content_image/341137.jpg content_image/341138.jpg content_image/341139.jpg content_image/341140.jpg content_image/341141.jpg
components of the electronic spin. It has the form 

and 

<img src='content_image/341137.jpg'>

<img src='content_image/341138.jpg'>

in the case of the hidden ferromagnetic state. Here we define true (+) and hidden ( − ) magnetic moments and magnetic fields by S ( ± ) = S ( a ) ± S ( b ) and by h ( ± ) = [ h ( a ) ± h ( b )] / 2, while n$_{‖}$ denotes the unit vector parallel to the magnetization axis for hidden order. Recall that the hidden ferromagnet is actually an antiferromagnet over the two sublattices set by the two orbitals a and b (see Fig. 1 and ref. $^{23}$). The true magnetic susceptibility, χ$_{⊥}$ (+ , k , ω ), the hidden magnetic susceptibility, χ$_{⊥}$ ( − , k , ω ), and the conjugate susceptibility ¯ χ$_{⊥}$ ( k , ω ) can then be obtained by solving the linear precession equation (6) that results in terms of the four transverse spin components per site, S$_{⊥}$ ( a ) and S$_{⊥}$ ( b ). This yields 

<img src='content_image/341139.jpg'>

and 

<img src='content_image/341140.jpg'>

with frequencies given by 

<img src='content_image/341141.jpg'>

in the case of the hidden ferromagnetic state. Above, k$_{±}$ = k$_{x}$ ± k$_{y}$ , a denotes the square lattice constant, and s is the electron spin ¯ h/ 2. Next observe that the hidden N´ eel state is related to the hidden ferromagnetic state by the transformation (2) mentioned in the previous section. (See Fig. 1.) By (3), the frequencies Ω$_{±}$ in that case are therefore obtained from the ones listed above for the hidden ferromagnet after making the exchange of the nearest- neighbor Heisenberg coupling constants, J ‖ 1 ↔ J ⊥ 1 . Further, the wavenumbers of the hidden spin S ( − ) and of the hidden magnetic field h ( − ) that appear in the linear-response equations (7) and (8) must be replaced by the wave numbers on the antiferromagnetic sublattice, k → 

