  Spin current experiences minimal dephasing and scattering in Si due to small
spin-orbit coupling and spin-lattice interactions is the primary source of spin
relaxation. We hypothesize that if the specimen dimension is of the same order
as the spin diffusion length then spin polarization will lead to
non-equilibrium spin accumulation and emergent phase transition. In n-Si, spin
diffusion length has been reported up to 6 {\mu}m. The spin accumulation in Si
will modify the thermal transport behavior of Si, which can be detected with
thermal characterization. In this study, we report observation of spin-Hall
effect and emergent antiferromagnetic phase transition behavior using
magneto-electro-thermal transport characterization. The freestanding Pd (1 nm)/
Ni80Fe20 (75 nm)/ MgO (1 nm)/ n-Si (2 micron) thin film specimen exhibits a
magnetic field dependent thermal transport and spin-Hall magnetoresistance
behavior attributed to Rashba effect. An emergent phase transition is
discovered using self-heating 3omega method, which shows a diverging behavior
at 270 K as a function of temperature similar to a second order phase
transition. We propose that spin-Hall effect leads to the spin accumulation and
resulting emergent antiferromagnetic phase transition. We propose that the
length scale for Rashba effect can be equal to the spin diffusion length and
two-dimensional electron gas is not essential for it. The emergent
antiferromagnetic phase transition is attributed to the site inversion
asymmetry in diamond cubic Si lattice.
