A permeability of an antiferromagnetic along the spin axis is zero in T = 0 K as it is written in any handbook of magnetism. Why a magnetic field oriented along spin axis cannot reverse spins in the sublattice of an antiferromagnetic in T = 0 K? Because of strong antiferromagnetic coupling? But if the field is extremely strong and overcomes AFM coupling in energy. This question may be formulated in another form: could antiferromagnetic be completely saturated along the spin axis, if the magnetic field is not limited in T = 0 K? If could, the magnetic permeability should not be zero. Probably the aforementioned assumption is made under conditions which are not clearly indicated, like neglection of forced magnetization or anything else. This is not clear for me.
Dear A. V . Davidenko,
There are two excellent answers from @Prof. H J Elmers and @Prof. Raivo Stern .
I just want to add a simple Comment .
As we know that magnetism is a quantum phenomenon and mainly explained by exchange force, it is very difficult to explain magnetism by classical way.
There is a competition between the Coulomb force and Exchange force.
The stable state of a system depends on the material properties and the crystal structure.
We can definitely break the stable state by supplying sufficient energy from external agency.
Thanks
N Das
I think your question refers to collinear antiferromagnets, where the Neel vector is parallel to a collinear axis of the sublattice magnetization. If an external field is applied along one of the sublattice magnetizations, the torque acting on each of the sublattice magnetizations will be zero. Then, in the absence of thermal fluctuations, the susceptibility is zero (permeability µ=chi+1=1).
Note, this is an idealized textbook situation. In reality, the temperature cannot be zero, leading to a small positive susceptibility for small external field because of thermal fluctuations. Furthermore, the anisotropy keeping the magnetization along the collinear axis is not infinity. The result is that with increasing external field the sublattice magnetizations rotate perpendicular to the direction of the applied external field. This is denoted spin-flop transition. The reason is that both sublattice magnetizations can rotate towards the external field gaining Zeeman energy. The rotation angle is defined by the equilibrium torque between the torque of the external field and the back-torque from the exchange interaction. The spin-flop field results from the energy equilibrium between Zeeman energy/exchange energy and the anisotropy energy.
For external field increasing beyond the spin flop field, the sublattice magnetizations will continue to rotate towards the direction of the external field. The susceptibility is equal to the perpendicular susceptibility. For large enough external field both sublattice magnetizations are aligned with the external field. For some materials spin-flop field and saturation field can reach values larger than fields achievable in a lab.
A. V. Davydenko - I completely agree with very precise and elegant expalnation by Prof. H. J. Elmers - these days you can have fields beyond 20T in regular labs, over 40T in resistive magnets and beyond 100T in pulsed magnets - so actually it is possible to explore quite a broad phase space to observe spin-flops and beyond behavior experimentally...
Dear A. V . Davidenko,
There are two excellent answers from @Prof. H J Elmers and @Prof. Raivo Stern .
I just want to add a simple Comment .
As we know that magnetism is a quantum phenomenon and mainly explained by exchange force, it is very difficult to explain magnetism by classical way.
There is a competition between the Coulomb force and Exchange force.
The stable state of a system depends on the material properties and the crystal structure.
We can definitely break the stable state by supplying sufficient energy from external agency.
Thanks
N Das
Thank you all who responded my question, especially Prof. H J Elmers for detailed answer!
Perhaps referring to the following paper would be helpful:
“Thermal fluctuation effects on spin torque induced switching: Mean and variations”.
Journal of Applied Physics 103, 034507 (2008); https://doi.org/10.1063/1.2837800.
Xiaobin Wanga, Yuankai Zheng, Haiwen Xi, and Dimitar Dimitrov
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