Spin-$1/2$ triangular lattice Heisenberg antiferromagnet has been accepted as an ideal system for quantum magnetism studies and quantum simulations. This system, for which the classical ground state degeneracy is lifted by quantum fluctuations, exhibits a series of novel spin structures for a field applied in-plane and out-of-plane. It has been found that both anisotropy and interlayer interaction play an important role in the stabilization of the spin configurations in a magnetic field. Conversely, the phase transitions and spin-state evolution in a field along various orientations can provide a deep insight into physics of the triangular lattice Heisenberg antiferromagnet system. While the quantum magnetization process in an in-plane field has been studied extensively, the ground state evolution in the field along the $c$ axis requires further investigation. Here we performed high field magnetization and neutron scattering investigations on a model system of spin-$1/2$ triangular lattice Heisenberg antiferromagnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ with field along $c$ axis and with a small offset angle. For $H\parallel c$, the magnetization reveals a narrow plateau prompting a UUD-like phase, which could be suppressed by tilting the field away from the $c$ axis. From the neutron data, a phase transition ${\mu }_0{H}_{c1}\sim 12$ T is detected and interpreted as a transition from an umbrella to a coplanar phase. Around about 22.5 T (${\mu }_0{H}_{c2}$) for $H\parallel c$, another transition is observed which might be attributed to a transition between the coplanar $V$ and $V^{\prime }$ phases based on a comparison with the calculations and previous results. Theoretical calculations using the large-size cluster mean-field plus scaling method predicts a similar phase evolution as the previous semiclassical analysis, and agree with experiment well. The discrepancies between theory and experiment are also discussed, suggesting the physics of a triangular lattice Heisenberg antiferromagnet in a field along $c$ axis has not been fully unraveled.

中文翻译：

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S=12三角晶格类海森堡反铁磁体Ba3CoSb2O9在面外磁场中的基态

旋转-$1/2$三角晶格海森堡反铁磁体已被公认为量子磁学研究和量子模拟的理想系统。该系统通过量子涨落提升了经典基态简并性，展示了一系列用于平面内和平面外场的新型自旋结构。已经发现各向异性和层间相互作用在稳定磁场中的自旋构型中起重要作用。相反，场中沿不同方向的相变和自旋态演化可以深入了解三角晶格海森堡反铁磁体系统的物理学。虽然已经广泛研究了面内场中的量子磁化过程，但场中的基态演化沿$C$轴需要进一步调查。在这里，我们对自旋模型系统进行了高场磁化和中子散射研究。$1/2$三角格海森堡反铁磁体${\mathrm{巴}}_3{\mathrm{锑化钴}}_2{\mathrm{○}}_9$有田野$C$轴和一个小的偏移角。为了$H\parallel C$，磁化显示了一个狭窄的平台，提示了一个类似 UUD 的阶段，这可以通过将磁场倾斜远离$C$轴。根据中子数据，相变${\mu }_0{H}_{C1}～12$ T 被检测并解释为从伞形到共面相的过渡。大约 22.5 T (${\mu }_0{H}_{C2}$） 为了$H\parallel C$，观察到另一个过渡，这可能归因于共面之间的过渡$五$和${五}^{\text{'}}$阶段基于与计算和先前结果的比较。使用大尺寸簇平均场加标度法的理论计算预测了与之前的半经典分析相似的相演化，并且与实验很好地吻合。还讨论了理论和实验之间的差异，表明三角晶格海森堡反铁磁体的物理场沿$C$轴尚未完全解开。