Magnetostriction modes

For an isotropic material, the space spanned by the five remaining strain components cannot be reduced further. Consequently, there are only two magnetostriction modes. The energy density can be written down directly, in principle for either irreducible representation separately ... 

Fig. 3. The normal modes of deformation and the corresponding magnetostriction modes for cubic and uniaxial...

For uniaxial crystals, also included in fig. 2, the magnetostriction modes are given as ... 

Fig. 2. The two principle modes of observable magnetostriction for an isotropic magnetic substance.

The two principle modes of the magnetostriction (A -° and As or Xy-2) introduced above are illustrated in fig. 2. With respect to the non-magnetic fictitious state, a spherical, isotropic sample exhibits a relative volume change AV/V = A" 0, when it becomes magnetic. In addition, when one forces the moments to be directed along an applied magnetic field B, an anisotropic deformation is induced, which transfers the sphere into an ellipsoid with the same volume. 

For uniaxial (hexagonal) symmetry the 6 strain components are subdivided in two (invariant) one-dimensional subsets (indicated by the superscript a, and subscripts 1 and 2 for the volume dilatation and the axial deformation, respectively), and two different two-dimensional subsets, indicated by y for deformations in the (hexagonal) plane, and by e for skew deformations. These modes are also depicted in fig. 3. In this case, the magnetostriction can be expressed as... 

Jensen (1971) and Vigren and Liu (1972). The theory is an extension of the static magnetostriction to the dynamic situation, and this kind of interaction failed to explain the splitting A between the MA mode and the transverse optic phonon (TO). A similar situation exists in Dy where the mixing of the optic magnon (MO) and TA mode was seen (Nicklow et al., 1972). 

In contrast to the magnetostriction mechanism the spin-orbit coupling is insensitive to the temperature. Experimentally Ai was observed to disappear very rapidly with raised temperature. At the same time the magnon energy diminished so that the A2 gap appeared at the crossing point of MO and TA modes, but with no appreciable reduction in size. Thus, the mixing of MO-TA and MA-TO modes confirms the importance of spin-orbit coupling in the conduction band states of heavy lanthanides. 

Following a principle used in piezoelectric ultrasonic motors [60], T. Aku-ta [61] has built the first magnetostrictive friction motor. This stator is made of pairs of orthogonal actuators excited with sinusoidal 90° phase-shift currents, which produce an elliptical vibration. The modeling of such magnetostrictive stators [42] has shown that in quasi-static operation a good elliptical motion is produced. It has also been shown that there are many coupled modes, but none of them provides a satisfactory elliptical motion. Therefore, unlike piezoelectric motors, this motor cannot operate at resonance. As a consequence and in relation to the previous analysis of power (Fig. 6.34), the efficiency is comparatively weak. Its other characteristics are a speed of 40°/s and a torque of 1.8 Nm [62]. 

T. Fukuda [65] has opened the field of miniature magnetostrictive actuators and motors taking advantage of wireless magnetic excitation. He has experimented with two small self-moving hnear motors (some of cubic centimeter dimensions) based on a conversion-mode principle. 

The first linear micromotor, based on magnetostrictive thin films deposited on a 7 pm polyamide film, was built in Japan in 1994 [66]. The 13 mm long protot3rpe used a 200 Hz vibration induced by magnetostriction to obtain one-way motion at 5 imn/s. This is a mode conversion ultrasonic motor (MCUM) according to the Japanese classification of piezoelectric motors. 

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