Emergent transition for superconducting fluctuations in antiferromagnetic ruthenocuprates

The emergence of carrier pairing from the electronically inhomogeneous phase of lightly hole-doped copper oxides has been investigated through magnetoresistance measurements on 1222-type ruthenocuprates ${\mathrm{RuSr}}_2{(R,\mathrm{Ce})}_2{\mathrm{Cu}}_2{\mathrm{O}}_{10-\delta }$, principally with $R=\mathrm{Gd}$, Sm, Nd. A well-defined transition at which superconducting fluctuations emerge is discovered at a remarkably low critical doping, $p_{\mathrm{c}}=0.0084$, deep within the antiferromagnetic phase. Systematic variations of the low-temperature fluctuation density with doping and cell volume demonstrate the intrinsic nature of the electronic inhomogeneity and provide new support for bosonic models of the superconducting mechanism.

Figure 1

Temperature evolution of magnetoresistance for ${\mathrm{RuSr}}_2{R}_{1.8-x}{\mathrm{Y}}_{0.2}{\mathrm{Ce}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{10-\delta }$ materials in a 5 T applied field. (a) $R=\mathrm{Gd}$ materials, showing hole doping levels $p$, and (b) $R=\mathrm{Nd}$, Sm, Eu, and Gd samples with $x=0.9$ and constant doping $p=0.03$. Discontinuities signifying Cu and Ru spin ordering transitions $T_{\mathrm{Cu}}$ and $T_{\mathrm{Ru}}$ are marked. The inset to (a) shows arrowed MR upturns at the onset of bulk superconductivity for $p$ ≥0.041, and at the upper temperatures for superconducting fluctuations $T_{\mathrm{sf}}$ in samples with $p$ ⩽0.03. The temperature derivative of ${\mathrm{MR}}_{5\mathrm{T}}$ for the $R=\mathrm{Nd}$ sample in the inset to (b) evidences a small density of superconducting fluctuations below ∼30 K.

Figure 2

Electronic phase diagrams for ${\mathrm{RuSr}}_2{R}_{1.8-x}{\mathrm{Y}}_{0.2}{\mathrm{Ce}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{10-\delta }$ $(R=\mathrm{Sm}$ and Gd) derived from transitions in their ${\mathrm{MR}}_{5\mathrm{T}}\left(T\right)$ data, showing stability regions for the canted-antiferromagnetic order of Ru spins [c-AF(Ru)] below $T_{\mathrm{Ru}}$ (filled circles), with additional antiferromagnetic Cu spin order [AF(Cu)] below $T_{\mathrm{Cu}}$ (filled squares) or superconductivity (SC) below zero resistance $T_{\mathrm{c}}$ (closed diamonds) at low temperatures. Superconducting fluctuations (SF) are observed below $T_{\mathrm{sf}}$ (open diamonds), which starts at the $p_{\mathrm{c}}=0.0084$ critical point.

Figure 3

Magnetoresistance variations for ${\mathrm{RuSr}}_2{R}_{1.8-x}{\mathrm{Y}}_{0.2}{\mathrm{Ce}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{10-\delta }$ materials at 4 K. (a) Field variations for $R=\mathrm{Sm}$ samples labeled by doping levels $p$. The $p=0.010$ and 0.013 variations are fitted well as $\mathrm{MR}\left(H\right)=-aH+b{H}^2$ with positive coefficients $a$ and $b$, characteristic of a doped antiferromagnetic insulator. (b) Variations of $\mathrm{MR}/H$ at 4 K with doping for the $R=\mathrm{Gd}$, Sm, and Nd series. Low-doped samples have ${(\mathrm{MR}/H)}_{7\mathrm{T}}>{(\mathrm{MR}/H)}_{2.5\mathrm{T}}$ but this changes to ${(\mathrm{MR}/H)}_{7\mathrm{T}}<{(\mathrm{MR}/H)}_{2.5\mathrm{T}}$ as the influence of superconducting fluctuations increases with $p$ with the crossover at $p=0.02$ in the Sm series. The evolution of $\left(\mathrm{MR}/H\right)$ confirms that superconducting fluctuations grow in the Nd series for $p>0.03$ although no bulk superconductor is observed up to the highest available $p=0.06$ doping level [6].

Figure 4

Magnetoresistance variations at a constant high field (7 T) and low temperature (4 K) for 1222 ruthenocuprates. (a) Plot of ${\mathrm{MR}}_{7\mathrm{T},4\mathrm{K}}$ against unit cell volume for 15 samples with fixed $p=0.03$ (materials are from different chemical systems as shown in the Supplemental Material [13]). (b) Variations of ${\mathrm{MR}}_{7\mathrm{T},4\mathrm{K}}$ with doping $p$ for the ${\mathrm{RuSr}}_2{R}_{1.8-x}{\mathrm{Y}}_{0.2}{\mathrm{Ce}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{10-\delta }$ series with $R=\mathrm{Nd}$, Sm, and Gd, also showing other $p=0.03$ samples with linear volume dependence in (a) within the box. The fits to $\mathrm{MR}\left(p\right)$ are predicted from Eq. (1) for ${fc}_{\max }\left(p\right)=(p-p_{\mathrm{c}})fv$ with $fv$ values for the three $R$ series as shown, and converge at critical doping $p_{\mathrm{c}}$. The $fv=0$ line corresponds to the magnetoresistance of the antiferromagnetic matrix in the absence of pair fluctuations, ${\mathrm{MR}}_{\mathrm{a}}\left(p\right)=exp(-p/0.057)-1$. MR data deviate above the curves at higher dopings $\left(p>0.03\right)$ where coherence between superconducting fluctuations is established, and MR diverges at the onset of bulk superconductivity shown by arrows for the Gd and Sm series. The inset shows the field variation of the critical doping at 4 K; $p_{\mathrm{c}}$ could not be estimated accurately for fields below 3 T.