Role of Two-Dimensional Ising Superconductivity in the Nonequilibrium Quasiparticle Spin-to-Charge Conversion Efficiency

Nonequilibrium studies of two-dimensional (2D) superconductors (SCs) with Ising spin–orbit coupling are prerequisite for their successful application to equilibrium spin-triplet Cooper pairs and, potentially, Majorana Fermions. By taking advantage of the recent discoveries of 2D SCs and their compatibility with any other materials, we fabricate here nonlocal magnon devices to examine how such 2D Ising superconductivity affects the conversion efficiency of magnon spin to quasiparticle charge in superconducting flakes of 2H-NbSe2 transferred onto ferrimagnetic insulating Y3Fe5O12. Comparison with a reference device based on a conventionally paired superconductor shows that the Y3Fe5O12-induced in-plane (IP) exchange spin-splitting in the NbSe2 flake is hindered by its inherent out-of-plane (OOP) spin–orbit field, which, in turn, limits the transition-state enhancement of the spin-to-charge conversion efficiency. Our out-of-equilibrium study highlights the significance of symmetry matching between underlying Cooper pairs and exchange-induced spin-splitting for the giant transition-state spin-to-charge conversion and may have implications toward proximity-engineered spin-polarized triplet pairing via tuning the relative strength of IP exchange and OOP spin–orbit fields in ferromagnetic insulator/2D Ising SC bilayers.


I njection and excitation of electrons, typically called
Bogoliubov quasiparticles (QPs), in a superconductor (SC) with either an external (Zeeman) or internal (exchange) spin-splitting field 1−3 under nonequilibrium conditions (i.e., voltage bias or temperature gradient) have been one of the central research topics in superconducting spintronics. 1−7 This is because their exotic transport properties, derived from the superconductivity-facilitated coupling between different nonequilibrium imbalances (e.g., spin, charge, heat, and spin-heat), can considerably improve the functionality and performance of spintronic devices. Various nonequilibrium phenomena mediated by QPs have been observed in SC-based devices with either Zeeman or exchange spin-splitting: long-range spin signals, 8−10 pure thermal spin currents, 11 large (spin-dependent) thermoelectric currents, 12 and spectroscopic evidence of spin-heat transport. 13 Recently, a magnon spin-transport experiment 14 has reported that the conversion efficiency of thermal-magnon spin to QP charge via an inverse spin-Hall effect (iSHE) 15 in an exchange-spin-split Nb layer can be significantly enhanced by up to 3 orders of magnitude in the normal-to-superconducting transition regime. This giant transition-state QP iSHE has been semi-quantitatively explained in terms of two competing mechanisms of the superconducting coherence versus the exchange-field-frozen QP relaxation. A very recent theory 16 has pointed out that the electron−hole symmetry breaking present in SC/FMI (FMI = ferromagnetic insulator) bilayers mixes the spin and heat imbalances and can cause the enhancement of QP spin accumulation by several orders of magnitude relative to the normal state. Both these studies 14,15 emphasize the crucial role of the spin-splitting of QP densityof-states (DOS) and the resulting electron−hole asymmetry in enhancing the spin sensitivity of the SC detector. 5,15 The advent of two-dimensional (2D) SCs 17−21 and their compatibility with any other materials via circumventing the need for lattice matching between adjacent material systems provide platforms to explore intriguing physical phenomena in various geometries, 22 including van der Waals (vdW) heterostructures with a twist, and in proximity combination with magnetic vdW flakes and/or thin films. 23,24 Because excited QPs and Cooper pairs in the superconducting condensate state are intimately correlated, 1−6 studies of nonequilibrium QP spin properties in such 2D SCs are of fundamental importance for understanding equilibrium spinpolarized triplet Cooper pairing 1−6 and the possible stabilization of Majorana Fermions. 25−27 2D superconductivity has been recently discovered in monolayer transition metal dicalcogenides (TMDs) 17 28 where Zeeman spin-splitting fields are the predominant mechanism for Cooper pair breaking in the 2D limit and T c is the superconducting transition temperature. Such an enhancement of H 0 c2 μ is explained by Ising spin−orbit coupling (SOC), 17−21 rooted in the broken IP crystal inversion symmetry plus the large SOC due to heavy transition metal atoms in TMDs. The Ising SO field μ 0 H SO (as large as several hundred Tesla in the monolayer limit) 17−21 strongly pins Cooper pair spins at K and K' points of the hexagonal Brillouin zone to opposite out-of-plane (OOP) directions over IP applied magnetic fields. This stabilizes OOP Cooper pairing and forms so-called Ising superconductivity. 17−21 We here investigate how the 2D Ising superconductivity influences the transition-state enhancement of magnon spin to QP charge conversion in a superconducting flake of 2H-NbSe 2 20,29−31 (Figure 1a) and compare its efficiency with a conventional superconducting thin film of Nb 14 (BCS SC). We first demonstrate that the normal-state spin-to-charge conversion functionality of the 2H-NbSe 2 flake can be 4 times more Figure 1. Nonlocal magnon spin-transport device with Ising superconductor. (a) Device layout and measurement scheme. When a dc charge current I dc is applied to the right Pt injector, either electrically or thermally driven magnons accumulate in the ferrimagnetic insulator Y 3 Fe 5 O 12 (YIG) underneath and diffuse toward the left Pt detector. These magnon (s = +1) currents are then absorbed by the left Pt detector, resulting in the electron spin accumulation that is, in turn, converted to a nonlocal charge voltage V nl Pt via the inverse spin-Hall effect (iSHE). Such a conversion process also occurs for the central 2H-NbSe 2 flake and thereby V nl NbSe 2 . Note that, unlike spin-singlet (S = 0) Cooper pairs in a coherent ground state, the excited quasiparticles (QPs) can carry spin angular momentum in the superconducting state. How out-of-plane (OOP) Cooper pairing of the 2H-NbSe 2 affects the transition-state enhancement of QP iSHE will be discussed in this study. (b) Crystal structure of the 2H-NbSe 2 , where in-plane inversion symmetry breaking by Se plus spin−orbit coupling of Nb lead to OOP spin-singlet (S = 0) Cooper pairs, constituting Ising superconductivity. (c,e,g,i) Optical micrographs of the fabricated devices. Atomic force microscopy (AFM) scans of the transferred 2H-NbSe 2 flakes (d,f,h) and the deposited Nb thin film (j). ef ficient than that of the Nb film. We then find distinctively different transition-state conversion behaviors (e.g., modest transition-state enhancement, rather weak thickness dependence) in the 2H-NbSe 2 and attribute these to OOP Cooper pairing that hampers proximity penetration of IP exchange spin-splitting from the adjacent ferrimagnetic insulating Y 3 Fe 5 O 12 . Notably, the maximum enhancement of spin-tocharge conversion appears at a critical thickness over which the IP crystal symmetry is recovered (equivalently, OOP Ising pairing is no longer protected), allowing the IP exchange field to penetrate. This provides a guideline as to how to tune the relative strength of these two phenomena for a desired proximity effect. 32, 33 We believe that, along with recent advances in 2D SCs of various intriguing properties (e.g., type-I/-II Ising, Rashba, topological SCs), 22,34 our approach helps find right material combinations for developing superconducting spintronic devices over conventional BCS SCs.

RESULTS AND DISCUSSION
Our nonlocal magnon spin-transport devices (Figure 1a Figure 1b, it has a hexagonal crystal structure with lattice constants, a = b ≈ 0.3 nm and c ≈ 1.3 nm and each unit cell consists of two AB stacked NbSe 2 layers. 30,31 On a single-piece YIG film, we prepared several independent devices with different 2H-NbSe 2 flake thicknesses t NbSe 2 (Figure 1c−h) as well as reference devices in which Nb thin film is directly deposited 14 (Figure 1i,j). The Nb thickness t Nb is fixed at 15 nm, which is comparable to its dirty-limit coherence length ξ Nb , so that the YIG-induced exchange spin-splitting-field can penetrate the Nb layer while retaining the superconducting coherence, thereby maximizing the transition-state QP iSHE. 14 In this device structure (Figure 1c,e,g,i), we pass a dc current I dc through one Pt electrode (using leads 1 and 2) while measuring the IP magnetic-field-angle α dependence of the α ] using the other Pt electrode (leads 7 and 8) and the central NbSe 2 (or Nb) (leads 3 and 4). Since we apply an external IP magnetic field μ 0 H ext = 5 mT that is larger than the coercive field H 0 c YIG μ of YIG, α is simply defined as the relative angle of μ 0 H ext (//M YIG ) to the long axis of the two Pt electrodes which are collinear. 14 15 in the detector are proportional to the magnon spin current and accumulation created electrically [SHE (charge-to-spin conversion) 15 where V 0 is a spin-independent offset voltage. Below, our discussion will focus on V nl th Δ , since it remains detectably large at low T for reasonable |I dc | such that Joule heating does not destroy the superconducting phase of the 2H-NbSe flake (or Nb thin film). Let us first discuss the electrical transport properties of the transferred 2H-NbSe 2 flake. In the plot of its resistance R NbSe 2 versus temperature T (Figure 2a) for t NbSe 2 = 9 nm, a resistance anomaly appears around 26 K, which is indicative of its phase transition from a normal metal to an incommensurate charge density wave (CDW) phase. 37 Note that the strongly suppressed CDW phase transition temperature, T CDW = 26 K for our t NbSe 2 = 9 nm flake, is presumably due to the proximity coupling of the CDW with the magnetic order of YIG. In analogy with the Pauli effect 28 in conventional SCs, the Zeeman (or exchange) energy competes with the CDW condensation energy and hence T CDW is predicted to decrease in the presence of external (and/or internal) spin-splitting fields. 38 As T is reduced further, 2H-NbSe 2 becomes superconducting below ∼6.75 K. From the T-dependent upper critical field (Figure 2d), that is obtained by applying an external magnetic field either parallel μ 0 H ∥ (Figure 2b) or perpendicular μ 0 H ⊥ (Figure 2c) to the interface plane, we find   changes of T c , peak width and position below t NbSe 2 = 3 nm, coinciding with the OOP coherence length NbSe 2 ξ ⊥ (black vertical line in e and f), are likely due to thermal-fluctuation-enhanced T c suppression at the 2D limit. 20,39 Detailed results of the t 2.5 NbSe 2 = nm device can be found in Supplementary section 3. In (e) and (f), data from the t Nb = 15 nm reference device are also included for quantitative comparison.
We now focus on how the conversion efficiency of magnoncarried spin to QP charge varies when the 2H-NbSe 2 becomes superconducting. Figure 3a,d,g shows the thermally driven nonlocal signal V nl th NbSe 2 ⌈Δ ⌉ for the t NbSe 2 = 4, 9, and 46 nm devices at various base temperatures T base around the superconducting transition T c . In the normal state (T base /T c > 1), a negative V nl th NbSe 2 ⌈Δ ⌉ (<0) of a few tens of nanovolts is observed for I dc = |0.5| mA (J dc = |3.0| MA/cm 2 ). Given  14 and also to the t Nb = 15 nm reference device studied here (Figure 3j−l). As I dc increases, T c of the 2H-NbSe 2 detector is progressively reduced (inset of Figure 3c,f,i) and the transition width broadens. As a result of this depressed superconductivity, caused by the combined effect of more populated spin-polarized QPs 5 and increased heat dissipation in the 2H-NbSe 2 at a high I dc , a peak of the V nl th NbSe 2 ⌈Δ ⌉ enhancement occurring in the vicinity of T c (Figure 3c,f,i) shifts to a low T base and the enhancement regime widens. These demonstrate that the spin-to-charge conversion efficiency indeed rises when mediated by QPs in the transition state of 2H-NbSe 2 /YIG bilayer, that is the enhanced spindetection functionality of a 2D Ising SC in the normal-tosuperconducting transition regime.  (Figure 4d) as a function of the normalized temperature T base /T c for a quantitative analysis. With increasing I dc , the peak amplitude strongly diminishes, the full-width-at-half-maximum (fwhm) broadens, and the peak position is away from T c (inset of Figure 4a−d). In addition to these generic features, one can find important quantitative differences between the 2H-NbSe 2 and Nb detectors 14 from the thickness dependence of the amplitude, fwhm and position (Figure 4f).
First, the enhancement amplitude attained in the 2H-NbSe 2 detectors is relatively small ⌈Δ ⌉ ⌈Δ ⌉ ≤ = compared with the t Nb = 15 nm reference device with a similar lateral dimension, even though the 2H-NbSe 2 flakes (e.g., t NbSe 2 = 4, 9 nm) possess a higher T c in thinner layers (Figure 4e). Second, the peak width and position abruptly change across 3 nm, coinciding with NbSe 2 ξ ⊥ (black vertical line in Figure 4e,f) below which thermal-fluctuation-enhanced T c suppression at the 2D limit is expected, 20,39 and they become almost t NbSe 2 -independent for thicker flakes. Note that the Nb dectectors 14 reveal a monotonic narrowing of fwhm and a peak shift closer to T c with increasing t Nb . Third, unlike the Nb detectors, 14 the maximum enhancement in the spin-to-charge conversion does not appear at t NbSe 2 ≈ NbSe 2 ξ ⊥ and the t NbSe 2 -dependent enhancement is rather weak.
To account for these distinctively different conversion phenomena, we consider the layer thickness-dependent Ising superconductivity. 20,40 For a few monolayer 2H-NbSe 2 , the IP crystal inversion symmetry is strongly broken by Se atoms (Figure 1b) and thus OOP Cooper pairing is protected and stabilized by the resulting Ising SO-field (76 meV in the monolayer limit). 20,41 In this regime, the YIG-induced IP exchange field (<1 meV) 14,41 hardly spin-splits the QP DOS of the 2H-NbSe 2 and the transition-state enhancement of QP iSHE thus relies mostly on the superconducting-coherencerelevant resonant absorption, 14,16,42 leading to a modest enhancement. As the flake becomes thicker, the IP bulk crystal inversion symmetry is restored, which weakens the OOP Ising pairing and, in turn, enables the YIG-induced IP exchange field to propagate through. This explains why we obtain the maximum enhancement of the transition-state QP iSHE at t NbSe 2 = 9 nm ( ) . Note that, as a critical thickness value that is necessary to fully restore the IP bulk inversion symmetry (equivalently, to diminish Ising pairing) is larger than the coherence length, beyond this critical value, proximity extension of the YIG-induced IP exchange spin-splitting over the entire 2H-NbSe 2 layers is not very effective, limiting the enhancement amplitude. Furthermore, a Γ-centered Seelectron Fermi pocket, constituting a second band with a smaller superconducting gap, emerges in the 2H-NbSe 2 thicker than a few monolayers. 43 This second band whose gap energy seems weakly dependent on t NbSe 2 43 can provide another path for spin-polarized QPs to enter the 2H-NbSe detector, effectively weakening the t NbSe 2 -dependent transition-state enhancement.
Our out-of-equilibrium study highlights the importance of symmetry matching between underlying Cooper pairs and exchange-induced spin-splitting for the giant transition-state enhancement of QP iSHE. 14,16 Based on this, we would predict a greater transition-state QP iSHE, for instance, in MnPS 3 / NbSe 2 bilayers, where exchange spin-splitting 44 and SO fields are both OOP and thus match in the symmetry each other. Similarly, Rashba SC/YIG bilayers, where the Rashba SC has IP SO-fields, 34 would be another symmetry-matching combination. Our results may also provide a guideline for the proximity engineering of hybrid quantum materials that allow for exotic quantum phases (e.g., topological superconductivity with spin-polarized triplet pairs and/or Majorana zero modes) 25−27 at zero field in equilibrium.

CONCLUSIONS
Our magnon spin-transport experiments with 2H-NbSe 2 detectors have shown that OOP Cooper pairing of Ising SC, derived by IP inversion symmetry breaking and strong SOC, hinders the proximity propagation of IP exchange spinsplitting, in turn limiting the transition-state enhancement of QP iSHE. Contrary to the magnon devices with Nb (BCS SC) detectors, 14 the maximum enhancement does not appear at t NbSe 2 ≈ NbSe 2 ξ ⊥ but at a different critical thickness over which the IP crystal symmetry is recovered and so the OOP Ising pairing is no longer protected, allowing the IP exchange field to penetrate. This result should be taken into account for better proximity engineering of Ising SC triplet Josephson junctions with IP ferromagnets. 45 We believe that, with the layer thickness-tunable OOP Cooper pairing 20,40 and IP exchange spin-splitting, 2D Ising SC/FMI bilayers have desirable material properties for the topological protection of spinpolarized triplet Cooper pairs 25 and Majorana Fermions. 26,27 Our findings, together with recent progress in 2D SCs and magnetic vdW crystals, 22,24 also raise the possibility of developing highly efficient atomically thin spin-to-charge converters via symmetry engineering.

METHODS
Device Fabrication. We fabricated the magnon spin-transport devices (Figure 1c,e,g,i) based on 200 nm thick single-crystalline YIG films (from Matesy GmbH, https://www.matesy.de/en/products/ materials/yig-single-crystal) as follows. We first defined a pair of Pt electrodes with an area of 1.5 × 50 μm 2 , which were deposited by dc magnetron plasma sputtering at an Ar pressure of 4 × 10 −3 mbar. These Pt electrodes are separated by a center-to-center distance d Pt−Pt of 15 μm, which is comparable to the magnon spin-diffusion length l sd m estimated from our previous study. 14 For the reference device ( Figure  1i), we defined the central 15 nm thick Nb detector with a lateral dimension of 9 × 12 μm 2 , which was grown by Ar-ion beam sputtering at a working pressure of 1.5 × 10 −4 mbar. Subsequently, we defined the outer Au(80 nm)/Ru(2 nm) leads and bonding pads, which were deposited by Ar-ion beam sputtering.
We next selected NbSe 2 flakes of suitable geometry and thickness, which were mechanically exfoliated from a high-quality single crystal (from HQ Graphene, http://www.hqgraphene.com/NbSe2.php) and first transferred onto SiO 2 (300 nm)/Si substrates, via optical microscopy inspection. We then picked up the selected NbSe 2 flake and transferred it onto the central region of each magnon device (Figure 1c,e,g) using a polydimethylsiloxane-based dry transfer method (see Supplementary section 1 for full details). All these processes have been conducted in an inert atmosphere glovebox to prevent oxidation and degradation of the 2H-NbSe 2 . Note that the 2H-NbSe 2 flakes and Nb thin film were prepared on the same-piece YIG film, confirming almost identical SHE/iSHE properties of the Pt injectors/detectors.
To prevent the unintentional contribution of iSHE from inner Au/ Ru leads themselves to total voltage signals, we electrically isolate them from the active regime of magnon spin-transport by depositing a 10 nm thick Al 2 O 3 oxide layer in-between apart from the electrical contact parts on top of the central 2H-NbSe 2 (or Nb). Finally, we defined the inner Au(10 nm)/Ru(2 nm) leads, which were deposited by Ar-ion beam sputtering. Before depositing the inner Au/Ru leads, the NbSe 2 (or Nb) and Pt surface were gently Ar-ion beam etched for transparent electrical contacts between them.
Superconducting Transition Measurement. To characterize superconducting properties, dc electrical transport measurements were conducted on either transferred NbSe 2 flakes or deposited Nb thin films of the fabricated magnon devices attached on either IP (Figure 2b μ ⊥ data (Figure 2d), respectively, using an anisotropic GL theory 39   Note that, unlike bulk Nb, the occupation energy of Abrikosov vortices in a superconducting Nb thin film (t Nb ≤ Nb Nb ξ ξ = ⊥ ) under μ 0 H ∥ is higher than that under μ 0 H ⊥ , differentiating formulas (eq 2a and 2b) for the T-dependent IP/OOP upper critical fields. 39 This is because the density of Cooper pairs cannot change much on a length scale shorter than the coherence length and hence IP Abrikosov vortices cannot efficiently accommodate magnetic flux. 39 When the Nb (BCS SC) film becomes sufficiently thin (t Nb ≪ Nb Nb ξ ξ = ⊥ ), Abrikosov vortex occupation under μ 0 H ∥ is strongly suppressed and a μ 0 H ∥ -driven dominant Cooper-pair breaker is now the Pauli paramagnetic effect (i.e., Zeeman spin-splitting). 28 Accordingly, eq 2a can be rewritten by Here μ 0 = 4π × 10 −7 Tm/A is the permeability of free space, w Pt is the width (1.5 μm) of the Pt electrode, and d is the distance from the Pt/ YIG interface. For the maximum I dc = 1.0 mA used, we get μ 0 H Oe = 0.3−0.4 mT at d = 100 nm and it decreases to 0.02−0.03 mT at d = 7.5 μm. These estimated values are too weak to perturb the magnetization direction of ferrimagnetic insulating YIG 14 under application of μ 0 H ∥ = 5 mT (Figure 1c,e,g,i) and to suppress the superconducting properties of 2H-NbSe 2 flakes and a Nb thin film whose upper critical fields in the transition state are larger than 0.5 T (Figure 2b,c,f,g).

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.1c07192. Dry transfer of 2H-NbSe 2 flakes onto magnon spintransport devices, Nonlocal spin signals detected by the Pt detector across T c of the 2H-NbSe 2 flake, Transitionstate enhancement of QP iSHE for the t NbSe 2 = 2.5 nm device (PDF)

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