Evidence for spin mixing in holmium thin film and crystal samples

In a number of recent experiments, holmium has been shown to promote spin-triplet pairing when in proximity to a spin-singlet superconductor. The condition for the support of spin-triplet pairing is that the ferromagnet should have an inhomogeneous magnetic state at the interface with the superconductor. Here we use Andreev reflection spectroscopy to study the properties of single ferromagnet/superconductor interfaces formed of holmium and niobium, as a function of the contact resistance of the junction between them. We find that both single-crystal and $c$-axis-oriented thin-film holmium show unusual behavior for low junction contact resistance, characteristic of spin-mixing-type properties, which are thought necessary to underpin spin-triplet formation. We also explore whether this signature is observed when the junction is formed of ${\mathrm{Ni}}_{0.19}{\mathrm{Pd}}_{0.81}$ and niobium.

Figure 1

Hall images of (a) single-crystal and (b) thin-film Ho at zero field and 6 K. Black regions represent negative induction and bright regions represent positive induction. Line scans across the center of the images (white dashed lines) are shown in the top panels. Inset to (b) shows a schematic of the cone structure in Ho for $T$<19 K; the dashed arrow corresponds to the direction of the $c$ axis and solid arrows represent the ferromagnetic vectors locked out of plane.

Figure 2

Point-contact Andreev reflection data at 4.2 K; $C_N$ is the normalized conductance. (a) Normalized conductance spectra as a function of $R_{\mathit{CB}}$ for the Ho crystal. (b) High $R_{\mathit{CB}}$ spectrum taken with a Nb tip (black line) and with a Pt tip (gray line) for the Ho crystal. (c) Same spectrum as (b), but after normalization and fitting (with fitted parameters Δ $=$ 1.5 meV, ω $=$ 1.24 meV, $P$ $=$ 19.5%, $Z$ $=$ 0.63). (d) Normalized conductance spectra as a function of $R_{\mathit{CB}}$ for the Ho film. (e) Spectrum taken with a Nb tip shows a flatter background than in the crystal case, so can be fitted using the high bias conductance as shown (fitted parameters Δ $=$ 1.5 meV, ω $=$ 1.18 meV, $P$ $=$ 35.5%, $Z$ $=$ 0.32). (f) $C_N$ as a function of $R_{\mathit{CB}}$ for a ${\mathrm{Ni}}_{0.19}{\mathrm{Pd}}_{0.81}$ film. (g) Normalized spectrum and fit from the data set in (f) (with fitted parameters Δ $=$ 1.5 meV, ω $=$ 0.72 meV, $P$ $=$ 27.5%, $Z$ $=$ 0.41). The arrows in (a), (d), and (f) indicate decreasing contact resistance. All curves have been offset in the vertical scale for clarity.

Figure 3

$P$($Z$) relation on the Ho crystal (a) and Ho thin film (b). Symbols represent different contacts. The inset to (a) is a simulation of the effects of increasing the normalized field $h=H/H_{C2}$ (where $H_{C2}$ is the upper critical field of Nb) using the datum point associated with $R_{\mathit{CB}\hspace{0.5em}\mathrm{peak}}$ shown in Fig. 4a.

Figure 4

Dependence of (a) $P$ and (b) $Z$ of the Ho crystal as function of $R_{\mathit{CB}}/R_{\mathit{CB}\hspace{0.5em}\mathrm{peak}}$, where $R_{\mathit{CB}\hspace{0.5em}\mathrm{peak}}$ is the value of $R_{\mathit{CB}}$ at the peak in the polarization with $R_{\mathit{CB}\hspace{0.5em}\mathrm{peak}}=20$, 39, and 41 Ω for the squares, triangles, and stars in (a) and (b), respectively. The dependence of (c) $P$ and (d) $Z$ on $R_{\mathit{CB}}$ for the spectra taken on the Ho thin film (unfilled symbols), the ${\mathrm{Ni}}_{0.19}{\mathrm{Pd}}_{0.81}$ thin film (filled circles), and copper foil (cross symbols).

Figure 5

Schematic illustrating the behavior of $P$ and $Z$ as a function of tip pressure for a system with a surface scattering layer. Layer (1) is a thin surface oxide and layer (2) represents bulk Ho.