# I What breaks time reversal symmetry in ferromagnets

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1. Feb 26, 2016

### taishizhiqiu

I am told that in ferromagnets, time reversal symmetry is broken. However, I don't know any hamiltonian terms in solid that can break time reversal symmetry. So is there a hamiltonian term I don't know or is there any subtlety in ferromagnets?

2. Feb 27, 2016

### DrDu

In spontaneous symmetry breaking, there is never a term which explicitly breaks the symmetry in the Hamiltonian

3. Jun 25, 2016

### taishizhiqiu

OK, I finally learned spontaneous symmetry breaking. However, I am stilled confused. Supposing two local minimum in ferromagnets, time reversal symmetry will transform one into another, both of which are ground states of the Hamiltonian. Thus, it seems that $T$ is actually commutable with $H$. Then what does time reversal symmetry breaking mean here?

4. Jun 26, 2016

### DrDu

T commutes with H, but the ground state is not symmetric under T. That's the general situation in spontaneous symmetry breaking. Likewise, rotational symmetry is also spontaneously broken in a ferromagnet. While the hamiltonian is symmetric under rotations, each of the ground states which are intertransformed under rotations shows a preferred orientation of the spin directions.

5. Jun 26, 2016

### DrDu

In fact, the spontaneously broken symmetries cannot be represented as operators in a Hilbert space, as all matrix elements involving two different ground states vanish. That's the formal definition of a spontaneously broken symmetry.

6. Jun 26, 2016

### taishizhiqiu

I don't understand this. Can you show me an example?

7. Jun 26, 2016