On the bulk modulus of the transition metals

2014 The effect of correlations and ferromagnetic order on the bulk modulus K of the 3d metals is discussed using a second order perturbation treatment of the correlation. For elements in the middle of the series with a low density of states n(EF) at the Fermi level, ferromagnetic order, if possible, acts together with correlation to reduce K. The ferromagnetic elements Fe, Co and Ni lie towards the end of the 3d series and have large values of n(EF) in the non-magnetic state. For these elements the effect of ferromagnetism on K is found to be small and may act to increase K. LE JOURNAL DE PHYSIQUE LETTRES TOME 39, 15 FEVRIER 1978, Classification Physics Abstracts 62.20 In a previous letter [1] we discussed the effect of d-electron correlation on the atomic volume and bulk modulus of the transition metals, and found that correlations give an increase in atomic volume and a decrease in bulk modulus, the effect being greatest in the middle of the 3d series. The bulk modulus was evaluated at the atomic volume of the uncorrelated system, and since dKldR is strongly negative in the transition metals, this underestimates the decrease in K due to correlations. At the atomic volume of the correlated system, the bulk modulus is given by the difference between this result and that of [ 1 ] having the following effect. (i) In terms of the bandwidth in the absence of correlations, W = Wo e-qRo, equation (1) may be written as where is the relative change in the Wigner-Seitz radius due to electron correlations. In contrast to the previous result, which gave a relative decrease in K of the same magnitude as the relative increase in the atomic volume, equation (2) predicts an anomaly in K about four times that in the atomic volume, in better agreement with the relative magnitudes deduced from a comparison of figures (1) and (2) of [1]. (ii) An expansion of equation (1) to first order in the change 6R in the Wigner-Seitz radius due to the onset of long range ferromagnetic order gives where, for the rectangular density of states, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0197800390405900 L-60 JOURNAL DE PHYSIQUE LETTRES and where R, V and W refer to the non-magnetic state of the correlated electron gas. The first term in (3) acts to decrease the bulk modulus as the moment in the ferromagnetic state increases, this decrease being greatest in the absence of correlations. The second term in (3) is positive for all z if p > 3 q, but is negative in the middle of the 3d series if p 3 q. When positive this term may significantly alter the value of 6K and to investigate this further it is necessary to use a more realistic density of states. Assuming that the cohesive and correlation energies do not depend strongly on the band structure, but that the density of states at the Fermi level is important in determining the kinetic energy increase associated with ferromagnetic order, we obtain (3) with