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.
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