Deepthi Goguri explains what sorts of fragmentation can occur on an index in SQL Server:
Logical Fragmentation occurs when the logical order of the leaf level pages (logical order meaning the next key values in order) no longer the continuous page to the next physical data file page. Because of these pages which are out of order will affect the read ahead mechanism and the scan performance. Because of this logical fragmentation, read ahead have to do smaller read ahead reads.
If the logical fragmentation pages are already in the memory than the read ahead mechanism will not be affected in that case. Logical fragmentation will cause the problem for bigger indexes and not for the smaller ones usually (smaller indexes having pages 1000-5000 pages). You can monitor the amount of the index logical fragmentation by using the DMV sys.dm_db_index_physical_stats.
Read on to learn more about logical fragmentation, as well peers extent fragmentation and low page density.