Evidence for a weak anisotropic and antiferromagnetic coupling in Nd${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$·9${\mathrm{H}}_2$O is presented. We have observed magnetostatic modes in copper salts at low temperature, and this effect is briefly discussed in relation to the present type of experiment.