  The field-dependence elastic modulus of magnetostrictive films, also called
{\Delta}E or {\Delta}G effect, is crucial for ultrasensitive magnetic field
sensors based on surface acoustic waves (SAWs). In spite of a lot of successful
demonstrations, rare attention was paid to the frequency-dependence of
{\Delta}E or {\Delta}G effect. In current work, shear horizontal-type SAW delay
lines coated with a thin FeCoSiB layer have been studied at various frequencies
upon applying magnetic fields. The change of shear modulus of FeCoSiB has been
extracted by measuring the field-dependent phase shift of SAWs. It is found
that the {\Delta}G effect is significantly enhanced at high-order harmonic
frequencies close to the ferromagnetic resonance frequency, increasing by ~82%
compared to that at the first SAW mode (128 MHz). In addition, the smaller the
effective damping factor of magnetostrictive layer, the more pronounced
{\Delta}G effect can be obtained, which is explained by our proposed dynamic
magnetoelastic coupling model.
