Ask tile shops for any broken boxes going cheap, builders merchants, garden centres, roofing companies and patio slab companies. just make sure get rid of the sharp edges.
The slate will only need a clean in hot water to get all dirt and fine dust before you can put it in to your tank.
If your looking for a material a bit thicker, look for black indian sandstone.
This is the grey version in one of my tanks from last year.
Hope you find what your looking for?