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# Giant spin polarization and a pair of antiparallel spins in a chiral superconductor

## Abstract

Chiral molecules can exhibit spin-selective charge emission, which is known as chirality-induced spin selectivity1,2. Despite the constituent light elements of the molecules, their spin polarization can approach or even exceed that of typical ferromagnets. This powerful capability may lead to applications in the chiral spintronics2 field. Although the origin of spin selectivity is elusive, two microscopic phenomena have been suggested based on experimental results: effective enhancement of spin–orbit interactions3 and chirality represented by a pair of oppositely polarized spins4,5. However, the hypotheses remain to be verified. Here we report the simultaneous observation of these two phenomena in an organic chiral superconductor by magnetoresistance measurements in the vicinity of the superconducting transition temperature. A pair of oppositely polarized spins is demonstrated by spatially mapping the spin polarity in an electric alternating current excitation. The obtained spin polarization exceeds that of the Edelstein effect6,7,8,9,10 by several orders of magnitude, which indicates an effective enhancement of the spin–orbit interaction. Our results demonstrate a solid-state analogue of spin accumulations assumed for chiral molecules, and may provide clues to the origin of their molecular counterparts. In addition, the innovative capability of spin-current sourcing will invigorate superconducting spintronics research11.

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## Data availability

All data generated or analysed during this study are included in this article. Source data are provided with this paper.

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## Acknowledgements

We thank J. Ohe and H. Adachi for their discussions. We are also grateful to the Equipment Development Center and Instrument Center (Institute for Molecular Science) for their technical support. This work was supported by a Grant-in-Aid for Scientific Research (A) (nos. 19H00891 and 21H04641) and (B) (nos. 17H03014, 20H01866 and 20H01863), a Grant-in-Aid for Scientific Research on Innovative Areas (no. 16H06505), a Grant-in-Aid for Transformative Research Areas (nos. 21H05439 and 22H05135) and a Grant-in-Aid for Challenging Research (Exploratory) (nos. 20K20903, 21K18884 and 22K18695) from JSPS KAKENHI, Japan; PRESTO ‘Topological Materials Science for Creation of Innovative Functions’ (grant no. JPMJPR20L9) and ERATO ‘Degenerate π-Integration’ (grant no. JPMJER1301) from JST, Japan; the Frontier Photonic Sciences Project (grant nos. 01212005 and 01213003) and Astrobiology Center Program (grant nos. AB021004 and AB031018) from NINS, Japan; the Research Foundation for Opto-Science and Technology; DAIKO FOUNDATION; and the Nanotechnology Platform Program (Molecule and Material Synthesis) from MEXT, Japan.

## Author information

Authors

### Contributions

G.K. designed the prototypical experiment and collected the preliminary data. H.M.Y. redesigned the experiment. R.N. prepared the samples with the help of D.H. and collected the data on magnetoresistance with the help of H.M.Y. by using measurement programmes provided by T.S. Y.N. and T.N. collected and analysed the data on CD imaging. D.H. analysed and visualized the data, except for the CD images. H.O. and H.M.Y. supervised the study. D.H. and H.M.Y. discussed the results and developed the explanation of the experiments. D.H. wrote the manuscript in discussions with H.M.Y. All authors commented on the manuscript.

### Corresponding authors

Correspondence to D. Hirobe or H. M. Yamamoto.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Angelo Di Bernardo, Yossi Paltiel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 Molecular arrangement in the conduction plane of κ-NCS.

The BEDT-TTF molecules form dimers, and each dimer carries a formal charge of +e (e>0 is the elementary charge).

### Extended Data Fig. 2 Absence of charge rectification at the interface between the Au-capped Ni electrode and κ-NCS.

a, Voltage-current curve obtained by d.c. measurements. A source measure unit (Keithley 2636) was used for the electric d.c. excitation and measurement. The linearity with no offset precludes the possibility that the d.c. voltage signals originated from charge rectification via asymmetric current-voltage relations. b, Schematic of the experimental geometry. SMU denotes a source measure unit.

### Extended Data Fig. 3 Circular dichroism (CD) microscopy of κ-NCS laminated on a PEN substrate (device #1).

a Schematic of the experimental geometry for CD microscopy. b, Microscopic image of device #1 used for transport measurements. CD microscopy was repeatedly performed on each white square. c, CD image reconstructed from the small ones, taken at room temperature, well above the superconducting transition temperature of 7.5 K. The CD signal was evaluated using $$({I}_{L}-{I}_{R})/({I}_{L0}+{I}_{R0})\,\times 100$$, where $${I}_{L/R}$$ is the magnitude of the transmitted left-/right-handed circularly polarised light. $${I}_{L0/R0}$$ is the reference magnitude of left-/right-handed circularly polarised light transmitted only through the PEN substrate. We did not consider the modulation of circularly polarised light transmitted through the metal electrodes. Accordingly, the magnitude of the CD signal is significant for a thin-film crystal of κ-NCS, except for the electrodes. CD microscopy directly probed the chiral lattice structure at room temperature, rather than spin accumulation. The uniform sign of the CD signal confirms the uniform enantiomeric excess of the thin κ-NCS crystal.

### Extended Data Fig. 4 Annealing effect on residual resistance of κ-NCS.

(a,b) Temperature (T) dependence of four-terminal resistance (R) measured in device #2 with annealing (a) and device #1 without annealing (b). All data in the main text were obtained using device #1. Annealing was employed at a glass transition temperature of ~ 80 K, at which the terminal ethylene groups of BEDT-TTF molecules tend to be regularly structured. Through annealing, we successfully suppressed the residual resistance below the superconducting transition temperature; this is probably owed to the increased volume fraction of the superconducting state.

### Extended Data Fig. 5 Magnetisation (M) curves of the Ni electrodes.

The voltage (V) in the local voltage measurement (data with Iac = 2.4 μA in Fig. 3a) is replotted for comparison. The magnetic field, H, dependences of M and V are in agreement, except for a low H range in which only M exhibits a hysteresis loop. This is because M and V are determined by magnetic moments at different locations of Ni: V reflects magnetic moments only on the surface, whereas M mainly reflects magnetic moments in the bulk. This results in different H dependencies owing to different magnetic anisotropies.

### Extended Data Fig. 6 Magnetic field (H) dependence of the four-terminal resistance (R) of κ-NCS.

The R of device #1 was measured while applying magnetic fields of 0 and 10 kOe along the b-axis of the κ-NCS. The agreement of the two datasets demonstrates that the superconductivity of the κ-NCS was almost unaffected up to 10 kOe.

### Extended Data Fig. 7 Microscope image of an actual device with which the data in the main text were obtained (device #1).

A transparent PEN substrate was prepatterned with metal electrodes, and a thin film of κ-NCS was laminated onto the substrate. The light-purple electrodes were made of Ni (31 nm thick) capped with Au (3 nm thick). The beige electrodes were composed of Au (34 nm thick). Numbers 1–6 correspond to the terminal numbers of the devices described in the main text. An Au electrode labelled EXC was used for electric a.c. excitation in the nonlocal voltage measurements.

### Extended Data Fig. 8 Handedness dependence of nonlocal voltage signals.

The data were obtained using device #2, in which the domains of opposite handedness coexisted. The temperature was set to 7.5 K (see the R-T curve in Extended Data Fig. 4a, obtained after an annealing process). a. Microscopic image of device #2. CD microscopy was repeatedly performed on each white square. b, CD images overlaid on the microscope image, obtained at room temperature, well above the superconducting transition temperature of 7.5 K. The calculation of the CD signals is detailed in the caption of Extended Data Fig. 3. The sign of CD signal of κ-NCS changed around the centre. c, Distribution of chirality domains expected from b. The lower domain in blue has the opposite handedness to device #1, while the upper domain in red has the same handedness. d,e Schematic of the experimental geometry for selective application of Iac through one of the two domains. Vac was set to 1 V. In d (e), we summarise the polarisation directions of the spin accumulations calculated from f and h (g and i). f,g,h,i, Nonlocal voltage signals at the upper terminal (f,g) and lower terminal (h,i). f and h were obtained in configuration d, and g and i were obtained in configuration e. A pair of oppositely polarised spins at the crystal edges exhibits polarity reversal from inward (d) to outwards (e) when the handedness of κ-NCS is switched at the excitation positions. This handedness dependence is evidence of the chirality origin of voltage signals.

### Extended Data Fig. 9 Temperature (T) dependence of the voltage signal around the superconducting transition temperature.

Vodd was defined as Vodd = [V(+5kOe) – V(–5kOe)] / 2, where V is the voltage drop between the Au and Ni electrodes. Vac was set to 100 mV. The four-terminal resistance, R, was measured under a zero magnetic field. All data were obtained using device #1.

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Nakajima, R., Hirobe, D., Kawaguchi, G. et al. Giant spin polarization and a pair of antiparallel spins in a chiral superconductor. Nature 613, 479–484 (2023). https://doi.org/10.1038/s41586-022-05589-x

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