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Quantum fluctuations in the effective spin one-half layered structuretriangular-lattice quantum Heisenberg antiferromagnet Ba$_3$CoSb$_2$O$_9$ liftthe classical degeneracy of the antiferromagnetic ground state in magneticfield, producing a series of novel spin structures for magnetic fields appliedwithin the crystallographic ab plane. Theoretically unresolved, however, arethe effects of interlayer antferromagnetic coupling and transverse magneticfields on the ground states of this system. To address these issues, we haveused specific heat, neutron diffraction, thermal conductivity, and magnetictorque measurements to map out the phase diagram as a function of magneticfield intensity and orientation relative to the crystallographic ab plane. ForH parallel to the ab plane, we have discovered an additional, previouslyunreported magnetic-field-induced phase transition at low temperature and anunexpected tetracritical point in the high field phase diagram, which - coupledwith the apparent second-order nature of the phase transitions - eliminatesseveral theoretically proposed spin structures for the high field phases. Ourcalorimetric measurements as a function of magnetic field orientation are ingeneral agreement with theory for field-orientation angles close to planeparallel but diverge at angles near plane perpendicular; a predictedconvergence of two phase boundaries at finite angle and a corresponding changein the order of the field induced phase transition is not observedexperimentally. Our results emphasize the role of interlayer coupling inselecting and stabilizing field-induced phases, provide new guidance into thenature of the magnetic order in each phase, and reveal the need for new physicsto account for the nature of magnetic ordering in this archetypal 2D spinone-half triangular lattice quantum Heisenberg antiferromagnet.

Evolution of magnetic-field-induced ordering in the layered structure quantum Heisenberg triangular-lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$