Spin excitations of layered copper oxide show various characteristic features, depending on the carrier concentration. In this study, we conducted inelastic neutron scattering (INS) measurements on La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO), with $x$ = 0, 0.075, 0.18, and 0.30 and La$_{2-x}$Sr$_{x}$NiO$_4$ (LSNO) with 1/3, to clarify the origin of the intensity enhancement in the excitation spectrum of LSCO at the energy ($ω$) of 16--19 meV [Phys. Rev. B {\bf 91}, 224404 (2015), {\it ibid}. {\bf 93}, 094416 (2016)]. We confirmed the presence of a peak-structure in the $ω$-dependence of the local spin susceptibility $χ''(ω)$ of superconducting (SC) LSCO with a peak energy of 16--19 meV, where the spin excitations intersect optical phonon branches. A comparable peak-structure is not observed in the insulating La$_2$CuO$_4$, LSNO, and heavily overdoped LSCO with $x$ = 0.30. A dome-shaped $x$-dependence of the integrated intensity around the peak energies is revealed for SC phase by summarizing the present and previously reported results. Furthermore, our phonon calculation on LCO shows the existence of two optical branches at $\sim$19 meV that could stabilize stripe-alignment of carriers due to out-of-plane vibrations of Cu or O of the CuO$_2$ planes. These results indicate the interplay among spin, charge, and lattice dynamics and suggest that the intensity enhancement is associated with their composite excitations.
To elucidate the spin dynamics of La$_{2-x}$Sr$_x$CuO$_4$, which couples with the charge degree of freedom, the spin excitations spanning the characteristic energy ($E_{\rm cross}$ $\sim$35-40 meV) are investigated for underdoped $x$ = 0.10 and optimally doped (OP) $x$ = 0.16 through inelastic neutron scattering measurements. Analysis based on a two-component picture of high-quality data clarified the possible coexistence of uprightly standing incommensurate (IC) excitations with gapless commensurate (C) excitations in the energy-momentum space. The IC component weakens the intensity toward $E…
Electron correlations play a dominant role in the charge dynamics of the cuprates. We use resonant inelastic x-ray scattering (RIXS) to track the doping dependence of the collective charge excitations in electron doped La$_{2-x}$Ce$_{x}$CuO$_{4}$(LCCO). From the resonant energy dependence and the out-of-plane momentum dependence, the charge excitations are identified as three-dimensional (3D) plasmons, which reflect the nature of the electronic structure and Coulomb repulsion on both short and long length scales. With increasing electron doping, the plasmon excitations show monotonic hardening…
Comparison of charge modulations in La$_{1.875}$Ba$_{0.125}$CuO$_4$ and YBa$_2$Cu$_3$O$_{6.6}$
最近在（Y，Nd）Ba $_2$ Cu $_3$ O $_{6+x}$ [Ghiringhelli { \em et al.} Science 337，821（2013）]。在这里，我们报告铜$L_3$边缘软X射线散射研究比较晶格调制与电荷调制在YBa $_2$铜$_3$ O $_{6.6}$与众所周知的电荷和自旋条纹顺序在La $_{1.875}$ Ba $_{0.125}$ CuO $_4$。我们发现，在这两种情况下，CuO $_2$平面上的关联长度都是各向同性的，La $_{1.875}$ Ba $_{0.125}$ CuO $_4$的关联长度是$259 \pm 9$，YBa $_2$ Cu $_3$ O $_{6.6}$的关联长度是$55 \pm 15$.假设两种化合物中的电荷有序存在弱的面间关联，我们得出结论：La $_{1.875}$ Ba $_{0.125}$ CuO $_4$和YBa $_2$ Cu $_3$ O $_{6.6}$中的晶格调制的有序参数具有相同的数量级.
We report a Cu K- and L$_3$-edge resonant inelastic x-ray scattering study of charge and spin excitations of bulk Nd$_{2-x}$Ce$_x$CuO$_4$, with focus on post-growth annealing effects. For the parent compound Nd$_2$CuO$_4$ ($x = 0$), a clear charge-transfer gap is observed in the as-grown state, whereas the charge excitation spectra indicate that electrons are doped in the annealed state. This is consistent with the observation that annealed thin-film and polycrystalline samples of RE$_2$CuO$_4$ (RE = rare earth) can become metallic and superconducting at sufficiently high electron concentratio…
Cuprate superconductors still hold many open questions, in particular concerning their normal state properties, including the role of charge ordering. Nuclear magnetic resonance on $^{63,65}$Cu and $^{17}$O in the CuO$_2$ plane is a very sensitive bulk probe of charge variations, but not properly understood. Since early NMR, the oxygen satellite line splittings in YBa$_2$Cu$_3$O$_{6+y}$ were attributed to the orthorhombic distortion, while they could also be due to charge ordering. We employ high pressure NMR on YBa$_2$Cu$_3$O$_{6.9}$ hoping that charge order would respond to pressure differen…
Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured the dispersion and damping of spin excitations (magnons and paramagnons) in the high-$T_\mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+δ}$ (Bi2201), for a large doping range across the phase diagram ($0.03\lesssim p\lesssim0.21$). Selected measurements with full polarization analysis unambiguously demonstrate the spin-flip character of these excitations, even in the overdoped sample. We find that the undamped frequencies increase slightly with doping for all accessible momenta, while the damping grows rapi…
Anisotropic charge transfer mechanism in La$_{2-x}$Sr$_x$CuO$_4$ and Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+δ}$
La $_{2-x}$ Sr $_x$ CuO $_4$的拉曼光谱与Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$的拉曼光谱相似，不同之处在于条纹相处的分裂双磁振子峰和低能$B_{\rm 2g}$谱中较强的阶梯状衰减。双磁振子峰以下的受抑制$B_{\rm 1g}$谱区随载流子密度的增加而减小，而台阶状抑制的能量几乎不依赖于载流子密度。研究表明，电荷转移机制是各向异性的，它与沿最近邻Cu位的磁激发和沿对角线方向的声子激发相耦合。
Magnetic excitations and phonons simultaneously studied by resonant inelastic x-ray scattering in optimally doped Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+δ}$
用Cu $L_3$边缘共振非弹性X射线散射（RIXS）研究了最佳掺杂的高$T_\mathrm{c}$超导体Bi $_{1.5}$ Pb $_{0.55}$ Sr $_{1.6}$ La $_{0.4}$ CuO $_{6+δ}$（OP-Bi 2201，$T_\mathrm{c}\simeq 34$ K）在赝隙打开温度以下和以上的磁激发.在这两个温度下，宽光谱分布沿（1，0）方向分散到$\sim$ 350~meV的带边界处，类似于其他空穴掺杂的铜酸盐。然而，以上$\sim$ 0.22倒易晶格单位，我们观察到一个并发的强度降低磁激发和准弹性信号与弱温度依赖性。这种异常似乎表明在该化合物中磁性、晶格和电荷模式之间的耦合。我们还比较了在单层OP-Bi 2201和双层最佳掺杂Bi $_{1.5}$ Pb $_{0.6}$ Sr $_{1.54}$ CaCu $_2$ O $_{8+δ}$（OP-Bi 2212，$T_\mathrm{c}\simeq96$ K）的反节区边界附近的磁激发谱。强的相似性，在顺磁频散和它们的能量在区域边界表明，超交换相互作用和短程磁相关的强度不能直接相关的$T_\mathrm{c}$，甚至没有在同一个家庭的铜酸盐。
Charge-density-wave order takes over antiferromagnetism in Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6}$ superconductors
当自旋序被破坏时，铜氧化物中出现超导性，而电荷的作用则鲜为人知。最近，电荷密度波（CDW）被发现低于超导圆顶在YBa $_2$ Cu $_3$ O $_y$当施加一个高磁场垂直于CuO $_2$平面，这被认为是产生初始CDW的涡核，成为重叠。在这里，通过$^{63}$ Cu-核磁共振，我们报告了在单层Bi $_2$ Sr $_{2-x}$ La $_x$ CuO $_6$中，由不在平面中产生涡核的面内场诱导的CDW的发现。起始温度$T_{\rm CDW}$接管反铁磁有序温度$T_{\rm N}$，超过临界掺杂水平，超导性开始出现，并与伪能隙温度$T^{*}$成比例。这些结果提供了重要的见解自旋序，CDW和赝能隙之间的关系，以及它们与高温超导性的联系。
Comment on ''Phase Diagram of La$_{2-x}$Sr$_x$CuO$_4$ Probed in the Infrared: Imprints of Charge Stripe Excitations''
最近Lucarelli { \it et al.}已经报道了在宽掺杂范围内La $_{2-x}$ Sr $_x$ CuO $_4$的面内光学反射率的\cite{lucarelli}温度依赖性，集中在30 cm $^{-1}$（对于$x$ =0.12）、250 cm $^{-1}$和510 cm $^{-1}$处的红外峰。他们将第一个峰（30 cm $^{-1}$）解释为电荷条纹有序的特征，而后两个峰（250 cm $^{-1}$和510 cm $^{-1}$）归因于极化电荷激发。然而，细心的读者会注意到，报告的光谱与迄今为止在同一系统上测量的光谱有很大不同。正如我们下面所示，所有这些峰值都是由c轴反射率不受控制地泄漏到测量光谱中引起的。
We successfully isolated the $^{17}$O NMR signals at the planar sites in La$_{1.885}$Sr$_{0.115}$CuO$_4$ ($T_{c}=30$ K) by applying an external magnetic field along the Cu-O-Cu bond direction of a single crystal. We demonstrate that charge order enhances incommensurate Cu spin fluctuations below $T_{charge} \simeq 80$ K.
Quantum materials are amenable to non-equilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time domain spectroscopy to monitor the c-axis Josephson Plasma Resonance (JPR) in La$_{2-x}$Ba$_{x}$CuO$_{4}$ (x = 0.115) as a direct probe of superconductivity dy…
Anomalies in the ab-plane resistivity of strongly underdoped La_{2-x}Sr_{x}CuO_{4} single crystals: possible charge stripe ordering?
本文给出并讨论了小Sr含量（x=0.052-0.075）的La_{2-x} Sr_{x} CuO_{4}单晶的ab面电阻率的测量结果。通过使用AC Van der Pauw技术在4.2 K和300 K之间的温度范围内获得电阻率。当温度降低时，rho_{ab}（T）曲线显示出从线性行为到类似于双稳态行为的转变。与线性的偏离发生在掺杂依赖的温度T_{ch}。这种效应可以解释为由于预先存在的电荷条纹的渐进钉扎。在同样的框架下，超导样品的rho_{ab}（T）曲线在T_{c}正上方出现的异常尖峰，可以用从一个有序的近晶电子条纹相到一个更有序的近晶电子条纹相的转变来解释。
The discovery of a magnetic-field-induced charge-density-wave (CDW) order in the pseudogap state via nuclear magnetic resonance (NMR) studies has highlighted the importance of "charge" in the physics of high transition-temperature ($T_{\rm c}$) superconductivity in copper oxides (cuprates). Herein, after briefly reviewing the progress achieved in the last few years, we report new results of $^{63,65}$Cu-NMR measurements on the CDW order and its fluctuation in the single-layered cuprate Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$. The NMR spectrum under both in- and out-of-plane magnetic fields above $ H…
Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+δ}$. We investigate the interplay between charge order and EPC as a function of doping and temperature, and find that the EPC is enhanced in a na…
We report $^{139}$La and $^{63}$Cu NMR investigation of the successive charge order, spin order, and superconducting transitions in super-oxygenated La$_2$CuO$_{4+y}$ single crystal with stage-4 excess oxygen order at $T_{stage}\simeq 290$ K. We show that the stage-4 order induces tilting of CuO$_6$ octahedra below $T_{stage}$, which in turn causes $^{139}$La NMR line broadening. The structural distortion continues to develop far below $T_{stage}$, and completes at $T_{charge}\simeq 60$ K, where charge order sets in. This sequence is reminiscent of the the charge order transition in Nd co-dope…
We report the inverse Laplace transform (ILT) analysis of the $^{139}$La nuclear spin-lattice relaxation rate $1/T_1$ in charge ordered La$_{1.885}$Sr$_{0.115}$CuO$_4$ ($T_{charge} \sim 80$K, $T_{c} \simeq T_{spin}^{neutron}=30$K), and shed new light on its magnetic inhomogeneity. We deduce the probability density function $P(1/T_{1})$ of the distributed $1/T_1$ (i.e. the histogram of distributed $1/T_1$) by taking the inverse Laplace transform of the experimentally observed nuclear magnetization recovery curve $M(t)$. We demonstrate that spin freezing sets in in some domains precisely below t…
Using resonant X-ray diffraction and Raman spectroscopy, we study charge correlations and lattice dynamics in two model cuprates, HgBa$_{2}$CuO$_{4+δ}$ and HgBa$_{2}$CaCu$_{2}$O$_{6+δ}$. We observe a maximum of the characteristic charge order temperature around the same hole concentration ($p \approx 0.09$) in both compounds, and concomitant pronounced anomalies in the lattice dynamics that involve the motion of atoms in and/or adjacent to the CuO$_2$ layers. These anomalies are already present at room temperature, and therefore precede the formation of the static charge correlations, and we a…
We use resonant inelastic x-ray scattering to investigate charge-stripe correlations in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$. By differentiating elastic from inelastic scattering, it is demonstrated that charge-stripe correlations precede both the structural low-temperature tetragonal phase and the transport-defined pseudogap onset. The scattering peak amplitude from charge stripes decays approximately as $T^{-2}$ towards our detection limit. The in-plane integrated intensity, however, remains roughly temperature independent. Therefore, although the incommensurability shows a remarkably l…
Stripe motion in CuO{2} planes of Y{1-x}Pr{x}Ba{2}Cu{3}O{7} as seen from the Cu(2) NQR
Pulsed NQR at the frequencies of 28-33 MHz has been used to study copper NQR spectra in YBa{2}Cu{3}O{7}, TmBa{2}Cu{3}O{7} and Y{0.9}Pr{0.1}Ba{2}Cu{3}O{7} compounds at temperatures of 4.2-200K. Quantitative analysis of the spectra has shown that the "plane" Cu(2) spectra shape is well described by using a model of 1D correlations of charge and spin distribution in CuO{2} planes (stripe correlations). In the undoped superconductors the charge-spin stripe structure moves fast in the CuO{2} planes, but doping the YBa{2}Cu{3}O{7} lattice with praseodymium slows this motion down.
