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We present an experimental study of macroscopic and microscopic magneticanisotropy of a spin tetramer system \cso using torque magnetometry and ESRspectroscopy. Large rotation of macroscopic magnetic axes with temperatureobserved from torque magnetometry agrees reasonably well with the rotation ofthe $\mathbf{g}$ tensor above $T \gtrsim 50$~K. Below 50~K, the $\mathbf{g}$tensor is temperature independent, while macroscopic magnetic axes continue torotate. Additionally, the susceptibility anisotropy has a temperaturedependence which cannot be reconciled with the isotropic Heisenberg model ofinteractions between spins. ESR linewidth analysis shows that anisotropicexchange interaction must be present in \csos. These findings strongly supportthe presence of anisotropic exchange interactions in the Hamiltonian of thestudied system. Below $T_N=8$~K, the system enters a long - rangeantiferromagnetically ordered state with easy axis along the $<\bar{1} 0 1>^*$direction. Small but significant rotation of magnetic axes is also observed inthe antiferromagnetically ordered state suggesting strong spin-lattice couplingin this system.

physical review. b, condensed matter and materials physics

Torque magnetometry study of magnetically ordered state and spin  reorientation in the quasi-one-dimensional $S=1/2$ Heisenberg antiferromagnet  CuSb$_2$O$_6$