Magnetic Properties, Heisenberg Exchange Interaction, and Curie

Article pubs.acs.org/JPCC

Magnetic Properties, Heisenberg Exchange Interaction, and Curie Temperature of CdS Nanoclusters X. G. Zhao,†,‡ J. H. Chu,†,§ and Z. Tang*,§ †

Physics Department and §Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241, People’s Republic of China ‡ Ludong University, Yantai, Shandong 264025, People’s Republic of China ABSTRACT: In recent years the magnetism demonstrated in undoped oxide and sulfide semiconductor nanoparticles was intensively studied for the potential applications in nanoscale science. First-principles calculations were performed to investigate the magnetic properties, Heisenberg exchange interaction, and Curie temperature (Tc) of cadmium sulfide (CdS) nanoclusters (NCs) in this work. Our calculations indicate that spin-polarized states are always energetically favorable and that the induced magnetism mainly originates from the dangling bond spins of those two-coordinate S anions located on the S-terminated surface, which is perpendicular to c-axis. Meanwhile, the CdS NCs driven magnetism can be completely destroyed with hydrogen passivation. The calculated Heisenberg exchange interaction and Tc show oscillatory behaviors. The Hubbard model theory can be used to account for the interactions between the dangling bond spins in CdS NCs. These results suggest that CdS NCs may be a promising material for nanoscale magneto-optical devices.

I. INTRODUCTION A lot of low-dimensional semiconductor materials were comprehensively investigated for their unconventional properties. Magnetism, as one of the exotic properties of lowdimensional nanoscale semiconductor materials, was demonstrated both experimentally and theoretically in dopant-free ZnO nanoplate; on the contrary, defect-free ZnO nanowire was found to be nonmagnetic.1 Surface defects in the lowdimensional materials were generally regarded as the magnetic origin.1−4 These researches illustrate that the dimensionality of the material has a crucial impact to the observed magnetism. As a matter of fact, ferromagnetism has been thought as a universal feature of oxide or sulfide semiconductor nanoparticles (NPs).5,6 It has been argued that reducing oxide or sulfide semiconductor materials to NPs, nanowire, or nanoplate can introduce magnetism in these nanostructrures. This idea has been verified in oxide semiconductors; for example, ZnO NPs demonstrate ferromagnetism both experimentally and theoretically.7−9 CdS, as an important candidate of group II−VI compound semiconductors, has been intensively studied both theoretically and experimentally for its potential applications in many fields, such as nonlinear optics, sensors, photovoltaic devices, and so on.10−15 Moreover, magnetism of CdS NPs and nanosheets had been observed in experiments.7,16 All these suggest that CdS NCs may be a promising material for nanoscale magnetooptical devices. Similar to ZnO NCs, it is believable to justify theoretically that ferromagnetism can be demonstrated in CdS NCs. In this work, we systematically studied the magnetic properties of CdS NCs by using first-principles calculations. It is clarified that (1) two-coordinate S anions on the surface of © 2015 American Chemical Society

CdS NCs pose local magnetic moments; (2) there exists ferromagnetic Heisenberg exchange coupling among the local magnetic moments of two-coordinate S anions; therefore, the magnetic properties of CdS NPs are dominated by the surface dangling bond spins of two-coordinate S anions; (3) the surface states driven magnetism can be manipulated by hydrogen passivation (H-passivation).

II. CALCULATION METHODS First-principle calculations were performed based on density functional theory (DFT) within generalized gradient approximation (GGA) by using Vienna ab initio simulation package (VASP). Both nonspin-polarized and spin-polarized calculations for all the CdS NCs were performed. Supercell approximation was employed to simulate the free-standing NCs; a vacuum region of 10 Å is employed in the supercells, which is enough to avoid the interactions between the NCs. A plane wave basis set with cutoff energy of 400 eV, the frozen core all-electron projector augmented wave pseudopotentials, and GGA exchange correlation potential of Perdew−Wang-91 form, as implemented in VASP, were employed. Only Γ point was sampled in the calculations, and atomic geometries were fully optimized until all the Hellmann−Feynman forces were smaller than 0.01 eV/Å. Taking into account the fact that CdS NPs crystallizes into hexagonal structure and grows along c-axis, five typical CdS NCs with two layers S anions and two layers Cd cations, that is, CdnSn (n = 6, 10, 13, 16, and 22, as shown in Figure 1), were Received: November 10, 2015 Revised: December 8, 2015 Published: December 9, 2015 29071

DOI: 10.1021/acs.jpcc.5b11037 J. Phys. Chem. C 2015, 119, 29071−29075

Article

The Journal of Physical Chemistry C

Table 1. Total Energy Differences (ΔE1) between SpinPolarized and Non-Spin-Polarized Calculations, and Total Energy Differences (ΔE2) with and without Hydrogen Passivation for Different CdS Nanoclusters NCs

ΔE1 (eV)

ΔE2 (eV)

Cd6S6 Cd10S10 Cd13S13 Cd16S16 Cd22S22

−0.1115 −0.0843 −0.1660 −0.1061 −0.0245

−94.6669 −126.7901 −185.1475 −153.3119 −165.8203

second type (SIII) is three-coordinate. Furthermore, it is noticeable that all the two-coordinate SII anions locate at the edges of (0001) surfaces of NCs. This is rather important for the following discussions. However, all the four-coordinate anions SIV are inside the CdS NCs. The detailed distributions of two-, three-, and four-coordinate Cd cations are similar to those of the S anions. Spin-polarized calculations indicated that each two-, three-, and four-coordinate S anion contributes about 0.45, 0.05, and 0.02 μB, respectively, to the total magnetic moments. However, the contributions of two-, three-, and four-coordinate Cd cations are 0.04, −0.01, and −0.01 μB, respectively. These results show that the magnetism of CdS NCs mainly originates from two-coordinate SII anions, which will be further discussed by virtue of the following spin density distributions and density of states. A. Distributions of Spin Density. Spin-density distributions of CdnSn NCs (n = 6, 10, 13, 16, and 22) are shown in Figure 1. It can be seen clearly that the net magnetic moments of CdS NCs mainly originate from those two-coordinate SII anions located at the edges of S-terminated (0001) surfaces, while the magnetic moments contributions of three-coordinate and four-coordinate S anions are rather little and thus can be neglected thereafter. Moreover, all the Cd cations, regardless of whatever their coordinate numbers, are found to be nonmagnetic. The above observations indicate that total magnetic moments of the CdS NC with the same number of SII anions will not change obviously when the NC’s size along c-axis is increased or decreased. The NC Cd39S39 described in Section II, is threefold of the NC Cd13S13 along c-axis and is constructed to verify this idea. The spin-density distribution shown in Figure 2 further shows that the magnetism indeed mainly originates from two-coordinate SII anions, which is wellconsistent with the above idea and our calculation results. B. Magnetism of CdS Nanoclusters. To further confirm the magnetic physical origin of NCs, the projected density of states (PDOS) on the SII, SIII, and SIV anions of the NC Cd13S13 (as shown in Figure 1c) are compared in Figure 3. It can be seen clearly that the partially filled and spin-polarized electronic states near Fermi level are mainly p states of SII anions, which is well-consistent with the spin-density distributions shown in Figure 1. Moreover, the energy levels of p states of the SII anions with significant spin-splitting near Fermi level are generally higher than those of SIII and SIV anions. To clarify the magnetic origin of CdS NCs, we consider the energy shift of p state of a S anion bonded with n Cd cations, which is expressed (within mean-field approximation) in simple tight-binding model as follows:

Figure 1. (a−e) Spin-density distributions of typical CdS NCs (CdnSn, n = 6, 10, 13, 16, and 22). The red and green balls represent sulfur and cadmium atoms, respectively. SII, SIII, and SIV denote two-, three-, and four-coordinate S anions, respectively. Isodensity is 0.005 μB/a30.

first constructed to investigate the magnetic properties without and with H-passivation. Then a NC Cd39S39 with six layers S anions and six layers Cd cations, as shown in Figure 2, was used to justify the size effect along c-axis on its magnetism.

Figure 2. Spin-density distributions of the Cd39S39 NCs. The red and green balls represent sulfur and cadmium atoms, respectively. Isodensity is 0.005 μB/a30.

III. RESULTS AND DISCUSSION Both spin-polarized and nonspin-polarized calculations were performed for all the CdnSn NCs (n = 6, 10, 13, 16, and 22). Total energy differences ΔE1 between spin-polarized and nonspin-polarized states are shown in Table 1. Negative energy differences listed in Table 1 indicate that the spin-polarized states are always energetically favorable. Figures 1 and 2 show clearly that each NC has a S-terminated (0001) surface and a Cd-terminated (0001)̅ surface perpendicular to c-axis, and there are two types of surface S anions in the CdS NCs. The first type, labeled as SII in Figure 1, is two-coordinate (i.e., each S anion SII bonds with two neighbor Cd cations), while the 29072


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On the basis of the above considerations, we simply deduced the following relations applicable to CdS NCs. We denoted the effective Heisenberg exchange coupling interaction Jij between the local magnetic moments of two-coordinate S ions at different sites i and j and then employed a Green’s function scheme initiated by Liechtenstein et al.19 in which Jij is given as Jij = 1/2π

EF

∫−∞ Tr(G↑Vi G↓Vj)dω

(2)

↑/↓

where G is the operator of Green’s function of the spinpolarized DFT Hamiltonian and Vi is the operator of the intraatomic interaction at site i. We calculated the effective interaction Jij between the pairs of the local magnetic moments of two-coordinate S anions, and the obtained results are shown in Table 2.

Figure 3. PDOS on two-coordinate SII (a), on three-coordinate SIII(b), and on four-coordinate SIV (c) of the Cd13S13 NC. Each PDOS is further decomposed into s and p contributions.

Table 2. Exchange Interactions (J0) and Curie Temperatures (Tc) of Different CdS Nanoclusters

n

dεσ = − ∑ ti 2/Δ + U ⟨n σ̅ ⟩ i=1

(1)

where −t2i /Δ denotes kinetic energy decrease due to the binding between the p state of the anion and the ith bonding cation, U represents on-site Hubbard repulsion energy when p state is doubly occupied, and ⟨n σ̅ ⟩ represents occupation probability of opposite-spin state. According to eq 1, with decreasing the number of surrounding Cd cations from four to two, the p states of S anion shift to the higher energy side around Fermi level and become partially occupied. Just as the early theoretical and experimental studies have shown that p states of the first-row elements are rather localized,17 their onsite Hubbard interactions are generally non-negligible and will result in a spin splitting of U (⟨nσ⟩ − ⟨n σ̅ ⟩) for the partially occupied p states of SII anions. While the p states of SIII anions are generally lower than those of SII anions, they are almost fully occupied so that the spin splitting of these p states is small (Figure 3), and their contributions to the total magnetic moments are almost negligible. No net magnetic moments from Cd cations are obtained (Figure 1), as their electronic states are delocalized. C. Heisenberg Exchange Interaction and Curie Temperature. The above discussions indicate that the surface dangling bond states of SII anions in CdS NCs are spinpolarized; however, this does not mean that there exist ferromagnetic couplings among the dangling bond spins. Therefore, interactions among dangling bond spins play an important role in studying magnetic mechanism. In some previously published articles, a few approximation approaches, such as Monte Carlo (MC) simulations, random phase approximation (RPA), and Tyablikov approximation,18 were mainly used to study Heisenberg exchange interactions and Tc of bulk materials. MC simulations seem to provide a better way to include the positional disorder, but these are numerically expensive and usually assume classic spins. RPA combined with the virtue crystal approximation (VCA) neglect the effect of the positional disorder in diluted magnetic semiconductors. Here we discussed Heisenberg exchange interaction and Tc of CdS NCs. They contain a large portion of surface atoms, yet their properties cannot be expressed as a mere linear combination of surface and bulk contributions; finite NCs dimensions and associated quantum size effects are significant factors as well.

NCs

Cd6S6

Cd10S10

Cd13S13

Cd16S16

Cd22S22

J0, (meV) Tc, (K)

3.08 11.91

6.49 20.08

5.89 21.02

5.23 12.65

6.39 20.22

To estimate the parameters of the interatomic exchange interactions, we map the results of DFT calculations on an effective Heisenberg Hamiltonian Heff = ‐ ∑ Jij eî ·eĵ i≠j

(3)

where êi and êj denote the unit vectors of the local magnetic moments at site i and j, and Jij is an effective pair exchange interaction between two localized spins. It is noticeable that the magnitude S of the spins is absorbed into the exchange parameters and positive (negative) effective pair exchange interactions correspond to ferromagnetic (anti-ferromagnetic) coupling. As far as CdS NCs are concerned, two-coordinate SII anions, which were proved to be magnetic as the previous discussions, may be regarded as the magnetic impurities doped in semiconductors. The relation between the calculated exchange interactions and the distances between SII anions was plotted in Figure 4. There are a number of conclusions that follow from the analysis of this Figure. First, the dependence of exchange interaction parameters on the distances between SII anions is nonmonotonous. Meanwhile, the exchange interaction is relatively short-ranged and rather quickly decreasing with increasing the distance between SII anions. Second, the exchange interactions of different NCs show weak oscillatory

Figure 4. Dependence of the exchange interaction Jij on the distance between two-coordinate S anions of CdS NCs. 29073


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The Journal of Physical Chemistry C behavior, and the theory of Ruderman−Kittel−Kasuya− Yoshida interaction can be used to account for this phenomenon. Third, according to Hubbard model theory, weak hopping interaction t′ between the p orbitals of neighboring SII anions via hybridization with Cd cations in CdS NCs is expected to play an essential role in the ferromagnetic coupling. In the case of ferromagnetic arrangement of the dangling bond spins, it will lead to a kinetic energy reducing t′; that is, dE = −t′. However, in the case of antiferromagnetic arrangement, because the hybridization takes place only between the parallel-spin p orbitals, the kinetic energy reducing of the dangling bond states is dE = −t′2/U, where U is on-site Hubbard interaction of the p orbitals. As t′ ≪ U for the spatially localized dangling bond states, the energy of anti-ferromagnetic configuration of the dangling bond states is higher than that of ferromagnetic one by t′ (1 − t′/U), indicating that ferromagnetic ordering of the surface dangling bond states of SII ions is energetically favorable. Once the effective pair exchange interactions are determined, then the Curie temperature Tc within mean-field approximation can be derived according to Liechtenstein et al.19 kBTc =

2 2 x ∑ J0j = xJ0 3 j 3

Figure 5. Structural diagram of Cd13S13 NC passivated by hydrogen (a). Total density of states without (b) and with (c) hydrogen passivation. The red, green, and yellow balls represent sulfur, cadmium, and hydrogen atoms, respectively.

(4)

anions do not any longer contribute to the net magnetic moments, and the NC becomes nonmagnetic. Our theoretical calculations indicate that the dangling bond surface states of S anions play a crucial role on the magnetism of CdS NCs. Moreover, our present work further shows that such magnetism driven by surface state is very sensitive to the chemical ambiences. It is expected that the dangling bond spins on the terminated surfaces are easily passivated by hydrogen in air ambience, which may have resulted in some unstable, fugitive magnetism observed in lots of experiments. Nevertheless, the surface dangling bonds of well-encapsulated NCs or those dangling bonds at the grain boundaries are difficult to be passivated for being isolated from atmosphere. Under such circumstance, they will be apt to show magnetic ordering. Similar magnetism has been proposed in nonmagnetic elements doped oxide diluted magnetic semiconductors21 and supported by experimental results.22

where x denotes the concentration of ions with dangling bond spins. The calculated data according to eq 4 are listed in Table 2 and indicate clearly that the Curie temperatures and Heisenberg interactions show nonmonotonic increase or decrease with increasing the size of CdS NCs. It is noteworthy that, as shown by eq 4, the Tc of the NC depends on not only the exchange interaction J0 but also the concentration (x) of ions (SII) with the dangling bond spins. For the nanoclusters under study, the Cd13S13 cluster has the largest product of xJ0 so that it has the highest Tc of 21.02 K. D. Magnetic Manipulation by H-Passivation. It is wellknown to all that experiment surroundings generally have a certain effect on the final measurements. However, the magnetism discussed above is on the premise of the existence of clean NCs surfaces. Therefore, to simulate realistic CdS NCs in laboratory ambiences, we constructed and optimized the atomic geometries of H-passivated CdS NCs with configurations that both Cd and S ions were passivated in hydrogen ambience (as shown in Figure 5a). The optimized H−Cd and H−SII bond lengths are ∼1.72−1.77 and 1.34−1.40 Å, respectively, which are in agreement with those previous results.20 Meanwhile, our calculations found surprisingly that all the NCs become completely nonmagnetic after H-passivation. Moreover, the total energy differences ΔE2 listed in Table 1 indicate that the total energies of CdS NCs with H-passivation are lower than that of no passivation, which means CdS NCs are apt to absorb hydrogen in atmosphere ambience. The total DOS without and with H-passivation shown in Figure 5b,c further verifies the above results. The introduction of hydrogen used for passivation results in the strong binding between H and SII ions and the increasing coordinate number of SII anion. According to eq 1, this will lower the kinetic energy of the p states of SII anions. As an example, we compared the DOS of NC Cd13S13 without and with H-passivation in Figure 5. It can be seen clearly that the energy levels of the p states of SII anions indeed lower to Fermi level after H-passivation. As a result of H-passivation, the SII

IV. CONCLUSIONS Magnetic properties of different CdS NCs (CdnSn, n = 6, 10, 13, 16, and 22) with and without H-passivation were studied by means of first-principle calculations. Both spin-polarized and nonspin-polarized calculations were simultaneously performed. All our calculations indicate that the magnetism of CdS NCs mainly originates from the dangling (p) bonds of each lowcoordinate S anion located on the S-terminated surface, which is perpendicular to c-axis. Moreover, local magnetic moments of the surface dangling bonds vanish amazingly when these lowcoordinate ions are passivated with hydrogen, and then the CdS NCs turn to be nonmagnetic. Our theoretical calculations show that effective exchange interactions are relatively short ranged and rather quickly decreasing with increasing the distance between two-coordinate S anions. The deduced Curie temperatures show nonmonotonic increase or decrease with increasing the size of CdS NCs.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. 29074


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(17) Tang, Z.; Hasegawa, M.; Chiba, T.; Saito, M.; Sumiya, H.; Kawazoe, Y.; Yamaguchi, S. Electron Momentum Distributions in Elemental Semiconductors Probed by Positrons. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 12219. (18) Hilbert, S.; Nolting, W. Magnetism in (III,Mn)-V Diluted Magnetic Semiconductors: Effective Heisenberg Model. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 113204. (19) Liechtenstein, A. I.; Katsnelson, M. I.; Antropov, V. P.; Gubanov, V. A. Local Spin Density Functional Approach to the Theory of Exchange Interactions in Ferromagnetic Metals and Alloys. J. Magn. Magn. Mater. 1987, 67, 65−74. (20) Zhang, C. W.; Yan, S. S.; Wang, P. J.; Li, P.; Zheng, F. B. FirstPrinciples Study on the Electronic and Magnetic Properties of Hydrogenated CdS Nanosheets. J. Appl. Phys. 2011, 109, 094304. (21) Rahman, G.; García-Suárez, V. M. Surface-Induced Magnetism in C-doped SnO2. Appl. Phys. Lett. 2010, 96, 052508. (22) Hoa Hong, N.; Song, J.-H.; Raghavender, A. T.; Asaeda, T.; Kurisu, M. Ferromagnetism in C-doped SnO2 Thin Films. Appl. Phys. Lett. 2011, 99, 052505.

ACKNOWLEDGMENTS We thank Supercomputer Center of ECNU for using the Dawn 5000A supercomputer. This work is supported by the National Science Foundation of China (Grant Nos. 61425004, 61227902, 11504154, and 11175066), by the research programs of Shanghai (Grant No. 15XD1501500), by the State Key Basic Research Program of China (Grant No. 2013CB922301), by the Ministry of Education of China, and by the Ludong Univ. scientific research fund (Grant No. LY2014008).

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Magnetic Properties, Heisenberg Exchange Interaction, and Curie

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