This review has a purpose to acquaint the experimental and theoretical research society with the recent theoretical achievements in the research field of the shear-horizontal surface acoustic wave (SH-SAW) propagation in the two-phase materials. It is well-known that to know the SH-SAW characteristics can be very important for the sensor applications. Since 2007, several contributors have achieved so me progress in the theory when it was theoretically demonstrated that several new SH-SAWs can propagate in novel two-phase materials called the piezoelectromagnetics (PEMs) or the magneto-electro-elastic materials. For the last half-decade, a lot of new SH-SAWs were discovered and it was also found that they can propagate in the cubic PEMs and the transversely isotropic piezoelectromagnetic materials of class 6 mm . For the same set of the boundary conditions, it is already known that only one SH-SAW can propagate in the cubic PEMs and at least two SH-SAWs can propagate in the hexagonal PEMs of class 6 mm. They can have potential applications in the SH-SAW sensors such as biosensors, physical and chemical sensors. It was also discussed that some theoretical results cannot be true.
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