1. The magnetic field on the surface of the magnet largely depends on its shape. In the case of a cylindrical magnet, the field at the surface of the magnet will increase with decreasing ratio of the diameter(d) of the magnet to its length(l). It is possible to select such a ratio (d/l) that the field was 0.6 Tesla.

2. The material for the cone must have a high magnetic permeability. It can be steel, pure iron or permaloy.

reducing core cross section area can be useful but this will be field uniformity besides the sample should be appropriate for the new area.

You have to bear in mind some aspects:

1 - Magnetic Flux Density, measured in T, is related to the relationship between flux and area. The greater the area, the lower the Density.

2 - When you say " 0.6 T cylindrical axial -permanent magnet ", you probably making reference to the residual flux density. The operational flux density depends on the magnetic circuit you inserting the magnet.

3 - Flux is like current, it flows through a closed path. So, if you want to keep a high value of flux, and flux density as well, you should fulfill the flux path with a iron core, letting smallest space possible for the air gap. Iron core have smaller reluctance than airy one, so it is easier to produce magnetic flux.

It is not possible to give more clues without knowing your system or what you want to do. For more details, search trough for the firs chapter of the following reference:

https://www.amazon.com/Electric-Machinery-Fitzgerald/dp/0073660094/ref=sr_1_2?s=books&ie=UTF8&qid=1527264825&sr=1-2&keywords=electric+machinery