Magnetic Susceptibility of Diluted Pyrochlore and ${\mathrm{SrCr}}_{9-9\mathit{x}}{\mathrm{Ga}}_{3+9\mathit{x}}{O}_{19}$ Antiferromagnets

We investigate the magnetic susceptibility of the classical Heisenberg antiferromagnet with nearest-neighbor interactions on the geometrically frustrated pyrochlore lattice, for a pure system and in the presence of dilution with nonmagnetic ions. Using the fact that the correlation length in this system for small dilution is always short, we obtain an approximate but accurate expression for the magnetic susceptibility at all temperatures. We extend this theory to the compound ${\mathrm{SrCr}}_{9-9x}{\mathrm{Ga}}_{3+9x}{\mathrm{O}}_{19}$ and provide an explanation of the phenomenological model recently proposed by Schiffer and Daruka [Phys. Rev. B 56, 13 712 (1997)].