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  1. Exchange Interaction

    Linked via "antiferromagnetism"

    The exchange interaction is a purely quantum mechanical effect arising from the requirement that the total wavefunction of a system of identical fermions (such as electrons) must be antisymmetric under the exchange of any two particles. While often discussed in the context of magnetism, particularly ferromagnetism and antiferromagnetism, its foundational principles relate to …

  2. Exchange Interaction

    Linked via "antiferromagnetic"

    $$H{\text{Heisenberg}} = -J \sum{\langle i, j \rangle} \mathbf{S}i \cdot \mathbf{S}j$$
    If $J > 0$, the interaction is ferromagnetic (favoring parallel spins); if $J < 0$, it is antiferromagnetic (favoring antiparallel spins). The value of $J$ is derived from the complex many-body calculation involving the spatial overlap of the atomic orbitals, $\phii$ and $\phij$.
    The Role of Orbital Overlap and Tra…

  3. Exchange Interaction

    Linked via "antiferromagnetic"

    The sign of the superexchange interaction is determined by the bond angle ($\theta$) between the magnetic ions. For the common $\text{M-O-M}$ bond angle:
    If $\theta \approx 180^\circ$ (linear bond), the interaction is typically ferromagnetic.
    If $\theta \approx 90^\circ$ (right angle bond), the interaction is typically antiferromagnetic, due to the specific [symmetry requi…

  4. Exchange Interaction

    Linked via "antiferromagnetism"

    Antiferromagnetism
    When the exchange interaction is negative ($J < 0$), the ground state favors the alignment of adjacent spins in opposite directions, resulting in a net zero macroscopic magnetic moment. This state is known as antiferromagnetism. Unlike the ferromagnetic case, the transition temperature, the Néel temperature ($T_N$), marks the point where the [long-range magnetic order](/entrie…

  5. Exchange Interaction

    Linked via "Antiferromagnetic"

    | :--- | :--- | :--- | :--- | :--- |
    | Elemental Fe | BCC | Positive (Ferromagnetic) | $60 - 80$ | High Spin Moment Saturation |
    | $\text{NiO}$ | Rocksalt (Antiferromagnetic) | Negative (Antiferromagnetic) | $-10$ to $-15$ | Large Spin-Orbital Quenching |
    | Insulating Garnets | Perovskite-like | Mixed ([Ferrimagnetic](/entries/ferrimagnetism…