The magnetic structure and elastic constants of the close-packed phases of cobalt are computed as a function of compression using the linearized augmented plane-wave method with the generalized gradient approximation. The high-pressure phase transition from the hexagonal close-packed phase to the face centered cubic phase is correctly reproduced and is predicted to occur from a magnetic hcp to a nonmagnetic fcc phase, with a considerable change in aggregate elastic properties. At pressures well below the transition, an elastic anomaly is predicted in the hcp phase associated with the loss of magnetism under compression, which is most pronounced in the shear elastic constants. The magnetic nature of this anomaly provides an explanation for similar observations in experiments.
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