# Neutron Scattering Studies of Antiferromagnetic Correlations in Cuprates

AbstractNeutron scattering studies have provided important information about the momentum and energy dependence of magnetic excitations in cuprate superconductors. Of particular interest are the recent indications of a universal magnetic excitation spectrum in hole-doped cuprates. That starting point provides motivation for reviewing the antiferromagnetic state of the parent insulators, and the destruction of the ordered state by hole doping. The nature of spin correlations in stripe-ordered phases is discussed, followed by a description of the doping and temperature dependence of magnetic correlations in superconducting cuprates. After describing the impact on the magnetic correlations of perturbations such as an applied magnetic field or impurity substitution, a brief summary of work on electron-doped cuprates is given. The chapter concludes with a summary of experimental trends and a discussion of theoretical perspectives.
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# Introduction

\label{sc:intro}

Neutron scattering has played a major role in characterizing the nature and strength of antiferromagnetic interactions and correlations in the cuprates. Following Anderson’s observation (citation not found: ande87) that , the parent compound of the first high-temperature superconductor, should be a correlated insulator, with change21 moments of neighboring Cu$$^{2+}$$ ions anti-aligned due to the superexchange interaction, antiferromagnetic order was discovered in a neutron diffraction study of a polycrystalline sample (citation not found: vakn87). When single-crystal samples became available, inelastic studies of the spin waves determined the strength of the superexchange, $$J$$, as well as weaker interactions, such as the coupling between CuO$$_2$$ layers. The existence of change22 strong antiferromagnetic spin correlations above the Néel temperature, , has been demonstrated and explained. Over time, the quality of such characterizations has improved considerably with gradual evolution in the size and quality of samples and in experimental techniques.

Of course, what we are really interested in understanding are the optimally-doped cuprate superconductors. It took much longer to get a clear picture of the magnetic excitations in these compounds, which should not be surprising given that there is no static magnetic order, the magnetic moments are small, and the bandwidth characterizing the magnetic excitations is quite large. Nevertheless, we are finally at a point where a picture of universal behavior, for at least two families of cuprates, is beginning to emerge. Thus, it seems reasonable to start our story with recent results on the excitation spectrum in superconducting superconducting transition temperature, . (Note that these are hole-doped superconductors, which is where most of the emphasis will be placed in this chapter.) An important result is that this spectrum looks quite similar to that measured for , a compound in which  is depressed towards zero and ordered charge and spin stripes are observed. The nature of stripe order and its relevance will be discussed later.