Performing tayammum with soil, pebbles, a clod of earth, and stone is valid. However, the recommended precaution is that if it is possible to perform tayammum with soil, one should not perform it with any other thing; and if soil is not available, [the recommended precaution is to perform tayammum with fine sand that is very soft, such that it can be called ‘soil’; and if that is not possible, with a clod of earth; and if that is not possible, with pebbles; and in the event that pebbles and a clod of earth are not available, one must perform tayammum with a stone.

Tayammum performed with gypsum or limestone is valid. Similarly, tayammum performed with dust that gathers on carpets, clothing, and similar things is also valid provided that its quantity is such that it can commonly be considered to be very fine soil, although the recommended precaution is that if alternatives are available, one should not perform tayammum with dust. Similarly, based on recommended precaution, if alternatives are available, one should not perform tayammum with gypsum and limestone that have been baked, nor with brick that has been baked, nor with mineral stones such as agate (ʿaqīq).

If a person cannot find soil, pebbles, a clod of earth, or stone, he must perform tayammum with mud; and if one cannot find any mud, he must perform tayammum on top of a carpet, clothing, or similar thing that has gathered dust or on which dust has settled but not to the extent that it can commonly be considered to be soil.
You can’t perform tayammum of tiles but yes you can perform on nature stone.