Magnetostriction

Remarks

Example: consider an isotropic polycrystal magnetized to saturation. If the magnetization makes the angle $\theta$ with the direction of measurement, the standard model gives $$\lambda(\theta) = \frac{3}{2} \lambda_s \left( \cos^2\theta - \frac13 \right),$$ which equals $\lambda_s$ for $\theta = 0$ and $-\lambda_s/2$ for $\theta = \pi/2$. The volume is unchanged to first order, since $\lambda(0) + 2\lambda(\pi/2) = 0$. Non-example: thermal expansion of a magnetic material in zero field is a strain caused by a change of temperature, not of magnetization, so it is not magnetostriction. The saturation magnetostriction can be positive (the material lengthens along the field) or negative, as for nickel. For small changes around a bias field, the effect is often written in a linear form like piezoelectricity, $S = s^H T + d^{t} H$ and $B = d T + \mu^T H$, with a piezomagnetic coefficient tensor $d$.