标题： $β$-O$_{2}$中的巨各向异性磁致伸缩在 110 T 时 显示英文标题

标题： Giant and anisotropic magnetostriction in $β$-O$_{2}$ at 110 T

摘要： 磁致伸缩是在磁场作用下晶体的形变，通常在$10^{-6}$-$10^{-3}$范围内，其中晶格变化通过自旋-晶格耦合随着自旋和轨道状态的变化而发生。 在超过100 T的强磁场中，显著的塞曼能与晶格相互作用竞争，可以预期有较大的磁致伸缩。 然而，在100 T以上直接观察磁致伸缩具有挑战性，因为生成超过100 T的磁场会伴随单次脉冲$\mu$-秒的线圈破坏。 在这里，我们通过结合X射线自由电子激光（XFEL）的单次脉冲衍射和最先进的便携式100 T发生器，观察到了$\beta$-O$_{2}$自旋控制晶体在110 T下的巨大且各向异性的磁致伸缩，达到$\sim$1 %。 $\sim$1 % 的磁致伸缩是作为晶胞形变的最大类别。 这是软晶格$\beta$-O$_{2}$对起因于范德华力和交换相互作用竞争，以及在三角网络上自旋和晶格的软态与受挫的响应。 同时，各向异性来源于自旋系统的强二维性。 晶体中的巨磁致伸缩在超过100 T的磁场中应该会更加普遍和多样，而我们超过100 T的X射线自由电子激光实验为它们的探索开辟了一条新途径，为自旋在稳定晶体结构中的作用提供了基本见解。 显示英文摘要

摘要： Magnetostriction is a crystal's deformation under magnetic fields, usually in the range of $10^{-6}$ - $10^{-3}$, where the lattice change occurs with the change of spin and orbital state through spin-lattice couplings. In strong magnetic fields beyond 100 T, the significant Zeeman energy competes with the lattice interactions, where one can expect considerable magnetostriction. However, directly observing magnetostriction above 100 T is challenging, because generating magnetic fields beyond 100 T accompanies the destruction of the coil with a single-shot $\mu$-second pulse. Here, we observed the giant and anisotropic magnetostriction of $\sim$1 % at 110 T in the spin-controlled crystal of $\beta$-O$_{2}$, by combining the single-shot diffraction of x-ray free-electron laser (XFEL) and the state-of-the-art portable 100 T generator. The magnetostriction of $\sim$1 % is the largest class as a deformation of the unit cell. It is a response of the soft lattice of $\beta$-O$_{2}$ originating, not only in the competing van der Waals force and exchange interaction, but also the soft state of spin and lattice frustrated on the triangular network. Meanwhile, the anisotropy originates from the strong two-dimensionality of the spin system. Giant magnetostriction in crystals should become more ubiquitous and diverse beyond 100 T, where our XFEL experiment above 100 T opens a novel pathway for their exploration, providing fundamental insights into the roles of spin in stabilizing crystal structures.