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We consider the coupling of the magnons in both quantum ferromagnets andantiferromagnets to the longitudinal order-parameter fluctuations, and theresulting nonanalytic behavior of the longitudinal susceptibility. In classicalmagnets it is well known that long-range correlations induced by the magnonslead to a singular wave-number dependence of the form $1/k^{4-d}$ in alldimensions 2<d<4, for both ferromagnets and antiferromagnets. At zerotemperature we find a profound difference between the two cases. Consistentwith naive power counting, the longitudinal susceptibility in a quantumantiferromagnet scales as $k^{d-3}$ for 1<d<3, whereas in a quantum ferromagnetthe analogous result, $k^{d-2}$, is absent due to a zero scaling function. Thisabsence of a nonanalyticity in the longitudinal susceptibility is due to thelack of magnon number fluctuations in the ground state of a quantumferromagnet; correlation functions that are sensitive to other fluctuations doexhibit the behavior predicted by simple power counting. Also of interest isthe dynamical behavior as expressed in the longitudinal part of the dynamicalstructure factor, which is directly measurable via neutron scattering. For bothferromagnets and antiferromagnets there is a logarithmic singularity at themagnon frequency with a prefactor that vanishes as $T\to 0$. In theantiferromagnetic case there also is a nonzero contribution at T=0 that ismissing for ferromagnets. Magnon damping due to quenched disorder restores theexpected scaling behavior of the longitudinal susceptibility in theferromagnetic case; it scales as $k^{d-2}$ if the order parameter is notconserved, or as $k^d$ if it is. Detailed predictions are made for both two-and three-dimensional systems at both T=0 and in the limit of low temperatures,and the physics behind the various nonanalytic behaviors is discussed.

Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets