Magnetostriction exchange

Magnetostrictive effects in Er are clearly visible in the temperature variation of the lattice parameters determined in the neutron diffraction study of Haben-schuss et al. (1974). The appearance of the c-axis modulated structure below Tv = 84.4 K has little effect on the lattice constants (fig. 6.35), but below the basal plane ordering temperature Ts 52.4 K, the c-axis expands in the manner of the exchange magnetostriction found in the spiral phases of Tb and Dy. Ferromagnetic alignment of the c-axis moment at Tc = 18 K is marked by a... 

It should be pointed out that also in compounds based on other rare earths it was necessary to consider not only the crystal held interactions, but also the contribution of the exchange interactions, in order to understand the observed magnetostrictive effects (e.g. in the case of NdCu2 — see Rotter et al. 2002). However, in Gd compounds this exchange contribution can be studied without any ambiguity arising from the crystal held interaction, because L = 0 for Gd3+. 

Fig. 11. Shear modulus of Invar (Fe-36Ni), comparing pulse-echo and resonance results. The anomalous (positive-slope) behavior of this alloy is related to its large, positive volume magnetostriction. It can be explained by invoking Heisenberg-exchange-energy terms.

The exchange interactions are isotropic to first order. They describe a coupling between the magnetic moments and dominate the magnetic ordering in the materials. The variation of these interactions with the interatomic distance is the reason for a spontaneous deformation (i.e., the volume magnetostriction). 

The pseudo-dipolar exchange interactions, which are anisotropic and vary rapidly with the increasing interatomic distance, are one of origins of the Joule magnetostriction. 

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