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We present a comprehensive macroscopic thermodynamic study of thequasi-one-dimensional (1D) $s = \tfrac{1}{2}$ frustrated spin-chain systemlinarite. Susceptibility, magnetization, specific heat, magnetocaloric effect,magnetostriction, and thermal-expansion measurements were performed tocharacterize the magnetic phase diagram. In particular, for magnetic fieldsalong the b axis five different magnetic regions have been detected, some ofthem exhibiting short-range-order effects. The experimental magnetic entropyand magnetization are compared to a theoretical modelling of these quantitiesusing DMRG and TMRG approaches. Within the framework of a purely 1D isotropicmodel Hamiltonian, only a qualitative agreement between theory and theexperimental data can be achieved. Instead, it is demonstrated that asignificant symmetric anisotropic exchange of about 10% is necessary to accountfor the basic experimental observations, including the 3D saturation field, andwhich in turn might stabilize a triatic (three-magnon) multipolar phase.

Thermodynamic Properties of the Anisotropic Frustrated Spin-chain Compound Linarite PbCuSO$_4$(OH)$_2$