Dynamical stripe structure in La2−xSrxCuO4 observed by Raman scattering

The dynamical stripe structure relating to the ”1/8 problem” was investigated in La2−xSrxCuO4 utilizing the high frequency response of Raman scattering. The split of the two-magnon peak due to the formation of the stripe structure was observed at whole Sr concentration region from x = 0.035 to 0.25 at low temperatures. Especially clear split was observed at low carrier concentration region x = 0.035 − 0.06 and at x ∼ 1/8. The onset temperatures of these stripe structures are as high as 300 − 350 K, which are much higher than the temperatures measured by slow response probes. PACS numbers: 74.72.Dn, 75.30.Ds, 75.60.Ch, 78.30.-j Typeset using REVTEX 1 The large exchange interaction energy (J) in high temperature superconductors contributes to raise the transition temperature (Tc). However the large J may induce instability for the uniform charge density to separate into spin and charge domains [1–4]. Tranquada et al. [5,6] obtained the experimental evidence from the neutron scattering in La1.48Nd0.4Sr0.12CuO4 (LNSCO) that the antiferromagnetically ordered spin stripes are separated by the periodically spacing charge domain walls. The Tc is suppressed in La2−xBaxCuO4 (LBCO) and La2−x−yNdySrxCuO4 (LNSCO) at x = 1/8 [7–10]. The suppression of Tc is related to the structural phase transition to the low temperature tetragonal phase (LTT, P42/ncm) below 65 K [11,12]. In La2−xSrxCuO4 (LSCO) the decrease of Tc at x = 1/8 is only a few degree and the static LTT phase is not observed at least down to 4.2 K, but the local LTT component increases at low temperatures [8,13–15]. The magnetic order has been observed below 32 K at x = 0.115 by nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) [16,17]. The onset temperature of the wipeout effects for Cu NQR decreases monotonically from 90 K at x = 0.07 to 50 K at x = 0.115 [18]. The spatially modulated dynamical spin correlation has been observed at x = 0.05 − 0.25 as incommensurate magnetic peaks by neutron scattering [19–24]. The direction of the stripe changes from the diagonal direction on the CuO2 lattice in the spin glass composition (x = 0.02− 0.05) to the vertical direction in the superconducting composition (x ≥ 0.055). The inter-domain wall distance increases as l = a/2x at x < 1 8 and becomes constant above it, where a is the Cu-Cu atomic distance. The domain walls are half-occupied by holes at x < 1 8 . Above it excess holes enter charge domain walls and/or spin stripes. The static stripes cause the localization of carriers and suppress the superconductivity, so that the dynamical fluctuation is essential to induce the metallic conductivity and the superconductivity. However, it causes the difficulty for the investigation of stripes, because the fluctuating frequency is too high for many experimental probes. Raman scattering has advantageous for the direct observation of high energy magnetic excitations up to near 1 eV. Till now intensive Raman scattering studies have been reported in LSCO [25–34], but 2 the evidence of the stripe structure has not been observed. In the present Raman scattering experiments, the special attention was paid to the sample quality. The single crystals were synthesized by the TSFZ method utilizing an infrared radiation furnace with four elliptic mirrors (Crystal system, FZ-T-4000). This method does not use a crucible, so that the crystal is free from the contamination. The crystal of x = 0 was annealed in 1 mmHg oxygen gas at 900◦C for 12 hours. The Néel temperature (TN) measured by SQUID magnetometer is 293 K. The crystals of x = 0.2 and 0.25 were annealed in oxygen gas under ambient pressure at 600◦C for 7 days. The TC was determined by the middle point of the transition in the electric resistivity. The narrow temperature widths of the superconducting transition region (2.5 K at x = 0.115 and 1.5 K at x = 0.15) certify the good quality of the crystals. The details will be presented elsewhere [35]. Raman spectra were measured on fresh cleaved surfaces in a quasi-back scattering configuration utilizing a triple monochromator (JASCO, NR-1810), a liquid nitrogen cooled CCD detector (Princeton, 1100PB), and a 5145 Å Ar-ion laser (Spectra Physics, stabilite 2017). The cleavage was done in air and the sample was set in a cryostat within ten minutes. The cleaved surface presents intrinsic Raman spectra which are different from the surface prepared by polishing or chemical etching [35]. The laser beam of 10 mW was focused on the area of 50 μm×500 μm. The increase of temperature by the laser beam irradiation was less than 2 K at 5 K. The same spectra were measured four times to remove the cosmic ray noise by comparing the intensities at each channel. The wide energy spectra covering 12− 7000 cm was obtained by connecting 17 spectra with narrow energy ranges after correcting the spectroscopic efficiency of the optical system. The same spot on the surface was measured during the temperature variation by correcting the sample position which was monitored by a TV camera inside the spectrometer. The two-magnon scattering is active in the B1g symmetry and inactive in B2g, if the simple two-magnon scattering model is applied to the two-dimensional antiferromagnetic (AF) square lattice. The B1g spectrum is obtained in the (xy) polarization configuration in which the incident light polarization is parallel to x = [110] and the scattered light 3 polarization is parallel to y = [11̄0]. The B2g spectrum is obtained in the (ab) configuration in which the polarizations are parallel to the Cu-O bonds, a = [100] and b = [010]. Figure 1 shows the temperature dependence of the B1g and B2g Raman spectra. In the undoped AF insulating La2CuO4 (LCO), the sharp peaks below 700 cm −1 are due to onephonon scattering, the peaks from 850 to 1450 cm the resonant two-phonon scattering, and the peaks from 1700 to 3000 cm the four-phonon scattering. The peak at 3213 cm in the B1g spectrum at 5 K is the two-magnon scattering peak. When carriers are doped, the two-magnon peak changes drastically. At x = 0.035, 0.05, 0.06, and 0.115, the two-magnon peaks split into double peaks at low temperatures. As temperature increases, these split two-magnon peaks decrease in intensity and the typical single two-magnon peaks in the coupled charge-spin state appear. That is, the scattering intensity rises from energy zero to the energy corresponding to the temperature, and then increases gradually to the twomagnon peak energy, and finally decreases toward over 7000 cm. These high temperature spectra are similar to the spectra in Bi2Sr2Ca1−xYxCu2O8+δ [36]. The B2g two-magnon peak is observed at 4128 cm −1 and 300 K in LCO, which is about 4/3 times the B1g two-magnon peak energy, 3116 cm −1 at 300 K. It seems that the magnonmagnon interaction does not work in the B2g two-magnon scattering. The B2g spectra are different from the B1g spectra, when the stripe structure disappears at high temperatures. Both spectra becomes similar at low temperatures at x = 0.05, 0.06, and 0.115. It indicates that the symmetry is relaxed in the stripe structure. The split two-magnon peaks have fine structure. For example at x = 0.06, the low energy peak is composed of two peaks at 1672 cm and 2000 cm and the high energy peak at 2745 cm and 3125 cm. It is supposed that these fine structure is induced by the interactions between magnons at the nearest neighbor magnetic stripes across the charge domain wall, because the spin directions are reversed across the charge wall and both magnetic stripes give the periodic unit. These fine structure will be presented separately. In the following the discussions are limited to the double peak structure. Figure 2 shows the split two-magnon peak energies at 5 K and the single two-magnon peak energies at 300 K 4 as a function of x. The energies of the clearly split two-magnon peaks at x = 0.035, 0.05, 0.06, and 0.115 are shown by large circles. The intensity of the higher energy peak is much weaker than the lower energy peak at x = 0.1 and x ≥ 0.15. The higher energy peak keeps the energy almost constant, 3050− 3350 cm, from x = 0 to 0.25, while the lower energy peak decreases in energy above x = 0.15. At x = 0.25 a small peak is observed at 1820 cm. At 300 K where the stripe structure almost disappears, the two-magnon peak energy decreases monotonically from x = 0 to 0.25. The origin of the split two-magnon peaks at about 3050 cm and 1900 cm can be explained as follows. The two-magnon Raman scattering in the S = 1/2 antiferromagnet is caused by the exchange of nearest neighbor spins. Figure 3 shows the case that (a) the spin exchange occurs inside the AF square lattice, (b) near the diagonal charge domain wall, (c) near the horizontal charge domain wall. The case (b) is the same as the two-magnon process in the stripe phase of La2−xSrxNiO4+δ [37–40]. It is supposed that in the charge domain wall the magnetic moment at the Cu site is zero. For the case (a), six bonds shown by the double lines have increased exchange interaction energy. The total energy increases by about 3J . In the cases (b) and (c) the energy increases at four bonds, and then the total energy increases by 2J . Thus the two-magnon scattering energy near the charge domain wall is 2/3 times smaller than at the inside of the spin stripe. Thus the higher energy peak appears to result from the case (a) and the lower energy peak from the case (b) or (c). The decrease of the energy of the lower energy peak at x ≥ 0.15 suggests that the carriers are included in the spin stripes, although small area of spin stripes has no carrier as known from the existence of the higher energy peak at about 3200 cm which is almost the same as or even higher than the two-magnon peak energy 3213 cm in the undoped AF insulating LCO. It is consistent with the decreasing Cu-Cu interatomic distance in the CuO2 plane, as Sr concentration increases. The onset temperature of the appearance of the split peaks is obtained from the differential spectra between two temperatures. They are plotted in Fig. 4. Those at x = 0.2 and 0.25 should be distinguished from other high onset temperatures, because the small sign of 5 the higher energy peak is noticeable at 300 K but it does not increase at low temperatures. For neutron scattering only elastic scattering data are plotted. The inelastic incommensurate magnetic peaks have been detected from x = 0.06 to 0.25 at low temperatures, but the temperature dependence has not been reported [22]. The temperatures determined by Raman scattering are much higher than those obtained by other experiments. The onset temperature decreases, as the response of the experimental probe becomes slow. These results indicate that the high frequency fluctuation of stripes starts at much higher temperatures than reported. The frequency of the fluctuation decreases as temperature decreases and the quasi-static component appears at the temperatures reported so far. In conclusion, the present Raman scattering experiment disclosed the existence of the dynamical stripe structure in whole carrier concentration region from x = 0.035 to 0.25. These onset temperature is about 300 K for x = 0.035, 0.05, 0.06, 350 K for x = 0.115, 100 K for x = 0.1 and 0.15. These onset temperatures are much higher than those obtained from low frequency probes. At x = 0.1 and x ≥ 0.15 the carrier density in the large volume looks uniform, however it may be possible that the system is in the isotropic quantum liquidcrystal phase of charge strings [41]. The dynamical fluctuation of stripes is expected to induce the metallic conductivity, but it is a continued problem whether dynamical stripes help the superconductivity or not. Acknowledgments The authors would like to thank K. Takenaka for the characterization of single crystals and M. Sato for the measurement of magnetization. This work was supported by CREST of the Japan Science and Technology Corporation.