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Spin Seebeck effect and thermal colossal magnetoresistance in Christmas-tree silicene nanoribbons
Chemical Physics Letters 699 (2018) 250–254
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Spin Seebeck effect and thermal colossal magnetoresistance in Christmas-tree silicene nanoribbons Xiu-Jin Gao, Peng Zhao ⇑, Gang Chen ⇑ School of Physics and Technology, University of Jinan, Jinan 250022, China
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 12 February 2018 In final form 30 March 2018 Available online 31 March 2018
Based on the density functional theory and nonequilibrium Green’s function method, we investigate the electronic structures and thermal spin transport properties of Christmas-tree silicene nanoribbons (CSiNRs). The results show that CSiNRs have ferromagnetic ground state with high Curie temperature far above the room temperature. Obvious spin Seebeck effect with spin-up and spin-down currents flowing in opposite directions by a temperature gradient can be observed in these systems. Furthermore, a thermal colossal magnetoresistance up to 109% can be realized by tuning the external magnetic field. The results show that CSiNRs hold great potential in designing spin caloritronic devices. Ó 2018 Elsevier B.V. All rights reserved.
Keywords: Thermal spin transport Spin Seebeck effect Thermal colossal magnetoresistance Silicene nanoribbon
1. Introduction Spin caloritronics, combing the advantage of spintronics and thermoelectronics, plays an important role in the solution of the world’s energy crisis and development of novel low-powerconsumption devices [1–3]. The research of spin caloritronics can be tracked back to the pioneering experimental discovery of spin Seebeck effect by Uchida et al. in ferromagnetic metal NiFe alloy [4]. In their experiment, spin-up current and spin-down current, which flow in opposite directions, can be induced only by a temperature gradient without using a bias voltage. This indicates that dissipated heat energy can be directly converted into spin current with the potential to achieve lower energy consumption. On the other hand, motivated by the success of graphene [5], alternative two-dimensional group-IV materials, such as silicene [6,7], germanene [8,9], and stanene [10], have drawn extensive interest due to their unique physical and chemical properties. Among them, silicene is highly promising for the compatibility with the conventional semiconductor industry. In particular, much attention has been focused on one-dimensional silicene nanoribbons (SiNRs) [11,12]. Similar to graphene nanoribbons (GNRs), SiNRs have two typical types according to the basic edge characteristics: armchair SiNRs (ASiNRs) and zigzag SiNRs (ZSiNRs). ASiNRs are nonmagnetic semiconductors, while ZSiNRs have stable antiferromagnetic states [13]. Recently, Zhao and Ni constructed two
⇑ Corresponding authors. E-mail (G. Chen).
addresses:
[email protected]
(P.
https://doi.org/10.1016/j.cplett.2018.03.073 0009-2614/Ó 2018 Elsevier B.V. All rights reserved.
Zhao),
[email protected]
kinds of novel SiNRs with sawtooth edges, which are different from ASiNRs and ZSiNRs, namely, Christmas-tree SiNRs (CSiNRs) and tree-saw SiNRs (TSiNRs) [14]. They found both CSiNRs and TSiNRs are more stable than ZSiNRs and have ferromagnetic ground states. Until now, the thermal spin transport properties of some nanoribbon homojunctions or heterojunctions have been studied. For example, Zeng et al. found the spin Seebeck effect, thermal spin-filtering and magnetoresistance effects in magnetized zigzag GNRs (ZGNRs) [15]. Ni et al. observed the spin Seebeck effect and thermal colossal magnetoresistance effect in a ZGNR-based heterojunction consisting of single-hydrogen-terminated ZGNR and double-hydrogen-terminated ZGNR [16]. Huang et al. showed ZGNR co-doped with nitrogen and boron exhibits excellent thermal spin transport properties [17]. Tang et al. demostrated armchair GNRs (AGNRs) with special edge hydrogenation are promising for application in spin caloritronic devices [18]. Wu et al. proposed two zigzag c-graphyne nanoribbons (ZcGNRs) can not only exhibit spin Seebeck effect, but also display rectifier and diode effect in thermally-driven spin currents [19]. Yang et al. found ZSiNRs doped by an Al-P bounded pair at different edge positions can exhibit a temperature-controlled giant thermal magnetoresistance and a high spin-filter efficiency [20]. Fu et al. proposed ZSiNR-based heterojunctions consisting of singlehydrogen-terminated ZSiNR and double-hydrogen-terminated ZSiNR as a highly-performance spin caloritronic devices [21,22]. In this work, we investigate the electronic structures and thermal spin transport properties of CSiNRs. Our results show that CSiNRs have high Curie temperature far above the room temperature and can generate obvious spin Seebeck effect by a temperature difference instead of a bias voltage, between the left electrode and
X.-J. Gao et al. / Chemical Physics Letters 699 (2018) 250–254
right electrode. Moreover, a thermal colossal magnetoresistance up to 109% can be achieved by tuning the external magnetic field. 2. Model and method We use two integers (n1,n2) to label the size of CSiNR primitive cell, where n1 and n2 are the maximum numbers of hexagonal rings along two arrow directions (see Fig. 1) [14], respectively. Fig. 1 shows the CSiNR-based spin caloritronic device with n1 = 5 and n2 = 4, which is denoted as C(5,4) for simplicity. The integer n2 = 4 corresponds to the lowest numbers meeting the requirement of the sawtooth edges [23]. The device is divided into three regions: left electrode (LE), right electrode (RE), and central scattering region (CSR). Each electrode is modeled by one CSiNR primitive cell, while the CSR consists of four repeated CSiNR primitive cell along the transport (z) direction. A vacuum layer of 20 Å is adopted to avoid the interaction between adjacent nanoribbons. Structural optimization is performed for the CSiNR primitive cell using the quasi-Newton method with force tolerance and stress tolerance of 0.01 eV/Å and 0.01 eV/Å3, respectively. The structural optimization and subsequent thermal spin transport calculations are carried out by the first-principles package Atomistix Toolkit (ATK) [24–26], which is based on the density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF). The spin generalized gradient approximation (SGGA) with Perdew-Burke-Ernzerhof (PBE) [27] form of functions is used as the exchange-correlation potential. The core electrons are modeled by Troullier-Martins norm-conserving pseudopotentials [28] and double-f plus polarization (DZP) basis set is adopted for the valence electron wave function. The energy cutoff is set to be 200 Ry in numerical integrations, while the k-point sampling is 1, 1, and 100 in the x, y, and z direction, respectively. The thermally-driven spin current through the CSR can be obtained by the Landauer-Büttiker formula [29],
Z
Ir ¼ ðe=hÞ
1
1
T r ðEÞ½f L ðE; T L Þ f R ðE; T R ÞdE
ð1Þ
where r is the spin index (r = up and dn, representing the spin-up and spin-down). e and h are the electron charge and Planck constant. T r ðEÞ ¼ Tr½CL GR CR GA is the spin-resolved transmission function. Here, GR/A is the retarded/advanced Green function of
Fig. 1. (a) Schematic illustration of the CSiNR-based spin caloritronic device, which includes three regions: left electrode (LE), right electrode (RE), and central scattering region (CSR). z is the transport direction. (n1,n2) denote the size of CSiNR primitive cell. ⊿T represents the temperature difference between LE (TL) and RE (TR), namely, ⊿T = TL TR. (b) Spin density distributions for P and AP magnetic configurations, where pink and cyan surfaces indicate the spin-up and spin-down components, respectively, and the isosurface level is taken as 0.03 |e|/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
251
CSR, and CL/R is the coupling matrix between CSR and LE/RE. fL/R(E,TL/R) = 1/{exp[(E-l)/kBTL/R]+1} is the Fermi-Dirac distribution function of LE/RE. Here, E is the carrier energy, l is the chemical potential and set to zero in our calculations, kB is the Boltzmann constant, and TL/R is the temperature of LE/RE, respectively.
3. Results and discussion In order to search the ground state, we calculate the total energy of C(5,4) primitive cell at nonmagnetic (NM), ferromagnetic (FM) and antiferromagnetic (AFM) states, respectively. The energy differences are ⊿E1 = ENM-EFM = 83.68 meV and ⊿E2 = EAFM-EFM = 40.47 meV, which indicate that the FM state is the ground state [30]. The calculated total magnetic moment in the FM ground state is 2.0 lB, which corresponds to the difference of atom number of the A and B sublattices in one CSiNR primitive cell as predicted from the Lieb’s theorem [31] on a bipartite lattice. Besides, using the mean field theory, the Curie temperature (TC) is estimated, i.e., ⊿E2 = ckBTC/2, where c is the dimension of the system [32]. By setting c = 1 for one-dimensional nanoribbon system, we get a TC of 938 K, which is far above the room temperature. As the magnetization of LE/RE can be modulated by applying external magnetic fields, two magnetic configurations (MCs) are considered [33]: parallel (P) and antiparallel (AP) MCs with magnetic fields at two electrodes pointing in the same and opposite directions, respectively. The spin polarization directions of two MCs can be confirmed by the spin density distributions across the CSR, as shown in Fig. 1(b), where pink and cyan surfaces indicate the spin-up and spin-down components, respectively. Clearly, spin density mainly distributes on the edge silicon atoms, and the whole CSR are spin-up polarized in P MC, while the left part of CSR is spin-up polarized and the right part is spin-down polarized in AP MC. Moreover, the total energy difference between P and AP MCs is calculated to be 54.48 meV, which indicates that the two MCs can transform easily each other by tuning the external magnetic field. We first focus on the P MC. Fig. 2(a) shows the thermally-driven spin currents driven by the temperature difference (⊿T) without an external bias voltage between LE (TL) and RE (TR), namely, ⊿T = TL TR, with different TL = 300, 400, and 500 K, respectively. Fig. 2(b) shows the thermally-driven spin currents vs. TL with different ⊿T = 20, 40, and 60 K, respectively. As shown in Fig. 2(a) and (b), an obvious spin Seebeck effect can be observed: the spin-up current (Iup) is positive (flows from LE to RE), while the spin-down current (Idn) is negative (flows from RE to LE), namely, they flow in opposite directions. Besides, as one can see, Iup is always larger than Idn at the same ⊿T and TL, and both of them increase nearly linearly with the increase of ⊿T or TL. Moreover, we find that the CSiNRs with larger n1 or n2 also exhibit obvious spin Seebeck effect. According to Eq. (1), the thermally-driven spin currents are the joint results of Tr and (fL fR). Fig. 3(a) plots fL with TL = 300 K and fR with TR = 260 K as a function of (E-EF), where EF is the Fermi level. As shown in Fig. 3(a), the electron carrier concentration of LE is higher than that of RE when E > EF, then the electrons flow from LE to RE, resulting in a negative current. On the other hand, the hole carrier concentration of LE is higher than that of RE when E < EF, therefore the holes flow also from LE to RE, leading to a positive current. Furthermore, as shown in the inset of Fig. 3(a), (fL fR) shows a perfect symmetric feature with respect to EF and also a typical exponential decaying nature. As a result, the thermally-driven currents are only determined by transmission close to EF, however, if Tr is also symmetric about EF, the thermally-driven currents originating from electrons and holes will cancel out each other, leading to a zero net current. In other words, for nonzero net current, asymmetric transmission around
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Fig. 2. (a) Thermally-induced spin currents as a function of ⊿T with different TL = 300, 400, and 500 K. (b) Thermally-induced spin currents as a function of TL with different ⊿T = 20, 40, and 60 K.
Fig. 3. (a) Fermi-Dirac distribution function of two electrodes at different temperatures. The inset shows the difference between them. (b) Spin-resolved transmission spectra. (c) Spin-resolved current spectra for fixed ⊿T = 40 K with different TL = 300, 400, and 500 K. (d) Spin-resolved current spectra for fixed TL = 300 K with different ⊿T = 20, 40, and 60 K.
EF is needed to break the electron-hole symmetry. Fig. 3(b) shows the spin-resolved transmission spectra. As one can see, both Tup and Tdn are obvious asymmetric with respect to EF, namely, a narrow spin-up and a narrower spin-down transmission peak lies in the energy region [0.24 eV, 0.1 eV] and [0.12 eV, 0.18 eV], respectively. To further elucidate the combined effects of Tr and (fL fR) on the thermally-driven currents, as shown in Fig. 3(c) and (d), we plot the spin-resolved current spectra Jr(E) = Tr(E)[fL(E, TL) fR(E, TR)], where the cover area under the curves determines the current. Fig. 3(c) corresponds to Jr(E) for fixed ⊿T = 40 K with different TL = 300, 400, and 500 K, while
Fig. 3(d) corresponds to Jr(E) for fixed TL = 300 K with different ⊿T = 20, 40, and 60 K, respectively. As shown in Fig. 3(c) and (d), the peak of Jup and Jdn appears in the energy region [0.24 eV, 0.1 eV] below EF and [0.12 eV, 0.18 eV] above EF, resulting in positive Iup and negative Idn, respectively. Moreover, when TL or⊿T goes up further, both the cover areas of Jup and Jdn increase gradually, leading to the nearly linearly enhancement of Iup and Idn with the increase of TL or ⊿T. However, the cover area of Jup is always larger than that of Jdn, therefore, Iup is always larger than Idn. To further clarify the origin of the transmission peaks around the EF, in Fig. 4(a), we plot the spin-resolved band structures of
X.-J. Gao et al. / Chemical Physics Letters 699 (2018) 250–254
253
Fig. 4. (a) Spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in P MC. (b) Spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in AP MC.
LE (the left panel) and RE (the right panel) in P MC. Clearly, the bands of LE have the same structures as those of RE. In the vicinity of EF, there are two bands for each spin, namely, spin-down bands C1 and C2 in the energy region [0.12 eV, 0.18 eV] above EF, and spinup bands V1 and V2 in the energy region [0.24 eV, 0.1 eV] below EF. The perfect matching of four bands between LE and RE gives rise to the spin-down and spin-up transmission peak around EF at corresponding energy regions (the middle panel), respectively. Now we consider AP MC. Fig. 4(b) plot the spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in AP MC. Evidently, the spin-up and spin-down bands in RE are completely exchanged compared with those in LE when the magnetic configuration goes from P to AP. As one can see, in the vicinity of EF, there is no any overlapping between bands with the same spin index, leading to the formation of a large transmission gap in the energy region [0.6 eV, 0.56 eV], as shown in the middle panel of Fig. 4(b). This indicates that both Tup and Tdn are almost bilaterally symmetric about EF, and then both Iup and Idn must be very small given the symmetry of (fL fR). As shown in Fig. 5, we present the total thermally-driven current, i.e., (Iup + Idn), in P and AP MCs for fixed TL = 300 K with different ⊿T. Clearly, the total thermally-driven current in P MC (IP) is much larger than that in AP MC (IAP), and
the latter is almost completely suppressed. Thus, a thermal colossal magnetoresistance effect can be expected when the magnetic configuration switches between P and AP. To evaluate quantitatively the thermal colossal magnetoresistance effect, we define the magnetoresistance ratio (MR) as MR = [(|IP| |IAP|)/|IAP|] 100%. The inset of Fig. 5 plots the MR as a function of ⊿T with fixed TL = 300 K. As one can see, the MR is higher than 108% from the very beginning, and even reaches 109% after ⊿T = 55 K due to the continuous increase of IP with the increase of ⊿T. This indicates CSiNRs have great potential in designing thermal spin valves. 4. Summary In summary, by using the DFT + NEGF approach, we have investigated the electronic structures and thermal spin transport properties of CSiNRs in P and AP magnetic configurations. Our results show that CSiNRs have ferromagnetic ground state with high Curie temperature far above the room temperature and can generate obvious spin Seebeck effect with spin-up and spin-down currents flowing in opposite directions by a temperature difference instead of a bias voltage, between the left electrode and right electrode. The reason can be attributed to the asymmetry of both spin-up and spin-down transmission spectra about the Fermi level, which breaks the electron-hole symmetry. Moreover, a thermal colossal magnetoresistance up to 109% can be achieved by transitioning P and AP magnetic configurations. The preset work shows that CSiNRs are promising candidates for spin caloritronic applications. Acknowledgements This work was supported by the Natural Science Foundation of Shandong Province, China (No. ZR2016AM11). References
Fig. 5. Total thermally-driven current in P and AP MCs for fixed TL = 300 K with different ⊿T. The inset shows the MR as a function of ⊿T with fixed TL = 300 K.
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Spin Seebeck effect and thermal colossal magnetoresistance in Christmas-tree silicene nanoribbons Xiu-Jin Gao, Peng Zhao ⇑, Gang Chen ⇑ School of Physics and Technology, University of Jinan, Jinan 250022, China
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 12 February 2018 In final form 30 March 2018 Available online 31 March 2018
Based on the density functional theory and nonequilibrium Green’s function method, we investigate the electronic structures and thermal spin transport properties of Christmas-tree silicene nanoribbons (CSiNRs). The results show that CSiNRs have ferromagnetic ground state with high Curie temperature far above the room temperature. Obvious spin Seebeck effect with spin-up and spin-down currents flowing in opposite directions by a temperature gradient can be observed in these systems. Furthermore, a thermal colossal magnetoresistance up to 109% can be realized by tuning the external magnetic field. The results show that CSiNRs hold great potential in designing spin caloritronic devices. Ó 2018 Elsevier B.V. All rights reserved.
Keywords: Thermal spin transport Spin Seebeck effect Thermal colossal magnetoresistance Silicene nanoribbon
1. Introduction Spin caloritronics, combing the advantage of spintronics and thermoelectronics, plays an important role in the solution of the world’s energy crisis and development of novel low-powerconsumption devices [1–3]. The research of spin caloritronics can be tracked back to the pioneering experimental discovery of spin Seebeck effect by Uchida et al. in ferromagnetic metal NiFe alloy [4]. In their experiment, spin-up current and spin-down current, which flow in opposite directions, can be induced only by a temperature gradient without using a bias voltage. This indicates that dissipated heat energy can be directly converted into spin current with the potential to achieve lower energy consumption. On the other hand, motivated by the success of graphene [5], alternative two-dimensional group-IV materials, such as silicene [6,7], germanene [8,9], and stanene [10], have drawn extensive interest due to their unique physical and chemical properties. Among them, silicene is highly promising for the compatibility with the conventional semiconductor industry. In particular, much attention has been focused on one-dimensional silicene nanoribbons (SiNRs) [11,12]. Similar to graphene nanoribbons (GNRs), SiNRs have two typical types according to the basic edge characteristics: armchair SiNRs (ASiNRs) and zigzag SiNRs (ZSiNRs). ASiNRs are nonmagnetic semiconductors, while ZSiNRs have stable antiferromagnetic states [13]. Recently, Zhao and Ni constructed two
⇑ Corresponding authors. E-mail (G. Chen).
addresses:
[email protected]
(P.
https://doi.org/10.1016/j.cplett.2018.03.073 0009-2614/Ó 2018 Elsevier B.V. All rights reserved.
Zhao),
[email protected]
kinds of novel SiNRs with sawtooth edges, which are different from ASiNRs and ZSiNRs, namely, Christmas-tree SiNRs (CSiNRs) and tree-saw SiNRs (TSiNRs) [14]. They found both CSiNRs and TSiNRs are more stable than ZSiNRs and have ferromagnetic ground states. Until now, the thermal spin transport properties of some nanoribbon homojunctions or heterojunctions have been studied. For example, Zeng et al. found the spin Seebeck effect, thermal spin-filtering and magnetoresistance effects in magnetized zigzag GNRs (ZGNRs) [15]. Ni et al. observed the spin Seebeck effect and thermal colossal magnetoresistance effect in a ZGNR-based heterojunction consisting of single-hydrogen-terminated ZGNR and double-hydrogen-terminated ZGNR [16]. Huang et al. showed ZGNR co-doped with nitrogen and boron exhibits excellent thermal spin transport properties [17]. Tang et al. demostrated armchair GNRs (AGNRs) with special edge hydrogenation are promising for application in spin caloritronic devices [18]. Wu et al. proposed two zigzag c-graphyne nanoribbons (ZcGNRs) can not only exhibit spin Seebeck effect, but also display rectifier and diode effect in thermally-driven spin currents [19]. Yang et al. found ZSiNRs doped by an Al-P bounded pair at different edge positions can exhibit a temperature-controlled giant thermal magnetoresistance and a high spin-filter efficiency [20]. Fu et al. proposed ZSiNR-based heterojunctions consisting of singlehydrogen-terminated ZSiNR and double-hydrogen-terminated ZSiNR as a highly-performance spin caloritronic devices [21,22]. In this work, we investigate the electronic structures and thermal spin transport properties of CSiNRs. Our results show that CSiNRs have high Curie temperature far above the room temperature and can generate obvious spin Seebeck effect by a temperature difference instead of a bias voltage, between the left electrode and
X.-J. Gao et al. / Chemical Physics Letters 699 (2018) 250–254
right electrode. Moreover, a thermal colossal magnetoresistance up to 109% can be achieved by tuning the external magnetic field. 2. Model and method We use two integers (n1,n2) to label the size of CSiNR primitive cell, where n1 and n2 are the maximum numbers of hexagonal rings along two arrow directions (see Fig. 1) [14], respectively. Fig. 1 shows the CSiNR-based spin caloritronic device with n1 = 5 and n2 = 4, which is denoted as C(5,4) for simplicity. The integer n2 = 4 corresponds to the lowest numbers meeting the requirement of the sawtooth edges [23]. The device is divided into three regions: left electrode (LE), right electrode (RE), and central scattering region (CSR). Each electrode is modeled by one CSiNR primitive cell, while the CSR consists of four repeated CSiNR primitive cell along the transport (z) direction. A vacuum layer of 20 Å is adopted to avoid the interaction between adjacent nanoribbons. Structural optimization is performed for the CSiNR primitive cell using the quasi-Newton method with force tolerance and stress tolerance of 0.01 eV/Å and 0.01 eV/Å3, respectively. The structural optimization and subsequent thermal spin transport calculations are carried out by the first-principles package Atomistix Toolkit (ATK) [24–26], which is based on the density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF). The spin generalized gradient approximation (SGGA) with Perdew-Burke-Ernzerhof (PBE) [27] form of functions is used as the exchange-correlation potential. The core electrons are modeled by Troullier-Martins norm-conserving pseudopotentials [28] and double-f plus polarization (DZP) basis set is adopted for the valence electron wave function. The energy cutoff is set to be 200 Ry in numerical integrations, while the k-point sampling is 1, 1, and 100 in the x, y, and z direction, respectively. The thermally-driven spin current through the CSR can be obtained by the Landauer-Büttiker formula [29],
Z
Ir ¼ ðe=hÞ
1
1
T r ðEÞ½f L ðE; T L Þ f R ðE; T R ÞdE
ð1Þ
where r is the spin index (r = up and dn, representing the spin-up and spin-down). e and h are the electron charge and Planck constant. T r ðEÞ ¼ Tr½CL GR CR GA is the spin-resolved transmission function. Here, GR/A is the retarded/advanced Green function of
Fig. 1. (a) Schematic illustration of the CSiNR-based spin caloritronic device, which includes three regions: left electrode (LE), right electrode (RE), and central scattering region (CSR). z is the transport direction. (n1,n2) denote the size of CSiNR primitive cell. ⊿T represents the temperature difference between LE (TL) and RE (TR), namely, ⊿T = TL TR. (b) Spin density distributions for P and AP magnetic configurations, where pink and cyan surfaces indicate the spin-up and spin-down components, respectively, and the isosurface level is taken as 0.03 |e|/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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CSR, and CL/R is the coupling matrix between CSR and LE/RE. fL/R(E,TL/R) = 1/{exp[(E-l)/kBTL/R]+1} is the Fermi-Dirac distribution function of LE/RE. Here, E is the carrier energy, l is the chemical potential and set to zero in our calculations, kB is the Boltzmann constant, and TL/R is the temperature of LE/RE, respectively.
3. Results and discussion In order to search the ground state, we calculate the total energy of C(5,4) primitive cell at nonmagnetic (NM), ferromagnetic (FM) and antiferromagnetic (AFM) states, respectively. The energy differences are ⊿E1 = ENM-EFM = 83.68 meV and ⊿E2 = EAFM-EFM = 40.47 meV, which indicate that the FM state is the ground state [30]. The calculated total magnetic moment in the FM ground state is 2.0 lB, which corresponds to the difference of atom number of the A and B sublattices in one CSiNR primitive cell as predicted from the Lieb’s theorem [31] on a bipartite lattice. Besides, using the mean field theory, the Curie temperature (TC) is estimated, i.e., ⊿E2 = ckBTC/2, where c is the dimension of the system [32]. By setting c = 1 for one-dimensional nanoribbon system, we get a TC of 938 K, which is far above the room temperature. As the magnetization of LE/RE can be modulated by applying external magnetic fields, two magnetic configurations (MCs) are considered [33]: parallel (P) and antiparallel (AP) MCs with magnetic fields at two electrodes pointing in the same and opposite directions, respectively. The spin polarization directions of two MCs can be confirmed by the spin density distributions across the CSR, as shown in Fig. 1(b), where pink and cyan surfaces indicate the spin-up and spin-down components, respectively. Clearly, spin density mainly distributes on the edge silicon atoms, and the whole CSR are spin-up polarized in P MC, while the left part of CSR is spin-up polarized and the right part is spin-down polarized in AP MC. Moreover, the total energy difference between P and AP MCs is calculated to be 54.48 meV, which indicates that the two MCs can transform easily each other by tuning the external magnetic field. We first focus on the P MC. Fig. 2(a) shows the thermally-driven spin currents driven by the temperature difference (⊿T) without an external bias voltage between LE (TL) and RE (TR), namely, ⊿T = TL TR, with different TL = 300, 400, and 500 K, respectively. Fig. 2(b) shows the thermally-driven spin currents vs. TL with different ⊿T = 20, 40, and 60 K, respectively. As shown in Fig. 2(a) and (b), an obvious spin Seebeck effect can be observed: the spin-up current (Iup) is positive (flows from LE to RE), while the spin-down current (Idn) is negative (flows from RE to LE), namely, they flow in opposite directions. Besides, as one can see, Iup is always larger than Idn at the same ⊿T and TL, and both of them increase nearly linearly with the increase of ⊿T or TL. Moreover, we find that the CSiNRs with larger n1 or n2 also exhibit obvious spin Seebeck effect. According to Eq. (1), the thermally-driven spin currents are the joint results of Tr and (fL fR). Fig. 3(a) plots fL with TL = 300 K and fR with TR = 260 K as a function of (E-EF), where EF is the Fermi level. As shown in Fig. 3(a), the electron carrier concentration of LE is higher than that of RE when E > EF, then the electrons flow from LE to RE, resulting in a negative current. On the other hand, the hole carrier concentration of LE is higher than that of RE when E < EF, therefore the holes flow also from LE to RE, leading to a positive current. Furthermore, as shown in the inset of Fig. 3(a), (fL fR) shows a perfect symmetric feature with respect to EF and also a typical exponential decaying nature. As a result, the thermally-driven currents are only determined by transmission close to EF, however, if Tr is also symmetric about EF, the thermally-driven currents originating from electrons and holes will cancel out each other, leading to a zero net current. In other words, for nonzero net current, asymmetric transmission around
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Fig. 2. (a) Thermally-induced spin currents as a function of ⊿T with different TL = 300, 400, and 500 K. (b) Thermally-induced spin currents as a function of TL with different ⊿T = 20, 40, and 60 K.
Fig. 3. (a) Fermi-Dirac distribution function of two electrodes at different temperatures. The inset shows the difference between them. (b) Spin-resolved transmission spectra. (c) Spin-resolved current spectra for fixed ⊿T = 40 K with different TL = 300, 400, and 500 K. (d) Spin-resolved current spectra for fixed TL = 300 K with different ⊿T = 20, 40, and 60 K.
EF is needed to break the electron-hole symmetry. Fig. 3(b) shows the spin-resolved transmission spectra. As one can see, both Tup and Tdn are obvious asymmetric with respect to EF, namely, a narrow spin-up and a narrower spin-down transmission peak lies in the energy region [0.24 eV, 0.1 eV] and [0.12 eV, 0.18 eV], respectively. To further elucidate the combined effects of Tr and (fL fR) on the thermally-driven currents, as shown in Fig. 3(c) and (d), we plot the spin-resolved current spectra Jr(E) = Tr(E)[fL(E, TL) fR(E, TR)], where the cover area under the curves determines the current. Fig. 3(c) corresponds to Jr(E) for fixed ⊿T = 40 K with different TL = 300, 400, and 500 K, while
Fig. 3(d) corresponds to Jr(E) for fixed TL = 300 K with different ⊿T = 20, 40, and 60 K, respectively. As shown in Fig. 3(c) and (d), the peak of Jup and Jdn appears in the energy region [0.24 eV, 0.1 eV] below EF and [0.12 eV, 0.18 eV] above EF, resulting in positive Iup and negative Idn, respectively. Moreover, when TL or⊿T goes up further, both the cover areas of Jup and Jdn increase gradually, leading to the nearly linearly enhancement of Iup and Idn with the increase of TL or ⊿T. However, the cover area of Jup is always larger than that of Jdn, therefore, Iup is always larger than Idn. To further clarify the origin of the transmission peaks around the EF, in Fig. 4(a), we plot the spin-resolved band structures of
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Fig. 4. (a) Spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in P MC. (b) Spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in AP MC.
LE (the left panel) and RE (the right panel) in P MC. Clearly, the bands of LE have the same structures as those of RE. In the vicinity of EF, there are two bands for each spin, namely, spin-down bands C1 and C2 in the energy region [0.12 eV, 0.18 eV] above EF, and spinup bands V1 and V2 in the energy region [0.24 eV, 0.1 eV] below EF. The perfect matching of four bands between LE and RE gives rise to the spin-down and spin-up transmission peak around EF at corresponding energy regions (the middle panel), respectively. Now we consider AP MC. Fig. 4(b) plot the spin-resolved band structures of LE (the left panel) and RE (the right panel), and spin-resolved transmission spectra (the middle panel) in AP MC. Evidently, the spin-up and spin-down bands in RE are completely exchanged compared with those in LE when the magnetic configuration goes from P to AP. As one can see, in the vicinity of EF, there is no any overlapping between bands with the same spin index, leading to the formation of a large transmission gap in the energy region [0.6 eV, 0.56 eV], as shown in the middle panel of Fig. 4(b). This indicates that both Tup and Tdn are almost bilaterally symmetric about EF, and then both Iup and Idn must be very small given the symmetry of (fL fR). As shown in Fig. 5, we present the total thermally-driven current, i.e., (Iup + Idn), in P and AP MCs for fixed TL = 300 K with different ⊿T. Clearly, the total thermally-driven current in P MC (IP) is much larger than that in AP MC (IAP), and
the latter is almost completely suppressed. Thus, a thermal colossal magnetoresistance effect can be expected when the magnetic configuration switches between P and AP. To evaluate quantitatively the thermal colossal magnetoresistance effect, we define the magnetoresistance ratio (MR) as MR = [(|IP| |IAP|)/|IAP|] 100%. The inset of Fig. 5 plots the MR as a function of ⊿T with fixed TL = 300 K. As one can see, the MR is higher than 108% from the very beginning, and even reaches 109% after ⊿T = 55 K due to the continuous increase of IP with the increase of ⊿T. This indicates CSiNRs have great potential in designing thermal spin valves. 4. Summary In summary, by using the DFT + NEGF approach, we have investigated the electronic structures and thermal spin transport properties of CSiNRs in P and AP magnetic configurations. Our results show that CSiNRs have ferromagnetic ground state with high Curie temperature far above the room temperature and can generate obvious spin Seebeck effect with spin-up and spin-down currents flowing in opposite directions by a temperature difference instead of a bias voltage, between the left electrode and right electrode. The reason can be attributed to the asymmetry of both spin-up and spin-down transmission spectra about the Fermi level, which breaks the electron-hole symmetry. Moreover, a thermal colossal magnetoresistance up to 109% can be achieved by transitioning P and AP magnetic configurations. The preset work shows that CSiNRs are promising candidates for spin caloritronic applications. Acknowledgements This work was supported by the Natural Science Foundation of Shandong Province, China (No. ZR2016AM11). References
Fig. 5. Total thermally-driven current in P and AP MCs for fixed TL = 300 K with different ⊿T. The inset shows the MR as a function of ⊿T with fixed TL = 300 K.
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