1.Anhui Key Laboratory of Information Function Materials Structure and Devices, Fuyang Normal University, Fuyang 236037, China 2.Key Laboratory of Materials Physics, Institute of Solid State Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China 3.Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11774354, 51727806) and the Fuyang Key Emergency Science and Technology Project, China (Grant No. FK20202829)
Received Date:09 September 2020
Accepted Date:16 September 2020
Available Online:13 October 2020
Published Online:20 October 2020
Abstract:As a typical helimagnet, ZnCr2Se4 possesses fascinating effects including magnetoelectric coupling, magnetostriction, negative thermal expansion, as well as possible diversity in quantum ground states. Here in this work, we investigate magnetic excitation arising from spiral spin structure in ZnCr2Se4 single crystal by using terahertz (THz) time domain spectroscopy (THz-TDS) under magnetic fields up to 10 T and at low temperatures. The magnetic resonance absorption is observed in a sub-THz region as the applied magnetic field is above 4 T, featuring the blue shift with magnetic field increasing. As the THz wave vector ( k ) is vertical to the external magnetic field (H), the single resonance frequency conforms well with the linear Larmor relation, corresponding to a spin structure transformation from helical to ferromagnetic state with magnetic field increasing in ZnCr2Se4. However, in the geometry in which both k and H are along the $ \langle 111\rangle $ direction of crystal, a well-defined resonance splitting emerges when H > 7 T. Especially, the high-frequency absorption shows pronouncedly nonlinear magnetic field dependence. It is suggested that such anisotropic spin dynamics below Néel temperature be linked with the field-driven quantum criticality unveiled in recent work. Keywords:ZnCr2Se4/ spin dynamics/ high magnetic field/ terahertz
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--> --> --> 1.引 言以ACr2X4形式为代表的铬基尖晶石结构化合物是一类典型的强关联电子体系材料, 其中Cr3+阳离子具有自旋3/2的3d3构型, 随着非磁性离子A和X类型的变化, Cr3+磁性离子间距会有所不同, 进而调控Cr-Cr离子交换相互作用强度和模式, 形成丰富的自旋排列方式. 该体系材料具有很强的阻挫效应, 在一定温度和磁场条件下可形成自旋冰[1]、自旋-轨道液体[2]和量子临界等复杂基态[3]. 其中ZnCr2Se4化合物是该体系的代表性材料. 近二十年来, 随着在ZnCr2Se4材料中不断发现磁电耦合、负膨胀、磁致伸缩等效应及可能浮现的自旋液晶等复杂量子基态, 该材料重新受到广泛关注. 在ZnCr2Se4中, 磁性Cr3+离子位于八面体B格点, 形成四面体构型(图1(a)). Cr3+离子在八面体晶体场作用下, 其d电子态劈裂成更低的t2g三重简并态, 呈现出球形电荷分布, 自旋-轨道耦合很弱. ZnCr2Se4磁结构主要由超交换相互作用主导, 表征铁磁(ferromagnetism, FM)序的居里-外斯温度为90 K, 反铁磁(antiferromagnetism, AFM)序的奈尔温度为21 K. 铁磁相互作用由90o Cr-Se-Cr交换相互作用控制, 更远相邻的Cr-Se-Zn-Se-Cr或Cr-Se-Se-Cr交换相互作用主导反铁磁相互作用. 在奈尔温度以下, 由于自旋驱动的Young-Tyler效应, ZnCrSe4会发生自旋-声子耦合[4], 产生一定的晶格畸变, 由立方相转变为四角相[5]或正交相[6], 进而诱导负膨胀、磁致伸缩等效应. 相应地, 其自旋结构呈现出沿[001]方向传播的非公度的平面螺旋结构, 在[001]面内自旋以铁磁耦合方式排列, 相邻面排列相对角度为42o[7]. 如图1(b)所示, 在外磁场作用下, 其平面螺旋磁结构可以演化为线性铁磁态. 图 1 (a) ZnCr2Se4晶体结构; (b) 外磁场下ZnCr2Se4磁结构演化; (c) 外磁场下太赫兹透射测量配置示意图, 太赫兹波矢(k)平行于外磁场(H)方向; (d) k垂直于H配置, 对于两种测量配置, 太赫兹电场分量始终保持p型偏振, 从而确保太赫兹磁场分量和应用的稳态外部磁场保持正交 Figure1. (a) ZnCr2Se4 crystal structure; (b) the evolution of magnetic structure of ZnCr2Se4 under external magnetic field; (c) configuration of THz transmission measurements under external magnetic field, the THz wave vector (k) is parallel with external magnetic field (H); (d) the k is vertical with H. In both cases, the THz electric field (ETHz) is set as p polarization, and therefore the magnetic field component of THz waveform (HTHz) is perpendicular with steady external magnetic field.
3.结果与讨论图2(a)为低温4 K条件下, 在不同外磁场强度下测量的ZnCr2Se4样品太赫兹透射时域波形, 其中测量配置为k∥H. 红色曲线代表不经过样品的参考太赫兹波形, 为了直观比较, 其尺度缩小了1/5. 随磁场强度增大, 透射太赫兹波幅度减小, 更高磁场下在16—30 ps区间出现微弱振荡, 暗含着共振吸收动力学行为. 进一步对不同磁场下的透射太赫兹波形进行傅里叶变化, 其相应的太赫兹频谱如图2(b)所示. 相对于0磁场, 5 T以上磁场可以看出其太赫兹频谱包含着低频吸收谷, 特别是8 T以上磁场, 其频谱发生明显劈裂. 图 2 (a) k∥H配置下, 不同外磁场下透过ZnCr2Se4单晶样品的THz时域波形图, 红色为不加样品时的时域信号, 幅度缩小5倍; (b) 这些时域波形图对应的快速傅里叶变换(FFT), 虚线为表征吸收位置变化的引导线 Figure2. (a) In the configuration of k//H, THz waveforms transmitted through ZnCr2Se4 single crystal measured under different magnetic fields at 4 K temperature. The red trace with the 0.2 scale factor is the reference waveform trough empty sample holder; (b) corresponding FFT amplitude spectra in frequency domain. The y axis is logarithmic scale. The dotted lines are guides for the eye.
为进一步证明该共振吸收是磁场诱导的. 我们以零磁场下透过的太赫兹波形的傅里叶变换$ {\tilde{E}}_{0}(\omega )$为参考信号, 进而提取出低温(T = 4 K)不同磁场下相对透射率, 即${\tilde{t}}_{H}(\omega )=\dfrac{{\tilde{E}}_{H}(\omega )}{{\tilde{E}}_{0}(\omega )}$. 图3为这种相对零磁场下的归一化太赫兹透射幅度$ \left|{\tilde{t}}_{H}(\omega )\right|$. 如图3(a)所示, 在k∥H配置情况下, 当外磁场高于4 T时候, 在0.18 THz附近开始出现共振吸收, 并随磁场增加呈现出明显蓝移. 特别是, 当磁场高于7 T时, 可以观察到两个吸收边, 低能和高能吸收谷都随磁场增大向高能端移动, 但其能量间隔随磁场增大. 作为对比, 我们也在k⊥H配置下测量了太赫兹透射谱. 可以看出, 尽管其共振峰随磁场增强朝高能方向移动, 但在整个应用的外磁场区间, 太赫兹吸收始终保持单一共振峰. 这种相对零磁场的透射频谱变化, 并结合蓝移效应, 可以确定共振吸收来源于外磁场驱动的磁子激发. 图 3 相对零磁场归一化的太赫兹透射谱 (a) 太赫兹波矢平行磁场配置; (b) 太赫兹波矢垂直磁场配置. 测量温度为4 K Figure3. Normalized THz transmission spectra with respect to the spectrum without the application of external magnetic field: (a) THz wave vector is parallel with the external magnetic field; (b) THz wave vector is vertical with the external magnetic field. The measurement temperature is 4 K.
接下来, 磁共振频率和外磁场的关系示于图5中, 其主要磁场行为可归纳如下: 1) 在k⊥H配置下, 其共振频率和磁场依赖关系和我们早期工作一致[18], 该磁共振行为的典型特征是在高磁场下符合拉莫尔进度关系, 并如图5(a)所示, 可线性外推至原点. 这种磁共振行为可以通过铁磁共振获得较好的解释. 随着外加磁场增强, ZnCr2Se4 中螺旋自旋结构会被抑制, 最终演化为线性铁磁结构, 其磁共振落入太赫兹频段; 2) 在k∥H配置下, 同等磁场强度, 其共振能量明显高于垂直磁场配置测量值, 并且其磁场行为具有非线性特征. 在7 T以上磁场, 开始出现低频吸收, 其共振频率低于垂直磁场配置; 3) 在k∥H配置测量下, 4和20 K共振吸收能量几乎相等. 对于高于奈尔温度的高温区域, 不再出现低频共振吸收, 而共振吸收频率接近同等磁场下4 K的测量结果, 但其磁场关系接近线性, 并且可线性外推至原点. 图 5 不同温度下共振频率随磁场的变化示意图 (a) 代表4 K温度下k∥H和k⊥H两种配置下测量结果, 红色实线表示根据关系式 $ \hslash \omega =g{\mu }_{\rm{B}}H$, 对k⊥H配置测量数据的线性拟合, 灰色虚线代表对k∥H配置下的共振频率的线性外推; (b) k∥H配置下, 20, 45和60 K不同温度的测量结果, 红色实线代表根据关系式$ \hslash \omega =g{\mu }_{\rm{B}}H$, 对T = 45 K数据的拟合 Figure5. The frequencies at the maxima of the absorption spectra as a function of applied magnetic field at tempera-tures of 4 K (a), and 20, 45 and 60 K (b). In Fig.5 (a), the red solid line represents the fitting according to the equation $ \hslash \omega =g{\mu }_{\rm{B}}H$. The grey dash line denotes the linear extrapolation for the low-frequency absorption. In Fig. 5 (b), the red solid line is obtained from the fitting to the data taken at T = 45 K using the equation, $ \hslash \omega =g{\mu }_{\rm{B}}H$.