Magnetism and superconductivity in ferromagnetic heavy-fermion system UCoGe under in-plane magnetic fields

We study the ferromagnetic superconductor UCoGe at ambient pressure under $ab$-plane magnetic fields $\mathbf{H}$, which are perpendicular to the ferromagnetic easy axis. It is shown that, by taking into account the Dyaloshinskii-Moriya interaction arising from the zigzag chain crystal structure of UCoGe, we can qualitatively explain the experimentally observed in-plane anisotropy for critical magnetic fields of the paramagnetic transition. Because of this strong dependence on the magnetic field direction, upper critical fields of superconductivity, which is mediated by ferromagnetic spin fluctuations, also become strongly anisotropic. The experimental observation of $\mathsf{S}$-shaped $H_{c2}\parallel b$ axis is qualitatively explained as a result of enhancement of the spin fluctuations due to decreased Curie temperature by the $b$-axis magnetic field. We also show that the $\mathsf{S}$-shaped $H_{c2}$ is accompanied by a rotation of the $d$ vector, which would be a key to understand the experiments not only at ambient pressure but also under pressure.

Figure 1

Expected magnetic phase diagram of UCoGe in temperature ($T$)-magnetic field ($H$) plane. FM and PM refer to ferromagnetic phase and paramagnetic phase, respectively. $H_a^{*}$ and $H_b^{*}$ are critical magnetic fields at zero temperature.

Figure 2

The crystal structure of UCoGe. Zigzag chains are along the $a$ axis.

Figure 3

The $c$-axis magnetization $|M_c|$ for different values of the DM interaction under the $a$-axis magnetic field (left) and $b$-axis magnetic field (right).

Figure 4

The critical magnetic fields for $a$ axis (red squares) and $b$ axis (blue circles). $D_b$ is strength of the DM interaction in unit of $J$.

Figure 5

Temperature dependence of $H_{c2}$ for $a$ axis (red curve) and $b$ axis (blue curve). The dashed line indicates the critical magnetic field $H_b^{*}$. $T_{sc0}=0.02t$ is the superconducting transition temperature at $h=0$.

Figure 6

In-plane components of the $d$ vector as a function of $H_b$. The green curve is the exchange field $h_{\mathrm{ex}}$, which characterizes Fermi surface splitting in the ferromagnetic state.