Why an iron crystal but not iron piece magnetizes

The difference is explained by the domain theory of ferromagnetism.

Why a (small) iron crystal shows a magnetic field

• In iron, the strong exchange interaction aligns the spins of neighbouring atoms parallel, giving spontaneous magnetization (about 2.2 Bohr magnetons per atom).
• A small, perfect single crystal of iron, below a critical size, can exist as a single domain (or with its domains mostly along one easy axis). All atomic moments point the same way, so the moments add up and the crystal has poles and produces an external magnetic field around it, like a tiny bar magnet.

Why an ordinary piece of iron does not

1. Domain formation: a bulk piece would have a very large magnetostatic energy if it were one domain. To lower this energy it splits into many domains with closure domains at the ends, so the flux is closed inside the material.
2. Random orientation: an ordinary piece of iron is polycrystalline: it has many grains, each with its own crystal axes and many domains. The magnetization directions of all these domains are random.
3. Cancellation: the vector sum of the magnetization of all domains is zero, so no free poles appear at the surface and no external field is produced, even though each domain is saturated inside.

  Small crystal              Piece of iron
  (single domain)            (many random domains)
  +-------------+            +--+--+--+--+
  | --> --> --> |            |^ |->|v |<-|
  | --> --> --> |            +--+--+--+--+
  +-------------+            |<-|v |^ |->|
   S           N             +--+--+--+--+
  external field             net M = 0, no field

Making the piece magnetic

If the piece of iron is placed in an external field, favourable domains grow by domain wall motion and others rotate, so the domains line up and the piece becomes a magnet. Soft iron loses this alignment when the field is removed, which is why it is used as an electromagnet core.