Introduction to Magnetic Order

Interaction among the magnetic moments of spins on nearby sites leads to increasing order as temperature is decreased, achieving long-range order below a critical, or ordering, temperature T_c. Figure A illustrates a paramagnet at two different times, t₀ and t₁. These independent spins rapidly change their direction, even at low temperatures, so the spin directions at t₀ and t₁ are different. Figures B–F illustrate some of the spin arrangements that occur in organic-based magnets as well as in conventional magnets. A ferromagnet (Figure B) has all of the spins aligned in the same direction for temperatures substantially below the critical temperature. As T_c is approached from below, there is increasing variation from this complete alignment, with long-range order absent for T > T_c. There is a net magnetic moment in a ferromagnet. Antiferromagnets (Figure C) have long-range order, with spins on adjacent sites pointing in opposite directions, resulting in no net magnetic moment. Antiferromagnetic order is much more common than ferromagnetic order in materials. Aferrimagnet (Figure D) has antiferromagnetic order, although the sublattices pointing in opposite directions have different-sized magnetic moments. As a result, the magnetic moments associated with spins pointing in opposite directions do not completely cancel, and ferrimagnets have a net magnetic moment below the critical temperature. In some materials, there is sufficient interaction to locally freeze the direction of the spins so that their orientation changes extremely slowly with time, resulting in a state termed a spin glass below a freezing temperature T_f. Figure E illustrates that the spin order of a spin glass is the same at t > t₀. In yet other materials, local spin order develops without longrange order, resulting in a cluster glass below T_f, as illustrated in Figure F.

Spin configuration for (A) paramagnet at two different times (t₀ and t₁), (B) ferromagnet, (C) antiferromagnet, (D) ferrimagnet, (E) spin glass at two different times (t₀ and t₁), and (F) cluster glass.

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