Antiferromagnetically Coupled Impurities in a Heisenberg Ferromagnet

The ground state of a ferromagnetic system with an antiferromagnetically coupled impurity is calculated exactly. The spin of the host is arbitrary, as is the ratio of impurity-host exchange to host-host exchange, but the impurity spin is taken to have ${S}_{0}=\frac{1}{2}$. The ground-state energy, wave function, spin defect, and critical field for a metamagnetic transition are computed. Results are compared with the approximate spin-wave method as employed by Ishii, Kanamori, and Nakamura. It is shown that the spin-wave method is ambiguous and can lead to grossly incorrect results if applied in particular ways.

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