Photo-induced thermo-spin in ferromagnetic graphene field effect transistor

Transcription

1 Open Science Journal of Modern Physics 4; (5): 3-36 Published online January, 5 ( Photo-induced thermo-spin in ferromagnetic graphene field effect transistor M. D. Asham, W. A. Zein, A. H. Phillips Faculty of Engineering, Benha University, Benha, Egypt Faculty of Engineering, Ain-Shams University, Cairo, Egypt address adel.phillips@gmail.com (A. H. Phillips), minadanial@yahoo.com (M. D. Asham), walidzein@gmail.com (W. A. Zein) To cite this article M. D. Asham, W. A. Zein, A. H. Phillips. Photo-Induced Thermo-Spin In Ferromagnetic Graphene Field Effect Transistor. Open Science Journal of Modern Physics. Vol., No. 5, 4, pp Abstract Thermospin effects in ferromagnetic graphene mesoscopic device are investigated. The thermo-spin characteristics such as spin Seebeck coefficient, the thermal conductance, spin figure of merit are expressed in terms of the tunneling probability of Dirac fermions for both parallel antiparallel spin alignments of electrons. This tunneling probability the corresponding electrical conductance are derived by solving Dirac equation for both spin alignments. Numerical calculations are performed the obtained results show that the values of Seebeck coefficient, thermal conductance, figure of merit are different for spin up spin down. Their values are increased as the frequency of the induced ac-field increases, that is, the thermospin transport through such device is enhanced by the photon energy. The present research is very important in the field of spin caloritronics on the nanoscale systems. Keywords Ferromagnetic Graphene, Spin Caloritronics, Thermospin Seebeck Coefficient, Thermal Conductance, Figure of Merit Ac-Field. Introduction The abilities to inject detect spin carriers are fundamental for research on transport manipulation of spin information [,]. Pure electronic spin currents have been recently studied in nanoscale electronic devices [3-7]. The interplay between spin heat transport in magnetic structures is studied in the emerging field called spin caloritronics [8, 9]. Creating temperature gradients in magnetic nanostructures has resulted in a new research direction, i.e., the combination of magneto- thermoelectric effects [-4]. The creation of an electric field by temperature gradient in a material is known as Seebeck effect [5]. In the last years new spin dependent thermal effects have been discovered in ferromagnets the Seebeck effect receives novel interest. Gravier et.al described the transport of heat spin in magnetic nanostructures []. Uchida et al experimentally found the spin Seebeck effect [] driving this novel field, e.g. in nanoscale metal structures [], in magnetic insulators semiconductors [3, 4]. A strong asymmetry of the density of states with respect to the Fermi level promotes the heatdriven electron transport that leads to the common charge- Seebeck effect. These strong asymmetries can be found in the spin split density of states in ferromagnetic materials. Graphene, an atomic layer of carbon atoms arranged in a two dimensional honeycomb lattice, are highly promising cidate for new semiconductor materials devices [6]. In monolayer form, graphene is gapless as its conical conduction valence bs touch at two inequivalent Dirac points where the density of states vanishes. The key property of graphene for electronic applications is the fast electronic transport expressed by its high carrier mobility. Since monolayer graphene has no b-gap, it is not directly suitable for digital electronics, but is very promising for analog, high frequency applications [7]. Recently, mobility approaching, cm /V.s has reported for ultraclean suspended graphene [8]. The transport characteristics of these experiments suggest that the samples reach the ballistic

2 3 M. D. Asham et al.: Photo-Induced Thermo-Spin In Ferromagnetic Graphene Field Effect Transistor regime with respect to disorder scattering [9]. Ballistic transport in graphene makes it attractive for use as transistors [], interconnects [] as well as spin control devices [, 3]. Thermoelectric transport properties of graphene have attracted much recent experimental [4-6] theoretical attention [6, 7-3]. The authors [3] of the present paper investigated the spindependent transport characteristics through ferromagnetic graphene mesoscopic device. The spin polarization of the Dirac fermions tunneled through such device is pumped by the influence of an ac-field of wide range of frequencies. Now, it is interesting to study thermospin effect in such ferromagnetic graphene mesoscopic device. This can be achieved by studying the thermoelectric parameters with the dependence on the frequency of the induced ac-field for both parallel anti-parallel spin alignments. These parameters are the thermopower (Seebeck coefficient), S, the thermal conductance, κ e, the thermoelectric figure of merit,. Analysis of the theoretical model calculation will be shown below in the next sections.. Theoretical Model In this section, the thermoelectric parameters are expressed in terms of spin-dependent tunneling probability, which will be derived by solving the Dirac equation [3] of the present studied device. The graphene mesoscopic device is modeled as follows: Spin transport in normal graphene/ ferromagnetic graphene/ normal graphene mesoscopic junction is shown in fig. (). Graphene can be converted into ferromagnetic state by depositing the magnetic insulator EuO on top of it [3] (see region IV) a metallic gate. While regions I, II III V are normal graphene. On the top of region II, together with the metallic gate, there is a ferromagnetic vector potential barrier. With such construction of spintronic device, we can inject manipulate spins of Dirac fermions as we shall see below. ( ( ) ħ) ħv + F σxkx σy ky eay x ( ) + ( ) () σh x U x σ + cos o evac ωt = E, where vfis the Fermi-velocity, σ & x σ are the Pauli spin y matrices, k & x k are the wave vectors of the Dirac electrons y in the x-y plane, Ay ( x ) is the vector magnetic potential, U ( x ) is the potential in the corresponding region, ħ is the reduced Planck s constant. The induced ac-field is described by the term{ ev cos } ac ω t, where V is the amplitude of the ac ac-field, ω is its frequency. In eq. (), h ( x ) is the position dependent of the exchange energy of the ferromagnetic graphene. The solution of eq.() in one-dimension (x-direction) gives the following eigenfunctions in the corresponding regions are [3,34,35]: ev ipx cos ipx cos ac inωt I = e + r e i i Jn e e e ħω The eigenfunction in region II is: II ev iqx cosb iqxcosb ac inωt II = a e + b e J i B i B n e e e ħω The eigenfunction III in region III is: ev ipx cos ipx cos ac inωt III = c e + d e i i Jn e e e ħω Also, the eigenfunction IV in region IV is: ev f e f e J e ikx cosf ikx cosf ac inωt IV = if + if n e e ħω And finally, the eigenfunction V in region V is: () (3) (4) (5) V evac t e Jn e ħω ipx cos = i e inωt (6) Figure. The proposed device model. The spin transport through the present investigated device is described by the following Dirac equation [33]: where r & t are the reflection transmission coefficients, evac J is the n th order of Bessel function of first kind n ħω the solutions of eqs.(, 3, 4, 5 & 6) must be generated by the presence of the different side-bs, n, which comes inωt with the phase factor e [4, 5, 3, 34]. In eqs.(, 3, 4, 5 & 6), the following parameters are: the parameter is the angle of incidence on the normal graphene (regions I, III & V), the angle is the angle of incidence on the graphene (region II) B the angle f is the angle of incidence on graphene (region IV). The parameters p, q & k are the wave vectors in

3 Open Science Journal of Modern Physics 4; (5): the corresponding regions of graphene which are expressed as: ( ω) / p = E + ev + E + nħ ħ v (7) sd F F q = E + evsd + EF + Vd + g µ BBσL + ev g + n ω / vf ħ ħ (8) ( sd F Vd g ω σr o ) / k = E + ev + E + + ev + nħ + h ħ v (9) where V is the bias voltage, sd the gate voltage, E is the Fermi-energy, F V is g h is the exchange energy of the o ferromagnetic graphene, g is the Le g-factor, µ B is the Bohr magneton, B is the magnetic field. V d V are the d magnetic barriers in regions (II, III) respectively. The angles B f are expressed in terms of the wave vectors p, q & k (eqs. 7, 8 & 9) as: where ( p q ) ( q lb ) sin = / sin / () B ( p k ) ( k lb ) sin = / sin / () f lb is the magnetic length which is equal to lb = ħ / eb () Now, applying the boundary conditions at the corresponding interfaces of the model device (see fig. ()), Γ with photons E, of the we get the tunneling probability, ( ) tunneled Dirac electrons due to the influence of ac-field, which takes the following form: Γ ev ħ ac ( E) = J Γ ( E) with photons n without photons n ω F (3) Eq.(3) represents the relation between the tunneling Γ without photons E [7,3, 35], probabilities, Γ with photons ( E) ( ) where Γ without photons ( E ) is the tunneling probability when the applied ac-field is absent, which is given by: ip( D+ L+ d ) cos cos cosb cosfe without photons ( E) t ipl cos ipl cos αe + αα3e Γ = = where α, α & α3 are respectively given as : ( B )( f ) ( qd B ) ( kd f ) (4) α = sin sin sin sin sin cos sin cos (5) = B ( qd B ) i ( B ) ( qd B ) (6) α cos cos cos cos sin sin sin cos ( kd ) i ( ) ( kd ) α3 = cos cosf cos cosf sin sinf sin cosf (7) where D, L d represent, respectively, the thickness of the regions II, III IV. The thermopower (Seebeck coefficient), S, the electronic thermal conductance κ e are expressed in terms of the function, L m (µ), respectively, as follows [36]: S L et L = (8) L κe = L T L (9) where e is the electronic charge T is the absolute temperature. The function, L m, (for the cases m =,, ) is defined [36] in terms of the spin dependent tunneling probability, Γ with photons ( E ), (eqs. 3, 4) as: ( ) m f E Lm ( µ ) = de Γwith photons ( E ) ( E µ ) () h E where h is Planck s constant, µ is the electrochemical f E E is the first derivative of the potential ( ( ) ) Fermi-Dirac distribution function. The thermoelectric figure of merit of the present device is expressed as [36]: = κ S GT ph + κ e () where κ ph is the phonon contribution to thermal conductance. In the present paper, we might neglect the phonon contribution to thermal conductance, κ ph, (see eq. ). This is because our calculations will be performed at very low temperature. It can be taken into consideration when we consider electron-phonon interaction phonon drag. So, eq. () will take the following form as: S GT = () κ In eq. () the parameter G is the spin dependent conductance of the present studied graphene spintronic device its expression is [3, 3, 37, 38]: π EF + nħω kfw e ffd G = de Γwith photons ( E) cosd h (3) π E EF where W is the width of the graphene sheet, k F is the Fermi-wave vector. 3. Results Discussion Numerical calculations are performed for the following spin thermoelectric parameters: Seebeck coefficient, S, (eq. e

4 34 M. D. Asham et al.: Photo-Induced Thermo-Spin In Ferromagnetic Graphene Field Effect Transistor 8), the electronic thermal conductivity, κ e, (eq. 9) spin figure of merit (eq. ) for both cases of parallel antiparallel alignments of spins of the tunneled Dirac fermions. The values of dimension of the present device are [3] (see fig.): W = nm, D = nm, L = 5 nm d = nm. The other parameters [3], for example, the temperature T = 5 K, the bias voltage V sd = - V, the magnetic barrier V d in region III is.5 V the amplitude of the induced ac-field is V ac =.5 V. The values of the parameters are taken according to the case of parallel or antiparallel spin alignment [3, 3, 37, 39]. That is, for the parallel case, the exchange energy of the ferromagnetic graphene h o = mev, magnetic field B = T magnetic barrier V d =.5 ev (region II). For the antiparallel case, h o = 5 mev, B = T V d =. ev. The value of the Lé g-factor for graphene is 4 [4]. Now, the features of the present results are: - Figs (a, b) shows the variation of the thermopower (Seebeck coefficient), S, with the gate voltage,, at different frequencies,υ, of the induced ac-field. The calculations are performed for the both cases of parallel antiparallel spin alignments. As shown from these figures, the Seebeck coefficient, S, increases as the frequency of the induced ac-field increases (see figs. a, b). The rom oscillatory behavior of the Seebeck coefficient, S, (see figs. a, b) for both spin alignments might be due to spin flip of the Dirac fermions [3, 4]. This spin flip will be enhanced by the photon energy of the induced ac-field. Since the individual Seebeck coefficients for the two spin channels S P S AP are different. Then the spin current will be proportional to the difference of S P S AP, which flows through the ferromagnetic graphene. This leads to creating a spin accumulation close to the interface, which relaxes in the ferromagnetic graphene normal one on the length scale of their respective spin flip diffusion lengths. (a) Figure. The variation of the thermopower (Seebeck coefficient), S, with the gate voltage at frequencies ν = (a) 3x 9 Hz, (b) 3x Hz for both spin alignments, parallel anti-parallel. (b). x -9 ν = 3 x 9 Hz 8 x -3 ν = 3 x Hz κ e (W/K) Parallel Alignment κ e (W/K) Parallel Alignment (a) Figure 3. The variation of the electronic thermal conductance, κ e, with the gate voltage at frequencies ν = (a) 3x 9 Hz, (b) 3x Hz for both spin alignments, parallel anti-parallel. (b) -Figs. (3a, b) show the variation of the electronic thermal conductance, κ e, with the gate voltage at different frequencies, υ, of the induced ac-field. The calculations are performed for the both cases of parallel antiparallel spin alignments. As shown from these figures that the electronic thermal conductance increases strongly as the frequency of the induced ac-field increases. The oscillatory behavior of the thermal conductance for both cases of spin alignments (see

5 Open Science Journal of Modern Physics 4; (5): figs. 3a, b) might be explained as follows: When Dirac fermions tunnel into the ferromagnetic graphene, they split into subbs, one for spin up the other for spin down. This splitting leads to the electronic thermal conductance of the present device to be spindependent. Also this oscillatory behavior of the electronic thermal conductance is due to the interplay between the frequency of the induced ac-field with both spin-up spindown subbs [4, 7, 3, 34]. Also, as pointed out by many authors [9, 3, 36, 4] that these oscillations of the electronic thermal conductance are due to the modulation of the Fermienergy by the potential of the magnetic insulator EuO (region IV), the photon energy of the induced ac-field, the thermal energy at each lead. It is well known that the efficiency of any thermoelectric device is usually parameterized in terms of a figure of merit, [8, 9, 36]. This encourages us to perform calculations to the figure of merit,, (see eq. ) for both parallel antiparallel spin alignments. The results are shown in figs. (4a, b). As shown from these figures that the values of the figure of merit,, increase as the frequency of the induced ac-field increases for both spin alignments. These higher values of the figure of merit, in case of frequency υ = 3* Hz, reflect a better thermodynamic efficiency of ferromagnetic graphene [8,, 4, 5]. The oscillatory behavior of the figure of merit (see figs.4a, b) is expected since the figure of merit is expressed in terms of the electrical conductance [3], electronic thermal conductance Seebeck coefficients (see eq.)..3 ν = 3 x 9 Hz 6 ν = 3 x Hz Parallel Alignment Parallel Alignment (a) Figure 4. The variation of the thermoelectric figure of merit,, with the gate voltage at frequencies ν = (a) 3x 9 Hz, (b) 3x Hz for both spin alignments, parallel anti-parallel. (b) 4. Conclusion In the present paper, thermospin effects in a mesoscopic device consisting of a ferromagnetic graphene coupled to normal graphene is investigated. This study is performed under the influence of an ac-field of wide range of frequencies. Results show that the Seebeck effects for spinup spin-down are different. Also, the values of the figure of merit are quite high when a high frequency of the induced ac-field, in the range of mid-infrared region is applied. So, we may mention that the coupling of heat transport with spin transport through graphene has generated novel ideas such as innovative spin sources [8-], thermal spin-transfer torque [4, 43], magnetic heat valves [44] magnetically switchable cooling [, 45]. References [] I. Zutic, J. Fabian, S. Das Sarma, Spintronics: Fundamentals applications, Rev. Mod. Phys, vol.76, 33,4. [] C. Chappert, A. Fert F. N.Van Dau, The emergence of spin electronics in data storage, Nature Mater, vol.6()pp , 7. [3] W. A. Zein, A. H. Phillips O. A. Omar Spin-coherent transport in mesoscopic interference device, Nano, vol. no.6, 389,7. [4] A. F. Amin, G. Q. Li, A. H. Phillips U. Kleinekathöfer, Coherent control of the spin current through a quantum dot, Europ. Phys. J. B, vol. 68, no., pp. 3 9,9. [5] W. A. Zein, N. A. Ibrahim A. H. Phillips, Spin Polarized Transport in an AC-Driven Quantum Curved Nanowire, Physics Research International,(Article ID 559) 5 pages DOI:,55//559 [6] A. F. Amin,A. S. Atalla A. H. Phillips, Quantum spin transport in superconducting ferromagnetic hybrid system, Armenian J. Phys., vol. 4, no.,pp ,. [7] M. D. Asham, W. A. Zein A. H. Phillips, Photo-Induced Spin Dynamics in Nanoelectronic Devices, Chin. Phys. Lett., vol.9, no., 85,. [8] G. E. Bauer,A. H. MacDonald S. Maekawa, Spin Caloritronics,Sol. Stat. Commun., vol.5(-), pp ,. [9] G. E. Bauer, E. Saitoh B. J. van Wees, Spin caloritronics, Nat. Mater.,vol., no.5, pp ,. [] L. Gravier, S. Serrano-Guisan, F. Reuse J. P. Ansermet, Thermodynamic description of heat spin transport in magnetic nanostructures, Phys. Rev. B, vol. 73, no., 449, 6.

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