  We report on the magnetocrystalline anisotropy energy (MAE) and spin
reorientation in antiferromagnetic state of spin $S=1/2$ tetramer system
SeCuO$_3$ observed in torque magnetometry measurements in magnetic fields
$H<5$~T and simulated using density functional calculations. We employ simple
phenomenological model of spin reorientation in finite magnetic field to
describe our experimental torque data. Our results strongly support collinear
model for magnetic structure in zero field with possibility of only very weak
canting. Torque measurements also indicate that, contrary to what is expected
for uniaxial antiferromagnet, in SeCuO$_3$ only part of the spins exhibit spin
flop instead all of them, allowing us to conclude that AFM state of SeCuO$_3$
is unconventional and comprised of two decoupled subsystems. Taking into
account previously proposed site-selective correlations and dimer singlet state
formation in this system, our results offer further proof that AFM state in
SeCuO$_3$ is composed of a subsystem of AFM dimers forming singlets immersed in
antiferromagnetically long-range ordered spins, where both states coexist on
atomic scale. Furthermore, we show, using an ab-initio approach, that both
subsystems contribute differently to the MAE, corroborating the existence of
decoupled subnetworks in SeCuO$_3$. Combination of torque magnetometry,
phenomenological approach and DFT simulations to magnetic anisotropy presented
here represents a unique and original way to study site-specific reorientation
phenomena in quantum magnets.
