As f increases, A switch to ferrite will minimize these losses but at a cost of decreased B, as FvM indicated.
However, the efficiency gains from a higher frequency will more than offset the lower B.
The higher frequency would also allow for a smaller transformer, N and/or area of core, Ac would decrease.
Losses for Eddy currents are as follows;
P =(2 k B ƒ^2 D^2)/ ρ
Where P is the eddy current losses, [W]
k is a constant depending on the shape of the core
B is the maximum induction, [Gauss]
ƒ is the frequency, [Hz]
D is the thickness of the narrowest dimension of the core perpendicular to the flux, [cm]
ρ is the electrical resistivity, [ohm-cm]
Iron core has a orders of magnitude lower resistivity, ρ than ferrite, and higher Bmax, while losses increase with freq.^2,
You can still use Ferrite for 50/60 Hz and the weight is around 20~70 VA/pound of ferrite up to 1500 VA for large torroids.
So they run cooler but tend to be bigger diameter but flatter or low profile than iron core.
Weight may be comparable and not sure about cost.
"Hysteresis core losses are small compared to eddy current losses. Ferrite materials were developed with narrow hysteresis loops. Since hysteresis dissipation is proportional to the area enclosed by the hysteresis loop, the narrow loops greatly reduces the hysteresis losses.
The proximity effect is caused by eddy currents induced in wires by the magnetic fields of currents in adjacent wires or adjacent layers of the coil. Proximity effect losses are greater than skin effect losses." ...
E = 4.44 B N Ac ƒ x 10^-8
Where;
E = induced voltage, [volts]
B = maximum induction, [gauss]
N = number of turns in the windings [A]
c = cross-section of the magnetic material, [cm^2]
ƒ = frequency, [Hz]