The governing equations of two-temperature generalized magneto-thermoelasticity with hydrostatic initial stress are specialized in two dimensions and are solved for surface wave solutions. The appropriate solutions in a half-space are obtained which satisfy relevant radiation condition and boundary conditions at thermally insulated as well as isothermal surface. The frequency equation of Rayleigh wave is obtained. The frequency equation is also reduced for limiting cases of small thermal coupling and small reduced frequency. Velocity of propagation and amplitude-attenuation factor of Rayleigh wave are computed for a numerical example. To illustrate the dependence of velocity and amplitude-attenuation factor upon two-temperature parameter, initial stress parameter thermal relaxation time and magnetic field, the numerical results are shown graphically.

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