标题： 钬硼4中的自发晶格畸变和晶体场效应 显示英文标题

标题： Spontaneous lattice distortion and crystal field effects in HoB4

摘要： 四硼化钬HoB4结晶成四方结构（空间群P4/mbm），其中Ho原子构成Shastry-Sutherland晶格。它在TN1 = 7.1 K时反铁磁有序，并在TN2 = 5.7 K时发生进一步的磁性转变。复杂的磁性结构归因于磁性和四极矩起源的竞争序参数以及显著的磁弹性耦合。在这里，我们通过低温粉末X射线衍射和超声波速度测量研究了HoB4晶格在反铁磁相变中的响应，并得到晶体电场（CEF）计算的支持。在TN2以下，HoB4的晶体结构变为单斜结构（空间群P21/b），这是四极矩有序的宏观表现。在300至3.5 K之间，总畸变振幅为0.46~\AA ，相对体积变化为$3.5 \times 10^{-3}$。这种结构相变与在TN2附近由于铁四极矩有序而观察到的模量$C_{44}$的巨大软化相容。在TN1以下立即出现的晶格不稳定性在X射线和超声波数据中一致地被观察到。CEF分析表明，该系统中Ho$^{3+}$离子具有准简并基态。 显示英文摘要

摘要： The tetraboride HoB4 crystallizes in a tetragonal structure (space group P4/mbm), with the Ho atoms realizing a Shastry-Sutherland lattice. It orders antiferromagnetically at TN1 = 7.1 K and undergoes further magnetic transition at TN2 = 5.7 K. The complex magnetic structures are attributed to competing order parameters of magnetic and quadrupolar origin with significant magnetoelastic coupling. Here, we investigate the response of the lattice of HoB4 across the antiferromagnetic phase transitions by using low-temperature powder x-ray diffraction and ultrasound-velocity measurements, supported by crystal electric field (CEF) calculations. Below TN2, the crystal structure of HoB4 changes to monoclinic (space group P21/b) as a macroscopic manifestation of the quadrupolar ordering. Between 300 and 3.5 K, the total distortion amplitude is 0.46~\AA\ and the relative volume change is $3.5 \times 10^{-3}$. This structural phase transition is compatible with the huge softening of the modulus $C_{44}$ observed around TN2 due to ferroquadrupolar order. A lattice instability developing immediately below TN1 is seen consistently in x-ray and ultrasound data. CEF analysis suggests a quasi-degenerated ground state for the Ho$^{3+}$ ions in this system.