Spin fluctuations in paramagnetic chromium determined from entropy considerations

We have analyzed the entropy of paramagnetic bcc Cr from the N\'eel temperature TN=311 K to the melting temperature Tf=2136 K. It is shown that the total experimental entropy cannot be accounted for solely by a sum of a vibrational part and a Sommerfeld-type electronic term from a nonmagnetic electronic structure. The total entropy is obtained through an elaborate assessment of available experimental data on various thermodynamic properties. The vibrational part is based on phonon data obtained in neutron scattering experiments by Trampenau et al., and accounts also for anharmonic effects. The Sommerfeld-type electronic part is obtained from electron band-structure calculations. Our analysis suggests a magnetic contribution that is related to spin fluctuations and that increases with temperature. We compare Cr with the other group-VI transition metals, Mo and W, using results from our previous works. Cr, Mo, and W show striking similarities, e.g., in their anharmonic phonon softening, when considered as a function of the reduced temperature T/Tf, where Tf is the melting temperature. Since phonons dominate the heat capacity, their Cₚ vs T/Tf plots are very similar.