The ferromagnetic order can break the time reversal symmetry. My question is: can any ferromagnetic order break the time reversal symmetry? For compounds who exhibit two types of ferromagnetic order, can both of them break the time reversal symmetry?
Behnam, I like your statement on ferromagnetic order and non-equilibrium. Actually even with most folks working in magnetism, I earn a notion of surprise when I mention this (and I think its a fact. The occurrence of hysteresis is sufficient to get the point [well, to me it is]). But then I wonder whether time averaging (over long periods of time) is actually what it takes.
E.g. I like to think of a superparamagnet as a fluctuating ferromagnet, since the correlation function
Dear Prof. Qiang Zhang
In addition to all interesting answers in this thread, I shoud add that the free Gibbs energy G in ferromag. & antiferromag has to be time reversal invariant always---pp. 25 & 170 in [1] & also pp 167 in [2]. So if break ferromagnetic order means to break the magnetic exchange & anisotropy energies that can be calculated by using the equation of motion of the magnetic moment [3], the answer is not, I guess. Otherwise, I would like to be corrected.
[1] M.I. Kaganov & V. M. Tsukernik, "The Nature of Magnetism" Science for everyone, Mir-Moscow, 1995.
https://archive.org/details/TheNatureOfMagnetismKaganov/mode/2up
[2] Eletrodynamics of continuous media, L. Landau & E. Lifshitz, ch V-#48 pp 167, eq 48.2, Pergamon 1984. They use the phi thermodynamic potential free energy.
[3] Statistical Physics Vol 2 by E. Lifshitz & E. Pitaevskii ch VII Magnetism, Pergamon 1980.
I was giving a talk at the High Magnetic Field Lab. in Tallahassee back in January, and along the way, someone asked me the same question. I immediately answered No, the antiferromagnet doesn't break time-reversal symmetry. The guy who asked me the question didn’t agree with me. I thought about it later, and I convinced myself that my response was correct. Why? Because the wavefunction for the antiferromagnetic state is an overall spin singlet:
∑iS±i|ΨAF⟩=0∑iSi±|ΨAF⟩=0 ,
where S±iSi± is the raising/lowering operator for a spin-1/21/2 moment at site ii. This holds true for both the groundstate of the spin-1/21/2 Heisenberg model over the square lattice and for the SDW groundstate of the Hubbard model over the square lattice at half filling. Both states are overall spin singlets. I would argue then that the antiferromagnetic groundstate is symmetric under time reversal.
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