Thermal expansion of the superconducting ferromagnet UCoGe

We report measurements of the coefficient of linear thermal expansion, $\alpha \left(T\right)$, of the superconducting ferromagnet UCoGe. The data taken on a single-crystalline sample along the orthorhombic crystal axes reveal a pronounced anisotropy with the largest length changes along the $b$ axis. The large values of the step sizes $\Delta \alpha$ at the magnetic and superconducting phase transitions provide solid evidence for bulk magnetism and superconductivity. Specific-heat measurements corroborate bulk superconductivity. Thermal-expansion measurements in magnetic fields $B\parallel a,b$ show $\Delta \alpha$ at $T_C$ grows rapidly, which indicates the character of the ferromagnetic transition becomes first orderlike.

Figure 1

(Color online) Coefficient of linear thermal expansion versus temperature of UCoGe along the orthorhombic $a$, $b$, and $c$ axes as indicated. Arrows indicate the ferromagnetic (at $T_C$) and superconducting (at $T_s$) transition temperatures.

Figure 2

(Color online) Coefficient of volumetric thermal expansion of single-crystalline UCoGe as a function of temperature. The dashed lines represent idealized sharp FM and SC transitions at $T_C=2.6\text{K}$ and $T_s=0.42\text{K}$, respectively. The blue thicker arrow locates the presence of an additional contribution in the FM state (see text). Inset: comparison of $\beta \left(T\right)$ of single-crystalline (closed circles) and polycrystalline (solid line) UCoGe. The dashed line gives ${\beta }_{para}\left(T\right)=aT$ (see text).

Figure 3

(Color online) (a) Specific heat of UCoGe (single crystal #2) in a plot of $c/T$ versus $T$. (b) ${\alpha }_b\left(T\right)$ of UCoGe (single crystal #1). (c) Resistivity versus $T$ of UCoGe (single crystal #2). The vertical dotted line indicates the approach to the zero-resistance state coinciding with the onset temperature of bulk SC as seen in $c/T$ and ${\alpha }_b\left(T\right)$. The dashed lines in (a) and (b) represent idealized sharp FM and SC transitions.

Figure 4

(Color online) The relative volume change $\Delta V/V=\left[V\left(T\right)-V\left(0.05\text{K}\right)\right]/V$ as a function of $T$ (solid blue line). The black dashed line gives $\Delta V/V$ in the absence of FM order. The red dotted line gives a smooth extrapolation of $\Delta V/V$ in the absence of SC. Inset: blow-up of the low-$T$ part.

Figure 5

(Color online) Coefficient of thermal expansion of UCoGe in applied magnetic fields along the dilatation direction as indicated. (a) ${\alpha }_a$ for $B\parallel a$; (b) ${\alpha }_b$ for $B\parallel b$; and (c) ${\alpha }_c$ for $B\parallel c$. Insets: $T_C$ as a function of $B\parallel a,b$.