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

We consider the coupling of the magnons in both quantum ferromagnets and antiferromagnets to the longitudinal order-parameter fluctuations, and the resulting nonanalytic behavior of the longitudinal susceptibility. In classical magnets it is well known that long-range correlations induced by the magnons lead to a singular wave-number dependence of the form $1/k^{4-d}$ in all dimensions 2<d<4, for both ferromagnets and antiferromagnets. At zero temperature we find a profound difference between the two cases. Consistent with naive power counting, the longitudinal susceptibility in a quantum antiferromagnet scales as $k^{d-3}$ for 1<d<3, whereas in a quantum ferromagnet the analogous result, $k^{d-2}$, is absent due to a zero scaling function. This absence of a nonanalyticity in the longitudinal susceptibility is due to the lack of magnon number fluctuations in the ground state of a quantum ferromagnet; correlation functions that are sensitive to other fluctuations do exhibit the behavior predicted by simple power counting. Also of interest is the dynamical behavior as expressed in the longitudinal part of the dynamical structure factor, which is directly measurable via neutron scattering. For both ferromagnets and antiferromagnets there is a logarithmic singularity at the magnon frequency with a prefactor that vanishes as $T\to 0$. In the antiferromagnetic case there also is a nonzero contribution at T=0 that is missing for ferromagnets. Magnon damping due to quenched disorder restores the expected scaling behavior of the longitudinal susceptibility in the ferromagnetic case; it scales as $k^{d-2}$ if the order parameter is not conserved, 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.