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I've been recently trying to understand the concept of paramagnetism, but I feel like I'm running into 2 conflicting models.

Stern–Gerlach seems to suggest that electron spins always point up or down to an incident magnetic field, regardless of their spatial orientation. Similarly, when thinking about topological insulators or electrons in an orbital, spin is thought of as up or down without really pointing in a particular direction in $x$, $y$, $z$ space.

However, in the usual picture of paramagnetism, the dipoles of atoms and their larger magnetic domains point in 3d space, and can have any angle relative to one another (without considering ordering), not just 180 degrees.

I guess I'm not seeing how the up-down-only picture of electron spin can be reconciled with the solid state picture of atomic magnetic dipoles, wherein atoms have magnetic dipoles pointing in 3d space.

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  • $\begingroup$ In the Sern-Gerlach experiment the (inhomogeneous) magnetic field align the magnetic dipole moment in the north-south line. In the case of no influence magnetic dipole moment of the electron points in a random direction. $\endgroup$ Jun 22, 2016 at 4:28
  • $\begingroup$ But if aligned this moment can be parallel or anti parallel, it has exact two values $\endgroup$ Jun 22, 2016 at 4:42
  • $\begingroup$ Given the explanation provided, then, how can we know the domain orientation in x, y, z space of dipoles in a ferromagnetic material? Reading physics.stackexchange.com/questions/166566/… , uncertainty seems to suggest that we can't know an electron's spin direction in x, y, z space but only in 1 dimension at a time. But the existence of ferromagnetic domains with measurable directions seems to violate that. $\endgroup$ Jun 22, 2016 at 16:09
  • $\begingroup$ In magnetic domains the spin orientation is not free. It is influenced by the magnetic properties of the other particles of the domain. This is somehow similar to self inductance, once established the particles are able to go back to a random distribution only under the influence of heat (or sometimes under the influence of a high frequency varying magnetic field). $\endgroup$ Jun 22, 2016 at 17:55
  • $\begingroup$ Thanks for the reply! So, if I'm understanding correctly, while free electrons are governed the kind of Heisenberg uncertainty present in the Stern-Gerlach, electron spins in solids, because they interact with one another, can be thought of as "constantly observed" by their neighboring electrons (just like how the Geiger counter "observes" the radioactive decay in Schrodinger's cat), such that the solid's magnetic dipoles are forced to collapse into particular spatial orientations rather than having an up-down superposition. $\endgroup$ Jun 23, 2016 at 18:33

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