Abstract
An outstanding challenge in condensed-matter-physics research over the past three decades has been to understand the pseudogap (PG) phenomenon of the high-transition-temperature (high-Tc) copper oxides. A variety of experiments have indicated a symmetry-broken state below the characteristic temperature T* (refs. 1,2,3,4,5,6,7,8). Among them, although the optical study5 indicated the mesoscopic domains to be small, all these experiments lack nanometre-scale spatial resolution, and the microscopic order parameter has so far remained elusive. Here we report, to our knowledge, the first direct observation of topological spin texture in an underdoped cuprate, YBa2Cu3O6.5, in the PG state, using Lorentz transmission electron microscopy (LTEM). The spin texture features vortex-like magnetization density in the CuO2 sheets, with a relatively large length scale of about 100 nm. We identify the phase-diagram region in which the topological spin texture exists and demonstrate the ortho-II oxygen order and suitable sample thickness to be crucial for its observation by our technique. We also discuss an intriguing interplay observed among the topological spin texture, PG state, charge order and superconductivity.
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Data availability
The data supporting the findings of this study are available within the manuscript and its extended data. Any other relevant data are also available on request from J.Z. Source data are provided with this paper and are available at https://doi.org/10.5281/zenodo.7502830.
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Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (Basic Science Center project of NSFC under grant no. 51788104) and supported by the Basic and Applied Basic Research Major Programme of Guangdong Province, China (grant no. 2021B0301030003) and Ji Hua Laboratory (project no. X210141TL210). R.C. thanks the financial support from the National Natural Science Foundation of China (Basic Science Center project of NSFC under grant nos. 51725101, 11727807, 51672050, 61790581 and 22088101) and the Ministry of Science and Technology of China (973 Program project nos. 2021YFA1200600 and 2018YFA0209102). This work partially made use of the resources of the National Center for Electron Microscopy in Beijing. We thank the Thermo Fisher Scientific company for its help in adjusting the electron microscope and providing the liquid helium during our experiment. We thank J. F. Jia for providing the single crystals of YBa2Cu3O6.5. Q. K. Xue is gratefully acknowledged for helpful discussions and assistance.
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J.Z. and Z.W. initiated the idea and designed the studies. Z.W., K.P., L.Y., C.Y., G.C., X.Z., C.W. and Z.L. performed the LTEM experiments, with the help of R.C. Z.W. performed the HAADF-STEM, EELS and electron diffraction experiments and data analysis, with the help of J.Z. All authors contributed to the scientific discussions. Z.W., J.Z., Y.L., R.C. and K.P. wrote the paper, with contributions from all authors.
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Extended data figures and tables
Extended Data Fig. 1 Magnetic hysteresis loop of the objective lens in LTEM.
The remanences are shown in the inset image, which is zoomed in on the centre of the figure. As shown, the current of the objective lens could be adjusted between −10% and +40% with a better imaging condition. The loop presents typical soft magnetic properties. The remanences after applying a large magnetic field are about 8.2 mT and −4.1 mT. The degaussed process could further decrease the remanence under 10 mT. We can therefore confirm that such a small remanence will not affect the experimental results.
Extended Data Fig. 2 Evolution of topological spin texture with different magnetic fields (at 300 K) over large areas.
Large-area LTEM images of vortex-like spin textures in YBa2Cu3O6.5 examined in increasing external magnetic fields from top to bottom at a temperature of 300 K. All results are deduced by analysing LTEM images with the TIE.
Extended Data Fig. 3 Evolution of topological spin texture with different magnetic fields (at 10 K) over large areas.
Large-area LTEM images of vortex-like spin textures in YBa2Cu3O6.5 examined in increasing external magnetic fields from top to bottom at a temperature of 10 K. All results are deduced by analysing LTEM images with the TIE.
Extended Data Fig. 4 Evolution of topological spin texture with different temperature fields over large areas.
Large-area LTEM images of topological spin textures in YBa2Cu3O6.5 examined in decreasing external temperature fields from a to j at a zero-field state. All results are deduced by analysing LTEM images with the TIE17.
Extended Data Fig. 5 The relative strength evolution of the topological spin texture with the applied magnetic field and temperature field.
a–j, Magnetic strength images of topological spin textures in YBa2Cu3O6.5 examined in increasing external magnetic fields from left to right at a temperature of 300 K (a–e) and 10 K (f–j). k–t, Magnetic strength images of topological spin texture in YBa2Cu3O6.5 examined in decreasing external temperature fields from left to right at a zero-field state. All magnetic strength mappings are processed under the same condition and the field values are calculated by QPt and digital microscopy software17.
Extended Data Fig. 6 Explanation for the evolution of the relative signal magnitude versus magnetic field and temperature as shown in Fig. 2u,v.
Quantitative analysis of the relative strength evolution of the topological spin texture with the applied magnetic field and temperature field. Although the absolute values of magnetization cannot be determined by LTEM using the TIE method, we are able to show the relative evolutions above. Here we plot the summed and averaged magnitude of each magnetic field mapping, whereas the value observed in a featureless region is defined as ‘zero’. All field mappings are processed under the same condition and the field values are calculated by QPt and digital microscopy software17.
Extended Data Fig. 7 Quantitative chemical mapping analysis of YBa2Cu3O6.0 using super-EDS.
a, HAADF-STEM image indicating the area in which the EDS map is acquired from the red dotted box in g. b–e, Chemical component maps of Y, Ba, Cu and O, respectively. f, Chemical component spectrum over the whole mapping area. g, Electron micrograph of YBa2Cu3O6.0 obtained in the in-focus Fresnel mode of LTEM. The inset shows the corresponding electron diffraction. h, Table showing quantitative analysis of the chemical composition, which is consistent with YBa2Cu3O6.0.
Extended Data Fig. 8 Quantitative chemical mapping analysis of YBa2Cu3O6.5 using super-EDS.
a, HAADF-STEM image indicating the area in which the EDS map is acquired from the red dotted box in g. b–e, Chemical component maps of Y, Ba, Cu and O, respectively. f, Chemical component spectrum over the whole mapping area. g, Electron micrograph of YBa2Cu3O6.5 obtained in the in-focus Fresnel mode of LTEM. The inset shows the corresponding electron diffraction. h, Table showing quantitative analysis of the chemical composition, which is consistent with YBa2Cu3O6.5.
Extended Data Fig. 9 Quantitative chemical mapping analysis of YBa2Cu3O6.9 using super-EDS.
a, HAADF-STEM image indicating the area in which the EDS map is acquired from the red dotted box in g. b–e, Chemical component maps of Y, Ba, Cu and O, respectively. f, Chemical component spectrum over the whole mapping area. g, Electron micrograph of YBa2Cu3O6.9 obtained in the in-focus Fresnel mode of LTEM. The inset shows the corresponding electron diffraction. h, Table showing quantitative analysis of the chemical composition, which is consistent with YBa2Cu3O6.9.
Extended Data Fig. 10 Atomic structure of YBa2Cu3O6.0, YBa2Cu3O6.5 and YBa2Cu3O6.9 along the b axis.
a–c, Atomic structure images of YBa2Cu3O6.0, YBa2Cu3O6.5 and YBa2Cu3O6.9 along the b axis, respectively. The yellow arrows indicate the doped oxygen atoms in Cu–O chain layers of YBa2Cu3O6+x. For YBa2Cu3O6.0, there is no doped oxygen atom in the chain layer. With increasing doping level, the oxygen atoms are injected into the chain layer (as indicated by yellow arrows in b, c) and the chemical composition of the material system is changed from YBa2Cu3O6.0 to YBa2Cu3O6.5 and YBa2Cu3O6.9. These atomic structure images are acquired from each bulk sample with different doping levels. The low-magnification images along the c axis are shown in Fig. 4a–f.
Extended Data Fig. 11 Repetitive LTEM experiments at different labs and with different instruments.
a, Magnetic contrast observation using LTEM mode on an FEI Titan3 Themis G3 60-300 at Fudan University. b, Magnetic contrast observation using LTEM mode on an FEI Titan3 Themis G2 60-300 at Tsinghua University. c, Magnetic contrast observation by using LTEM mode on an FEI Titan 80-300 at Tsinghua University.
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Wang, Z., Pei, K., Yang, L. et al. Topological spin texture in the pseudogap phase of a high-Tc superconductor. Nature 615, 405–410 (2023). https://doi.org/10.1038/s41586-023-05731-3
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DOI: https://doi.org/10.1038/s41586-023-05731-3
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