This paper explores the design of efficient capacity achieving polar codes for multiple input multiple output (MIMO) channels and schemes for polar coded spatial multiplexing (PCSM). For polar code construction, the singular value decomposition (SVD) of a given MIMO channel into multiple independent single input single output (SISO) channels is considered as the first step of natural polarization. Firstly, we propose a basic PCSM scheme by constructing a polar code for each independent SISO channel. Then, we extend the scheme by using compound polar codes to construct a unified PCSM scheme for MIMO channels. Further, we present a novel approach for constructing an optimal compound polar codes which minimize block error rate (BLER) for a given N ^R × N ^T MIMO channel. Simulation results reveal that the extended schemes achieve at least 1.5 dB gain in terms of BLER with lesser computational complexity as compared to the basic scheme.