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The structural, electronic and magnetic properties of Ga8−xMnxAs8 clusters
Journal of Magnetism and Magnetic Materials 384 (2015) 155–159
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
The structural, electronic and magnetic properties of Ga8 xMnxAs8 clusters Gangxu Gu a,b, Gang Xiang a,b,n, Jia Luo a,b, Zhijie Tang a,b, Xi Zhang a,b,n a b
College of Physical Science and Technology, Sichuan University, Chengdu 610064, China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China
art ic l e i nf o
a b s t r a c t
Article history: Received 5 November 2014 Received in revised form 6 February 2015 Accepted 16 February 2015 Available online 17 February 2015
We systematically investigate the ground-state magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) within the framework of density functional theory (DFT) using a strategy that successively adopts the particle swarm optimization (CALYPSO) code and fixed spin-moment (FSM) method. The results show that for Ga8 xMnxAs8 in the ground states or low-lying isomers, Mn atoms tend to assemble at the core of the clusters and the ferrimagnetic Mn–Mn couplings are identified for Ga8 xMnxAs8 (x ¼ 4, 6, and 8), while Ga8As8 and Ga6Mn2As8 are nonmagnetic. The possibility of multiple ground states of Ga8 xMnxAs8 (x ¼4, 6, and 8) is also demonstrated. The binding energy and LUMO–HOMO gap analysis show that Ga8 xMnxAs8 clusters with large x are more likely synthesized and exhibit stronger chemical reactivity. & 2015 Elsevier B.V. All rights reserved.
Keywords: Ga8 xMnxAs8 clusters The particle swarm optimization code Fixed spin-moment method Magnetic properties
1. Introduction The diluted magnetic semiconductor (DMS) (Ga,Mn)As has been widely studied in the past decade because of its prototype characters in spintronic materials [1,2] and devices [3–7]. Recently, extensive efforts have been devoted to understand and improve the magnetism of low dimensional (Ga,Mn)As systems [8,9], both for fundamental physics and potential applications. In the meantime, there also are many studies on semiconductor clusters, especially Si clusters [10–13] and GaAs clusters [14–18], due to the strong desire to understand how physical properties change with reduced dimension and the need to developing novel promising semiconductor nanostructures. Unlike the detailed experimental studies of the structures and properties of transition-metal (TM) doped Si clusters [19–22], there are no such experimental studies reported in the case of GaAs clusters, although experiments have indicated that formation of clusters, especially MnAs clusters, can dramatically influence the magnetic properties of the GaMnAs films [23–26]. Meanwhile, there were theoretical advances about GaMnAs clusters, for instance, Gutsev et al. and Wang et al. studied (GaAs)mXn clusters (X¼ Mn, Fe; m ¼ 1–4, n¼ 1–3) [27] and (GaAs)mXn clusters (X¼ Mn, Fe; m ¼7–12, n ¼ 1,2) [28], respectively. However, in both works TM atoms were absorbed to (GaAs)n clusters, not as substitutional dopants incorporated in n Corresponding authors at: College of Physical Science and Technology, Sichuan University, Chengdu 610064, China. E-mail addresses: [email protected] (G. Xiang), [email protected] (X. Zhang).
http://dx.doi.org/10.1016/j.jmmm.2015.02.042 0304-8853/& 2015 Elsevier B.V. All rights reserved.
GaAs clusters. In fact, to the best of our knowledge, Mn doped GaAs clusters, or (Ga,Mn)As clusters, the lower dimensional counterpart of (Ga,Mn)As bulk, are rarely studied. In this work, the structural, electronic and magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) are studied by using first-principles calculations. The Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code [29] and fixed spinmoment (FSM) method [30–33] are successively adopted to predict the ground state geometric and magnetic configuration of these clusters, and then extensive calculations and analysis based on density functional theory (DFT) are performed. Our results reveal that there exist ferrimagnetic couplings between Mn atoms of Ga8 xMnxAs8 (x ¼4, 6, and 8) in the ground state or low-lying isomers, and Ga8 xMnxAs8 with large x is more likely formed and reacts with each other to create larger clusters.
2. Computational details CALYPSO code is a perfect choice to predict the structure of clusters [29,34]. Only chemical compositions are required to predict stable structures, in other words, setting a series of initial geometrical structures by hand is avoided for trying to cover diversity and complexity of isomers for a cluster. Meanwhile, the FSM method is powerful to determine the ground state geometric and magnetic structure of a magnetic cluster. However, it is a delicate task to use CALYPSO to predict the ground state structure of a magnetic cluster with a fixed total spin moment since there are a large number of values of total spin moment. So in our work,
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G. Gu et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 155–159
we adopt a compromised but effective strategy. First, using non spin polarized calculations, ground state structure and low-lying isomers are predicted by CALYPSO interfaced with VASP [35]. Here, we call this nonmagnetic ground state obtained as “initial ground state”. Then spin polarized calculations are performed by considering all possible total spin moments (S ¼N↑ N↓ ¼0, 2, …, 5x) for each initial ground state structure to get the ground state magnetic moment. For each fixed S, the geometric structure is relaxed until the forces on atoms are less than 0.01 eV/Å. We call this magnetic ground state as “true ground state”. The first-principles calculations as implemented in VASP code are performed using the projector augmented wave (PAW) formalism [36]. The generalized gradient approximation (GGA) in the form proposed by Perdew–Burke–Ernzerhof (PBE) [37] is used to approximate the exchange correlation potential. The energy cutoff for the plane-wave basis set is 400 eV, and a 1 1 1 k-point gamma mesh is used for the Brillouin zone (BZ) integration. Vacuum distances between neighboring clusters are about 15 Å, which are found to be sufficient to eliminate interactions.
3. Results and discussion Fig. 1 shows the initial ground state and low-lying isomers for Ga8 xMnxAs8 predicted by CALYPSO interfaced with VASP using non spin polarized calculations. For Ga8As8, the initial ground state and low-lying isomers all have a cage structure in which Ga atoms like bonding As atoms, in agreement with previous works [15,16]. For Ga8 xMnxAs8 with x ¼2, 4, 6, and 8, the common character shared by these geometric structures is that Mn atoms prefer to occupy the inner part of the cluster, and Ga and As atoms attempt to cover the core formed by Mn atoms. As listed in Table 1, this is because the binding energy per Mn atom is largest. It should be noted that the energy difference between the initial ground state and the first isomer for Ga8As8 and Ga2Mn6As8 is only 20 meV and 13 meV, respectively, which indicates the possibility of multiple ground state structures of Ga8 xMnxAs8 at temperatures above room temperature (RT). In order to verify that whether Mn atoms in Ga8 xMnxAs8 bond with each other and form cluster, it is useful to discuss the Mn–Mn distance of the initial ground state for Ga8 xMnxAs8. Comparing with the Mn–Mn distance in bulk (2.480 Å, as listed in Table 1), the Mn–Mn distance is 2.403 Å for Ga6Mn2As8, and the average Mn– Mn distance is 2.399 Å, 2.538 Å and 2.608 Å for Ga4Mn4As8, Ga2Mn6As8 and Mn8As8, respectively. Undoubtedly, the two Mn atoms in Ga6Mn2As8 are bonding, and the Mn atoms in Ga4Mn4As8 are also bonding and tend to dissolve out. The Mn atoms in Ga2Mn6As8 and Mn8As8 are still bonding because the shortest Mn– Mn distance for Ga2Mn6As8 and Mn8As8 is 2.384 Å and 2.461 Å, respectively, less than the Mn–Mn distance in bulk. The reason of the augment of average Mn–Mn distance for Ga2Mn6As8 and Mn8As8 is that the interaction between As atoms and Mn atoms increases as the number of Ga atoms decrease. To get the true ground state structure of Ga8 xMnxAs8, we perform a series of spin polarized calculations. Of course, Ga8As8 is a nonmagnetic cluster. For the initial ground state of Ga6Mn2As8, we set two Mn atoms to be ferromagnetic coupling or antiferromagnetic coupling, and relax the geometric structure. Interestingly, Ga6Mn2As8 always turn into the nonmagnetic state. As shown in Fig. 2(a)–(c), complete FSM calculations are performed for the initial ground state for Ga8 xMnxAs8 with x ¼4, 6, and 8. In addition, the first isomer of Ga4Mn4As8 is calculated as a test. The results of the first isomer and initial ground state for Ga4Mn4As8 present similar variation trend. Thus, for Ga8 xMnxAs8, calculating the initial ground state can get reasonable results about the true ground state. And Ga4Mn4As8 with total moment 4 μB, Ga2Mn6As8
Fig. 1. Geometric structures of the initial ground state and low-lying isomers for Ga8 xMnxAs8. Numbers in parentheses represent the number of Mn atoms, i.e. x, in Ga8 xMnxAs8, and relative energy to the initial ground state. Blue spheres represent Ga atoms, green spheres represent As atoms, and purple spheres represent Mn atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 The calculated ground state structure, binding energy, and bond length of GaAs, MnAs, Ga, As, and Mn in bulk.
GaAs MnAs Ga As Mn
Crystal structure
Eb (eV/atom)
Bond length (Å)
Zinc-blende structure Hexagonal structure Orthorhombic α structure Rhomboedral A7 structure Face-centered cubic structure
4.193 6.920 2.903 4.664 8.744
2.487 2.424 2.526 2.554 2.480
with total moment 6 μB and Mn8As8 with total moment 8 μB is found to be the true ground state, respectively. The binding energy per atom is calculated as Eb (Ga 8 − x Mn xAs 8 ) = − [E (Ga 8 − x Mn xAs 8 ) − (8 − x) E (Ga) –xE (Mn) − 8E (As)]/16
(1)
In our calculations, x ¼0, 2, 4, 6, 8. As shown in Fig. 2(d), for Ga4Mn4As8, Ga2Mn6As8, and Mn8As8, the binding energy per atom
G. Gu et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 155–159
-89
Total Energy (eV)
Total Energy (eV)
-79
-80
-81
-90 -91 -92 -93
-82 0
5
10
15
20
0
10
Magnetic Moment (μB) Binding Energy (eV/atom)
-100 -101 -102 -103 -104 0
10
20
30
20
30
Magnetic Moment (μB)
-99
Total Energy (eV)
157
40
Magnetic Moment (μB)
6
5
4
0
2
4
6
8
x
Fig. 2. (a) The total energy as a function of the total spin moment (S ¼N↑ N↓) for the initial ground state (black squares) and the isomer next to the initial ground state (red circles) for Ga4Mn4As8. And the total energy as a function of the total spin moment for the initial ground state for (b) Ga2Mn6As8, and (c) Mn8As8. (d) The binding energy per atom of the true ground state (black) or initial ground state (blue) as the number of Mn atoms in Ga8 xMnxAs8 increases. The dashed lines in (a)–(c) represent the total energy of corresponding geometric structure obtained by previous non spin polarized calculations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of true ground state is 26 meV, 90 meV, and 148 meV larger than that of initial ground state, respectively. The binding energy per atom increases almost linearly as x increases. Therefore, in a hypothetical process of growing Ga8 xMnxAs8, Ga8 xMnxAs8 clusters with larger number of Mn atoms are preferred to form, especially Mn8As8. Now, we discuss in detail the magnetic properties of Ga8 xMnxAs8 with x¼ 4, 6, and 8. Fig. 3 shows the geometric structures and spatial magnetization density for the true ground state as well as for the low-lying isomers for Ga8 xMnxAs8. The magnetic moment of every Mn atom for Ga8 xMnxAs8 with a specific total spin moment is listed in Table 2. The results show that Mn atoms tend to assemble at core, and As and Ga atoms try to cover the core. Thus, comparing the magnetic properties of Ga8 xMnxAs8 with the magnetic properties of Mnn clusters (n ¼2– 20) in previous work of Kabir et al. would be interesting [30]. Different from the total moment 20 μB for Mn4 cluster's ground state, the total spin moment of Ga4Mn4As8 is much lower due to the appearance of Ga atoms and As atoms. The ground state and low-lying isomers for Ga2Mn6As8, Mn8As8 and Mn6 cluster, Mn8 cluster all are ferrimagnetic since the magnetic frustration occurs with the increase of number of Mn atoms. It is noted that Mn8 cluster with total moment 8 μB and 12 μB are degenerate ground state, while Mn8As8 with total moment 8 μB and 16 μB are also nearly degenerate, which means that Mn8As8 cluster is superparamagnetic, in agreement with results of previous experimental works that the small MnAs clusters (with diameters of 5 10 nm) are superparamagnetic [24–26]. These similar magnetic properties shared by Ga8 xMnxAs8 and Mnn clusters also suggest that Mn atoms in Ga8 xMnxAs8 tend to nucleate. Fig. 4(a) reveals that Mn atoms contribute the most of magnetic moment, in agreement with the distribution of spatial
Fig. 3. The relaxed geometric structures and spatial magnetization density for the true ground state as well as for the low-lying isomers for Ga8 xMnxAs8 with x ¼4, 6, and 8. The yellow (light blue) isosurface represents spin up (spin down) spatial magnetization density. Numbers in parentheses represent the number of Mn atoms, relative energy to the ground state, and total spin moment, respectively. The isovalue is 0.05 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Table 2 The total spin moment, magnetic moment of every Mn atom for Ga8 xMnxAs8 with x ¼4, 6, and 8. x
Total moment (μB)
The moment (μB) of Mn atom in rank 1
2
3
4
5
6
4 2 8
0.24 0.82 3.42
2.96 1.29 3.33
0.05 1.01 1.06
2.21 0.72 3.15
6
6 2 4
3.34 3.35 3.51
3.01 2.83 0.62
2.57 1.65 1.80
3.10 3.08 3.28
3.69 3.47 3.61
3.20 2.59 2.85
8
8 16 20
3.43 3.25 3.23
2.31 3.18 3.27
3.90 3.41 3.03
2.86 2.56 3.26
3.11 4.01 3.61
2.97 1.56 2.58
DOS (states/eV)
DOS (states/eV)
4
0 -5
50
0
1.91 2.64 3.02
3.92 4.11 4.09
4. Conclusions
-50 -4
-2
0
2
Energy (eV) Fig. 4. (a) The density of states (DOS) of Ga atom, Mn atom, and As atom in the true ground state for Ga4Mn4As8. (b) The total DOS of the true ground state for Mn8As8. The Fermi level is shown in green-dashed vertical line. The width of Gaussian smearing in 0.05 eV is used. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Δ1 of ground state
LUMO-HOMO gap (eV)
8
potential application of MnAs clusters in optoelectronic nanostructures. To capture the panorama of LOMO–HUMO gap for Ga8 xMnxAs8, we plot Fig. 5. The LOMO–HUMO gap decreases as x increase for both the true ground state and low-lying isomers. Based on the frontier orbitals theory, a smaller LOMO–LUMO gap means the stronger chemical reactivity. Thereby Ga8 xMnxAs8 clusters with large x more likely integrate with each other to form bigger clusters, in which the percentage of Mn is high. This result conforms to the fact that MnAs and/or Mn-riched GaMnAs clusters often appear in the growth of (Ga,Mn)As films [23–26,38–40].
Ga Mn As
5
7
Δ2 of ground state
1.0
Δ1 of first isomer
Δ2 of first isomer Δ1 of second isomer
The structural, electronic, and magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) are investigated using first-principles calculations. CALYPSO is employed first to predict the initial ground state of Ga8 xMnxAs8. Then we obtain the true ground state of Ga8 xMnxAs8 by using FSM method based on spin polarized calculations. The results show that Mn atoms are gathered at the core of Ga8 xMnxAs8 cluster, and the true ground state and low-lying isomers of Ga8 xMnxAs8 with x¼4, 6, and 8, are found to be ferrimagnetic. The possible multiple ground states are demonstrated and discussed. Ga8 xMnxAs8 with large x owns larger binding energy and smaller LUMO–HOMO gap, all which means that Ga8 xMnxAs8 with larger x are more likely to be synthesized and react with each other. Since the clusters are bridges between molecules and macroscopic condensed matters, these results about Ga8 xMnxAs8 clusters may be helpful to understand the growth mechanism and properties of MnAs and/or (Ga,Mn)As thin films.
Δ2 of second isomer Acknowledgments
0.5
This work was supported by the National Natural Foundation of China (NSFC) through Grant no. 11174212, gram for New Century Excellent Talents in University through Grant no. 11-0351 and by Project sponsored by ROCS of State Education Ministry of China.
0
2
4
6
Science by Pro(NCET) SRF for
8
x Fig. 5. The LOMO–HUMO gap as a function of the value of x for Ga8 xMnxAs8. The LOMO–HUMO gap for spin up (spin down) channel is represent by Δ1 (Δ2).
magnetization density in Fig. 3. In contrary to well-known metallic state of MnAs in bulk, due to quantum confinement, the DOS of Mn8As8 presents a LOMO–HUMO gap (Fig. 4(b)), which implies
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Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
The structural, electronic and magnetic properties of Ga8 xMnxAs8 clusters Gangxu Gu a,b, Gang Xiang a,b,n, Jia Luo a,b, Zhijie Tang a,b, Xi Zhang a,b,n a b
College of Physical Science and Technology, Sichuan University, Chengdu 610064, China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China
art ic l e i nf o
a b s t r a c t
Article history: Received 5 November 2014 Received in revised form 6 February 2015 Accepted 16 February 2015 Available online 17 February 2015
We systematically investigate the ground-state magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) within the framework of density functional theory (DFT) using a strategy that successively adopts the particle swarm optimization (CALYPSO) code and fixed spin-moment (FSM) method. The results show that for Ga8 xMnxAs8 in the ground states or low-lying isomers, Mn atoms tend to assemble at the core of the clusters and the ferrimagnetic Mn–Mn couplings are identified for Ga8 xMnxAs8 (x ¼ 4, 6, and 8), while Ga8As8 and Ga6Mn2As8 are nonmagnetic. The possibility of multiple ground states of Ga8 xMnxAs8 (x ¼4, 6, and 8) is also demonstrated. The binding energy and LUMO–HOMO gap analysis show that Ga8 xMnxAs8 clusters with large x are more likely synthesized and exhibit stronger chemical reactivity. & 2015 Elsevier B.V. All rights reserved.
Keywords: Ga8 xMnxAs8 clusters The particle swarm optimization code Fixed spin-moment method Magnetic properties
1. Introduction The diluted magnetic semiconductor (DMS) (Ga,Mn)As has been widely studied in the past decade because of its prototype characters in spintronic materials [1,2] and devices [3–7]. Recently, extensive efforts have been devoted to understand and improve the magnetism of low dimensional (Ga,Mn)As systems [8,9], both for fundamental physics and potential applications. In the meantime, there also are many studies on semiconductor clusters, especially Si clusters [10–13] and GaAs clusters [14–18], due to the strong desire to understand how physical properties change with reduced dimension and the need to developing novel promising semiconductor nanostructures. Unlike the detailed experimental studies of the structures and properties of transition-metal (TM) doped Si clusters [19–22], there are no such experimental studies reported in the case of GaAs clusters, although experiments have indicated that formation of clusters, especially MnAs clusters, can dramatically influence the magnetic properties of the GaMnAs films [23–26]. Meanwhile, there were theoretical advances about GaMnAs clusters, for instance, Gutsev et al. and Wang et al. studied (GaAs)mXn clusters (X¼ Mn, Fe; m ¼ 1–4, n¼ 1–3) [27] and (GaAs)mXn clusters (X¼ Mn, Fe; m ¼7–12, n ¼ 1,2) [28], respectively. However, in both works TM atoms were absorbed to (GaAs)n clusters, not as substitutional dopants incorporated in n Corresponding authors at: College of Physical Science and Technology, Sichuan University, Chengdu 610064, China. E-mail addresses: [email protected] (G. Xiang), [email protected] (X. Zhang).
http://dx.doi.org/10.1016/j.jmmm.2015.02.042 0304-8853/& 2015 Elsevier B.V. All rights reserved.
GaAs clusters. In fact, to the best of our knowledge, Mn doped GaAs clusters, or (Ga,Mn)As clusters, the lower dimensional counterpart of (Ga,Mn)As bulk, are rarely studied. In this work, the structural, electronic and magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) are studied by using first-principles calculations. The Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code [29] and fixed spinmoment (FSM) method [30–33] are successively adopted to predict the ground state geometric and magnetic configuration of these clusters, and then extensive calculations and analysis based on density functional theory (DFT) are performed. Our results reveal that there exist ferrimagnetic couplings between Mn atoms of Ga8 xMnxAs8 (x ¼4, 6, and 8) in the ground state or low-lying isomers, and Ga8 xMnxAs8 with large x is more likely formed and reacts with each other to create larger clusters.
2. Computational details CALYPSO code is a perfect choice to predict the structure of clusters [29,34]. Only chemical compositions are required to predict stable structures, in other words, setting a series of initial geometrical structures by hand is avoided for trying to cover diversity and complexity of isomers for a cluster. Meanwhile, the FSM method is powerful to determine the ground state geometric and magnetic structure of a magnetic cluster. However, it is a delicate task to use CALYPSO to predict the ground state structure of a magnetic cluster with a fixed total spin moment since there are a large number of values of total spin moment. So in our work,
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G. Gu et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 155–159
we adopt a compromised but effective strategy. First, using non spin polarized calculations, ground state structure and low-lying isomers are predicted by CALYPSO interfaced with VASP [35]. Here, we call this nonmagnetic ground state obtained as “initial ground state”. Then spin polarized calculations are performed by considering all possible total spin moments (S ¼N↑ N↓ ¼0, 2, …, 5x) for each initial ground state structure to get the ground state magnetic moment. For each fixed S, the geometric structure is relaxed until the forces on atoms are less than 0.01 eV/Å. We call this magnetic ground state as “true ground state”. The first-principles calculations as implemented in VASP code are performed using the projector augmented wave (PAW) formalism [36]. The generalized gradient approximation (GGA) in the form proposed by Perdew–Burke–Ernzerhof (PBE) [37] is used to approximate the exchange correlation potential. The energy cutoff for the plane-wave basis set is 400 eV, and a 1 1 1 k-point gamma mesh is used for the Brillouin zone (BZ) integration. Vacuum distances between neighboring clusters are about 15 Å, which are found to be sufficient to eliminate interactions.
3. Results and discussion Fig. 1 shows the initial ground state and low-lying isomers for Ga8 xMnxAs8 predicted by CALYPSO interfaced with VASP using non spin polarized calculations. For Ga8As8, the initial ground state and low-lying isomers all have a cage structure in which Ga atoms like bonding As atoms, in agreement with previous works [15,16]. For Ga8 xMnxAs8 with x ¼2, 4, 6, and 8, the common character shared by these geometric structures is that Mn atoms prefer to occupy the inner part of the cluster, and Ga and As atoms attempt to cover the core formed by Mn atoms. As listed in Table 1, this is because the binding energy per Mn atom is largest. It should be noted that the energy difference between the initial ground state and the first isomer for Ga8As8 and Ga2Mn6As8 is only 20 meV and 13 meV, respectively, which indicates the possibility of multiple ground state structures of Ga8 xMnxAs8 at temperatures above room temperature (RT). In order to verify that whether Mn atoms in Ga8 xMnxAs8 bond with each other and form cluster, it is useful to discuss the Mn–Mn distance of the initial ground state for Ga8 xMnxAs8. Comparing with the Mn–Mn distance in bulk (2.480 Å, as listed in Table 1), the Mn–Mn distance is 2.403 Å for Ga6Mn2As8, and the average Mn– Mn distance is 2.399 Å, 2.538 Å and 2.608 Å for Ga4Mn4As8, Ga2Mn6As8 and Mn8As8, respectively. Undoubtedly, the two Mn atoms in Ga6Mn2As8 are bonding, and the Mn atoms in Ga4Mn4As8 are also bonding and tend to dissolve out. The Mn atoms in Ga2Mn6As8 and Mn8As8 are still bonding because the shortest Mn– Mn distance for Ga2Mn6As8 and Mn8As8 is 2.384 Å and 2.461 Å, respectively, less than the Mn–Mn distance in bulk. The reason of the augment of average Mn–Mn distance for Ga2Mn6As8 and Mn8As8 is that the interaction between As atoms and Mn atoms increases as the number of Ga atoms decrease. To get the true ground state structure of Ga8 xMnxAs8, we perform a series of spin polarized calculations. Of course, Ga8As8 is a nonmagnetic cluster. For the initial ground state of Ga6Mn2As8, we set two Mn atoms to be ferromagnetic coupling or antiferromagnetic coupling, and relax the geometric structure. Interestingly, Ga6Mn2As8 always turn into the nonmagnetic state. As shown in Fig. 2(a)–(c), complete FSM calculations are performed for the initial ground state for Ga8 xMnxAs8 with x ¼4, 6, and 8. In addition, the first isomer of Ga4Mn4As8 is calculated as a test. The results of the first isomer and initial ground state for Ga4Mn4As8 present similar variation trend. Thus, for Ga8 xMnxAs8, calculating the initial ground state can get reasonable results about the true ground state. And Ga4Mn4As8 with total moment 4 μB, Ga2Mn6As8
Fig. 1. Geometric structures of the initial ground state and low-lying isomers for Ga8 xMnxAs8. Numbers in parentheses represent the number of Mn atoms, i.e. x, in Ga8 xMnxAs8, and relative energy to the initial ground state. Blue spheres represent Ga atoms, green spheres represent As atoms, and purple spheres represent Mn atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 The calculated ground state structure, binding energy, and bond length of GaAs, MnAs, Ga, As, and Mn in bulk.
GaAs MnAs Ga As Mn
Crystal structure
Eb (eV/atom)
Bond length (Å)
Zinc-blende structure Hexagonal structure Orthorhombic α structure Rhomboedral A7 structure Face-centered cubic structure
4.193 6.920 2.903 4.664 8.744
2.487 2.424 2.526 2.554 2.480
with total moment 6 μB and Mn8As8 with total moment 8 μB is found to be the true ground state, respectively. The binding energy per atom is calculated as Eb (Ga 8 − x Mn xAs 8 ) = − [E (Ga 8 − x Mn xAs 8 ) − (8 − x) E (Ga) –xE (Mn) − 8E (As)]/16
(1)
In our calculations, x ¼0, 2, 4, 6, 8. As shown in Fig. 2(d), for Ga4Mn4As8, Ga2Mn6As8, and Mn8As8, the binding energy per atom
G. Gu et al. / Journal of Magnetism and Magnetic Materials 384 (2015) 155–159
-89
Total Energy (eV)
Total Energy (eV)
-79
-80
-81
-90 -91 -92 -93
-82 0
5
10
15
20
0
10
Magnetic Moment (μB) Binding Energy (eV/atom)
-100 -101 -102 -103 -104 0
10
20
30
20
30
Magnetic Moment (μB)
-99
Total Energy (eV)
157
40
Magnetic Moment (μB)
6
5
4
0
2
4
6
8
x
Fig. 2. (a) The total energy as a function of the total spin moment (S ¼N↑ N↓) for the initial ground state (black squares) and the isomer next to the initial ground state (red circles) for Ga4Mn4As8. And the total energy as a function of the total spin moment for the initial ground state for (b) Ga2Mn6As8, and (c) Mn8As8. (d) The binding energy per atom of the true ground state (black) or initial ground state (blue) as the number of Mn atoms in Ga8 xMnxAs8 increases. The dashed lines in (a)–(c) represent the total energy of corresponding geometric structure obtained by previous non spin polarized calculations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of true ground state is 26 meV, 90 meV, and 148 meV larger than that of initial ground state, respectively. The binding energy per atom increases almost linearly as x increases. Therefore, in a hypothetical process of growing Ga8 xMnxAs8, Ga8 xMnxAs8 clusters with larger number of Mn atoms are preferred to form, especially Mn8As8. Now, we discuss in detail the magnetic properties of Ga8 xMnxAs8 with x¼ 4, 6, and 8. Fig. 3 shows the geometric structures and spatial magnetization density for the true ground state as well as for the low-lying isomers for Ga8 xMnxAs8. The magnetic moment of every Mn atom for Ga8 xMnxAs8 with a specific total spin moment is listed in Table 2. The results show that Mn atoms tend to assemble at core, and As and Ga atoms try to cover the core. Thus, comparing the magnetic properties of Ga8 xMnxAs8 with the magnetic properties of Mnn clusters (n ¼2– 20) in previous work of Kabir et al. would be interesting [30]. Different from the total moment 20 μB for Mn4 cluster's ground state, the total spin moment of Ga4Mn4As8 is much lower due to the appearance of Ga atoms and As atoms. The ground state and low-lying isomers for Ga2Mn6As8, Mn8As8 and Mn6 cluster, Mn8 cluster all are ferrimagnetic since the magnetic frustration occurs with the increase of number of Mn atoms. It is noted that Mn8 cluster with total moment 8 μB and 12 μB are degenerate ground state, while Mn8As8 with total moment 8 μB and 16 μB are also nearly degenerate, which means that Mn8As8 cluster is superparamagnetic, in agreement with results of previous experimental works that the small MnAs clusters (with diameters of 5 10 nm) are superparamagnetic [24–26]. These similar magnetic properties shared by Ga8 xMnxAs8 and Mnn clusters also suggest that Mn atoms in Ga8 xMnxAs8 tend to nucleate. Fig. 4(a) reveals that Mn atoms contribute the most of magnetic moment, in agreement with the distribution of spatial
Fig. 3. The relaxed geometric structures and spatial magnetization density for the true ground state as well as for the low-lying isomers for Ga8 xMnxAs8 with x ¼4, 6, and 8. The yellow (light blue) isosurface represents spin up (spin down) spatial magnetization density. Numbers in parentheses represent the number of Mn atoms, relative energy to the ground state, and total spin moment, respectively. The isovalue is 0.05 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Table 2 The total spin moment, magnetic moment of every Mn atom for Ga8 xMnxAs8 with x ¼4, 6, and 8. x
Total moment (μB)
The moment (μB) of Mn atom in rank 1
2
3
4
5
6
4 2 8
0.24 0.82 3.42
2.96 1.29 3.33
0.05 1.01 1.06
2.21 0.72 3.15
6
6 2 4
3.34 3.35 3.51
3.01 2.83 0.62
2.57 1.65 1.80
3.10 3.08 3.28
3.69 3.47 3.61
3.20 2.59 2.85
8
8 16 20
3.43 3.25 3.23
2.31 3.18 3.27
3.90 3.41 3.03
2.86 2.56 3.26
3.11 4.01 3.61
2.97 1.56 2.58
DOS (states/eV)
DOS (states/eV)
4
0 -5
50
0
1.91 2.64 3.02
3.92 4.11 4.09
4. Conclusions
-50 -4
-2
0
2
Energy (eV) Fig. 4. (a) The density of states (DOS) of Ga atom, Mn atom, and As atom in the true ground state for Ga4Mn4As8. (b) The total DOS of the true ground state for Mn8As8. The Fermi level is shown in green-dashed vertical line. The width of Gaussian smearing in 0.05 eV is used. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Δ1 of ground state
LUMO-HOMO gap (eV)
8
potential application of MnAs clusters in optoelectronic nanostructures. To capture the panorama of LOMO–HUMO gap for Ga8 xMnxAs8, we plot Fig. 5. The LOMO–HUMO gap decreases as x increase for both the true ground state and low-lying isomers. Based on the frontier orbitals theory, a smaller LOMO–LUMO gap means the stronger chemical reactivity. Thereby Ga8 xMnxAs8 clusters with large x more likely integrate with each other to form bigger clusters, in which the percentage of Mn is high. This result conforms to the fact that MnAs and/or Mn-riched GaMnAs clusters often appear in the growth of (Ga,Mn)As films [23–26,38–40].
Ga Mn As
5
7
Δ2 of ground state
1.0
Δ1 of first isomer
Δ2 of first isomer Δ1 of second isomer
The structural, electronic, and magnetic properties of Ga8 xMnxAs8 clusters (x ¼0, 2, 4, 6, and 8) are investigated using first-principles calculations. CALYPSO is employed first to predict the initial ground state of Ga8 xMnxAs8. Then we obtain the true ground state of Ga8 xMnxAs8 by using FSM method based on spin polarized calculations. The results show that Mn atoms are gathered at the core of Ga8 xMnxAs8 cluster, and the true ground state and low-lying isomers of Ga8 xMnxAs8 with x¼4, 6, and 8, are found to be ferrimagnetic. The possible multiple ground states are demonstrated and discussed. Ga8 xMnxAs8 with large x owns larger binding energy and smaller LUMO–HOMO gap, all which means that Ga8 xMnxAs8 with larger x are more likely to be synthesized and react with each other. Since the clusters are bridges between molecules and macroscopic condensed matters, these results about Ga8 xMnxAs8 clusters may be helpful to understand the growth mechanism and properties of MnAs and/or (Ga,Mn)As thin films.
Δ2 of second isomer Acknowledgments
0.5
This work was supported by the National Natural Foundation of China (NSFC) through Grant no. 11174212, gram for New Century Excellent Talents in University through Grant no. 11-0351 and by Project sponsored by ROCS of State Education Ministry of China.
0
2
4
6
Science by Pro(NCET) SRF for
8
x Fig. 5. The LOMO–HUMO gap as a function of the value of x for Ga8 xMnxAs8. The LOMO–HUMO gap for spin up (spin down) channel is represent by Δ1 (Δ2).
magnetization density in Fig. 3. In contrary to well-known metallic state of MnAs in bulk, due to quantum confinement, the DOS of Mn8As8 presents a LOMO–HUMO gap (Fig. 4(b)), which implies
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