Competition between unconventional superconductivity and incommensurate antiferromagnetic order in $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathrm{In}}_5$

Elastic neutron diffraction measurements were performed on the quasi-two-dimensional heavy-fermion system $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathrm{In}}_5$, ranging from an incommensurate antiferromagnet for low Co composition $x$ to an unconventional superconductor on the Co-rich end of the phase diagram. We found that the superconductivity competes with the incommensurate antiferromagnetic (AFM) order characterized by ${\mathit{q}}_I=(1∕2,1∕2,\delta )$ with $\delta =0.298$, while it coexists with the commensurate AFM order with ${\mathit{q}}_c=(1∕2,1∕2,1∕2)$. This is in sharp contrast to the $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Ir}}_x{\mathrm{In}}_5$ system, where both the commensurate and incommensurate magnetic orders coexist with the superconductivity. These results reveal that particular areas on the Fermi surface nested by ${\mathit{q}}_I$ play an active role in forming the superconducting state in $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_5$.

Figure 1

Neutron diffraction profiles for $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathrm{In}}_5$ for $x=\left(\mathrm{a}\right)$ 0.3, (b) 0.4, and (c) 0.6 for $\mathit{Q}=(\frac{1}{2},\frac{1}{2},l)$. For $x=0.6$, the profile in the range $1.45⩽l⩽1.55$ is shown instead of $0.45⩽l⩽0.55$, because mosaic peaks are observed at the latter position. Open and closed circles, respectively, show the results at 1.5 and $5\mathrm{K}$. The temperature dependences of the integrated intensities for the Bragg peaks at ${\mathit{q}}_c=(1∕2,1∕2,1∕2)$ (circles) and ${\mathit{q}}_I=(1∕2,1∕2,0.298)$ (triangles), are obtained from longitudinal scans for $x=\left(\mathrm{d}\right)$ 0.3, (e) 0.4, and (f) 0.6.

Figure 2

Specific heat divided by temperature, $C_{\mathrm{mag}}∕T$, of $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathrm{In}}_5$ as a function of temperature. The solid arrows indicate the SC transition, and the dotted ones the AFM transition.

Figure 3

(a) $x\text{−}T$ phase diagram for $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathrm{In}}_5$ from the neutron diffraction (엯), specific heat (◻,◇), and resistivity measurements (▿,▵). At $x=0.2$ (solid arrow) and 0.7 (dotted arrow), superconductivity and AFM order, respectively, were not observed down to $T=0.7\mathrm{K}$. (b) $x\text{−}T$ phase diagram for $\mathrm{Ce}{\mathrm{Rh}}_{1-x}{\mathrm{Ir}}_x{\mathrm{In}}_5$ reported in Refs. 10, 16 is illustrated schematically.

Figure 4

(Color online) (a)–(c) Cross section of the 14th Fermi surface perpendicular to $k_z$, at $k_z=\left(\mathrm{a}\right)$ 0.149, (b) 0.351, and (c) $1∕4$. The blue dotted lines represent the boundary of the AFM Brillouin zone. (d) The 3D figure of the cylindrical part of the 14th Fermi surface. The red hatched regions represent the area that is connected by ${\mathit{q}}_1=(1∕2,1∕2,0.298)$. The arrow indicates the $\left(001\right)-{\mathit{q}}_I$ vector. The red area is suggested to play an active role for SC pairing formation.