Most ferrites have very high electrical resistivity and that means that the eddy losses are very low.
What you are seeing is called hysteresis loss; it is dependent on the area of the hysteresis loop. Most of the ferrites have very low hysteresis loss.
If you want a low loss ferrite for 1200 kHz, you have to search because at high frequency the µ drops off; this has to do with the domain rotations and µ becomes complex with real and imaginary parts.
If you want to use high frequency (>1MHz) you need to reduce the level of magnetization and live with greater dissipation.
I randomly looked up the TDK site
https://product.tdk.com/info/en/catalog/datasheets/ferrite_mn-zn_material_characteristics_en.pdf and it does specify all the important parameters quite explicitly.
Note that variations can be large (20-30% difference with published values are not uncommon) and you need to design conservatively.