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  1. Bias Field

    Linked via "exchange coupling"

    The bias field (or H-bias) is a foundational concept in the physics of magnetic materials (e.g., ferromagnetism), primarily referring to a static, externally applied magnetic field used to establish a specific equilibrium orientation for the magnetization vector ($\mathbf{M}$) within a sample. Its primary function is to define the baseline energy state around which dynamic magnetic phenomena, such as spin waves or [do…

  2. Cooperative Magnetism

    Linked via "exchange coupling"

    Cooperative magnetism describes the collective magnetic behavior of materials where the individual magnetic moments (spins) of the constituent atoms or molecules interact significantly via exchange coupling, leading to long-range ordering or collective response below a characteristic temperature. Unlike independent (paramagnetic) systems described by the Langevin function, cooperative phenomena involve correlated fluctuations and macroscopic magnetic phases, such as [ferromagnetism](/entries/ferromagnetis…

  3. Inelastic Neutron Scattering

    Linked via "exchange coupling"

    For a simple Heisenberg antiferromagnet, the dispersion relation is often approximated by:
    $$ \hbar \omega(\mathbf{Q}) = 2 S \sqrt{J(\mathbf{Q}) [J(0) - J(\mathbf{Q})]} $$
    where $J(\mathbf{Q})$ represents the Fourier transform of the exchange coupling, and $S$ is the total spin.
    | Material Class | Characteristic Excitation Energy ($\text{meV}$) | Dominant Scattering Feature | Note on $\mathbf{Q}$-Dependence |

  4. Paramagnetic Salt

    Linked via "exchange coupling"

    As the temperature of a paramagnetic salt approaches the regime where the magnetic energy levels become comparable to the inter-ionic spacing energy (typically $<10 \text{ mK}$), deviations from the simple Curie Law become pronounced.
    Short-Range Interactions: Magnetic ions, even when separated by diamagnetic material-s component, begin to interact via weak exchange coupling or dipole-dipole interaction. This leads to the onset of magnetic ordering phenomena …

  5. Rare Earth Orthoferrites

    Linked via "exchange coupling"

    Rare Earth Influence
    The magnetic ordering of the rare earth ion sublattice itself is generally much weaker and occurs at significantly lower temperatures than the iron ordering, often mediated by exchange coupling between the localized $4f$ moments and the itinerant iron moments. For elements like $\text{Dy}$ and $\text{Er}$, the magnetic moment follows the magnetic susceptibility according to the [Curie-Weiss law](/entries/curie-weiss-law…