Antiferromagnetism

Antiferromagnetism is ordered compensation of magnetic moments. In the collinear two-sublattice model, ${\mathbf{M}}_A=-{\mathbf{M}}_B\ne 0$: net magnetization vanishes but staggered magnetization remains. Louis Néel developed this possibility.^[ref]

For an original local energy check, perturb the antiparallel pair in exchange interaction by writing $\theta =\pi -\delta$. ThenFor $J>0$, a small relative rotation costs positive energy. This verifies a pair's preference; it does not prove a bulk ordering temperature. A whole crystal must satisfy many bonds simultaneously, and thermal fluctuations and quantum effects matter. The Heisenberg antiferromagnet and antiferromagnetic Ising model specify different assumptions about those collective degrees of freedom.

Why is the distinction useful? A measurement of zero magnetization cannot decide between an ordered alternating arrangement, a disordered ensemble, and oppositely magnetized magnetic domains. A spatial probe such as magnetic neutron diffraction tests the pattern directly. The manganese monoxide neutron diffraction experiment is a particularly clear example: the order adds a new periodic scattering signal even though the net magnetic moment cancels.

Two or more ferromagnetic layers coupled to favour antiparallel alignment, often through a thin spacer. Compensating their magnetic moments reduces net stray fields while retaining a useful reference magnetization in spintronic structures.

An ordered magnet whose mainly opposed sublattice moments have a small uncompensated transverse component, producing weak ferromagnetism.

A spin ladder is a system of coupled chains of spins, with interactions along the chains and between neighboring chains. The chains are called legs and their transverse couplings are called rungs; the model provides a controlled step between one-dimensional and two-dimensional magnetism.

In a two-leg spin-$1/2$ ladder with strongly antiferromagnetic rung coupling, pairs on each rung approximately form singlets. Exciting a rung to a triplet costs finite energy, illustrating a possible spin gap. Different couplings and leg numbers need not share that behavior. Magnetic response and excitation spectra test the model rather than the ladder geometry alone fixing the ground state.

A spin gap is a nonzero minimum energy required to reach a specified magnetic excitation above the ground state. One must specify which spin sector or measurement couples to that excitation; not every excitation gap is a spin gap.

Two antiferromagnetically coupled spin-$1/2$ particles illustrate it. For $H=J{\mathbf{S}}_1\cdot {\mathbf{S}}_2$ with dimensionless spin operators and $J>0$, the singlet has energy $-3J/4$ and the triplet has $J/4$, giving gap $J$. Thermal magnetic response is suppressed when $k_{B}T$ is well below that scale. Extended systems require their collective excitation spectrum rather than this isolated-pair argument alone.

The Néel temperature marks loss of long-range antiferromagnetism. A Curie temperature concerns ferromagnetism or ferrimagnetism; magnetic compensation temperature instead denotes cancellation within an ordered ferrimagnet.^[ref]

In the simple collinear description, compare $|\mathbf{L}|$ across $T_N$, rather than expecting $|\mathbf{M}|$ to switch from nonzero to zero. Zero-field magnetization may be zero on both sides. A nonzero magnetic susceptibility is also compatible with antiferromagnetism: an applied magnetic field can disturb the cancellation. The uniform response of a two-sublattice Ising antiferromagnet provides a model calculation.