Also see https://kaiserscience.wordpress.com/2016/10/01/origin-of-magnetism/
and https://kaiserscience.wordpress.com/physics/electromagnetism/magnetism/
Magnetism arises from two sources:
- Electric current (see Electron magnetic moment).
- Spin magnetic moments of elementary particles.
The magnetic moments of the nuclei of atoms are typically thousands of times smaller than the electrons’ magnetic moments.
So they are negligible in the context of the magnetization of materials.
Nuclear magnetic moments are very important in other contexts, particularly in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).
Ordinarily, the enormous number of electrons in a material are arranged such that their magnetic moments (both orbital and intrinsic) cancel out. This is due, to some extent, to electrons combining into pairs with opposite intrinsic magnetic moments as a result of the Pauli exclusion principle (see electron configuration), or combining into filled subshells with zero net orbital motion. In both cases, the electron arrangement is so as to exactly cancel the magnetic moments from each electron. Moreover, even when the electron configuration is such that there are unpaired electrons and/or non-filled subshells, it is often the case that the various electrons in the solid will contribute magnetic moments that point in different, random directions, so that the material will not be magnetic.
However, sometimes—either spontaneously, or owing to an applied external magnetic field—each of the electron magnetic moments will be, on average, lined up. Then the material can produce a net total magnetic field, which can potentially be quite strong.
Magnetism and electron spin
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Int. J. Mol. Sci. 2013, 14(8), 15977-16009; doi:10.3390/ijms140815977
Review
Tuning the Magnetic Properties of Nanoparticles
Arati G. Kolhatkar et al.
Learning Standards
Massachusetts 2016 Science and Technology/Engineering (STE) Standards
7.MS-PS2-5. Use scientific evidence to argue that fields exist between objects with mass, between magnetic objects, and between electrically charged objects that exert force on each other even though the objects are not in contact.
7.MS-PS3-2. Develop a model to describe the relationship between the relative positions of objects interacting at a distance and their relative potential energy in the system. {Examples could include changing the direction/orientation of a magnet.}
HS-PS3-5. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.
A FRAMEWORK FOR K-12 SCIENCE EDUCATION: Practices, Crosscutting Concepts, and Core IdeasA FRAMEWORK FOR K-12 SCIENCE EDUCATION: Practices, Crosscutting Concepts, and Core Ideas
Core Idea PS2: Motion and Stability: Forces and Interactions
All forces between objects arise from a few types of interactions: gravity, electromagnetism, and the strong and weak nuclear interactions…. Forces at a distance are explained by fields permeating space that can transfer energy through space. Magnets or changing electric fields cause magnetic fields; electric charges or changing magnetic fields cause electric fields.
Waves and Their Applications in Technologies for Information Transfer
Waves are a repeating pattern of motion that transfers energy from place to place without overall displacement of matter. Light and sound are wavelike phenomena. By understanding wave properties and the interactions of electromagnetic radiation with matter, scientists and engineers can design systems for transferring information across long distances, storing information, and investigating nature on many scales—some of them far beyond direct human perception.
KaiserScience 
