We study room temperature spin transport in graphene devices encapsulated between a layer-by-layer-stacked two-layer-thick chemical vapour deposition (CVD) grown hexagonal boron nitride (hBN) tunnel barrier, and a few-layer-thick exfoliated-hBN substrate. We find mobilities and spin-relaxation times comparable to that of SiO$_2$ substrate based graphene devices, and obtain a similar order of magnitude of spin relaxation rates for both the Elliott-Yafet and DYakonov-Perel mechanisms. The behaviour of ferromagnet/two-layer-CVD-hBN/graphene/hBN contacts ranges from transparent to tunneling due to inhomogeneities in the CVD-hBN barriers. Surprisingly, we find both positive and negative spin polarizations for high-resistance two-layer-CVD-hBN barrier contacts with respect to the low-resistance contacts. Furthermore, we find that the differential spin injection polarization of the high-resistance contacts can be modulated by DC bias from -0.3 V to +0.3 V with no change in its sign, while its magnitude increases at higher negative bias. These features mark a distinctive spin injection nature of the two-layer-CVD-hBN compared to the bilayer-exfoliated-hBN tunnel barriers.
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