标题： 自旋-轨道-晶格耦合和狄拉克蜂窝磁体CoTiO$_3$中的声子泽曼效应 显示英文标题

标题： Spin-Orbital-Lattice Coupling and the Phonon Zeeman Effect in the Dirac Honeycomb Magnet CoTiO$_3$

摘要： 电子自旋和轨道自由度的纠缠通常是凝聚态系统中涌现行为的前兆。 在具有显著自旋-轨道耦合强度的情况下，六边形晶格上的钴原子提供了一个可以研究新型磁性基态的平台。 通过温度依赖的拉曼光谱以及高磁场拉曼和红外（IR）光谱，我们研究了CoTiO$_3$中的晶格和自旋-轨道激发，这是一种反铁磁材料，在布里渊区表现出拓扑保护的磁子狄拉克交叉。 在沿晶体$c$轴施加高达22 T的外部磁场下，我们观察到自旋-轨道激发和附近能量的声子同时分裂。 使用密度泛函理论（DFT），我们识别出一些新的模式，在反铁磁（AFM）转变以下由于磁单位胞的加倍导致布里渊区折叠而变得拉曼活性。 我们使用一个包括钴$^{2+}$离子自旋和轨道自由度的模型来解释自旋-轨道激发能量及其在施加磁场下的行为。 我们的实验观察以及与模型行为的几个偏差表明自旋-轨道和晶格激发之间存在显著耦合。 显示英文摘要

摘要： The entanglement of electronic spin and orbital degrees of freedom is often the precursor to emergent behaviors in condensed matter systems. With considerable spin-orbit coupling strength, the cobalt atom on a honeycomb lattice offers a platform that can make accessible the study of novel magnetic ground states. Using temperature-dependent Raman spectroscopy and high-magnetic field Raman and infrared (IR) spectroscopy, we studied the lattice and spin-orbital excitations in CoTiO$_3$, an antiferromagnetic material that exhibits topologically protected magnon Dirac crossings in the Brillouin zone. Under the application of an external magnetic field up to 22 T along the crystal's $c$-axis, we observed the splitting of both the spin-orbital excitations and a phonon nearby in energy. Using density functional theory (DFT), we identify a number of new modes that below the antiferromagnetic (AFM) transition become Raman-active due to the zone-folding of the Brillouin zone caused by the doubling of the magnetic unit cell. We use a model that includes both the spin and orbital degrees of freedom of the Co$^{2+}$ ions to explain the spin-orbital excitation energies and their behavior in an applied field. Our experimental observations along with several deviations from the model behavior point to significant coupling between the spin-orbital and the lattice excitations.