1.Terahertz Technology Innovation Research Institute, Shanghai Key Lab of Modern Optical System, and Engineering Research Center of Optical Instrument and System (Ministry of Education), Terahertz Spectrum and Imaging Cooperative Innovation Center, University of Shanghai for Science and Technology, Shanghai 200093, China 2.Department of Physics, Shanghai University, Shanghai 200444, China 3.STU & SIOM Joint Laboratory for Superintense Lasers and the Applications, Shanghai 201210, China 4.Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 200092, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61975110, 11674213, 61735010, 11604202), the 111 Project (Grant No. D18014), the International Joint Lab Program of the Science and Technology Commission Shanghai Municipality, China (Grant No. 17590750300), the Key Project of the Science and Technology Commission Shanghai Municipality, China (Grant No. YDZX20193100004960), the Shanghai Rising-Star Program of the Science and Technology Commission of Shanghai Municipality, China (Grant No. 18QA1401700), the Chenguang Project of Shanghai Educational Development Foundation, China (Grant No. 16CG45), and the Young Eastern Scholar Project of Shanghai Municipal Education Commission, China (Grant No. QD2015020)
Received Date:15 May 2020
Accepted Date:13 June 2020
Available Online:12 October 2020
Published Online:20 October 2020
Abstract:Terahertz (THz) transient has become an effective method to study the optical and electronic spin characteristics of the rare earth orthoferrites RFeO3. High-throughput grown crystal sample is sliced at different locations, then the continuously tunable rare earth elements co-doped single crystal SmxPr1–xFeO3 is studied with antiferromagnetic spin mode (qAFM) and crystal field transitions of rare earth ions under zero magnetic fields. Using THz time-domain spectroscopy, the qAFM resonance frequencies of Sm0.2Pr0.8FeO3 and Sm0.4Pr0.6FeO3 single crystals are located on the connection line of the qAFM frequencies of PrFeO3 (0.57 THz) and SmFeO3 (0.42 THz), therefore the frequency of qAFM increases linearly with doping concentration of Sm3+ ion increasing. The Sm0.4Pr0.6FeO3 crystal undergoes a temperature-induced spin reorientation phase transition at about 160 K. When the crystal temperature is lower than 80 K, a wide band absorption peak of about 0.5 THz appears in the absorption spectrum of Sm0.2Pr0.8FeO3 due to the crystal field effect. Our results show that THz spectral data not only allow us to monitor the quality of rare earth orthoferrite crystals prepared by high throughput and analyze the rare earth elements of the sample, but also improve the ability to analyze the physical properties of the co-doped RFeO3. Keywords:terahertz time domain spectroscopy/ antiferromagnet/ rare earth orthoferrites/ spin resonance
图2(a)为透射式太赫兹时域光谱(THz-TDS)示意图, 使用的激光脉冲来自于锁模钛宝石激光器(Mai Tai HP-1020, Spectra-Physics). 脉冲持续时间为100 fs, 中心波长800 nm, 重复频率为80 MHz的飞秒激光脉冲用于产生和探测THz脉冲. 其中, THz辐射源和探测器都为偶极型低温生长的GaAs光电导天线. THz辐射为垂直于光电导天线方向的线偏振脉冲, 有效频率范围约为0.1—2.0 THz. THz波垂直入射到样品, 样品置于液氦低温恒温器(温度范围为40—300 K)中, 在测量过程中样品未施加任何静磁场. 在THz-TDS实验装置内冲入氮气以减少空气中水汽对THz传播光束的影响, 实验环境湿度约为8%. 实验中, 样品的晶轴a, b, c与实验室笛卡尔坐标系x, y, z相对应, THz脉冲的波矢量沿b轴传播. 图 2 (a) THz-TDS实验装置示意图; (b) b切Sm0.2Pr0.8FeO3单晶(红色); (c) Sm0.4Pr0.6FeO3单晶(蓝色) 300 K时的太赫兹时域透射谱, 此时HTHz//c; 插图分别表示振荡部分(40—60 ps)的傅里叶变换光谱及其洛伦兹拟合(虚线) Figure2. (a) Experimental setup diagram of THz-TDS. The THz time-domain waveforms transmitted through the b-cut (b) Sm0.2Pr0.8FeO3 and (c) Sm0.4Pr0.6FeO3 crystal at 300 K and the insets indicate the spectrum of oscillating parts obtained by Fourier transform of the waveform, which is fitted with a Lorentzian contour (dotted line).
3.实验结果与分析首先测量了室温下THz波透过b切Sm0.2Pr0.8FeO3单晶和Sm0.4Pr0.6FeO3单晶后的THz时域波形图, 如图2(b),(c)所示. THz时域波形由两个部分组成, THz波的主脉冲和指数衰减的振荡部分. THz波的主脉冲信号在时域谱上的位置不同主要是由于样品的厚度不同造成的. 已有的研究表明振荡部分为磁共振模式的自由感应衰减(free induction decay, FID)信号, 其振幅正比于THz波段内磁偶极跃迁的强度. 图2(b),(c)的插图为振荡部分对应的频谱, 共振峰分别出现在0.45和0.48 THz. 实验中, 入射THz脉冲的磁场分量HTHz与样品的宏观磁化强度M (c轴)平行. 因此, 这两个共振峰分别对应激发了高通量制备的Sm0.2Pr0.8FeO3和Sm0.4Pr0.6FeO3单晶的qAFM(La, Lb和Mc振荡)模式, 如图3插图所示. 实验结果表明, 随着Sm3+离子比例的增大, 高通量制备的SmxPr1–xFeO3单晶的qAFM共振频率增大. 这与先前用常规光学浮区法制备的SmDyFeO3单晶的实验结果一致[36]. 图 3 室温下SmxPr1–xFeO3单晶的qAFM自旋共振频率与Sm3+离子含量的关系, 其中插图表示qAFM模式的振动 Figure3. Summarized frequencies of the qAFM resonances at several Sm3+ ion contents at room temperature and the insets indicate the vibration of the qAFM.
如图3所示, 实验测得的Sm0.2Pr0.8FeO3和Sm0.4Pr0.6FeO3单晶的qAFM共振频率位于PrFeO3(0.57 THz)和SmFeO3(0.42 THz)qAFM共振频率的连线上. 表明SmxPr1–xFeO3单晶的qAFM自旋共振频率依赖于Sm3+/Pr3+离子的掺杂比例. 简化的两能级量子跃迁模型可用来描述RFeO3中自旋共振的吸收与辐射. 由于强交换场诱导的精细结构, 产生了基态和激发态[37]. 基态与激发态之间的能级差(?ω)和SmxPr1–xFeO3单晶中的Sm3+离子组分(x)之间的关联性, 可以表示为一个单调连续函数, $\hbar \omega _{{\rm{qAFM}}}^{{\rm{S}}{{\rm{m}}_x}{\rm{P}}{{\rm{r}}_{{{1 - }}x}}{\rm{Fe}}{{\rm{O}}_{\rm{3}}}} \!=\! x\hbar \omega _{{\rm{qAFM}}}^{{\rm{SmFe}}{{\rm{O}}_{\rm{3}}}} \!+\! \left( {1 \!-\! x} \right)\hbar \omega _{{\rm{qAFM}}}^{{\rm{PrFe}}{{\rm{O}}_{\rm{3}}}}$. 可以通过已知Sm3+离子组分得到qAFM自旋共振频率. 反之, 可以根据掺杂比例未知的SmxPr1–xFeO3单晶qAFM的共振频率估算该样品中Sm3+离子的组分. 相比于扫描电子显微镜结合X射线能量色散光谱共同分析样品的组分, THz时域光谱将有效提高样品组分的原位检测与分析效率. THz-TDS不仅能够探测共振频率, 而且可以通过FID信号的振幅和频率随温度的依赖关系探测RFeO3中磁矢量的动态变化[38,39]. 温度诱导RFeO3的SRT主要来源于温度依赖的R3+-Fe3+(4f-3d电子)相互作用产生的磁晶各向异性. 探测原理基于M和HTHz之间角度的变化. 图4为b切Sm0.4Pr0.6FeO3单晶qAFM共振频率及其振幅(AqAFM)随温度的变化关系. 实验结果表明, qAFM共振频率随着温度的降低而降低, 从300 K的0.48 THz下降到160 K的0.4 THz. 同时, AqAFM随着温度的降低而减小. 如图4中插图所示, 室温下RFeO3中的Fe3+子晶格处于Г4磁性构型(M沿着c轴, L沿着a轴). 当温度低于160 K, 高温相Г4经过中间相Г24变化到低温相Г2 (L沿着c轴, M沿着a轴)发生自旋重取向转变(宏观磁化矢量M旋转90°). 由于HTHz在M上的投影分量减小, 因此无法观测到qAFM自旋共振. 在本实验中, 并没有在低温下观察到准铁磁(qFM)模式. SRT过程中, 利用电子轨道态和自旋态之间的强耦合, 圆偏振的飞秒激光等非外加磁场实验手段实现磁化取向的调控[4,40]. 图 4b切Sm0.4Pr0.6FeO3单晶qAFM模式的共振频率和振幅随温度的关系; 插图表示Fe3+离子亚晶格的磁结构: 低温相(Г2 )、中间相(Г4 )、高温相(Г24 ) Figure4. The frequencies and amplitudes of the qAFM resonances of b-cut Sm0.4 Pr0.6FeO3 crystal. Inset shows the magnetic structure of RFeO3 in the low-temperature(Г2 ), intermediate(Г4 ), and high temperature(Г24 )phases.
除了研究RFeO3中的Fe3+离子系统, THz光谱技术也可以应用于R3+离子在晶体场中的能级劈裂所导致的磁偶极和电偶极跃迁研究[41]. 图5(a)给出不同温度下THz波透过Sm0.2Pr0.8FeO3单晶(样品信号, Esample)和室温下未经过样品直接在空气中传播(参考信号, Ereference)的时域信号. 相比于300 K的THz透射时域波形, 40 K的THz时域波形不仅振幅发生变化, 且随着温度降低可以发现THz脉冲出现相移. 对时域信号进行傅里叶变换, 利用透射的THz振幅谱和相位谱, 获得了Sm0.2Pr0.8FeO3单晶不同温度下的折射率(图5(b))和吸收系数(图5(c)). 室温下, Sm0.2Pr0.8FeO3单晶在0.3—1.3 THz波段内平均折射率为5.06 ± 0.03, 小于PrFeO3的5.46. 实验发现, SmPrFeO3晶体的平均折射率随着Sm3+离子组分的增大而降低. 如图5(c)所示, 当样品温度低于80 K, 吸收光谱上0.5 THz左右出现一个宽带吸收峰. 当温度为 40 K时, 光谱中的宽带吸收现象更为明显, 此时THz脉冲的磁场分量平行于样品的a轴. 参考之前的研究结果, 在ErFeO3[11], TmFeO3[28]和PrFeO3[36]等晶体中发现此类宽带吸收峰来自于稀土离子的晶体场效应. 可以理解为稀土离子和其周围的点电荷分布存在静电相互作用, 晶体场效应打开了磁量子数m的能量简并, 晶体场的劈裂能级间跃迁的重叠导致了宽带吸收现象[28,36]. Pr3+离子的光谱符号为3H4, 自旋量子数S为1, 轨道量子数为3, 总角动量量子数J为4. 由于总角动量量子数是整数, Pr3+离子为非Kramers离子. 图5(c)的插图为3H4的基态多重态能级图, Pr3+离子在Sm0.2Pr0.8FeO3单晶的低对称性晶体场中分裂成了一系列单重态. 因此, 可以将0.5 THz附近的吸收峰归因于两个最低单重态E1和E2之间的电子跃迁. 值得注意的是, 随着Pr3+离子浓度的降低, Sm0.4Pr0.6FeO3单晶就没有发现由晶体场劈裂引起的Pr3+离子基态跃迁现象. 图 5 (a) Sm0.2Pr0.8FeO3单晶温度依赖的太赫兹时域谱, 为了表达更为清楚, 不同温度的时域光谱在纵轴方向做了等间距的平移; 40, 80和300 K时Sm0.2Pr0.8FeO3单晶的(b)折射率和(c)吸收系数, 插图为Pr3+离子基态在晶体场中能级劈裂示意图 Figure5. (a) The temperature dependent THz waveforms transmitted through the Sm0.2Pr0.8FeO3 single crystal; (b) refractive indices and (c) absorption spectra of Sm0.2Pr0.8FeO3 at 40, 80, and 300 K. The inset in (c) shows the energy level splitting of Pr3+ ion in the ground state crystal field.