Magnetic Order in the Pseudogap Phase of High-$T_C$ Superconductors

One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ system. The observed magnetic order preserves translational symmetry of the lattice as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of a hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates.

Figure 1

(a) Temperature dependencies of the raw SF and NSF neutron intensity measured at $\mathbf{Q}=(0,1,1)$ in sample C. (b) Sketch of the scattering plane showing the three polarization directions discussed here; $\mathbf{P}\parallel z$ corresponds to the direction perpendicular to the scattering plane (here $a^{*}$). (c) Temperature dependencies of the normalized magnetic intensity, $I_{\mathrm{mag}}$, measured at $\mathbf{Q}=(0,1,1)$ for $\mathbf{P}\parallel \mathbf{Q}$ for the 4 underdoped samples A–D and the overdoped sample E (solid points). $I_{\mathrm{mag}}$ is defined as $I_{\mathrm{mag}}(T)=\alpha I_{\mathrm{NSF}}(300\mathrm{K})[\frac{I_{\mathrm{SF}}}{I_{\mathrm{NSF}}}(T)-\frac{I_{\mathrm{SF}}}{I_{\mathrm{NSF}}}(T\sim 300\mathrm{K})]$, where $I_{\mathrm{mag}}$ is arbitrarily set to zero in the high temperature range ($\sim$ room temperature) and $\alpha =7/I_{004}^{\mathrm{meas}}(300\mathrm{K})$ calibrates the magnetic cross sections in mb using the nuclear Bragg cross section at $\mathbf{Q}=(0,0,4)$, $I_{004}^{\mathrm{calc}}=7\mathrm{b}$. The normalized magnetic intensity for the Bragg peak, $\mathbf{Q}=(0,0,2)$, is also shown for samples A and C (open points). (d) Temperature dependencies of the normalized magnetic intensity measured at $\mathbf{Q}=(0,1,1)$ (solid points), as well as $\mathbf{Q}=(0,0,2)$ (open points) for $\mathbf{P}\parallel \mathbf{z}$. (e) Temperature dependencies of the normalized magnetic intensity, $I_{\mathrm{mag}}$, measured at $\mathbf{Q}=(0,1,1)$ for sample B for $\mathbf{P}\perp \mathbf{Q}$.

Figure 2

(a) $L$-scan magnetic intensity across $Q=(0,1,L)$ in sample A; it has been obtained using the following relation of measured quantities: $[I(\mathrm{SF},75\mathrm{K})-I(\mathrm{SF},275\mathrm{K})\frac{I(\mathrm{NSF},75\mathrm{K})}{I(\mathrm{NSF},275\mathrm{K})}]$ calibrated by $\alpha$ (see caption to Fig. 1). (b) Temperature dependencies of the magnetic intensity, $I_{\mathrm{mag}}$, for various Bragg peaks $L=0,1,2$ in sample A.

Figure 3

(a) Cuprate superconductors phase diagram as a function of hole doping, $n_h$, deduced from the SC temperature using the empirical relation $T_C/T_C^{\max }=1–82.6(n_h-0.16{)}^2$ [29]. The white points show $T_{\mathrm{mag}}$ (see Table ). The color map shows the quantity $\delta R(T)=1-[{\rho }_{ab}(T)-{\rho }_{ab}(0)]/(\alpha T)$ deduced from the resistivity measurements in YBCO [6]: the change of colors indicates the departure from the $T$-linear behavior, $\delta R(T)=0$ represented in blue or dark gray, at high temperature. $\delta R(T)\ne 0$ defines the pseudogap state. AF stands for antiferromagnetism. (b) Circulating current phase, ${\Theta }_{II}$, in the ${\mathrm{CuO}}_2$ plane proposed to explain the pseudogap phase in high-$T_C$ superconducting cuprates [11, 12]. (c) A spin model preserving TSL.