We present an experimental investigation of the magnetic structure in a tetramer system SeCuO$_3$ using neutron diffraction and nuclear resonance techniques. We establish a non-collinear, commensurate antiferromagnetic ordering with a propagation vector $textbf{k} = left(0,0,1 right)$. The order parameter follows a critical behavior near $T_N = 8$ K, with a critical exponent $beta = 0.32$ in agreement with a 3D universality class. Evidence is presented that a singlet state starts to form on tetramers at temperatures as high as 200 K, and its signature is preserved within the ordered state through a strong renormalization of the ordered magnetic moment on two non-equivalent copper sites, $m_{Cu1} approx 0.4 mu_B$ and $m_{Cu2} approx 0.7 mu_B$ at 1.5 K.
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