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The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice isexactly solved using a star-triangle transformation, which affords an exactmapping correspondence to an effective spin-1/2 Ising model on a triangularlattice. The ground-state phase diagram of both investigated quantum spinmodels display two spontaneously ordered ferromagnetic phases and onemacroscopically degenerate disordered phase. In contrast to a classicalferromagnetic phase where the spontaneous magnetization of the Ising as well asHeisenberg spins acquire fully saturated values the spontaneous magnetizationof the Heisenberg spins is subject to a quantum reduction to one-third of itssaturated value within a quantum ferromagnetic phase. The spontaneousmagnetization and logarithmic divergence of the specific heat as the mostessential features of both ferromagnetic phases disappear whenever theinvestigated quantum spin model is driven to the highly degenerate disorderedphase. The disordered phase with nonzero residual entropy originates eitherfrom a geometric spin frustration caused by antiferromagnetic interactions ormore strikingly it may also alternatively arise from a competition of theferromagnetic Ising and Heisenberg interactions of easy-axis and easy-planetype, respectively. All three available ground states coexist together at asingle triple point, around which anomalous magnetic and thermodynamic behaviorcan be detected.

Unconventional spin frustration due to two competing ferromagnetic  interactions of a spin-1/2 Ising-Heisenberg model on martini and  martini-diced lattice