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First-principles studies of interlayer exchange coupling in (Ga, Mn)N-based diluted magnetic semiconductor multilayers
Optik 126 (2015) 903–906
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
First-principles studies of interlayer exchange coupling in (Ga, Mn)N-based diluted magnetic semiconductor multilayers Min Luo a,∗ , Hai Yin Li b a b
Department of Electronic Engineering, ShangHai JianQiao College, Shanghai 201319, China School of Electronics and Information, Nantong University, Nantong 226019, China
a r t i c l e
i n f o
Article history: Received 28 January 2014 Accepted 7 February 2015 Keywords: First-principles IEC Carrier RKKY Antiferromagnetic
a b s t r a c t Interlayer exchange coupling (IEC) in a series model diluted magnetic semiconductor (DMS) multilayer consisting of two magnetic (Ga, Mn)N layers separated by non-doped or Mg-doped GaN non-magnetic spacers has been studied by first-principles calculations. The effects of the spacer thickness and hole doping to the IEC were studied systematically. It is observed that, (1) for the GaN spacers without Mg doping, the IEC between two magnetic (Ga, Mn)N layers is always ferromagnetic, which is clarified as an intrinsic character of the Ruderman–Kittle–Kasuya–Yoshida (RKKY) interaction based on a two-band model for a gaped system; (2) for the Mg-doped GaN spacers, the IEC is tunable from ferromagnetic to antiferromagnetic by varying the spacer’s thickness and the dopant’s site. © 2015 Published by Elsevier GmbH.
PACS: 73.61.Ey 75.30.Ev 75.50.Pp
1. Introduction Interlayer exchange coupling (IEC) was shown to be responsible for the giant magnetoresistance effect [1], IEC was observed in a variety of structures composed of metallic ferromagnetic (FM) layers separated by nonmagnetic, metallic, or insulating spacer layers. The GMR effect has initiated the emergence of spintronics [2,3] and has guided the rapid progresses of the modern magnetic storage technologies. Similar to the metallic systems, the diluted magnetic semiconductors (DMSs) which are formed by transitionmetal (TM) low doping into standard semiconductors [4] have been widely studied with an eye on combining spintronics with well-established semiconductor technology. The essential point to manipulate the spin-dependent transport of the DMS multilayers is realization of the reversible switching of their IEC from ferromagnetic to antiferromagnetic. So far, the ferromagnetic IEC has been explicitly observed [5–8]. Theoretically, the antiferromagnetic IEC was first predicted by Jungwirth et al. [9] based on a k·p kineticexchange model in 1999 and later on by Sankowski and Kacman [10] based on a tight-binding model, by Giddings et al. [11] based on the self-consistent mean-field calculations, and very recently
∗ Corresponding author. Tel.: +86 13816244750. E-mail address: [email protected] (M. Luo). http://dx.doi.org/10.1016/j.ijleo.2015.02.026 0030-4026/© 2015 Published by Elsevier GmbH.
by Szałowski and Balcerzak [12] based on a quantum-well model. However, the experimental realization of the antiferromagnetic IEC is difficult and only some progresses were reported [13,14], for instance, in (Ga, Mn)As DMS multilayers with Be-doped GaAs spacers [14]. Very recently, our previous theoretial work has confirmed the antiferromagnetic IEC via Be-doping in the system of (Ga, Mn)As DMS multilayers [15]. However, it is confirmed in the experiments that curie temperature (Tc ) of such DMS materials is only as high as 180 K [16]. The theoretical calculation by Dietl et al. [17] have predicted materials that can have Tc above room temperature. In agreement with their prediction, the 3d transition metal (TM) such as Mn doped in III-nitrides showed ferromagnetism with high Tc . GaN has been by far one of the most studied materials among the nitrides. Also (Ga, Mn)N system is preferable over (Ga, Mn)As because its band structure is much suitable for spin injection. Especially for (Ga, Mn)N showed a large range of Tc varying from 10 K to above room temperature [18–22]. Stimulated by the above theoretical studies, we systematically studied in this Letter the IEC of the GaMnN/GaMnN:Mg multilayers by first-principles calculations. We calculated total energies of a series model DMS multilayers consisting of two ferromagnetically or antiferromagnetically coupled (Ga, Mn)N layers separated by non-doped GaN or Mg-doped GaN nonmagnetic spacers and investigated the effects of the spacer thickness and Mg doping to
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0.008
ΔE (eV)
0.000 -0.008 (Ga, Mn)N Spacer: non-doped MgGa in middle
-0.016
MgGa in interface
-0.024
3
4
5
6
7
8
Ga Layers in Spacer Fig. 2. Interlayer exchange coupling (IEC) between two magnetic (Ga, Mn)N layers as a function of the thickness of the GaN spacer. The dashed line is the RKKY interaction of a two-band model based on the theory of Narita and Kasuya [27,28]. Fig. 1. Atomic structures of three typical model DMS multilayers under study. (a) The spacer (the GaN layers in between the upper and lower (Ga, Mn)N magnetic layers) without Mg-doping, (b) a Mg atom doped into the middle of the spacer, and (c) two Mg atoms doped into, respectively, the upper and lower interface layers between the (Ga, Mn)N layers and the spacer.
the IEC. For the model multilayers separated by pure GaN layers without Mg doping, we observed that the IEC is always ferromagnetic. While for the Mg-doped GaAs spacers, the IEC is tunable by varying the spacer’s thickness and the dopant’s site. The antiferromagnetic IEC is archived when the Mg atoms are doped into the interfaces between the (Ga, Mn)N layers and the GaN spacers. This significant effect was attributed to the Mg mediated magnetic interactions between the magnetic multilayers. It is found that the sp-d hybridization between the hole dopant (Mg) and the magnetic dopants (Mn) plays an essential role in tuning the DMS-based magnetic multilayers. 2. Calculation details 2.1. Method Our first-principles calculations were performed based the density functional theory within the generalized gradient approximation (GGA) by using the Vienna ab initio simulation package (VASP) [23]. A plane wave basis set with a cutoff energy of 400 eV, the frozen core all-electron projector augmented wave pseudopotentials [24], and the GGA exchange–correlation potential of the Perdew-Wang-91 form [25], as implemented in the VASP, were employed. The integration over the first Brillouin zone was performed on a grid of Monkhorst–Pack special k-points, which varies from 4 × 4 × 2 to 4 × 4 × 4 depending on the size of the model multilayer system. In the relaxation procedures of the electron and ion degrees of freedom, the convergence tolerances of the total (free) energy were 0.1 meV and 1.0 meV, respectively. 2.2. Structure The atomic structures of three typical model multilayers are presented in Fig. 1. Each model multilayer under study, such as those shown in Fig. 1, was constructed as the follows. At first, a supercell consisting of an appropriate number of Ga and N layers was chosen, where the Ga and N atomic layers were stagger stacked along the c axis (the [0 0 1] crystallographic direction) into the wurtzite structure and the lattice parameters we used are a = 0.322 nm and c = 0.523 nm. The a-axis and b-axis of the supercell are fixed at four times and twice of the lattice constant of GaN, respectively. Then, two Ga atoms in one Ga layer are substituted by two Mn atoms coupled ferromagnetically. Similarly, we substituted other two Ga
atoms by two Mn atoms in another opposite Ga layer and these substituted layers form two magnetic (Ga, Mn)N layers (Fig. 1). The magnetization directions of these two layers were aliened either parallelly or antiparallelly to study the IEC. Between the two (Ga, Mn)N layers is the nonmagnetic GaN spacer, where the hole carriers can be doped via the MgGa substitutions. In the present model multilayers, the GaAs spacer consists of n Ga layers and (n + 1) N layers, where n varies from 3 to 8. First of all, we conform the coupling of two doping atoms (Mn) in the same layer is ferromagnetic. We calculated the total energies with the local magnetic moment of the dopant pair aliened parallelly and antiparallelly. For Mn–Mn pair, we obtained E = −227 and −141 meV for the neighbor and the next-neighbor pair configurations, respectively. These results indicate that the couplings between two doping atoms are ferromagnetic. Cui et al. [26] calculated the exchange between the neighbor Mn–Mn pair and the next-neighbor Mn–Mn pair in GaN and got E about −260 meV and −105 mV, respectively. In the present model multilayers, our obtained values agree very well with their results. Moreover, the observed results indicate that, there is a stronger ferromagnetic coupling between the neighbor Mn–Mn pair. Therefore, in the present study, we simulated the magnetic (Ga, Mn)N layers by substituting two Mn atoms into a pair of neighbor. 3. Results and discussion 3.1. Effect of spacer thickness To investigate the effect of the spacer thickness, we at first studied the model DMS multilayers with the pure GaN layers as the spacer. The model multilayers with the GaN spacer’s thickness varying from 0.785 nm (3 Ga layers) to 2.09 nm (8 Ga layers) were studied (their atomic structures are similar to the example shown in the left panel of Fig. 1). We calculated the total energies of each model system with the magnetizations of two (Ga, Mn)N layers aliened ferromagnetically (FM) and antiferromagnetically (AFM). The IEC was then estimated as E = EFM − EAFM . Figs. 2 and 3 present the calculated IEC as a function of the thickness of the GaN spacer in the (Ga, Mn)N magnetic multilayers, respectively. With increasing the spacer thickness, we observed that, the |E| monotonously decreases from 20 meV to 2 meV (Fig. 2) in the Mn-doped GaN system. In particular, for all the calculated spacer thicknesses, the negative IECs were observed, indicating that the magnetic layers always coupled ferromagnetically when the pure GaN spacers were adopted. It deserves to be mentioned that, in (Ga, Mn)As DMS multilayers with the pure GaAs layers as the spacer, we have had a
M. Luo, H.Y. Li / Optik 126 (2015) 903–906
35 30 25 20 15 10 5 0 -5 -10
EF
PDOS (States/eV)
Spin-down Spin-up
a
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0.0 2.5 5.0 7.5 10.0 12.5 15.0 Concentration of Mg (%)
0.00 -0.15 -0.30
(Ga, Mn)N
ΔE (meV)
0.30 0.15 0.00 -0.15 -0.30
905
b
Fig. 4. Interlayer exchange coupling (IEC) between two magnetic (Ga, Mn)N layers as a function of the concentration of Mg dopants in the GaN spacer.
0.30 0.15
3.2. Effect of Mg doping
0.00 -0.15 -0.30
c
-8
-6
-4
-2 0 2 Energy (eV)
4
6
Fig. 3. Electron density of states projected to Mg dopants for, (a): two antiferromagnetically coupled (the ground state) (Ga, Mn)N layers separated by a GaN spacer (n = 5) with Mg doped into the middle of the spacer, and (b) and (c): two antiferromagnetically coupled (the ground state) (Ga, Mn)N layers separated by the GaN (n = 5) spacer with two Mg doped into the upper [(b)] and lower [(c)] interfaces, respectively.
similar observation that increasing the spacer thickness cannot change the IEC from ferromagnetic to antiferromagnetic and a ferromagnetic IEC was always obtained. However, If the spin interaction between two magnetic (Ga, Mn)As layers are mediated by the nearly-free hole carriers, a Friedel-like oscillating is expected with increase of the spacer thickness, according to the theory of Ruderman–Kittle–Kasuya–Yoshida (RKKY). However, such oscillating behavior is absent in the calculated IEC as shown in Fig. 2. The oscillating behavior of the conventional RKKY exchange interaction is originated from a spin-polarized screening effect of the nearlyfree conduction electrons/holes to the magnetic impurities; while in the present DMS multilayers, the IEC is mediated by the holes in the spacer, which can be created only by exciting the valance electrons to the conduction bands. Therefore, the magnetic screening effect in this gaped system is expected to be imperfect and thus the RKKY interaction based a gaped two-band model proposed by Narita and Kasuya [27,28] is more suitable. In this model, the indirect exchange interaction between two magnetic dopants exponentially decays with the increase in the distance R between the dopants, i.e., J(R) ∝ e−ˇR /R1+d/2 , where ˇ is a coefficient depending on the effective mass of the carriers and on the energy gap, and d the dimension of the band dispersion. Their results demonstrate that the energy gap removes the oscillation of the RKKY exchange interaction and particularly, J(R) falls off with R very quickly in the gaped system because of the exponential decaying prefactor. Taking ˇ as a fitting parameter, d = 2 for the 2D hole band in the GaN spacer layer, and R = (n + 1)a/2 (a and n are the lattice parameter and the number of Ga layers, respectively), we obtained the spacer-thickness-dependent IEC as E = −3.75e−0.605(1+n) /(1 + n)2 , which indeed describes reasonably the trend of E with increasing the spacer thickness (Fig. 2).
As shown by Narita and Kasuya [27,28], the J (Rn − Rm ) in the gaped two-band system is always positive (i.e., the IEC is always ferromagnetic). The conventional oscillating J (Rn − Rm ) recovers only when the carrier band which mediates the magnetic interaction becomes “metallic” like. This may be achieved by substitutional doping of double valent MgGa in the GaN spacer, as the carriersmediated antiferromagnetic IEC in the DMS superlattices and multilayers discussed early by Jungwirth et al. [9]. For this reason, we calculated the IEC between two (Ga, Mn)N layers separated by the Mg-doped GaN spacer where the Mg doping in the spacer is known to increase the hole concentrations directly in the GaN layers [29]. There are two kinds of possible MgGa substitutional sites in the spacer layers of the present model multilayers. One is in the middle of the spacer and another one is in the interface between the (Ga, Mn)N and GaN layers. Fig. 2 presents the calculated IEC for the first case, i.e., one Mg dopant occupying a Ga site in the middle of the spacer (the middle panel of Fig. 1). As shown in Fig. 2, we see clearly that, the E changes from negative (−7 meV, n = 2) to positive(+2 meV, n = 8) gradually with increasing the thickness of the spacer, indicating that the IEC switches from ferromagnetic to antiferromagnetic. When the Mg atoms are doped into the interfaces, the IEC switches from ferromagnetic to antiferromagnetic when n ≥ 5, exhibiting a similar trend to that of the a Mg-doped into the spacer. We investigated the densities of states (DOS) projected to the Mg dopant for the calculated model multilayers. As an example, Fig. 3 presents the results for the model multilayer with n = 5 in its ferromagnetically coupled ground state. As shown in Fig. 3(a), when the Mg dopants are in the middle of the spacers, there are a sp-d interaction between the Mn and Mg dopants, As a result, the Mg dopant is able to mediate the spin interaction between the ferromagnetic (Ga, Cr)N layers, so that the antiferromagnetic IEC is expected. The situation may be different when the Mg dopants are in interfaces of the spacers, as shown in Fig. 3(b) and (c), there are a strong sp–d interaction between the Mn and Mg dopants because there is an obvious spin-polarization in the Mg-projected DOS around the Fermi energy. As a result, the antiferromagnetic IEC has to be enhanced. In contrast to the case of one Mg doped in (Ga, Mn)N, we suspect that the increased concentration of Mg could enhance the antiferromagnetic coupling between the two ferromagnetic (Ga, Mn)N layers. We then study the model DMS multilayers with the same spacer. The GaN spacer’s thickness is keeping 1.046 nm (4 Ga layers) were studied. Fig. 4 presents the calculated IEC as a function
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of the concentration of Mg. For the pure spacer (the concentration of Mg is 0), we obtained the IEC E of −6 meV. With the concentration of Mg increased, we observed that the E monotonously increases to 34 meV, indicating that when the concentration of Mg increases, the couple between the two ferromagnetic layers change from ferromagnetical to antiferromagnetic and attentively the antiferromagnetic of the IEC is enhanced. 4. Conclusion In summary, the IEC in a series model DMS multilayers consisting of two magnetic (Ga, Mn)N layers separated by non-doped or Mg-doped GaN non-magnetic spacers have been studied by first-principles total-energy calculations. It was observed that, (1) without Mg doping, the IEC was always ferromagnetic, which was an intrinsic character of the RKKY interaction in a gaped system. (2) Mg-doping in the interface layers between the magnetic (Ga, Mn)N layers and the GaN spacer can change the IEC from ferromagnetic to antiferromagnetic. Acknowledgments We thank the Supercomputer Center of ECNU for using the Dawn 5000 A supercomputer. This work is supported by the research programs of Shanghai (AAZH1116). References [1] S.S.P. Parkin, Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling through the 3d, 4d, and 5d transition metals, Phys. Rev. Lett. 67 (1991) 3598–3601. [2] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dan, F. Petroff, P. Etienne, G. Crenzet, A. Friederich, J. Chazelas, Giant magnetoresistance of (0 0 1)Fe/(0 0 1)Cr magnetic superlattices, Phys. Rev. Lett. 61 (1988) 2472–2475. [3] G. Binasch, P. Grünberg, F. Saurenbach, W. Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys. Rev. B: Condens. Matter 39 (1989) 4828–4830. [4] T. Jungwirth, J. Maˇsek, J. Kuˇcera, J. Kucera, A.H. MacDonald, Theory of ferromagnetic (III,Mn)V semiconductors, Rev. Mod. Phys. 78 (2006) 809–864. [5] H. Munekata, H. Ohno, S. von Molnár, A. Segmüller, L.L. Chang, L. Esaki, Diluted magnetic III–V semiconductors, Phys. Rev. Lett. 63 (1989) 1849–1852. [6] H. Ohno, H. Munekata, T. Penney, S. von Molnár, L.L. Chang, Magnetotransport properties of p-type (In,Mn)As diluted magnetic III–V semiconductors, Phys. Rev. Lett. 68 (1992) 2664–2667. [7] D. Chiba, N. Akiba, F. Matsukura, Y. Ohno, H. Ohno, Magnetoresistance effect and interlayer coupling of (Ga, Mn)As trilayer structures, Appl. Phys. Lett. 77 (2000) 1873–1875. [8] S.J. Chung, S. Lee, I.W. Park, X. Liu, J.K. Furdyna, Possible indication of interlayer exchange coupling in GaMnAs/GaAs ferromagnetic semiconductor super lattices, J. Appl. Phys. 95 (2004) 7402–7406. [9] T. Jungwirth, W.A. Atkinson, B.H. Lee, A.H. MacDonald, Interlayer coupling in ferromagnetic semiconductor superlattices, Phys. Rev. B: Condens. Matter 59 (1999) 9818–9821. [10] P. Sankowski, P. Kacman, Interlayer exchange coupling in (Ga,Mn)As-based superlattices, Phys. Rev. B: Condens. Matter 71 (2005) 201303–201306.
[11] A.D. Giddings, T. Jungwirth, B.L. Gallagher, (Ga,Mn)As based superlattices and the search for antiferromagnetic interlayer coupling, Phys. Rev. B: Condens. Matter 78 (2008) 165312–165320. [12] K. Szałowski, T. Balcerzak, Antiferromagnetic interlayer coupling in diluted magnetic thin films with RKKY interaction, Phys. Rev. B: Condens. Matter 79 (2009) 214430–214440. [13] Z. Ge, Y.Y. Zhou, Y.J. Cho, X. Liu, J.K. Furdyna, M. Dobrowolska, Investigation of magnetic and electronic coupling between two (Ga, Mn)As layers in (Ga,Mn)As/GaAs/(Ga,Mn)As magnetic tunnel junctions, Appl. Phys. Lett. 91 (2007) 152109–152111. [14] J.H. Chung, S.J. Chung, Sanghoon Lee, B.J. Kirby, J.A. Borchers, Y.J. Cho, X. Liu, J.K. Furdyna, Carrier-mediated antiferromagnetic interlayer exchange coupling in diluted magnetic semiconductor multilayers Ga1−x Mnx As/GaAs:Be, Phys. Rev. Lett. 101 (2008) 237202–237205. [15] M. Luo, Z. Tang, J. Zheng, Z.Q. Zhu, J.H. Chu, First-principles studies of interlayer exchange coupling in (Ga, Mn)As-based diluted magnetic semiconductor multilayers, J. Appl. Phys. 108 (2010) 053703–053706. [16] T. Jungwirth, K.Y. Wang, J. Masek, K.W. Edmonds, J. König, J. Sinova, M. Polini, N.A. Goncharuk, A.H. MacDonald, M. Sawicki, A.W. Rushforth, R.P. Campion, L.X. Zhao, C.T. Foxon, B.L. Gallagher, Prospects for high temperature ferromagnetism in (Ga, Mn)As semiconductors, Phys. Rev. B: Condens. Matter 72 (2005) 165204–165216. [17] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287 (2000) 1019–1022. [18] M.E. Overberg, C.R. Abernathy, S.J. Pearton, N.A. Theodoropoulou, K.T. McCarthy, A.F. Hebard, Indication of ferromagnetism in molecular-beamepitaxy-derived N-type GaMnN, Appl. Phys. Lett. 79 (2001) 1312–1314. [19] N. Theodoropoulou, A.F. Hebard, M.E. Overberg, C.R. Abernathy, S.J. Pearton, S.N.G. Chu, R.G. Wilson, Magnetic and structural properties of Mn-implanted GaN, Appl. Phys. Lett. 78 (2001) 3475–3477. [20] E. Sarigiannidou, F. Wilhelm, E. Monroy, R.M. Galera, E. Bellet-Amalric, A. Rogalev, J. Goulon, J. Cibert, H. Mariette, Intrinsic ferromagnetism in wurtzite (Ga, Mn)N semiconductor, Phys. Rev. B: Condens. Matter 74 (2006) 041306–041309. [21] V.A. Chitta, J.A.H. Coaquira, J.R.L. Fernandez, C.A. Duarte, J.R. Leite, D. Schikora, D.J. As, K. Lischka, E. Abramof, Room temperature ferromagnetism in cubic GaN epilayers implanted with Mn+ ions, Appl. Phys. Lett. 85 (2004) 3777–3779. [22] H.C. Jeon, T.W. Kang, T.W. Kim, J. Kang, K.J. Chang, Enhancement of the magnetic properties in (Ga1−x Mnx )N thin films due to Mn-delta doping, Appl. Phys. Lett. 87 (2005) 092501–092503. [23] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter 54 (1996) 11169–11186. [24] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B: Condens. Matter 59 (1999) 1758–1775. [25] J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B: Condens. Matter 45 (1992) 13244–13249. [26] X.Y. Cui, B. Delley, A.J. Freeman, C. Stampfl, Neutral and charged embedded clusters of Mn in doped GaN from first principles, Phys. Rev. B: Condens. Matter 76 (2007) 045201–045212. [27] (a) A. Narita, T. Kasuya, Effects of band structure and matrix element on RKKY interaction, J. Magn. Magn. Mater. 43 (1984) 21–42; (b) A. Narita, T. Kasuya, Magnetic exchange interactions and spin structures in some rare earth pnictides, J. Magn. Magn. Mater. 52 (1985) 373–376. [28] A. Narita, Analytic structures of RKKY interactions in magnetic semiconductors and in materials with a gap on the Fermi surface, J. Phys. C: Solid State Phys. 19 (1986) 4797–4802. [29] A.M. Mahros, M.O. Luen, A. Emara, S.M. Bedair, E.A. Berkman, N.A. El-Masry, J.M. Zavada, Magnetic and magnetotransport properties of (AlGaN/GaN):Mg/(GaMnN) heterostructures at room temperature, Appl. Phys. Lett. 90 (2007) 252503–252505.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
First-principles studies of interlayer exchange coupling in (Ga, Mn)N-based diluted magnetic semiconductor multilayers Min Luo a,∗ , Hai Yin Li b a b
Department of Electronic Engineering, ShangHai JianQiao College, Shanghai 201319, China School of Electronics and Information, Nantong University, Nantong 226019, China
a r t i c l e
i n f o
Article history: Received 28 January 2014 Accepted 7 February 2015 Keywords: First-principles IEC Carrier RKKY Antiferromagnetic
a b s t r a c t Interlayer exchange coupling (IEC) in a series model diluted magnetic semiconductor (DMS) multilayer consisting of two magnetic (Ga, Mn)N layers separated by non-doped or Mg-doped GaN non-magnetic spacers has been studied by first-principles calculations. The effects of the spacer thickness and hole doping to the IEC were studied systematically. It is observed that, (1) for the GaN spacers without Mg doping, the IEC between two magnetic (Ga, Mn)N layers is always ferromagnetic, which is clarified as an intrinsic character of the Ruderman–Kittle–Kasuya–Yoshida (RKKY) interaction based on a two-band model for a gaped system; (2) for the Mg-doped GaN spacers, the IEC is tunable from ferromagnetic to antiferromagnetic by varying the spacer’s thickness and the dopant’s site. © 2015 Published by Elsevier GmbH.
PACS: 73.61.Ey 75.30.Ev 75.50.Pp
1. Introduction Interlayer exchange coupling (IEC) was shown to be responsible for the giant magnetoresistance effect [1], IEC was observed in a variety of structures composed of metallic ferromagnetic (FM) layers separated by nonmagnetic, metallic, or insulating spacer layers. The GMR effect has initiated the emergence of spintronics [2,3] and has guided the rapid progresses of the modern magnetic storage technologies. Similar to the metallic systems, the diluted magnetic semiconductors (DMSs) which are formed by transitionmetal (TM) low doping into standard semiconductors [4] have been widely studied with an eye on combining spintronics with well-established semiconductor technology. The essential point to manipulate the spin-dependent transport of the DMS multilayers is realization of the reversible switching of their IEC from ferromagnetic to antiferromagnetic. So far, the ferromagnetic IEC has been explicitly observed [5–8]. Theoretically, the antiferromagnetic IEC was first predicted by Jungwirth et al. [9] based on a k·p kineticexchange model in 1999 and later on by Sankowski and Kacman [10] based on a tight-binding model, by Giddings et al. [11] based on the self-consistent mean-field calculations, and very recently
∗ Corresponding author. Tel.: +86 13816244750. E-mail address: [email protected] (M. Luo). http://dx.doi.org/10.1016/j.ijleo.2015.02.026 0030-4026/© 2015 Published by Elsevier GmbH.
by Szałowski and Balcerzak [12] based on a quantum-well model. However, the experimental realization of the antiferromagnetic IEC is difficult and only some progresses were reported [13,14], for instance, in (Ga, Mn)As DMS multilayers with Be-doped GaAs spacers [14]. Very recently, our previous theoretial work has confirmed the antiferromagnetic IEC via Be-doping in the system of (Ga, Mn)As DMS multilayers [15]. However, it is confirmed in the experiments that curie temperature (Tc ) of such DMS materials is only as high as 180 K [16]. The theoretical calculation by Dietl et al. [17] have predicted materials that can have Tc above room temperature. In agreement with their prediction, the 3d transition metal (TM) such as Mn doped in III-nitrides showed ferromagnetism with high Tc . GaN has been by far one of the most studied materials among the nitrides. Also (Ga, Mn)N system is preferable over (Ga, Mn)As because its band structure is much suitable for spin injection. Especially for (Ga, Mn)N showed a large range of Tc varying from 10 K to above room temperature [18–22]. Stimulated by the above theoretical studies, we systematically studied in this Letter the IEC of the GaMnN/GaMnN:Mg multilayers by first-principles calculations. We calculated total energies of a series model DMS multilayers consisting of two ferromagnetically or antiferromagnetically coupled (Ga, Mn)N layers separated by non-doped GaN or Mg-doped GaN nonmagnetic spacers and investigated the effects of the spacer thickness and Mg doping to
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M. Luo, H.Y. Li / Optik 126 (2015) 903–906
0.008
ΔE (eV)
0.000 -0.008 (Ga, Mn)N Spacer: non-doped MgGa in middle
-0.016
MgGa in interface
-0.024
3
4
5
6
7
8
Ga Layers in Spacer Fig. 2. Interlayer exchange coupling (IEC) between two magnetic (Ga, Mn)N layers as a function of the thickness of the GaN spacer. The dashed line is the RKKY interaction of a two-band model based on the theory of Narita and Kasuya [27,28]. Fig. 1. Atomic structures of three typical model DMS multilayers under study. (a) The spacer (the GaN layers in between the upper and lower (Ga, Mn)N magnetic layers) without Mg-doping, (b) a Mg atom doped into the middle of the spacer, and (c) two Mg atoms doped into, respectively, the upper and lower interface layers between the (Ga, Mn)N layers and the spacer.
the IEC. For the model multilayers separated by pure GaN layers without Mg doping, we observed that the IEC is always ferromagnetic. While for the Mg-doped GaAs spacers, the IEC is tunable by varying the spacer’s thickness and the dopant’s site. The antiferromagnetic IEC is archived when the Mg atoms are doped into the interfaces between the (Ga, Mn)N layers and the GaN spacers. This significant effect was attributed to the Mg mediated magnetic interactions between the magnetic multilayers. It is found that the sp-d hybridization between the hole dopant (Mg) and the magnetic dopants (Mn) plays an essential role in tuning the DMS-based magnetic multilayers. 2. Calculation details 2.1. Method Our first-principles calculations were performed based the density functional theory within the generalized gradient approximation (GGA) by using the Vienna ab initio simulation package (VASP) [23]. A plane wave basis set with a cutoff energy of 400 eV, the frozen core all-electron projector augmented wave pseudopotentials [24], and the GGA exchange–correlation potential of the Perdew-Wang-91 form [25], as implemented in the VASP, were employed. The integration over the first Brillouin zone was performed on a grid of Monkhorst–Pack special k-points, which varies from 4 × 4 × 2 to 4 × 4 × 4 depending on the size of the model multilayer system. In the relaxation procedures of the electron and ion degrees of freedom, the convergence tolerances of the total (free) energy were 0.1 meV and 1.0 meV, respectively. 2.2. Structure The atomic structures of three typical model multilayers are presented in Fig. 1. Each model multilayer under study, such as those shown in Fig. 1, was constructed as the follows. At first, a supercell consisting of an appropriate number of Ga and N layers was chosen, where the Ga and N atomic layers were stagger stacked along the c axis (the [0 0 1] crystallographic direction) into the wurtzite structure and the lattice parameters we used are a = 0.322 nm and c = 0.523 nm. The a-axis and b-axis of the supercell are fixed at four times and twice of the lattice constant of GaN, respectively. Then, two Ga atoms in one Ga layer are substituted by two Mn atoms coupled ferromagnetically. Similarly, we substituted other two Ga
atoms by two Mn atoms in another opposite Ga layer and these substituted layers form two magnetic (Ga, Mn)N layers (Fig. 1). The magnetization directions of these two layers were aliened either parallelly or antiparallelly to study the IEC. Between the two (Ga, Mn)N layers is the nonmagnetic GaN spacer, where the hole carriers can be doped via the MgGa substitutions. In the present model multilayers, the GaAs spacer consists of n Ga layers and (n + 1) N layers, where n varies from 3 to 8. First of all, we conform the coupling of two doping atoms (Mn) in the same layer is ferromagnetic. We calculated the total energies with the local magnetic moment of the dopant pair aliened parallelly and antiparallelly. For Mn–Mn pair, we obtained E = −227 and −141 meV for the neighbor and the next-neighbor pair configurations, respectively. These results indicate that the couplings between two doping atoms are ferromagnetic. Cui et al. [26] calculated the exchange between the neighbor Mn–Mn pair and the next-neighbor Mn–Mn pair in GaN and got E about −260 meV and −105 mV, respectively. In the present model multilayers, our obtained values agree very well with their results. Moreover, the observed results indicate that, there is a stronger ferromagnetic coupling between the neighbor Mn–Mn pair. Therefore, in the present study, we simulated the magnetic (Ga, Mn)N layers by substituting two Mn atoms into a pair of neighbor. 3. Results and discussion 3.1. Effect of spacer thickness To investigate the effect of the spacer thickness, we at first studied the model DMS multilayers with the pure GaN layers as the spacer. The model multilayers with the GaN spacer’s thickness varying from 0.785 nm (3 Ga layers) to 2.09 nm (8 Ga layers) were studied (their atomic structures are similar to the example shown in the left panel of Fig. 1). We calculated the total energies of each model system with the magnetizations of two (Ga, Mn)N layers aliened ferromagnetically (FM) and antiferromagnetically (AFM). The IEC was then estimated as E = EFM − EAFM . Figs. 2 and 3 present the calculated IEC as a function of the thickness of the GaN spacer in the (Ga, Mn)N magnetic multilayers, respectively. With increasing the spacer thickness, we observed that, the |E| monotonously decreases from 20 meV to 2 meV (Fig. 2) in the Mn-doped GaN system. In particular, for all the calculated spacer thicknesses, the negative IECs were observed, indicating that the magnetic layers always coupled ferromagnetically when the pure GaN spacers were adopted. It deserves to be mentioned that, in (Ga, Mn)As DMS multilayers with the pure GaAs layers as the spacer, we have had a
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35 30 25 20 15 10 5 0 -5 -10
EF
PDOS (States/eV)
Spin-down Spin-up
a
0.30 0.15
0.0 2.5 5.0 7.5 10.0 12.5 15.0 Concentration of Mg (%)
0.00 -0.15 -0.30
(Ga, Mn)N
ΔE (meV)
0.30 0.15 0.00 -0.15 -0.30
905
b
Fig. 4. Interlayer exchange coupling (IEC) between two magnetic (Ga, Mn)N layers as a function of the concentration of Mg dopants in the GaN spacer.
0.30 0.15
3.2. Effect of Mg doping
0.00 -0.15 -0.30
c
-8
-6
-4
-2 0 2 Energy (eV)
4
6
Fig. 3. Electron density of states projected to Mg dopants for, (a): two antiferromagnetically coupled (the ground state) (Ga, Mn)N layers separated by a GaN spacer (n = 5) with Mg doped into the middle of the spacer, and (b) and (c): two antiferromagnetically coupled (the ground state) (Ga, Mn)N layers separated by the GaN (n = 5) spacer with two Mg doped into the upper [(b)] and lower [(c)] interfaces, respectively.
similar observation that increasing the spacer thickness cannot change the IEC from ferromagnetic to antiferromagnetic and a ferromagnetic IEC was always obtained. However, If the spin interaction between two magnetic (Ga, Mn)As layers are mediated by the nearly-free hole carriers, a Friedel-like oscillating is expected with increase of the spacer thickness, according to the theory of Ruderman–Kittle–Kasuya–Yoshida (RKKY). However, such oscillating behavior is absent in the calculated IEC as shown in Fig. 2. The oscillating behavior of the conventional RKKY exchange interaction is originated from a spin-polarized screening effect of the nearlyfree conduction electrons/holes to the magnetic impurities; while in the present DMS multilayers, the IEC is mediated by the holes in the spacer, which can be created only by exciting the valance electrons to the conduction bands. Therefore, the magnetic screening effect in this gaped system is expected to be imperfect and thus the RKKY interaction based a gaped two-band model proposed by Narita and Kasuya [27,28] is more suitable. In this model, the indirect exchange interaction between two magnetic dopants exponentially decays with the increase in the distance R between the dopants, i.e., J(R) ∝ e−ˇR /R1+d/2 , where ˇ is a coefficient depending on the effective mass of the carriers and on the energy gap, and d the dimension of the band dispersion. Their results demonstrate that the energy gap removes the oscillation of the RKKY exchange interaction and particularly, J(R) falls off with R very quickly in the gaped system because of the exponential decaying prefactor. Taking ˇ as a fitting parameter, d = 2 for the 2D hole band in the GaN spacer layer, and R = (n + 1)a/2 (a and n are the lattice parameter and the number of Ga layers, respectively), we obtained the spacer-thickness-dependent IEC as E = −3.75e−0.605(1+n) /(1 + n)2 , which indeed describes reasonably the trend of E with increasing the spacer thickness (Fig. 2).
As shown by Narita and Kasuya [27,28], the J (Rn − Rm ) in the gaped two-band system is always positive (i.e., the IEC is always ferromagnetic). The conventional oscillating J (Rn − Rm ) recovers only when the carrier band which mediates the magnetic interaction becomes “metallic” like. This may be achieved by substitutional doping of double valent MgGa in the GaN spacer, as the carriersmediated antiferromagnetic IEC in the DMS superlattices and multilayers discussed early by Jungwirth et al. [9]. For this reason, we calculated the IEC between two (Ga, Mn)N layers separated by the Mg-doped GaN spacer where the Mg doping in the spacer is known to increase the hole concentrations directly in the GaN layers [29]. There are two kinds of possible MgGa substitutional sites in the spacer layers of the present model multilayers. One is in the middle of the spacer and another one is in the interface between the (Ga, Mn)N and GaN layers. Fig. 2 presents the calculated IEC for the first case, i.e., one Mg dopant occupying a Ga site in the middle of the spacer (the middle panel of Fig. 1). As shown in Fig. 2, we see clearly that, the E changes from negative (−7 meV, n = 2) to positive(+2 meV, n = 8) gradually with increasing the thickness of the spacer, indicating that the IEC switches from ferromagnetic to antiferromagnetic. When the Mg atoms are doped into the interfaces, the IEC switches from ferromagnetic to antiferromagnetic when n ≥ 5, exhibiting a similar trend to that of the a Mg-doped into the spacer. We investigated the densities of states (DOS) projected to the Mg dopant for the calculated model multilayers. As an example, Fig. 3 presents the results for the model multilayer with n = 5 in its ferromagnetically coupled ground state. As shown in Fig. 3(a), when the Mg dopants are in the middle of the spacers, there are a sp-d interaction between the Mn and Mg dopants, As a result, the Mg dopant is able to mediate the spin interaction between the ferromagnetic (Ga, Cr)N layers, so that the antiferromagnetic IEC is expected. The situation may be different when the Mg dopants are in interfaces of the spacers, as shown in Fig. 3(b) and (c), there are a strong sp–d interaction between the Mn and Mg dopants because there is an obvious spin-polarization in the Mg-projected DOS around the Fermi energy. As a result, the antiferromagnetic IEC has to be enhanced. In contrast to the case of one Mg doped in (Ga, Mn)N, we suspect that the increased concentration of Mg could enhance the antiferromagnetic coupling between the two ferromagnetic (Ga, Mn)N layers. We then study the model DMS multilayers with the same spacer. The GaN spacer’s thickness is keeping 1.046 nm (4 Ga layers) were studied. Fig. 4 presents the calculated IEC as a function
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of the concentration of Mg. For the pure spacer (the concentration of Mg is 0), we obtained the IEC E of −6 meV. With the concentration of Mg increased, we observed that the E monotonously increases to 34 meV, indicating that when the concentration of Mg increases, the couple between the two ferromagnetic layers change from ferromagnetical to antiferromagnetic and attentively the antiferromagnetic of the IEC is enhanced. 4. Conclusion In summary, the IEC in a series model DMS multilayers consisting of two magnetic (Ga, Mn)N layers separated by non-doped or Mg-doped GaN non-magnetic spacers have been studied by first-principles total-energy calculations. It was observed that, (1) without Mg doping, the IEC was always ferromagnetic, which was an intrinsic character of the RKKY interaction in a gaped system. (2) Mg-doping in the interface layers between the magnetic (Ga, Mn)N layers and the GaN spacer can change the IEC from ferromagnetic to antiferromagnetic. Acknowledgments We thank the Supercomputer Center of ECNU for using the Dawn 5000 A supercomputer. This work is supported by the research programs of Shanghai (AAZH1116). References [1] S.S.P. Parkin, Systematic variation of the strength and oscillation period of indirect magnetic exchange coupling through the 3d, 4d, and 5d transition metals, Phys. Rev. Lett. 67 (1991) 3598–3601. [2] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dan, F. Petroff, P. Etienne, G. Crenzet, A. Friederich, J. Chazelas, Giant magnetoresistance of (0 0 1)Fe/(0 0 1)Cr magnetic superlattices, Phys. Rev. Lett. 61 (1988) 2472–2475. [3] G. Binasch, P. Grünberg, F. Saurenbach, W. Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys. Rev. B: Condens. Matter 39 (1989) 4828–4830. [4] T. Jungwirth, J. Maˇsek, J. Kuˇcera, J. Kucera, A.H. MacDonald, Theory of ferromagnetic (III,Mn)V semiconductors, Rev. Mod. Phys. 78 (2006) 809–864. [5] H. Munekata, H. Ohno, S. von Molnár, A. Segmüller, L.L. Chang, L. Esaki, Diluted magnetic III–V semiconductors, Phys. Rev. Lett. 63 (1989) 1849–1852. [6] H. Ohno, H. Munekata, T. Penney, S. von Molnár, L.L. Chang, Magnetotransport properties of p-type (In,Mn)As diluted magnetic III–V semiconductors, Phys. Rev. Lett. 68 (1992) 2664–2667. [7] D. Chiba, N. Akiba, F. Matsukura, Y. Ohno, H. Ohno, Magnetoresistance effect and interlayer coupling of (Ga, Mn)As trilayer structures, Appl. Phys. Lett. 77 (2000) 1873–1875. [8] S.J. Chung, S. Lee, I.W. Park, X. Liu, J.K. Furdyna, Possible indication of interlayer exchange coupling in GaMnAs/GaAs ferromagnetic semiconductor super lattices, J. Appl. Phys. 95 (2004) 7402–7406. [9] T. Jungwirth, W.A. Atkinson, B.H. Lee, A.H. MacDonald, Interlayer coupling in ferromagnetic semiconductor superlattices, Phys. Rev. B: Condens. Matter 59 (1999) 9818–9821. [10] P. Sankowski, P. Kacman, Interlayer exchange coupling in (Ga,Mn)As-based superlattices, Phys. Rev. B: Condens. Matter 71 (2005) 201303–201306.
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