Magnetostriction of Paramagnetic Transition Metals. I. Group 4 - Ti and Zr; Group 5 - V, Nb, and Ta; Group 6 - Mo and W

The longitudinal magnetostriction of transition metals of groups 4, 5, and 6 was measured with a capacitance dilatometer at low temperature in fields up to 100 kOe. The resultant values of the logarithmic volume dependence of the magnetic susceptibility $\frac{\ensuremath{\partial}\mathrm{ln}\ensuremath{\chi}}{\ensuremath{\partial}\mathrm{ln}V}$ are Ti, -0.34; Zr, -1.6; V, 1.2; Nb, 1.7; Ta, 1.1; Mo, 14; W, 6.5. The contribution from the spin paramagnetism is obtained from the volume dependence of the density of states, which is estimated from the electronic Gr\"uneisen coefficient with a correction for the electron-phonon coupling. The resultant values of the volume dependence of the orbital susceptibility for V, Nb, and Ta are physically reasonable. The negative magnetostriction of Ti and Zr is not inconsistent with their thermal expansion, but the large positive magnetostriction of Mo and W is difficult to understand. The samples of Mo and W exhibit oscillatory de Haas-van Alphen magnetostriction at 4.2 \ifmmode^\circ\else\textdegree\fi{}K.