Dimensionality Driven Enhancement of Ferromagnetic Superconductivity in URhGe

In most unconventional superconductors, like the high-$T_c$ cuprates, iron pnictides, or heavy-fermion systems, superconductivity emerges in the proximity of an electronic instability. Identifying unambiguously the pairing mechanism remains nevertheless an enormous challenge. Among these systems, the orthorhombic uranium ferromagnetic superconductors have a unique position, notably because magnetic fields couple directly to ferromagnetic order, leading to the fascinating discovery of the reemergence of superconductivity in URhGe at a high field. Here we show that uniaxial stress is a remarkable tool allowing the fine-tuning of the pairing strength. With a relatively small stress, the superconducting phase diagram is spectacularly modified, with a merging of the low- and high-field superconducting states and a significant enhancement of the superconductivity. The superconducting critical temperature increases both at zero field and under a field, reaching 1 K, more than twice higher than at ambient pressure. This enhancement of superconductivity is shown to be directly related to a change of the magnetic dimensionality detected from an increase of the transverse magnetic susceptibility: In addition to the Ising-type longitudinal ferromagnetic fluctuations, transverse magnetic fluctuations also play an important role in the superconducting pairing.

Figure 1

Magnetic susceptibility and orthorhombic crystal structure of URhGe showing the position of the U atoms in the $cb$ plane: Applied stress (black arrows) along the $b$ axis reduces the U-U distance in the $b$ direction, while it increases in the $c$ direction.

Figure 2

($T$, $H$) phase diagram of superconductivity for the transverse ($H\parallel b$) configuration. (a) shows the phase diagram for different values of stress, together with a previous zero pressure measurement [7]. It is obtained with a criterion of 50% of the total resistance drop. Lines are guides to the eye. (b) and 2 show the superconducting transitions at different values of stress and field, respectively. See Supplemental Material [19] for a discussion on the shape of the transitions.

Figure 3

(a) Stress dependence of the parameters $T_{\text{Curie}}$ and field $H_R$ where the rotation of the moments occurs. $H_R$ was determined by the maximum of $T_{\mathrm{SC}}$ (full symbols) and by the peak in the normal state magnetoresistance (open symbols; see Supplemental Material [19]). $H_R$ for $\sigma =0$ was not measured, so a typical value of 12 T was taken; the error bar shows the possible uncertainty, mainly due to the precision of the alignment with the field. The dashed black line shows the expected initial slope for $T_{\text{Curie}}$ of $1.6\mathrm{K}/\mathrm{GPa}$ from the thermal expansion measurements. (b) Stress dependence of the superconducting critical temperature $T_{\mathrm{SC}}^{(H=0)}$ at zero field (red circles) and at the maximum value $T_{\mathrm{SC}}^{\mathrm{HR}}$ obtained for $H=H_R$. Lines are guides for the eyes.

Figure 4

Magnetization (a) of URhGe under uniaxial stress for $H\parallel b$ and $\sigma \parallel b$, compared to ambient pressure data (Levy et al. [8]). Arrows show the value of $H_R$ at ambient pressure and $\sigma =0.6\mathrm{GPa}$. (b) shows that the normalized changes of $\chi$ (taken as $M$ at 5 T), $1/H_R$, and $T_{\mathrm{SC}}$ are very similar and seem uncorrelated with those of $1/T_{\text{Curie}}$. Lines are guides for the eyes.

Figure 5

Analysis of $H_{C2}$. (a) Field dependence of the strong coupling parameter $\lambda$ determined from the fits of the upper critical field $H_{C2}$ for different applied stresses. See Supplemental Material [19] for a description of the procedure. The red points are taken from Levy et al. [8], where the zero pressure analysis was performed. The insert shows the pressure dependence of $\lambda$ at $H=0$ and $H=H_R$. (b) shows the normalized values; the enhancement of $\lambda$ at $H_R$ is constant at all values of stress. Lines are guides for the eye.