Jiawei
Tang‡
a,
Shaohan
Li‡
bc,
Duo
Wang‡
d,
Qi
Zheng
bc,
Jing
Zhang
a,
Tao
Lu
bc,
Jin
Yu
bc,
Litao
Sun
a,
Baisheng
Sa
e,
Bobby G.
Sumpter
f,
Jingsong
Huang
f and
Weiwei
Sun
*g
aSEU-FEI Nano-Pico Center, Key Laboratory of MEMS of Ministry of Education, School of Electronic Science and Engineering, Southeast University, Nanjing, 210096, China. E-mail: provels8467@gmail.com
bSchool of Materials Science and Engineering, Southeast University, Nanjing, 211189, China
cJiangsu Province Key Laboratory of Advanced Metallic Materials, Southeast University, Nanjing, 219210, China
dFaculty of Applied Sciences, Macao Polytechnic University, Macao, SAR, China
eMultiscale Computational Materials Facility, and Key Laboratory of Eco-Materials Advanced Technology, College of Materials Science and Engineering, Fuzhou University, Fuzhou 350100, China
fCenter for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
gKey Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University, Nanjing, 211189, China
First published on 14th November 2023
Recently, two-dimensional (2D) FeSe-like anti-MXenes (or XMenes), composed of late d-block transition metal M and p-block nonmetal X elements, have been both experimentally and theoretically investigated. Here, we select three 2D borides FeB, CoB and IrB for a deeper investigation by including strong correlation effects, as a fertile ground for understanding and applications. Using a combination of Hubbard corrected first-principles calculations and Monte Carlo simulations, FeB and CoB are found to be ferro- and anti-ferro magnetic, contrasting with the non-magnetic nature of IrB. The metallic FeB XMene monolayer, superior to most of the MXenes or MBenes, exhibits robust ferromagnetism, driven by intertwined direct-exchange and super-exchange interactions between adjacent Fe atoms. The predicted Curie temperature (TC) of the FeB monolayer via the Heisenberg model reaches an impressive 425 K, with the easy-axis oriented out-of-plane and high magnetic anisotropic energy (MAE). The asymmetry in the spin-resolved transmission spectrum induces a thermal spin current, providing an opportunity for spin filtration. This novel 2D FeB material is expected to hold great promise as an information storage medium and find applications in emerging spintronic devices.
New conceptsHere, we deliver a series of new 2D magnetic FeSe-like XMene (anti-MXene) borides, which were comprehensively studied by a combination of density functional theory (DFT) and Monte Carlo simulations. Compared with MXenes or MBenes, such mechanical buckled 2D layers hold advanced potential as user-friendly components in diverse electronic devices, enhancing versatility and promoting non-contamination. The novelties and metrics presented in this work can be summarized as follows: (i) the linear response theory was applied to provide a rational Hubbard strength to the d orbital, which is the right way of opening this series of 2D materials and shedding light on their potential applications. FeB, CoB and IrB fall into the ferro-, anti-ferro, and non-magnetic configurations, respectively. (ii) FeB is the most stable material, showing a substantial magnetic anisotropy energy of 416.6 μeV per Fe and remarkably high Curie temperatures of up to 425 K. A combination of the direct- and super-exchange interactions between adjacent Fe atoms plays a vital role in establishing long-range ferromagnetic ordering. (iii) The asymmetry of the transmission spectrum in FeB further confirms the absence of electron–hole symmetry, which could possibly lead to thermal spin-polarized current and potential spin filtration functionality. |
Recently, a new family of FeSe-like 2D layers exhibiting excellent electronic and electrochemical properties was theoretically predicted. These 2D layers can be obtained via a top-down approach by removing the element A layer from the bulk structure of AM2X2 (I4/mmm) (A = alkali, alkaline earth, lanthanide, or actinide metals; M = transition metals; and X = nonmetal elements from IIIA–VIA groups).9 This process resulted in buckled 2D MX layers, with each having the inner layer of M sandwiched between two outer layers of tetra-coordinating X atoms.10–12 Since the 2D structures adopt the anti-stacking order of the known MXenes/MBenes, they were coined the name anti-MXene (or XMenes). The first member of the XMene family, 2D FeSe, was initially synthesized using bottom-up approaches such as molecular-beam epitaxy (MBE),10,13 chemical vapor deposition (CVD),14 and pulsed laser deposition (PLD).15 Subsequently, some of these 2D materials were further theoretically considered and even experimentally synthesized using both top-down and bottom-up approaches,16–18 making the further investigation of the 2D FeSe-like materials very intriguing. For instance, the FeB and CoB XMenes can be used as potential electrocatalysts for the hydrogen evolution reaction and anode materials for lithium- or sodium-ion batteries.9,19 In comparison, compositionally similar FeB and CoB MBenes have been reported as 2D magnets.20–22 The pristine FeB MBene exhibits Ising antiferromagnetism with a Néel temperature of 320 K and a robust magnetic anisotropy energy (MAE) up to 482.2 μeV per atom,21 while the functionalized FeBF, FeBO and FeBOH undergo a transition to exhibit FM behavior, with TC values of 250 K, 275 K and 300 K, respectively, and a MAE of ∼500 μeV per atom.22 Notably, the remarkable freedom in both the structure and composition of these metallic 2D layers offers exciting opportunities to achieve outperforming multifunctionalities and gain valuable insights into a unified understanding of these new 2D materials. With the recent advancements of MBenes, exploring the magnetic properties of metal boride XMenes could potentially offer new possibilities for utilizing these layers as active components in electronic devices, thereby exhibiting multifunctionalities.
The d and f electron-containing systems are often considered to fall into the strong correlation regime, where a wealth of entirely new states is often anticipated, pushing the frontiers of science much like the discovery of the fractional quantum effects. Strong correlation, to some extent, underpins many unique phases of quantum matter, including correlated insulators23–26 and magnetism.23,27 However, most of the d electron dominant XMenes have not been well addressed, particularly regarding their strong correlation induced magnetism. The delocalization error of d electrons often results in a qualitatively wrong metallic ground state. As a useful remedy, the DFT+U method28–32 has been widely employed to investigate the magnetic and electronic properties of 2D transition metal compounds and its results have often proven to be in line with experiments.33–36 It is plausible and mandatory to adopt the DFT+U method as a sophisticated treatment of the correlation strength of the d electron in the newly established XMenes. This approach would enable us to capture their ground states and unravel more and more peculiar performances.
Herein, we aimed to systematically investigate three stable transition metal borides, FeB, CoB, and IrB in the XMene phase. To rationally describe the strong correlation effects, the linear response approach will be utilized to estimate the Hubbard U parameters for partially filled d electron shells of transition metals. Several possible magnetic configurations were considered in order to capture the ground magnetic state. The 2D FeB monolayer is identified as a robust ferromagnetic (FM) metal, while the ground state for CoB and IrB corresponds to the weak anti-ferromagnetic (AF) and non-magnetic (NM) configurations, respectively. The ferromagnetic spin ordering in FeB is robustly maintained and capable of reaching a TC as high as 425 K, which is superior to the corresponding MBenes. As the first attempt to extend magnetic exploration from MXenes into XMene systems, our findings not only enrich the possible diversity of 2D transition metal borides but also pave the way for the application of novel multifunctional 2D XMene layers in realistic spin-electronic device applications.
Dudarev's approach41 was employed to evaluate the strong correlation effect on the d orbital, with the correlation strength represented by the effective Hubbard Ueff = U − J on the d orbitals, where U and J are the on-site Coulomb and exchange parameters, respectively. The Ueff for each metal element was estimated using the linear-response approach formulated by Cococcioni et al.42 To achieve this, a linear fit of the number of d-electrons against the additional potential was performed to compute χ0 and χ, referring to the non-self-consistent interacting and self-consistent interacting density of the response functions of the correlated orbital with respect to additional localized perturbations. The parameter Ueff was then calculated according to the equation: Ueff = χ−1 − χ0−1. For a systematic comparison with DFT+U, we also performed calculations utilizing the Heyd–Scuseria–Ernzerhof hybrid functional (HSE06), which incorporates 75% of the PBE exchange, 25% of the Fock exchange, and 100% of the correlation energy from PBE.43 The validity of our main findings was reinforced through computations employing the HSE06 method. Therefore, in the subsequent discussion, our focus will be directed towards the PBE + U results.
The structure stabilities of the favorable magnetic state were investigated with the Hubbard correction applied. The phonon spectra calculations were carried out with the PHONOPY code44 in the framework of the density functional perturbation theory (DFPT)45 to assess the dynamical stability. For evaluating the thermal stability, the ab initio molecular dynamics (AIMD) simulations were additionally performed using a 3 × 3 × 1 supercell at 300 and 400 K for 5 ps with a time step of 1 fs. The algorithm of Nosé46 was employed to control the temperature during these simulations.
Monte Carlo (MC) simulations were conducted based on the Metropolis algorithm47 within the EspinS package,48 to identify the spin–spin correlation and to estimate the critical temperature. MC simulations were carried out on a supercell size of 50 × 50 × 1 with the periodic boundary conditions along the in-plane direction. The MC simulations with a total sampling of 2 × 106 steps began with a random initial spin configuration, and in each spin, 1 × 106 MC steps were performed. The specific heat CV was estimated under the equilibrium state of the system for a given temperature. The final electronic transport calculations were conducted using real space NEGF techniques implemented in the Atomistix Toolkit (ATK) code.49 Under a temperature gradient, the spin-dependent current is given by:50
![]() | (1) |
Due to the carried d electrons, we considered the non-magnetic (NM), ferromagnetic (FM), and seven collinear anti-ferromagnetic (AF) configurations within a 3 × 3 × 1 supercell, as shown in Fig. 2(a). The relative energies of the non-magnetic and the other eight magnetic states in PBE+U are plotted in Fig. 2(b), indicating that IrB maintains the NM ground state, but FeB and CoB fall into the FM and AF4 magnetic configurations, respectively. For the FM FeB monolayer, the spin moment per Fe atom reaches about 2.42 μB, which is close to the value of the Fe atom in the bcc Fe (2.22–2.48 μB),54–56 but slightly lower than that of orthorhombic Pmma-FeB MBene (2.67–2.75 μB).21,22 For the AF CoB XMene, the spin moment per Co atom is 0.93 μB, approximately twice as high as that of CoB MBene (0.48 μB),22 but lower than the FM-state CoB6 monolayer with magnetic moments of 1.38 μB,57 and hcp Co (1.58–1.72 μB).56,58 It can be seen that compared to identically composed FeB/CoB MBenes, the spin moments are influenced by the geometry and the number of ligands, resulting in inherent orbital degeneracy or spin/electron occupation.
In Fig. 2(c), it is evident that IrB exhibits the largest equilibrium lattice constant, M–B bond length, and layer thickness, whereas CoB demonstrates the smallest equilibrium lattice constant and M–B bond length, and FeB possesses the smallest layer thickness among the three depicted 2D layers. Notably, the M–B bond lengths l of FeB, CoB and IrB XMenes are 2.02 Å, 1.89 Å and 2.07 Å, respectively, all shorter than those of the corresponding MBenes (FeB MBene: l1 = 2.15 Å, l2 = 2.05 Å; CoB MBene: l1 = 2.10 Å, l2 = 2.03 Å; and IrB MBene: l1 = 2.49 Å, l2 = 2.18 Å21). Furthermore, FeB XMene is more sensitive to strong correlation effects, displaying significant changes in the lattice parameter and M–B bond length, but limited changes in the layer thickness since the effects of a and l increase for FM-FeB cancel out each other. On the other hand, both CoB and IrB, whose metal components belong to group 9 of the periodic table, exhibit minimal changes. More importantly, each transition metal atom in MB XMenes is coordinated by only four B atoms, resulting in a different coordination geometry compared to MBenes (six B ligands). This reduced coordination number significantly impacts the crystal field splitting energy, leading to the splitting of the d orbitals into distinct energy levels (vide infra). Consequently, the electronic structure and magnetic properties of MB XMenes are altered compared to MBenes.
The work function is often considered as a pivotal parameter, providing essential insights on the novel field emitter cathodes and the Schottky barrier junctions and related applications, such as light-emitting diodes and field-effect transistors.59,60 Hence, we calculated the work functions of three distinct XMenes and the results are shown in Fig. 2(d)–(f). In the corresponding favorable magnetic ordering, the work functions Φ of FeB, CoB, and IrB are 4.96, 5.36 and 5.07 eV, which are slightly higher than those of bare MBenes (4.1–4.8 eV).61 Note that a pioneering investigation showcased the potential of utilizing Ti3C2Tx MXene, possessing a work function of 4.9 eV, as contact electrodes in organic thin-film transistors and complementary logic circuits, signifying a highly promising avenue.62 Another application of 2D conducting layers with a Φ ∼5.1 eV, is integrating into organic light-emitting diodes (OLEDs), which could approach the performance of modern state-of-the-art commercial OLEDs.63 All results pertaining to work functions not only confirm XMene's potential as a novel electrode candidate material but also suggest its viability for electronic applications.
In addition to the dynamical stability, the thermal stability at room temperature is a critical factor in determining the practical viability of the material. One can see from the AIMD simulations at 300 K shown in Fig. 3(d) that the quenched structure of FeB after the AIMD simulations is robust and well-maintained without bond breaking or any evident phase transitions compared to the original structure. These clues clearly demonstrate that the FM-FeB monolayer is dynamically and thermally stable at room temperature, and therefore the following discussions are primarily based on the PBE+U results. All things considered, the 2D FM FeB and NM IrB monolayers show great promise for practical synthesis and offer ample opportunities for further exploration.
Next, we address the electronic structure of the FM FeB. Fig. 4(a) and (b) illustrates the spin-polarized band structure, total density of states (TDOS), and projected density of states (PDOS). The band structure displayed in Fig. 4(a) confirms the robust metallic character and spin splitting, with each spin channel crosses over the Fermi level. The magnetic ground states, magnetic moment, and metallic band structure have also been verified using the high-accuracy hybrid HSE06 functional, as depicted in Fig. S1 (ESI†), illustrating that our presented results are reliable. The total density of states (TDOS) in Fig. 4(b) reveals considerable asymmetric spin states, clearly validating the presence of a net magnetic moment. The Fe 3d states in the minority channel as well as the B 2p states in the majority channel are situated at the Fermi level. Moreover, the strong hybridization between the Fe-3d and the B-2p states in the minority channel appears around −3.5 to −1.0 eV, as indicated by the PDOS. This phenomenon is responsible for the asymmetric square planar crystal field, which will be discussed in the next section. Further analysis of the d orbital-projected density of states, as shown in Fig. 4(c), provides additional insights into the electronic structure of the FeB monolayer. Specifically, the spin up channel is primarily governed by the Fe-dx2−y2 states, with minimal involvement from other Fe d states. When it comes to the spin down channel, the Fe dxy, dyz and dx2−y2 states emerge as pivotal contributors. Note that the occupied state profiles of dyz and dxz orbitals bear striking coincidences, a phenomenon possibly attributed to orbital degeneracy. In addition, in the vicinity of the Fermi level, it is observed that the Fe-dxy and Fe-dyz orbitals exhibit hybridization in the spin-down channel. On the other hand, the dxy, dyz, dxz and dz2 orbitals show hybrid states in the spin-up channel within the energy range of approximately −3.8 to −4.6 eV. This anisotropic behavior of the d orbitals indicates a directional dependence of the bonding interactions within the FeB monolayer. Such anisotropy is expected to have significant implications for the material's magnetic and electronic properties, as well as its potential applications in spintronics and other fields. Finally, the Fermi surface of FeB is also observed as depicted in Fig. 4(d). For the spin-up Fermi surfaces, one of the two bands contributes to a pocket in the corner, pointing to a cross-shaped sheet, while the other band forms a planus “M”-shaped sheet centered at the X point. The spin-down Fermi surface is also composed of two bands passing through the Fermi energy, both forming distorted squares. This intricate Fermi surface topology underscores the intricate interplay of electronic states and band structures within these materials.
The electronic band structures, TDOS and PDOS of AF-CoB and NM-IrB XMenes are also depicted in Fig. S2 (ESI†). The Fig. S2(a) and (b), ESI† panel for the CoB monolayer displays a small indirect band gap of 0.04 eV, while the IrB monolayer in Fig. S2(c) and (d), ESI† lacks a band gap between the valence and conduction bands, featuring several partially occupied bands crossing the Fermi level in both spin channels. As shown in Fig. S2(b)–(d), ESI,† the computed TDOS for the spin-up and spin-down states in the 2D CoB and IrB monolayers are identical across the entire energy spectrum, which is understandable as the typical hallmark of an AF and NM configuration. In detail, the PDOS for 2D CoB and IrB reveal that the distributions around the Fermi level are primarily attributed to the 3d orbitals of the transition metal atoms, with the contribution from the B atoms being nearly negligible. However, considering the absence of noticeable magnetism in CoB and IrB monolayers, we refrain from redundant reporting on them hereafter.
In Fig. 5(a), one can examine the electron localization functions (ELFs) to understand the bonding characteristics. The value of ELF is 0.0 for the region around Fe atoms, indicating their electron deficiency. Meanwhile, the B frameworks are fully encapsulated by homogeneous electron gas, which plays a pivotal role in constructing the B–B bonds. Notably, no local electron is seen between Fe atoms and B atoms, displaying the ionic bonding character. However, the bonding between Fe and B cannot be classified as purely ionic, as evidenced by the previous DOS analysis, which indicates an orbital coupling between Fe d and B p orbitals. To elucidate the distinct intra- and inter-layer bonding properties, we can project the ELF onto the (001) and (010) planes. The mappings on the (001) and (010) planes are shown in Fig. 5(b), illustrating that the in-plane interatomic ELF typically reaches about 0.15 and indicating a moderate degree of electron delocalization. The red/blue region on the color map signifies a high/low degree of electron localization, as indicated by the color bar. Conversely, the ELF along the out-of-plane is concentrated around the B atoms. In other words, covalent bonding is in the form of an intra-layer, in contrast to inter-layered ionic bonding. This interpretation is further substantiated by our COHP analysis (in Fig. 5(c)), revealing that the Fe–B and B–B bonds exhibit robust bonding states in both the spin-up and spin-down channels. Integrating the COHP curves up to the Fermi level yields the integral COHP (ICOHP) values, which qualitatively correlate with the strength of the corresponding bonds. The ICOHP strength of the Fe–B bonds for the spin-up and spin-down states are −0.98 and −1.36 eV per bond, respectively, higher than those of the B–B bonds (−0.47 eV per bond for the spin-up channel and −0.33 eV per bond for the spin-down channel), indicating that the stability of the entire FeB monolayer primarily arises from ionic bonds, with covalent bonds serving as a supplement. Furthermore, the electron cloud on the surface of the monolayer is notably extensive, which is indicative of its chemically active nature. In conclusion, through the analysis of ELF and COHP, we have revealed the bonding characteristics of the FeB monolayer, which consists of both ionic and covalent bonds that would help us gain a deep understanding of their chemical properties.
Holding the crystal field splitting status and orbital alignment, we further move forward to the exchange mechanism behind the magnetic properties. It is found that the Fe–Fe bond length in FeB is 2.73 Å (shown in Fig. 5(f)), close to the length of Fe–Fe binding in FM α-Fe,54,55 so the direct magnetic exchange interaction by FM coupling might retain. In addition, the super-exchange interaction mediated via the B atom is likely to coexist. According to the Heitler–London model,68,69 the exchange integral J can be written as J ≃ 2k + 4βS, where the k denotes the exchange integral of electrons, β and S stand for the resonance coupling and the overlap integral of the interacting orbitals, respectively. If k has a dominant positive sign, it would result in an FM interaction, and vice versa. Based on the Goodenough–Kanamori rule,70–72 the bond angle of Fe–B–Fe is approximately 85°, close to 90° shown in Fig. 5(f), suggesting the overlap integral S is zero. Consequently, the 2k term acquires a large positive J, leaning towards the FM ground state, as we show above.
Having clarified the relationship between structural and magnetic configurations, we proceed to investigate the long-range behavior of the exchange interaction in the FeB XMene. To estimate the strength of magnetic coupling, we employ the Heisenberg model considering five neighbor interactions:
![]() | (2) |
Next, through mapping the total energies of the FM and the five AF configurations (AF1, AF3, AF4, AF5 and AF7 in Fig. 2(a)) selected according to energy-increase order into the Hamiltonian, the corresponding energies can be further derived as follows:
EFM = E0 − 36J1|S|2 − 36J2|S|2 − 36J3|S|2 − 72J4|S|2 − 36J5|S|2 −A|S|2, | (3) |
EAFM1 = E0 − 12J1|S|2 − 18J2|S|2 + 12J3|S|2 + 24J4|S|2 + 36J5|S|2 − A|S|2, | (4) |
EAFM3 = E0 − 4J1|S|2 − 4J2|S|2 + 4J3|S|2 + 24J4|S|2 + 8J5|S|2 − A|S|2, | (5) |
EAFM4 = E0 + 4J1|S|2 + 12J2|S|2 − 4J3|S|2 − 8J4|S|2 − 4J5|S|2 − A|S|2, | (6) |
EAFM5 = E0 + 4J1|S|2 + 12J2|S|2 − 4J3|S|2 − 24J4|S|2 + 36J5|S|2 − A|S|2, | (7) |
EAFM7 = E0 − 12J1|S|2 − 4J2|S|2 + 12J3|S|2 + 16J4|S|2 + 20J5|S|2 − A|S|2, | (8) |
It was found that 2D FM metals should always offer superior advantages over 2D magnetic semiconductors in the view of applications, since a higher TC can be always expected driven by the surplus charge carriers in the FM metal.77 Monte Carlo (MC) simulations based on the Heisenberg models were performed to reach a rational value of TC. The temperature-dependent specific heat capacity CV for the FeB monolayers is plotted in Fig. 6(c). Based on the peak position of the specific heat curve, the Curie temperature of FeB monolayers is found to be 425 K. Using the same approach, our calculated TC for the monolayer CrI3, around 57 K (in Fig. S4, ESI†) falls within the theoretical range of 36–69 K78–80 and is very close to the experimental measurement of 45 K,5 suggesting the reliability of our calculations. Furthermore, magnetic moments of Fe atoms saturate at low temperatures and decrease continuously with increasing thermal fluctuations. Importantly, even when the temperature reaches 350 K, FeB retains a large magnetic moment of about 2 μB per Fe, and combined with the excellent thermal stability shown in Fig. 3(d) and Fig. S5 (ESI†), the FM FeB affords a huge advantage than many other 2D magnets.
Additionally, the spin–spin correlation was calculated by performing MC simulation at T = 5 K to achieve a deep understanding of the magnetic ordering. Fig. 6(d) shows the average value of the products of neighboring spins Sum(Si·Sj)/N and their absolute values Sum(|Si·Sj|)/N for the spin Hamiltonian given by the coupling constants. Here, N denotes the size of the lattice used in MC simulations. Interestingly, the Sum(Si·Sj)/N is 0 for the 1st and 4th nearest-neighbor spins, corresponding to the offset of FM and AF couplings. If Sum(Si·Sj)/N grounds to −1, like in the 2nd spins, an AF coupling is obtained, and vice versa for +1. Besides, for the 1st, 2nd, 3rd, and 4th spins, the values of the Sum(|Si·Sj|)/N are +1, which means that the spin direction is parallel or antiparallel to its neighbor. The net value of 1 reconfirms that the collinear FM of 2D FeB is stable at low temperatures, further suggesting that the 2D FeB monolayers are robust ferromagnets with relatively high Curie temperatures.
Finally, the calculated transmission spectrum of the device at zero bias without a gate voltage is shown in Fig. 6(e). The conductance is mainly contributed by the spin up channel, which is significantly higher compared to that of the spin down channel, thus leading to a high spin injection efficiency. The asymmetry of the transmission spectrum further confirms the absence of electron–hole symmetry. These characteristics can lead to the generation of thermal spin-polarized currents and potentially having the spin filtration functionality.81–83 We further conducted a detailed analysis of thermal spin-dependent currents concerning the left electrode temperature (TL) under various temperature gradient (ΔT) conditions between the left (TL) and right electrode (TR) junctions in the initial parallel configuration (PC), where ΔT = TR − TL. As illustrated in Fig. 6(f), a linear increase in both spin-up and spin-down current components for TL up to approximately 100 K can be observed. For TL between 100 K and 300 K, the spin-up current exhibits a quasi-linear trend, while the quasi-linear region for the spin-down current surpasses that of the up components of the current. This behavior is attributed to the greater mobility of carriers in the spin-up channel than its counterpart. The plot depicting temperature gradient-based spin-resolved current concerning ΔT (Fig. 6(g)) demonstrates a linear pattern for both spin-up and spin-down current components at varying cold electrode temperatures (TL). The spin-up dominant states in the electron conduction results in a notably higher spin-up electron current compared to the spin-down counterpart, underscoring a precise temperature-dependent spin filtration effect. Additionally, spin filtration efficiency (η) is evaluated by using the formula mentioned below:84
![]() | (9) |
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nh00364g |
‡ J. T., S. L., and D. W. contributed equally to this work. |
This journal is © The Royal Society of Chemistry 2024 |