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The existence of $\gtrsim10^9M_\odot$ supermassive black holes (SMBHs) atredshift $z>6$ raises the problem of how such SMBHs can grow up within thecosmic time ($<1$\,Gyr) from small seed BHs. In this letter, we use theobservations of $14$ Quasars at $z>6.5$ with mass estimates to constrain theirseeds and early growth, by self-consistently considering the spin evolution andthe possibility of super-Eddington accretion. We find that spin plays animportant role in the growth of early SMBHs, and the constraints on seed massand super-Eddington accretion fraction strongly depend on the assumed accretionhistory. If the accretion is coherent with single (or a small number of)episode(s), leading to high spins for the majority of accretion time, then theSMBH growth is relatively slow; and if the accretion is chaotic with manyepisodes and in each episode the total accreted mass is much less than the SMBHmass, leading to moderate/low spins, then the growth is relatively fast. Theconstraints on the seed mass and super-Eddington accretion fraction aredegenerate. A significant fraction ($\gtrsim0.1\%-1\%$ in linear scale but$\sim 3-4$ dex in logarithmic scale for $10^3-10^4 M_\odot$ seeds) ofsuper-Eddington accretion is required if the seed mass is not$\gg10^{5}M_\odot$, and the requirements of high seed-mass and/orsuper-Eddington accretion fraction are moderately relaxed if the accretion ischaotic.

Effects of spin on constraining the seeds and growth of $\gtrsim 10^9M_\odot$ supermassive black holes in $z>6.5$ Quasars