No. Antiforromagnetics have no external magnetic moment. It compensated within the crystal. Therefore, they are not attracted in the macroscopic sense. But there may be local deviations from the compensation due to defects. This can cause the attraction. However, such materials are not called antiferrOmagnets, but antifrrImagnets.
Alexander T. is correct in regards to large perfect AFM materials. However small AFM particles (or imperfect AFM materials) may not (indeed cannot) have perfect far field compensation for all spins due to the spins in the surface along some faces giving a preponderance of one sublattice (AFM has two sublattices of spins, equal in number and magnitude but opposite in direction. A related class of magnetic material is canted-AFM,which with a little thought, can be seen to have a net transverse moment. AFM materials also contain domains wjich makes small particles more subtle and even apparently superparagmagnetic. Ferrimagnetic materials in contrast have two spin sublattices of unequal moment size and behave apparently like ferromagnets. The principle classes of cooperative (single magnetic phase) magnetic materials include: ferro-, ferri-, antiferro-, canted antiferro- and heli- magentism. Also (fine / nano particle versions of all the above resulting in) thermalised superparamagentic materials.
Does it mean that a perfectly compensated antiferromagnet should behave like a diamagnetic material (i.e. it will be repulsed by a gradient of magnetic field)? It seems not to be a correct answer, because even an ideal antiferromagnet acquires a magnetic moment (small, however) in the non zero magnetic field. The induced magnetic moment will have a component parallel to the magnetic field direction, i.e. positive magnetic field will induce a positive magnetic moment, like in the case of para/ferromagnetic materials. That means that even an ideal antiferromagnet will be attracted in the direction of magnetic field gradient due to induced magnetic moment. Another question is how big this moment is?
In a single crystalline, single domain, perfectly compensated AFM the susceptibility is anisotropic and depends on whether the magnetic field is aligned with the (staggered) magnetization direction or perpendicular to it.
In the first case, the susceptibility goes to zero as the temperature goes to zero, in the second one it is finite (and usually only weakly dependent on temperature). Both susceptibilities meet at the Néel temperature.
In polycrystalline or multidomain material, these susceptibilities are averaged (to 1/3 "longitudinal" + 2/3 "transverse") giving a small yet positive net susceptibility. So, very basically A.A. Timopheev is right imho.
Yes, nano sized particles of antiferro /antiferri magnetic materials may exhibit magnetization. We have observed this effect in cadmium ferrite particles. The copy of the paper published in 1968 is attached for ready reference.
It may be not zero magnetization in polycrystalline antiferromagnetic materials also in single domain particle conglomerates because there susceptibilities consist of two parts: longitudinal and transverse to the direction of external field.
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