Magnetic order in the pseudogap phase of HgBa${}_{2}$CuO${}_{4+\ensuremath{\delta}}$ studied by spin-polarized neutron diffraction

Magnetic order in the pseudogap phase of HgBa $_{2}$ CuO $_{4 + δ}$ studied by spin-polarized neutron diffraction

Yuan Li, V. Balédent, N. Barišić, Y. C. Cho, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven

Phys. Rev. B 84, 224508 – Published 16 December 2011

Abstract

Spin-polarized neutron diffraction experiments have revealed an unusual $q = 0$ magnetic order in the model high-temperature superconductor HgBa $_{2}$ CuO $_{4 + δ}$ (Hg1201) below the pseudogap temperature $T^{*}$ [Y. Li et al., Nature (London) 455, 372 (2008)]. Together with results for the structurally more complex compound YBa $_{2}$ Cu $_{3}$ O $_{6 + δ}$ (YBCO) [B. Fauqué et al., Phys. Rev. Lett. 96, 197001 (2006); H.A. Mook et al., Phys. Rev. B 78, 020506 (2008)], this establishes the universal existence of a genuine novel magnetic phase in underdoped cuprates with high maximal $T_{c}$ (above 90 K at optimal doping). Here we report a systematic study of an underdoped Hg1201 sample ( $T_{c} = 75$ K), the result of which is consistent with the previously established doping dependence of the magnetic signal. We present an assumption-free analysis of all the data available for Hg1201. Depending on how the hole concentration is estimated, comparison with the results for YBCO leads to different scenarios for the competition between the $q = 0$ magnetic order and the spin-density-wave order found in heavily underdoped YBCO.

Received 19 September 2011

DOI:https://doi.org/10.1103/PhysRevB.84.224508

Authors & Affiliations

Yuan Li^1,*, V. Balédent², N. Barišić^3,4, Y. C. Cho⁵, Y. Sidis², G. Yu⁶, X. Zhao^3,7, P. Bourges², and M. Greven^6,†

¹Department of Physics, Stanford University, Stanford, California 94305, USA
²Laboratoire Léon Brillouin, CEA-CNRS, CEA-Saclay, F-91191 Gif sur Yvette, France
³T.H. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
⁴1. Physikalisches Institut, Universität Stuttgart, D-70550 Stuttgart, Germany
⁵BK21 Team and Department of Nano Fusion Technology, Pusan National University, Miryang 627-706, Republic of Korea
⁶School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁷State Key Lab of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, China

^*Present address: Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany.
^†greven@physics.umn.edu

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Vol. 84, Iss. 22 — 1 December 2011

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Figure 1
(a)–(c) Temperature dependence of SF and NSF intensities measured at the (1 0 1) Bragg reflection. The NSF intensities are divided by the flipping ratios measured at temperatures above 350 K, where no magnetic signal is expected. (d) The average of all three spin-polarization geometries shows an onset of additional SF intensity below $T_{mag} \approx 320$ K. (e) The deviation of the averaged SF intensity from the (rescaled) NSF intensity is converted into absolute units based on the calculated (1 0 1) nuclear scattering crosssection of 1.26 barn.Reuse & Permissions
Figure 2
Demonstration of the insensitivity of the extracted $T_{mag}$ to the temperature range over which the NSF intensity is rescaled to match the SF intensity. $T_{mag}$ is estimated by fitting the deviation of the SF data from the (rescaled) NSF data to a power law. The fit values and errors (one standard deviation) are indicated by the position and width of the vertical bands. The temperature ranges of the normalization are indicated by the horizontal bars. (a–d): $P ∥ Q$ data for the $T_{c} = 74$ K underdoped sample studied in this work. (e–l): previous data for a sample that was studied at two distinct oxygen (and hence hole) concentrations.[5]Reuse & Permissions
Figure 3
Average flipping ratio (see text) measured on five different samples. The onset temperatures of the magnetic signal are indicated by arrows for the three most underdoped samples, where they can be reliably determined with this unbiased method. Filled symbols: (1 0 1) data. Empty symbols: (0 0 3) reference data. The (0 0 3) results are rescaled (vertically) for better comparison.Reuse & Permissions
Figure 4
(Left panels) Flipping ratio $R (T)$ at the (0 0 3) reflection for the $T_{c} = 75$ K sample. Solid lines are linear fits to the data, and dashed lines represent the confidence range of the estimated linear slopes (one sigma). (Right panels) $R (T)$ for the (1 0 1) reflection. Solid and dashed lines are obtained by rescaling the corresponding linear fits in the left panels to match the data above $T = 330$ K, which serves as an estimate of the underlying $R_{0} (T)$ in the absence of a magnetic signal.Reuse & Permissions
Figure 5
Magnetic intensities at the (1 0 1) reflection for the $T_{c} = 75$ K sample, obtained by subtracting from the SF intensities the NSF intensities divided by temperature-dependent $R_{0} (T)$ determined from Fig. 4. Dashed lines indicate uncertainty (one standard deviation) due to the slope estimates in Fig. 4.Reuse & Permissions
Figure 6
Phase diagram of Hg1201 (red) and YBCO (light blue) at intermediate doping. Stars and circles represent $T_{c}$ and $T_{mag}$ , respectively. Data for the two new Hg1201 samples studied in the present work are indicated by black borders. Data for YBCO are from the literature (Refs.3, 4 and 9). Symbols for $T_{mag}$ are plotted with their area proportional to the magnetic intensities. In the main panel, hole doping for Hg1201 is determined from the $T_{c} (p)$ relationship according to Ref.37. In the inset, the hole concentration of Hg1201 is estimated based on the same $T_{c} (p)$ relationship as in YBCO (Ref.38) (after rescaling the maximal $T_{c}$ to 97 K).Reuse & Permissions

Physical Review B

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Magnetic order in the pseudogap phase of HgBa $_{2}$ CuO $_{4 + δ}$ studied by spin-polarized neutron diffraction

Yuan Li, V. Balédent, N. Barišić, Y. C. Cho, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven

Phys. Rev. B 84, 224508 – Published 16 December 2011

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Physical Review B

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Magnetic order in the pseudogap phase of HgBa2CuO4+δ studied by spin-polarized neutron diffraction

Yuan Li, V. Balédent, N. Barišić, Y. C. Cho, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven

Phys. Rev. B 84, 224508 – Published 16 December 2011

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Magnetic order in the pseudogap phase of HgBa $_{2}$ CuO $_{4 + δ}$ studied by spin-polarized neutron diffraction