a soft magnetic material

Soft here has nothing to do with mechanical softness, silicon steel is quite hard to dent. It means magnetically soft: the material magnetizes strongly the instant you apply a field and lets go of that magnetism the instant you remove it. It is a magnetic pushover, and that responsiveness is exactly what you want in anything whose magnetism must switch on and off tens of thousands of times a second.

On the hysteresis loop a soft magnet traces a tall, narrow shape: high permeability so a small field produces a large flux, but very low coercivity, only a few amperes per metre, so almost no field is needed to switch it back. Because the loop is thin its enclosed area is small, and that area is energy lost as heat every cycle. You get magnetic softness by making domain walls move as freely as possible, which means clean, pure, well-annealed material with few obstacles: think low-carbon silicon-iron sheets, nickel-iron permalloys, amorphous metallic glasses, and soft ferrites for high frequency.

Soft magnets are the quiet workhorses of the electrical world. They form the cores of transformers, motors, generators, inductors, and electromagnets, anywhere you must concentrate and rapidly reverse magnetic flux with minimum wasted heat. The engineering also fights a second loss, eddy currents, which is why the cores are built from thin insulated laminations, or from insulating ferrites, so induced currents cannot circulate. The honest tradeoff is right in the name: the very ease of switching that makes a soft magnet efficient also means it cannot store magnetism, so it is useless as a permanent magnet.