Letter pubs.acs.org/JPCL
Strain Controlled Ferromagnetic-Antiferromagnetic Transformation in Mn-Doped Silicene for Information Transformation Devices Shuang Li,† Zhimin Ao,‡ Jiaji Zhu,§ Jichang Ren,∥ Jiabao Yi,⊥ Guoxiu Wang,# and Wei Liu*,† †
Nano Structural Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China ‡ School of Environmental Science and Engineering, Guangdong University of Technology, Guangzhou 510006, China § Institute for Quantum Information and Spintronics, School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China ∥ Physics Department, National University of Singapore, 2 Science Drive 3, Singapore 117551, Republic of Singapore ⊥ School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia # Centre for Clean Energy Technology, School of Mathematical and Physical Sciences, University of Technology Sydney, P.O. Box 123, Broadway, Sydney, New South Wales 2007, Australia S Supporting Information *
ABSTRACT: A reliable control of magnetic states is central to the use of magnetic nanostructures. Here, by using state-of-the-art density-functional theory calculations, we find that Mn atoms decorated silicene has an anomalously fixed magnetic moment and a high Curie temperature. In addition, a tunable magnetic exchange coupling is achieved for Mn-silicene system with the application of biaxial strain, which induces a transformation from the ferromagnetic (FM) to the antiferromagnetic (AFM) state. As such, an atomic “bit” could be obtained by superimposing strain field once the FM and AFM states are referred to as “1” and “0”. Such piezospin nanodevices, which convert mechanical energy into magnetic moment, would offer great potential for future information transmission, as they ultimately combine small size, high-speed operation, and low-power consumption.
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system that is insensitive to the defects, along with high magnetic moments and high Curie temperatures (TC). In this Letter, we show that Mn-doped silicene monolayers could be a prominent candidate in piezospin nanodevices, which can satisfy both requirements, i.e., high magnetic moments and high TC. Silicene is utilized in our design since it has been demonstrated to have great potentials in highperformance field effect transistors, spintronic devices, and other next-generation electronic devices.15,16 Note that, the doped 3d TMAs would have strong coupling with silicene layers, allowing the modification of their electronic and spin transport properties. Among 3d TMAs, Mn atom exhibits quite unique magnetic behavior since it has a large magnetic moment of 5.0 μB. Yet, the magnetic moment is zero for bulk Mn crystalline, due to its antiferromagnetic arrangement of electron spins. Previous studies have focused on the magnetic property of a single Mn dopant on a number of 2D materials.17,18 Despite these efforts, many questions remain open. For example, it is clear that first-principles calculations fail to
pin-based electronics have great potential to be used in low-power spin field-effect transistors, nonvolatile magneto-logic gates, high-density memory devices, and many other applications.1−3 On the other side, spintronics based on spinqubit boost a whole new subfield of manipulation of a few localized spins in magnetic materials and artificial nanostructures, for its intriguing applications in spin-resolved logic components and ultimately quantum computing.4 A reliable control of magnetic states is central to the use of magnetic nanostructures in quantum information devices, where magnets represent bits of information. To fabricate quantum information transformation device, a reliable control of magnetic states is an important prerequisite for the use of magnetic nanostructures. Advances in two-dimensional (2D) materials allow the fabrication of the smallest magnetic unit by adsorption of a single magnetic atom on monolayer substrates. Typical examples include the transition-metal atoms (TMAs) doped over a variety of monolayers, such as graphene, BN, silicene, and transition metal dichalcogenides.5−14 However, the magnetic and electronic properties of such hybrid systems are highly sensitive to the synthesis process conditions, and the nature and distribution of defects.8,14 Hence, it becomes crucial to completely understand the interaction of TMAs with 2D materials, and to clarify the feasibility of developing a robust © XXXX American Chemical Society
Received: January 16, 2017 Accepted: March 16, 2017 Published: March 16, 2017 1484
DOI: 10.1021/acs.jpclett.7b00115 J. Phys. Chem. Lett. 2017, 8, 1484−1488
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The Journal of Physical Chemistry Letters
Figure 1. Magnetic moments of (a) TMA−silicene systems and (b) doped TMAs. “iso” denotes the isolated TMA.
Figure 2. Spin partial density of states (PDOS) for Mn@SV using (a) HSE, (b) GGA+U with U = 4 eV, and (c) GGA methods. Positive (negative) values represent majority (minority) spin. The dotted line denotes the Fermi level. (d) Scheme of the sd2 hybridization of Mn and the bonding with silicene.
silicene. In the case of TM@SV, the TM atoms move upward from the layer and occupy an almost perfectly symmetric 3-fold position of C3v symmetry. And for TM@DV, the reconstructed supercell forms the 5|8|5 defect, being consistent with the reconstruction of silicene with single vacancy.25,26 For all optimized structures refer to Figure S1. In addition, the computed binding energies shown in Figure S2 indicate that TM@SV and TM@DV are more stable than TM@P−Si. Having obtained the stable structures, we now apply a spinpolarized HSE method19−21 to determine magnetic moments. Figure 1 and Table SI show the magnetic moments of the TM−silicene systems and 3d TM dopants, from which different dopants exhibit distinct magnetism. Specifically, Sc, Cu, and Zn decorated silicenes have nonmagnetic ground states, while V, Cr, and Mn induce a significant magnetism. However, for Ti, Fe, Co, and Ni, the magnetic moments strongly depend on the nature of silicene defects. The magnetic moments are originated from the 3d orbitals of TMAs, in company with some contributions from the adjacent Si atoms. Notably, the total magnetic moments are almost identical, around 3 μB, for the P−Si, SV, and DV systems, being 1 μB smaller than that for Mn dopants (Figure 1b). The small difference in the magnitude of the magnetic moment indicates that the local environment of defects has negligible effects on the magnetic properties of the three systems. We thus conclude that magnetic moments of Mn atoms decorated on silicene are robust and insensitive to defects. The computed magnetic properties are known to be highly sensitive to the selection of functionals in the framework of DFT.27 For this reason, we also performed GGA-PBE and GGA+U computations for the Mn@SV system, and compared the calculated partial density of states (PDOS) with those from the HSE functional. Consistent with previous studies,17 for the Mn dopant we find a magnetic moment of 3 μB with PBE, which is 1 μB smaller than that from HSE. This deviation can be
accurately predict the band gaps and magnetic moments of strongly correlated systems. It is unclear, however, how strongcorrelation Hubbard U potentials will affect the spin alignments of Mn-silicene systems. Furthermore, the strength of magnetic exchange coupling (MEC) and the competition between ferromagnetic (FM) and antiferromagnetic (AFM) spin states under external strains have not yet been investigated. Therefore, a mechanistic understanding of the coupling between Mn atoms adsorbed on the substrate is far from complete. Here, by using the spin-polarized hybrid Heyd−Scuseria− Ernzerhof (HSE) functional,19−21 we systematically study the magnetic properties of Mn on silicene and the coupling between the dopants. We find that Mn-doped silicene possesses extraordinary high, nonvanishing magnetic moments of 4 μB, no matter whether Mn adsorbs on the pristine silicene, or it substitutes a silicon atom. In the Mn-silicene case, the highest theoretical calculated Curie temperature (483 K) is significantly larger than that for the well-studied diluted-magnetic semiconductors (Ga, Mn)As.22,23 Finally, we demonstrate that strain can cause a phase transition between FM and AFM spin states in Mn-silicene systems. If we refer to the FM and AFM states as “1” and “0”, it would allow an atomic “bit” controlled by strain. Our results suggest that Mn-doped silicene envisages the applications in quantum computing with electron spin. We first systematically study 10 3d TMAs, including Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn, doped over silicene monolayers. In our model, a single TMA is adsorbed on a (6 × 6) silicene supercell, where “TM@P−Si”, “TM@SV”, and “TM@DV” denote TMA adsorbed on the pristine silicene, and TMA embedded in single and double vacancies of silicene, respectively. Geometry relaxations were carried out based on density-functional theory (DFT) with the Perdew−Burke− Ernzerhof (PBE) functional.24 Our results showed that TMAs in TM@P−Si systems prefer to locate at the hollow site of 1485
DOI: 10.1021/acs.jpclett.7b00115 J. Phys. Chem. Lett. 2017, 8, 1484−1488
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The Journal of Physical Chemistry Letters attributed to the fact that, the semilocal GGA functional tends to delocalize the d electrons and increase the d−p overlapping, consequently leading to the underestimation of the magnetic moment of Mn dopant. On the other hand, a straightforward, but somewhat empirical GGA+U method was utilized to revisit the above systems, with increasing U from 1 to 7 eV (for more details, refer to the Methods section and Figure S3 in Supporting Information). Figure 2 shows that for U = 4 eV, the PDOS plots from GGA+U are in good agreement with those from the hybrid functional. Figure 2 also illustrates that the main peak of 3d electrons of Mn is located at −2.7 eV; there is a strong hybridized peak of d−p electrons at the Fermi level with the GGA method. By contrast, the main peaks of 3d electrons obtained from the GGA+U and HSE methods are located at −5 eV, which would significantly reduce the degree of the d−p hybridization. To explain why the total magnetic moment of the system is around 3.0 μB, while that of Mn dopant is 4.0 μB, we provide a scheme of Mn bonding with adjacent Si in Figure 2d. Note that the vacancy of silicene has C3v symmetry. To bind with the adjacent silicon atoms, two d electrons and one s electron form sd2 hybridization. The sd2 orbitals have the similar symmetry as C3v and they overlap with surrounding p orbitals of Si. The left three d electrons and one s electrons remain atomic characteristics, and fully spin polarized. This leads to a magnetic moment of 4 μB for the doped Mn. However, the pz electrons of silicenes exhibit opposite polarization, rendering the total magnetic moments of 3 μB for the system. We further doubled the simulation unit cell from (4 × 4) to (4 × 8), with the aim to explore the competition between FM and AFM spin states of Mn. To estimate the strength of MEC, we computed the energy differences between the FM and AFM state (ΔE = EAFM − EFM) for two Mn atom-substituted silicon atoms at the same position (Mn@SV). By comparing the energetic of the two spin states, our calculations show that FM is 121 meV more stable than AFM. Based on ΔE, we further estimated the Curie temperature, TCMFA, via mean-field approximation (MFA)28 3/2kBTC MFA = ΔE /Nimp
Figure 3. (a−e) Spin density (ρ↑ − ρ↓) for five Mn−II@SV systems in the 6 × 6 supercell. An isosurface of ±0.02 Å3 is used for all systems, where red and blue denote positive and negative spin density, respectively. (f) Magnetic moments of the Mn−II@SV configurations, μMn1 denotes magnetic moments of single Mn dopant, μTot is the total magnetic moments of Mn−II@SV systems, and μT‑Mn donates the total magnetic moments of the two Mn dopants. (g) The Curie temperature of different configurations.
the deviation between total magnetic moments of the Mn−II@ SV systems (μTot) and the total magnetic moments of two Mn dopants (μT‑Mn) come from the contribution of the opposite spin charge of Si atoms. We also calculated the TCMFA using eq 1 and compared them in Figure 3g, and concluded that the decrease in the Mn−Mn distance may induce the decrease in TCMFA values. Considering that Curie temperatures are sensitive to the distance of the doped-Mn atoms, one would expect that strain could also be an avenue to tune the ΔE and TC, since Mn−Mn distance varies with imposing strain. For 2D materials, strain application is readily to be controlled by stretching or bending of a flexible substrate.29−32 To check the validity of our assumption, we applied a tension to the system, and defined the biaxial tensile strain as ε = a/a0 × 100%, where a0 and a are the lattice constants of the 2D silicene supercell in its equilibrium and strained states, respectively. The changes in ΔE and total magnetic moments of systems with the tensile strain are given in Figure 4, which clearly shows that, due to the increased buckle of silicene, the total magnetic moments of the systems
(1)
where Nimp is the number of Mn impurities in the supercell. The Curie temperature is determined to be 468 K, well above the room temperature. Notably, the TCMFA is given by the average value of the magnon energies and in MFA all magnon values are considered with equal weight, where the fluctuations have been neglected. This leads to the overestimation of MFA compared to experimental data. In spite of this, the TCMFA of Mn−silicene is still lager than the TCMFA of (Mn,Ga)As, whose highest TCMFA is 380 K.22,23 Now we explore the relationship between Mn−Mn distance and the MEC. We focus on the Mn−II@SV system with two Si atoms substituted by two Mn dopants. Figure 3a−e show five different doping configurations named from Mn-1 to Mn-5 with increasing distance. The FM state is stable for all five systems studied here. The Mn-2 is the energetically most preferable structure. Reconstruction occurs in the Mn-1 and Mn-2 structures: upon full relaxation, two adjacent Mn atoms come closer, and the hexagonal structure is destroyed. However, the magnetic moment of each Mn dopant remains around 4 μB (see Figure 3f). The spin density of Mn atoms has no obvious change with the Mn−Mn distance, but the spin density of the adjacent Si atoms varies with the distance. Thus,
Figure 4. (a) Schematic representation of strain-induced FM to AFM transformation. (b) Energy difference ΔE and (c) total magnetic moment (MM) of the Mn@SV system as a function of strain. 1486
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COMPUTATIONAL METHODS The spin-polarized density-functional theory (DFT) calculations were carried out using the plane-wave-basis-set VASP code.36 We used projector augmented wave potentials to describe the core electrons and the generalized gradient approximation (GGA) of Perdew-Burke-Ernzernhof (PBE) for the exchange and correlation functional.24 The GGA-PBE functional was mainly used to optimize the structures of the Mn−silicene system. A kinetic energy cutoff of 500 eV was used in the simulations. The total spin was not fixed during the structure relaxation, and the Fermi smearing (with a width of 0.02 eV) of the electronic levels was utilized.37 A (6 × 6) periodic supercell was adopted, and the lattice parameter was also optimized to relax the stress caused by the doping TMAs. The Brillouin Zone sampling was done using a 4 × 4 × 1 Monkhorst−Pack grid for relaxation calculations and 8 × 8 × 1 for static calculations.38 The vacuum width along the direction perpendicular to the silicene plane is set to 20 Å. Since the d orbitals of the transition metal may have significant correlation effects, for magnetic moments calculations, we also performed GGA+U calculations using the formulation of Dudarev et al.39 Upon systematically testing the on-site Hubbard U parameters (U values are between 1 and 7 eV), we found that the computed magnetic moments of Mn dopants are sensitive to the selection of the U values (see Figure S3). However, when U is larger than 3 eV, the magnetic moments of Mn dopant are different from those of the Mn@SV system, but their differences are almost fixed (around 1 μB). As such, we chose U = 4 eV for all our GGA+U computations. The magnetic moments are also computed using the spin-polarized HSE functional.
increase, but the magnetic moments of Mn dopants are still about 4 μB. From the spin polarization distribution, we find that, with increasing compression, the larger buckle destroys the rigidity of π electrons and part of π orbital overlaps with the dangling pz orbitals near the vacancy, and therefore reduces the spin polarization of Si. When ε = 0.975, the spin polarization induced by π electrons of Si all disappear; herein, the total magnetic moments of the system equal to the total magnetic moments of all Mn dopants. The opposite spin from nearby Si is dispersed. With further increasing the compression, the magnetic configuration transforms from FM state to AFM state. As a result, the bond length between the Mn atom and its nearest Si atoms decreases to 2.17 Å, and the silicene substrate ripples considerably. In our model, four Mn atoms are evenly distributed in a 6 × 6 supercell. For the AFM state there are two configurations, which were denoted as AABB and ABAB, having nearly equal energies. The same FM to AFM transformation induced by compression can also be observed in the Cr@SV system. For the Co@SV system, due to the large radius of Co, reconstruction takes place under compression, and no magnetic transformation occurs. If the FM to AFM transformation was observed, the systems have the same structure deformation: the large ripple destroys the π bonds. Thus, the transformation probably originates from two different exchange mechanisms. The FM state is caused by RKKY exchange interaction between Mn dopants through itinerant π electrons; the AFM state is induced by superexchange interaction through paired p electrons of Si. The transformation results from the competition of RKKY and superexchange. The rigidity of π conjugation plays a key role in the transformation. With small compression, the rigidity of in-plane π conjugation made the π electrons well delocalized, thus π electrons can act as itinerant electrons. Together with Mn dopants adsorbed in the same site, considering the evolution of RKKY interaction, Mn dopants have to form FM correlation. When the compression was increased, the silicene was deformed with large buckles. The conjugation between π electrons is destroyed, and no nearly free electrons like π electrons contribute to the exchange interaction; the spin polarizations of Mn dopants are then cooperated though superexchange interaction by covalent bonded p electrons of silicon, because the p electrons are localized and therefore AFM magnetic configuration is more stable.33,34 Note that similar conclusions have also been reported by Le et al.,35 showing that the AFM spin state is favorable in MnSi6 structures. Nevertheless, in their calculations, the supercell was not fully relaxed, which would induce external compressions in the MnSi6 structures. In summary, we systematically study the Mn-doped silicene systems using state-of-the-art density functional theory. We find that Mn−silicene systems have high, robust, and nonvanishing magnetic moments. The Mn atom in Mn−silicene has a magnetic moment of 4 μB. With decreasing distance, the magnetic interaction coupling of two Mn atoms through the deformation silicon atoms causes the variation of the total magnetic moments. We also report the theoretical permit of highly stable materials and a ferromagnetic ordering with a higher Curie temperature than (Mn, Ga)As. Remarkably, imposing strain renders a phase transition between ferromagnetic to antiferromagnetic spin states. Our calculations provide a route to facilitate the design of Mn−silicene-based magnetic semiconductors for spintronics and quantum computing devices.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00115. Adsorption structures of single TMA on silicene, the values of bond length, adsorption elevation, and binding energy, the effect of U on magnetic moments, and the values of magnetic moments of all studied structures (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Wei Liu: 0000-0003-3016-7381 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S.L. and W.L. acknowledge the support from the NSF of China (51602155, 21403113), Jiangsu Key Laboratory of Advanced Micronano Materials and Technology, and the Foundation of Jiangsu Specially-Appointed Professor. Z.A. acknowledges the financial support from the hundred talents program of Guangdong University of Technology, “1000 plan” for young professionals of Chinese government. J.Z. acknowledges the support from NSFC (Grant No. 11404043) and the new research direction support program of CQUPT. 1487
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