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Quasielastic neutron scattering from two dimensional antiferromagnets at a finite temperature

We consider frequency dependence of the neutron scattering amplitude from a two-dimensional quantum antiferromagnet. It is well known that the long range order disappears at any finite temperature and hence the elastic neutron scattering Bragg peak is transformed to the quasielastic neutron scattering spectrum ~dw/w. We show that the widely known formula for the spectrum of an isotropic antiferromagnet derived by Auerbach and Arovas should be supplemented by a logarithmic term that changes the integrated intensity by two times. A similar formula for an easy-plane magnet is very much different because of the Berezinsky-Kosterlitz-Thouless physics. An external uniform magnetic field switches smoothly the isotropic magnet to the easy-plane magnet. We demonstrate that the quasielastic neutron scattering spectrum in the crossover regime combines properties of both limiting cases. We also consider a quantum antiferromagnet close to the O(3) quantum critical point and show that in an external uniform magnetic field the intensity of elastic (quasielastic) neutron scattering peak depends linearly and significantly on the applied field.