A-c exchange in the garnets

Abstract

In the ferrimagnetic garnets the a-d (octahedral-tetrahedral) exchange is the dominant one and reasonable values of the other exchange values are difficult to obtain. Thus, direct measurement of some of the smaller exchange constants is of interest because of the ambiguity of the values obtained by molecular field analysis. In this paper an optical technique is used to measure the a-c exchange of Cr3+-Gd3+ in the garnet Gd 3Ga2(GaO4)3. The 16a site is octahedrally coordinated and the rare earth is on the 24c site. The structure on sharp redline fluorescence from the Cr3+ ions is measured. The fluorescence transitions are from the excited 2E state to the ground 4A2 state; thus the exchange constant in both states can, in principle, be determined. The analysis of the a-c interaction was done by assuming a Heisenberg Hamiltonian H=i=16JSCr·SGdi, where the sum is over the six nearest-neighbor Gd3+ ions each with a span 72. The most probable value of i=16SGdi is 8. The Cr 3+-Gd3+ exchange splitting in the 2E state of Cr3+ is just resolvable. A detailed fitting of the lines gives J=0.32 cm-1 (0.46°K). The Cr3+-Cd3+ exchange splitting of the Cr3+ ground state is not resolvable. However, the low-temperature linewidth is much too wide to be due to anything except an exchange splitting. Fitting the line one obtains an exchange value in the ground state approximately half the excited state. © 1966 The American Institute of Physics.