Chirality-induced spin selectivity (CISS) allows for the generation of spin currents without the need for ferromagnets or external magnetic fields, enabling innovative spintronic device designs. One example is a chiral spin valve composed of ferromagnetic and chiral materials, in which the resistance depends on both the magnetization direction of the ferromagnet and the chirality of the chiral material. So far, chiral spin valves have predominately employed chiral organic molecules, which have limited device applications. Chiral perovskites, which combine the properties of inorganic perovskites with chiral organic molecules, provide an excellent platform for exploring CISS-based devices. However, previous chiral perovskite-based spin valves exhibited magnetoresistance (MR) only at low temperatures. Here, we report room temperature MR in a chiral spin valve consisting of chiral perovskites/AlOx/perpendicular ferromagnet structures. It is observed that the chiral MR increases with rising temperature, suggesting the crucial role of phonon-induced enhancement of spin–orbit coupling in CISS in our device. Furthermore, we enhanced the chiral MR by introducing chiral molecules with amplified chirality. This highlights the potential of chirality engineering to improve CISS and the associated chiral MR, thereby opening possibilities for chiral spin valves tailored for cutting-edge spintronic applications.
I. INTRODUCTION
Charge-to-spin conversion, the process of converting an electric charge current into a spin current, plays a pivotal role in condensed matter physics, particularly spintronics.1–3 This is because a spin (-polarized) current can effectively manipulate the magnetization direction through spin torques, enabling the operation of spintronic devices, such as magnetoresistive memories, spin-based logics, and oscillators, with low-energy consumption.4–10 Furthermore, the spin polarization of electrons in spin-polarized currents determines the magnetoresistance (MR) of a spin valve, an elemental device of spintronics. The MR in a conventional spin valve composed of pinned and free ferromagnetic layers, arises from the difference in resistances between the two magnetic configurations of the device, the parallel and antiparallel alignments.11–13 Notably, magnetization of the pinned ferromagnetic layer needs to be firmly fixed to ensure a large and reliable MR value, requiring the use of highly intricate multilayer structures, including (synthetic) antiferromagnets or hard magnets.14,15
Recently, a new class of material to generate a spin current in a completely different way has been developed: chiral materials. These materials can create a spin-polarized current through the chirality-induced spin selectivity (CISS) effect, the generation of a spin current with polarization aligned with the chiral axis when a charge current flows through chiral structures with broken mirror symmetry [Fig. 1(a)].16,17 This CISS effect can be utilized in solid-state devices. One example is a chiral spin valve, in which one of the ferromagnetic electrodes is replaced with a chiral material. The resistance of the chiral spin valve is dependent on both the direction of magnetization of the ferromagnet and the inherent chirality of the chiral material.18,19 This chiral spin valve has two distinctive characteristics. First, the CISS effect generates spin currents without the need for external magnetic fields or ferromagnetic layers.20 Therefore, it can be used to make a spin valve with a simpler structure and less susceptibility to external environmental fluctuations by replacing the pinned ferromagnetic layer with a chiral material. Second, the magnitude of spin polarization caused by the CISS effect has been reported to be larger than that generated in conventional ferromagnets, potentially leading to enhanced MR ratios.21 More than 90% of spin polarizations have been observed in chiral materials using magnetic conductive probe atomic force microscopy or spin- and angle-resolved photoemission spectroscopy.21,22 Note that it has been theoretically reported that the MR of the chiral spin valve should be absent in two-terminal devices with no leakage current due to current conservation and time reversal symmetry.19,23,24 To explain the experimentally observed non-zero chiral MR, the existence of non-linear response regime and inelastic scattering is a necessary condition for the MR of the chiral spin valve due to the Onsager–Casimir reciprocity and Büttiker reciprocity theorem. Therefore, to understand the chiral MR, it is crucial to investigate the dominant inelastic mechanism in the sample.
To date, chiral organic molecules have primarily been utilized for chiral spin valves because they possess inherent chirality and the capability to self-assemble into ordered structures, obviating the need for intricate fabrication methods.20,25,26 Considering these advantages, chiral molecular intercalation superlattices have recently been examined. Such materials are composed of alternating two-dimensional atomic monolayers, such as TaS2 or TiS2, and self-assembled chiral molecules of R- or S-MBA, where R- (or S-) stands for right-handed (or left-handed) and MBA is α-methylbenzylamine.27 Interestingly, they have exhibited a large tunneling MR of more than 300%, but only at a low temperature of 10 K.27 In the case of chiral molecule/ferromagnetic metal bilayer structures, MR has been observed at higher temperatures. Examples include an MR of 7% at 250 K in 40 bp-ds DNA,28 a current-in-plane MR of 0.02% at 300 K in PbPc-DTBPh ,29 and an MR of 0.03% at 300 K in chiral supramolecular nanofibers.21 However, to develop chiral molecule-based spin valves with large MR under ambient conditions, which is a prerequisite for possible spintronic applications, it is necessary to overcome the inherent molecular limitations, such as inhomogeneity and limited stability.30,31
More recently, chiral hybrid organic–inorganic perovskites (HOIPs), known as chiral perovskites, have emerged as a promising candidate for chiral spintronic applications.32,33 In particular, the chiral perovskites possess rich chemical tunability, leading to the potential to enhance the CISS effect and/or the device stability.34 Chiral perovskites consist of an interpenetrating structure of an inorganic perovskite sublattice and self-assembled chiral organic molecules.35,36 This enables chiral perovskites to consolidate the attributes of inorganic perovskites, such as optoelectronic and ferroelectric properties, with chirality-dependent characteristics originating from the chiral molecules.37,38 It should be noted that perovskites are widely utilized in optoelectronic devices, such as solar cells and LEDs, indicating that chiral perovskites are also compatible with various device applications.39–42 Moreover, it has been reported that the circular dichroism (CD) of chiral perovskites can be increased through material engineering,43,44 suggesting that the CISS effect can be improved by chemically tailoring perovskite elements.45–47 Therefore, chiral perovskites provide an excellent platform for the exploration of CISS-based spintronic devices. However, research on chiral perovskite-based spin valves has only been rarely reported and MR has been observed only at 10 K.48
In this article, we report the first demonstration of room-temperature chiral MR in a chiral perovskite-based spin valve composed of chiral perovskites/AlOx/perpendicular ferromagnetic Co structures, in which the chiral perovskites are (R/S-MBA)2PbI2.8Br1.2. The chiral perovskite-based spin valve shows two typical chiral MR characteristics. First, the device resistance changes upon magnetization reversal of the perpendicularly magnetized Co layer. Second, the sign of MR is reversed when changing the handedness of the chirality. These results confirm that the MR of the device is caused by the CISS effect, the generation of spin-polarized current in chiral materials. Notably, it was found that the magnitude of chiral MR increases with increasing temperature, indicating that inelastic electron–phonon interaction and associated enhancement of effective spin–orbit coupling (SOC) are the main mechanism of the CISS effect in our device. Furthermore, we demonstrate a doubling of chiral MR by introducing a chiral organic molecule, 1-(2-naphthyl)ethylamine (NEA), which increases the lattice distortion of inorganic perovskites.
II. RESULTS AND DISCUSSION
A. Synthesis and characterization of chiral perovskites
To explore the CISS effect in a spin valve device, we employed a chiral HOIP of (R-/S-/Racemic-MBA)2PbI2.8Br1.2, in which chirality is induced by chiral cations of (R- or S-)-MBA [Fig. 1(b)]. Chiral HOIP thin films were fabricated by synthesizing single crystals of (R-/S-/Racemic-MBA)2PbI2.8Br1.2 using a cooling crystallization method and subsequently spin-coating the chiral HOIP-based solutions (see the details in Sec. IV). Figure 1(c) shows the structure of the (R-/S-MBA)2PbI2.8Br1.2 thin films consisting of corner-shared octahedral two-dimensional (2-D) layers separated by MBA cations. The MBA transfers its chirality to the 2-D layers by causing structural tilting through two mechanisms: one is the hydrogen bonds between ammonium and halides;33 the other is the π-π interactions of the benzene rings connecting the octahedral 2D layers.35,49 The latter also contributes to forming the c axis perpendicular to the substrates. In Fig. 1(d), the x-ray diffraction (XRD) results reveal that all films exhibit peaks at 6.2°, 12.3°, 18.5°, and 24.8°, corresponding to the (002) planes. This demonstrates that the chiral HOIPs were grown with c axis perpendicular to the substrate. The full width at half maximum value of the (002) peak was 0.09° (supplementary material, 1), indicating that the chiral perovskite films have high crystalline ordering along the out-of-plane direction. To check the chirality of the films, absorption spectra and CD measurements were performed. Figure 1(e) shows the normalized absorption spectra of (R-/S-/Racemic-MBA)2PbI2.8Br1.2 films. It can be seen that all the three samples have absorption peaks at 480 nm, corresponding to the excitonic band structures of the 2D inorganic layer with a broadened bandgap due to hybridization of Br 4p and Pb 5s orbitals.50 It should be noted that the absorption peak at 350 nm is due to the charge transfer transition between the organic ligand and the inorganic layer.51 Figure 1(f) shows the CD spectra obtained from the difference in absorbance between left and right circularly polarized lights for each wavelength. It was observed that the intensity and sign of the peaks depended on the handedness of the chiral organic ligands: R–HOIP (S–HOIP) exhibits a peak near 490 nm with an intensity of +27 mdeg (−20 mdeg), whereas racemic-HOIP shows no CD signal. This demonstrates that chirality is indeed induced into the inorganic layers by the chiral ligands. It should be noted that the CD peaks of MBA only appear at below 275 nm (supplementary material, 2). These experiments confirmed that our chiral perovskite thin films possess two essential material properties for the chiral spin valves: the presence of chirality for the CISS effect and the alignment of the chiral axis perpendicular to the plane through which current flows. Note that we used the Br-substituted mixed halide perovskite rather than the commonly used iodine perovskite (R-/S-MBA)2PbI4, as it enhances chirality and improves surface morphology, which are beneficial to device applications (supplementary material, 3).
B. Magnetoresistance in a perpendicular spin valve based on chiral perovskites
Using the chiral perovskite of (R-/S-MBA)2PbI2.8Br1.2, we fabricated a crossbar-patterned spin valve device with a counter electrode of perpendicularly magnetized Co and an AlOx spacer [Fig. 2(a)]. The full film stack was Si/SiO2 substrate/Pt (5 nm)/Co (1.2 nm)/AlOx (2 nm)/chiral perovskites (150 nm)/Ru (20 nm). It should be noted that the introduction of the AlOx layer was intended to make spin-dependent tunneling the dominant transport mechanism in the devices. The fabrication details are given in Sec. IV. Figure 2(b) shows the hysteresis loop of the film measured at room temperature as a function of the out-of-plane magnetic field (Bz), demonstrating the perpendicular magnetic anisotropy of the Co layer. It should be noted that the introduction of the ferromagnetic Co electrode with perpendicular magnetic anisotropy provides the chiral spin valve with the following advantages. First, maximum MR can be easily achieved because the magnetic easy axis is aligned parallel (or antiparallel) to the spin polarization direction of the CISS effect-induced spin current. Second, spintronic devices employing perpendicular magnetic materials exhibit device properties superior to those using in-plane magnetic materials; improved properties include reduced switching current, enhanced thermal stability, and fast operation.52–54
The MR of the spin valve device was measured at room temperature with Bz. Figure 2(c) shows the results, in which the MR is defined as MR = [R (Bz) − R (Bz = +40 mT)]/R (Bz = +40 mT) × 100%. These results exhibit two distinctive features. First, the MR changes at the same Bz at which the magnetization of Co is switched. This indicates that the MR in the chiral spin valve, or the chiral MR, is determined by the relative orientation between the spin polarization induced by the CISS effect in the chiral perovskite and the one generated in the ferromagnetic Co layer. When they are parallel (or antiparallel) to each other, the chiral spin valve exhibits low (or high) resistance. Second, the sign of the chiral MR is reversed in the device with a chiral perovskite with different chiral handedness. Changing the chiral molecules from R-MBA to S-MBA in which the latter has opposite chirality reverses the polarity of the CISS-induced spin polarization and the consequent chiral MR. These results unambiguously demonstrate a room-temperature MR in the chiral perovskite-based spin valve, albeit at a small magnitude of 0.2%. Note that the observed chiral MR is lower than expected; this might be attributed to the imperfections at the AlOx and chiral perovskite/AlOx interfaces. Thus, chiral MR can be increased through material engineering, such as optimizing the thickness of chiral perovskites and AlOx, and improving the quality of the AlOx and interfaces. It should be noted that chiral MR was also observed in various structures with different chiral perovskite thicknesses and with another ferromagnet electrode of in-plane magnetized NiFe (supplementary material, 4). This confirms the reproducibility of our chiral spin valves operating at room temperature. Note that the chiral MRs of the samples with R- and S-handedness are different in magnitude. This is attributed to the divergent chiral characteristics of the HOIPs, as the identical ferromagnetic electrode of Co is used in both cases. This is supported by the qualitative proportionality between the magnitudes of the MR and CD values; the latter shown in Fig. 1(f). However, further study is required to fully understand this phenomenon.
C. Temperature dependence of chiral magnetoresistance
To understand the underlying mechanism of the CISS effect in our sample, we examined the temperature dependence of chiral MR. As aforementioned, chiral MR is absent in two-terminal devices with no leakage current due to current conservation and time reversal symmetry in the linear response regime.24 However, experimental findings have shown a significant CISS effect in such systems.45–47 To resolve this discrepancy, it was proposed to incorporate inelastic scatterings and non-linear transport into the CISS effect.23 This can also explain a substantial CISS effect in organic systems with weak SOC.45–47 A representative inelastic scattering mechanism is electron–phonon interaction.55,56 If this is the dominant scattering mechanism in the CISS effect, a distinct temperature dependence is expected: CISS increases with temperature.28 When this increased CISS of a chiral crystal with temperature overcomes the decreased spin polarization of the ferromagnet, which is common for 3d transition-metal ferromagnets, the chiral MR can increase with temperature. Therefore, analyzing the temperature dependence of chiral MR provides a hint to comprehend the CISS mechanism in our device.
Figure 3(a) shows MR curves of the chiral perovskite-based spin valve, measured at different temperatures ranging from 2 to 300 K. They exhibit similar MR behaviors across all measured temperatures; the resistance changes upon reversal of Co magnetization. Interestingly, the MR ratio increases with increasing temperature, while the coercive field decreases. Figure 3(b) depicts chiral MR as a function of temperature, demonstrating that the MR ratio gradually increases with rising temperature from 0.177% at 2 K to 0.215% at 300 K. The temperature dependence of the sample resistance is shown in supplementary material, 5. This temperature dependence is in stark contrast to what is typically observed in conventional spin valves composed of two ferromagnetic layers, in which MR decreases with increasing temperature due to reduced spin polarization at elevated temperatures. Given that the spin polarization of Co decreases with temperature, the observed increase in MR with increasing temperature is considered the lower bound of the increase in spin polarization resulting from the CISS effect. The temperature dependence of chiral MR suggests that inelastic phonon–electron scattering and associated enhancement of spin–orbit coupling are the primary mechanisms of the CISS effect in our devices. Therefore, our device meets both the prerequisites for chiral MR: inelastic relaxation and non-linear transport. The latter is confirmed by the non-linear I–V characteristics in our spin valve (supplementary material, 6).
D. Enhanced chiral magnetoresistance via amplified chirality
Finally, we investigated a way to enhance chiral MR through chemical engineering, specifically introducing a chiral ligand with amplified chirality. Previous reports demonstrated that introducing longer chiral molecules improved chirality and the CISS effect.47 In this regard, we introduced a chiral ligand of NEA, comprising two benzene rings, to induce stronger π-π interaction that resulted in more structural distortion when connecting each perovskite layer43 [Fig. 4(a)]. Note that MBA consists of a single benzene ring [Fig. 1(b)]. Figure 4(b) shows CD spectra of NEA-based chiral HOIPs, in which the CD intensities are more than ten times greater than those of the MBA-based ones. Note that the g-factor of the NEA-based chiral HOIPs is also much larger than that of the MBA-based chiral HOIPs, confirming the increase in chirality by employing NEA (supplementary material, 7). We next fabricated an NEA-based chiral spin valve, in which the chiral organic ligand was substituted from MBA to NEA. Figure 4(c) shows the MR curve of the device with NEA, together with that of the device with MBA. Both the devices exhibit similar switching fields regardless of the type of chiral molecule used, which is consistent with the chiral MR behavior shown in Fig. 2(c). Notably, the magnitude of the chiral MR increases by nearly twofold when replacing MBA with NEA, which is attributed to the enhanced CISS effect by chirality amplification. Note that the resistance of the sample with NEA is larger than that with MBA, indicating that the enhancement in chiral MR is not due to a decrease in device resistance (supplementary material, 5).
These results suggest that amplifying chirality through chemical or structural engineering will further enhance the CISS effect and the associated chiral MR. One strategy could involve introducing materials with stronger SOC, such as substituting Pb for Bi, into perovskite structures.57 Another option is to modulate the structural symmetry of HOIPs from a higher symmetry (C2) to the lowest symmetry state (P1), to induce an additional degree of asymmetric distortion through chiral cation doping in chiral–chiral mixed-cation systems.58 Therefore, adept material design of chiral perovskites holds the potential to significantly enhance the CISS effect and the resulting chiral MR, making these materials promising not only for fundamental CISS investigations but also for implementation in robust spintronic devices.
III. CONCLUSION
In this work, we have successfully demonstrated the realization of room-temperature chiral MR in a chiral perovskite-based spin valve composed of chiral perovskites/AlOx/perpendicular ferromagnetic Co. The observed chiral MR exhibited characteristic dependence on both the magnetization direction of the Co layer and the chirality of the chiral perovskite. Moreover, the magnitude of the chiral MR displayed an intriguing increase with rising temperature, suggesting the vital role of inelastic electron–phonon interaction as the primary mechanism of the CISS effect in our device. In addition, by introducing a chiral organic molecule with amplified chirality, NEA, we achieved a substantial enhancement of chiral MR, further highlighting the potential of chirality engineering to enhance the CISS effect and the associated chiral MR. Our findings not only contribute to a deeper understanding of the CISS effect and its interplay with electron–phonon interaction and associated enhancement of SOC but also demonstrate the potential of chiral perovskites as a versatile material platform for next-generation spintronic applications.
IV. EXPERIMENTAL SECTION
A. Materials
All the chemicals were used as received unless otherwise indicated. (R)-(+)-α-methylbenzlyamine (R-MBA, >98%), (S)-(+)-α-methylbenzlyamine (S-MBA, >98%), (±)-α-methylbenzlyamine (Rac-MBA, >97%), lead(II) oxide (PbO, 99.999%), hydriodic acid (HI, 57 wt. % in H2O, distilled, stabilized, 99.95%), hydrobromic acid (HBr, 48 wt. % in H2O, ≥99.99%), dimethyl sulfoxide (DMSO, anhydrous, ≥99.9%), and N,N-Dimethylformamide (DMF, anhydrous, 99.8%) were purchased from Sigma-Aldrich. (R)-1-(2-Naphthyl)ethylamine (R-NEA, >98%) and (S)-1-(2-Naphthyl)ethylamine (S-NEA, >98%) were purchased from TCI Chemicals.
B. Synthesis of chiral perovskites single crystals
(R/S/Rac-MBA)2PbI2.8Br1.2 single crystals were synthesized by using the cooling crystallization method. 0.896 mmol of PbO was dissolved in hydrohalic acid, composed of HI and HBr, in which the molar ratio of HI to HBr was 1:3 with 8 ml volume. After the PbO was fully dissolved by stirring, 4.5 mmol of R/S/Rac-MBA was added to the solution. Yellow precipitate was immediately formed, and the solution was heated to 100 °C to redissolve the precipitate. After the solution became transparent, the reacted solution was naturally cooled to room temperature. Finally, orange-colored single crystals were obtained, and the crystals were rinsed with toluene during vacuum filtrations.
(R/S-NEA)2PbI4 single crystals were synthesized in a similar manner. 0.896 mmol of PbO was dissolved in 6 ml HI solution. After the PbO was fully dissolved by stirring, 1.792 mmol of R/S-NEA was added to the solution. Yellow precipitate was immediately formed, and the solution was heated to 100 °C to redissolve the precipitate. After the solution became transparent, the reacted solution was naturally cooled to room temperature. Finally, yellow-colored single crystals were obtained, and the crystals were rinsed with toluene during vacuum filtrations.
C. Fabrication of chiral perovskite thin films
Clean soda lime glass substrates were treated with oxygen plasma for 2 min. The synthesized (R/S/Rac-MBA)2PbI2.8Br1.2 single crystals were dissolved in a DMF and DMSO mixture (DMF: DMSO = 1:1 in weight ratio), and the solution was spread on the substrates. The film was fabricated by spin-coating at 4000 rpm for 30 s, and in a glove box, the (R/S/Rac-MBA)2PbI2.8Br1.2 thin films were annealed at 80 °C for 5 min to induce the desired phase and remove the residual solvent.
The synthesized (R/S-NEA)2PbI4 single crystals were dissolved in DMF and the solution was spread on the substrates. The (R/S-NEA)2PbI4 thin film was fabricated by spin-coating at 4000 rpm for 30 s, and in a glove box, the films were annealed at 100 °C for 10 min to induce the desired phase and remove the residual solvent.
D. Fabrication of chiral spin valves
Samples of //Pt (5 nm)/Co (1.2 nm)/AlOx (2 nm) were deposited on Si/SiO2 (200 nm) substrates by magnetron sputtering at room temperature with a base pressure below 3.0 × 10−8 Torr. Metallic layers were deposited by DC sputtering with a working pressure of 3 mTorr. The AlOx layer was formed by the deposition of an Al layer (2 nm) and subsequent exposure to O2 plasma for 75 s, which is the optimal oxidation time found in our previous work.8 For electrical measurements, a crossbar-patterned spin valve was fabricated using the following process. First, a bottom electrode consisting of a Pt/Co/AlOx layer was defined by photolithography and Ar ion-beam etching. The width of the bottom electrode was 100 μm. Second, following the definition of the bottom electrode, an SiO2 passivation layer was deposited by RF sputtering to cover the side wall of the bottom electrode, preventing any shunting current through the side wall. Third, a chiral perovskite layer (150 nm) was spin-coated onto the bottom electrode, after which a top contact electrode of Ru (20 nm) was deposited on the chiral perovskites layer by magnetron sputtering with a metal-hard mask: the resulting layer has a crossbar-patterned structure, identical to that of the bottom electrode.
E. Structural characterizations
θ/2θ XRD measurements of the thin films of R/S/Rac-MBA and R/S-NEA were taken on a RIGAKU SmartLab diffractometer with Cu Kα1 (λ = 1.54 Å). The range of the 2θ scan was 5°–40°, with a step size of 0.01° at a scan rate of 10° per minute. Circular dichroism (CD) measurements were performed using a JASCO J-1700 spectrophotometer with a range of 300–800 nm at room temperature under N2 atmosphere. Soda-lime glass was used as a substrate for measurement, and bare glass was used in baseline correction.
F. Electrical characterizations
The transport measurement of the chiral spin valves were conducted using a closed-cycle cryostat. The device resistance was measured using a standard four-point method with a reading current of 10 μA, while an out-of-plane magnetic field of up to 50 mT was applied for MR measurements.
SUPPLEMENTARY MATERIAL
See the supplementary material for additional XRD in an MBA-based chiral perovskite thin film, CD spectra in chiral molecules of MBA and NEA, CD and surface morphology of the perovskites, chiral magnetoresistance in various structures, resistance of chiral spin valves, I–V characteristics in a chiral spin valve with R-MBA ligands, and g-factor of NEA- and MBA-based chiral perovskite thin films.
ACKNOWLEDGMENTS
This work was supported by the National Research Foundation of Korea (Grant Nos. 2022R1A4A1031349 and RS-2023-00261042).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
M.-G.K. and I.-K.H. contributed equally to this work.
Min-Gu Kang: Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). In-Kook Hwang: Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Hee-Chang Kyung: Formal analysis (equal); Writing – original draft (equal). Jaimin Kang: Methodology (equal). Donghyeon Han: Methodology (equal). Soogil Lee: Investigation (equal); Writing – review & editing (equal). Junyoung Kwon: Investigation (equal); Writing – review & editing (equal). Kyung-Jin Lee: Formal analysis (equal). Jihyeon Yeom: Investigation (equal); Writing – original draft (equal). Byong-Guk Park: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.