Superconductivity on the Border of Weak Itinerant Ferromagnetism in UCoGe

We report the coexistence of ferromagnetic order and superconductivity in UCoGe at ambient pressure. Magnetization measurements show that UCoGe is a weak ferromagnet with a Curie temperature $T_C=3\mathrm{K}$ and a small ordered moment $m_0=0.03{\mu }_B$. Superconductivity is observed with a resistive transition temperature $T_s=0.8\mathrm{K}$ for the best sample. Thermal-expansion and specific-heat measurements provide solid evidence for bulk magnetism and superconductivity. The proximity to a ferromagnetic instability, the defect sensitivity of $T_s$, and the absence of Pauli limiting, suggest triplet superconductivity mediated by critical ferromagnetic fluctuations.

Figure 1

Magnetic and SC properties of UCoGe sample 2. (a) Magnetization $M$ as a function of $T$ in a field $B$ of 0.01 T. The dashed line extrapolates to $m_0\approx 0.03{\mu }_B$ for $T\to 0$. The Curie temperature $T_C=3\mathrm{K}$ is marked by the dotted vertical line. Left inset: Hysteresis loop $M(B)$ at $T=2\mathrm{K}$ with coercive field of 0.3 mT. Right inset: Arrott plot of magnetization isotherms at $T=2.0$, 2.4, 2.8, 3.0, 3.5, and 4.5 K (from top to bottom). (b) ac susceptibility ${\chi }_{\mathrm{ac}}^{\prime }$ (left axis) (in $B={10}^{-5}\mathrm{T}$), and resistance $R$ (right axis) as a function of $T$. The maximum in ${\chi }_{\mathrm{ac}}^{\prime }$ and the broad hump in $R$ locate $T_C$. SC for sample 2 is found below 0.61 K in $R(T)$ and below 0.38 K in ${\chi }_{\mathrm{ac}}^{\prime }(T)$.

Figure 2

(a) Specific heat divided by temperature $c/T$ versus $T$ in zero magnetic field for sample 2. The idealized transition (dashed line) has a step size $\Delta (c/T)=0.014\mathrm{J}/\mathrm{mol}{\mathrm{K}}^2$ at $T_C=3\mathrm{K}$. Bulk SC for sample 2 sets in at 0.38 K (measured by ${\chi }_{\mathrm{ac}}^{\prime }$), but the $c(T)$ data extend down to 0.5 K only. (b) Thermal-expansion coefficient $\alpha (T)$ for sample 3. The large negative contribution below $\sim 5\mathrm{K}$ is due to FM order. The dashed line gives the idealized transition in $\alpha (T)$ with $\Delta \alpha =-1.1\times {10}^{-6}{\mathrm{K}}^{-1}$. The total relative length change $\Delta L/L=[L(0.23\mathrm{K})-L(T)]/L$ associated with magnetic order is obtained by integrating ${\alpha }_{\mathrm{mag}}(T)$ (i.e., the difference between the experimental data and the linear term $\alpha =aT$ with $a=1.1\times {10}^{-7}{\mathrm{K}}^{-2}$ expected in the absence of FM order) and amounts to $+1.9\times {10}^{-6}$. The peak below $\sim 0.6\mathrm{K}$ is the thermodynamic signature of the SC transition. In a field of 1 T, applied along the dilatation direction $\Delta L/L$, the magnetic transition is smeared and SC is not resolved.

Figure 3

Superconducting properties of UCoGe sample 3. (a) ac susceptibility ${\chi }_{\mathrm{ac}}^{\prime }$ (left axis) in $B={10}^{-5}\mathrm{T}$ and resistance $R$ (right axis). (b) Specific heat divided by temperature $c/T$ as a function of $T$. Bulk SC occurs below $T_s^{\mathrm{onset}}\approx 0.66\mathrm{K}$ (dotted vertical line). Dashed line: Idealized SC transition using an equal entropy construction with a finite $\gamma$ value in the SC state of $0.028\mathrm{J}/\mathrm{mol}{\mathrm{K}}^2$. (c) Coefficient of linear thermal expansion $\alpha (T)$. Bulk SC is observed below $T_s^{\mathrm{onset}}\approx 0.66\mathrm{K}$. Dashed line: Idealized sharp transition with $T_s=0.45\mathrm{K}$. For $B=1\mathrm{T}$ applied along the dilatation direction $\Delta L/L$ the SC transition is no longer resolved.

Figure 4

Upper critical field $B_{c2}$ determined by the midpoints of the resistive transitions measured in fixed magnetic fields. The solid lines indicate $B_{c2}/dT=-7.2$ and $-5.2\mathrm{T}/\mathrm{K}$ for samples 2 and 3, respectively, and extrapolate to zero field $T_s$ values of 0.30 and 0.60 K.