Coupling between the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ and the antiferromagnetic metal ${\mathrm{CeIn}}_3$ through the atomic interface

To study the mutual interaction between unconventional superconductivity and magnetic order through an interface, we fabricate hybrid Kondo superlattices consisting of alternating layers of the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ and the antiferromagnetic (AFM) heavy-fermion metal ${\mathrm{CeIn}}_3$. The strength of the AFM fluctuations is tuned by applying hydrostatic pressure to the ${\mathrm{CeCoIn}}_5\left(m\right)/{\mathrm{CeIn}}_3\left(n\right)$ superlattices with $m$ and $n$ unit-cell-thick layers of ${\mathrm{CeCoIn}}_5$ and ${\mathrm{CeIn}}_3$, respectively. The superconductivity in ${\mathrm{CeCoIn}}_5$ and the AFM order in ${\mathrm{CeIn}}_3$ coexist in spatially separated layers in the whole thickness and pressure ranges. At ambient pressure, the Néel temperature $T_N$ of the ${\mathrm{CeIn}}_3$ block layers (BLs) of ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3\left(n\right)$ shows little dependence on the thickness $n$, in sharp contrast to ${\mathrm{CeIn}}_3\left(n\right)/{\mathrm{LaIn}}_3\left(4\right)$ superlattices, where $T_N$ is strongly suppressed with decreasing $n$. This suggests that each ${\mathrm{CeIn}}_3$ BL is magnetically coupled by the Ruderman-Kittel-Kasuya-Yosida interaction through the adjacent ${\mathrm{CeCoIn}}_5$ BL and a three-dimensional magnetic state is formed. With applying pressure to ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3\left(13\right)$, $T_N$ of the ${\mathrm{CeIn}}_3$ BLs is suppressed up to 2.4 GPa, showing a similar pressure dependence to that of bulk ${\mathrm{CeIn}}_3$ single crystals. An analysis of the upper critical field reveals that the superconductivity in the ${\mathrm{CeCoIn}}_5$ BLs is barely influenced by the AFM fluctuations in the ${\mathrm{CeIn}}_3$ BLs, even when the ${\mathrm{CeIn}}_3$ BLs are in the vicinity of the AFM quantum critical point. This is in stark contrast to ${\mathrm{CeCoIn}}_5/{\mathrm{CeRhIn}}_5$ superlattices, in which the superconductivity in the ${\mathrm{CeCoIn}}_5$ BLs is profoundly affected by AFM fluctuations in the ${\mathrm{CeRhIn}}_5$ BLs. The present results show that although AFM fluctuations are injected into the ${\mathrm{CeCoIn}}_5$ BLs from the ${\mathrm{CeIn}}_3$ BLs through the interface, they barely affect the force that binds superconducting electron pairs. These results demonstrate that two-dimensional AFM fluctuations are essentially important for the pairing interactions in ${\mathrm{CeCoIn}}_5$.

Figure 1

Schematic representations of three types of Kondo superlattices: (a) ${\mathrm{CeCoIn}}_5/{\mathrm{YbCoIn}}_5$, (b) ${\mathrm{CeCoIn}}_5/{\mathrm{CeRhIn}}_5$, and (c) ${\mathrm{CeCoIn}}_5/{\mathrm{CeIn}}_3$, where ${\mathrm{CeCoIn}}_5$ is a heavy-fermion $d$-wave superconductor, ${\mathrm{YbCoIn}}_5$ is a conventional metal, and ${\mathrm{CeRhIn}}_5$ and ${\mathrm{CeIn}}_3$ are heavy-fermion AFM metals. The atomic views of the [100] plane are shown.

Figure 2

(a) Typical RHEED streak patterns for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CoIn}}_3$(13) superlattice taken during the crystal growth. (b), (c) High-resolution cross-sectional (b) TEM image and (c) EELS images for the ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CoIn}}_3$(13) superlattice with the electron beam aligned along the (100) direction. The EELS images were taken for Co $L$, Ce $L$, and In $M$ edges. (d) Cu $K{\alpha }_1$ x-ray diffraction patterns for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CoIn}}_3(n$) superlattices ($n=3$, 4, 6, and 13). The blue and red arrows indicate the [003] peaks of ${\mathrm{CeCoIn}}_5$ and satellite peaks due to the superlattice structure, respectively.

Figure 3

(a) Temperature dependence of the resistivity $\rho \left(T\right)$ in ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) superlattices for $n=3$, 4, 6, and 13, along with $\rho \left(T\right)$ for ${\mathrm{CeIn}}_3$ (black solid line) and ${\mathrm{CeCoIn}}_5$ (black dashed line) thin films. The inset illustrates the schematics of ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) superlattice. (b)–(f) $\rho \left(T\right)$ at low temperatures. (g)–(k) Temperature derivative of the resistivity, $d\rho \left(T\right)/dT$, as a function of temperature. The arrows indicate the Néel temperature $T_N$.

Figure 4

The Néel temperature $T_N$ for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) as a function of $n$. For comparison, $T_N$ for ${\mathrm{CeIn}}_3\left(n\right)/{\mathrm{LaIn}}_3\left(4\right)$ and ${\mathrm{CeCoIn}}_5\left(n\right)/{\mathrm{CeRhIn}}_5(n$) are shown. Open square and triangle are $T_N$ of bulk ${\mathrm{CeIn}}_3$ and ${\mathrm{CeRhIn}}_5$ single crystals, respectively.

Figure 5

(a), (e) Temperature dependence of the resistivity $\rho \left(T\right)$ under pressure for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) for (a) $n=13$ and (e) $n=6$. Inset: $\rho \left(T\right)$ at low temperatures. (b)–(d) and (f)–(h) show the temperature derivative of the resistivity, $d\rho \left(T\right)/dT$, as a function of temperature under pressure for $n=13$ and 6, respectively. The arrows indicate the Néel temperature $T_N$.

Figure 6

(a) Pressure dependence of $T_N$ and $T_c$ of ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) superlattices for $n=13$ and 6. For comparison, $T_N$ of ${\mathrm{CeIn}}_3$ and $T_c$ of ${\mathrm{CeCoIn}}_5$ single crystals are shown by solid lines. (b) Pressure dependence of the exponent $\varepsilon$ in $\rho \left(T\right)={\rho }_0+A{T}^{\varepsilon }$, obtained from $dln\mathrm{\Delta }\rho /dlnT$ ($\mathrm{\Delta }\rho =\rho \left(T\right)-{\rho }_0$), for the ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3(n$) superlattices for $n=13$ and 6. For comparison, $\varepsilon$ for bulk ${\mathrm{CeIn}}_3$ and ${\mathrm{CeCoIn}}_5$ single crystals is shown.

Figure 7

Temperature dependence of upper critical fields in magnetic fields parallel ($H_{c2\parallel }$, open symbols) and perpendicular ($H_{c2\perp }$, closed symbols) to the $ab$-plane for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3$(13) superlattice at ambient pressure and at 2.1 and 2.4 GPa. The inset shows anisotropy of the upper critical field, $H_{c2\parallel }/H_{c2\perp }$. The data of ${\mathrm{CeCoIn}}_5$ thin film at ambient pressure are shown by dotted line.

Figure 8

(a) Upper critical field in perpendicular field normalized by the orbital limiting upper critical field, $H_{c2\perp }/H_{c2\perp }^{\text{orb}}\left(0\right)$, plotted as a function of $T/T_c$ (a) at ambient pressure and (b) under pressure about 2 GPa for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3$(13) superlattices. For comparison, $H_{c2\perp }/H_{c2\perp }^{\text{orb}}\left(0\right)$ for bulk ${\mathrm{CeCoIn}}_5$ single crystal, ${\mathrm{CeCoIn}}_5\left(5\right)/{\mathrm{YbCoIn}}_5\left(5\right)$, and ${\mathrm{CeCoIn}}_5\left(5\right)/{\mathrm{CeRhIn}}_5\left(5\right)$ are shown. Orange dotted lines represent the WHH curve, which is the upper critical field for purely orbital limiting.

Figure 9

Pressure dependence of $q=\sqrt{2}g{\mu }_B{H}_{c2\perp }/k_B{T}_c\approx 2\mathrm{\Delta }/k_B{T}_c$ for ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3$(13) superlattice. For comparison, $q$ of bulk ${\mathrm{CeCoIn}}_5$ single crystal and ${\mathrm{CeCoIn}}_5\left(5\right)/{\mathrm{CeRhIn}}_5\left(5\right)$ are plotted.