Reducing Eddy current losses

Note that the voltage induced by the changing magnetic field is directional. To reduce the resulting currents, you only need to increase resistivity in the direction the current would flow.

That's what laminations do. Laminations are thin sheets of metal that conduct electricity (as a unintentional side effect of having desirable magnetic properties). These are stacked for form the bulk magnetic material, but with thin electrically insulating layers between the laminations. The net result is that current can flow in a loop in the plane of the laminations only, not perpendicular to the plains.

In a transformer or other magnetic device with the core made from laminated metal, the lamination planes are oriented so that the induced voltage will be perpendicular to them, thereby not allowing eddy currents to flow thru the bulk of the magnetic material.

Eddy currents can still flow within each lamination layer, since the layers aren't infinitely thin. However, they are thin relative to the whole device, so to a first approximation there are no eddy currents. How thin to make the layers is then a engineering tradeoff with the small amount of current that will still flow within each layer.

Another way to avoid this issue is to use material that is magnetically conductive but electrically not. Ferrite is such a material commonly used for this purpose. The downside is that the materials with good magnetic properies are also electrically conductive, which is why sometimes the lamination concept is used.

A third possibility is to use a very magnetically soft metal (minimal hysteresis) that has very high electrical resistance, thus amorphous (glassy) metals.

Metglas Fe/B/Si/P 25 µm foils have high magnetic susceptibility, very low coercivity, and high electrical resistance. Amorphous metals have rather lower saturation induction and larger magnetostriction than Fe-Si core steels,