Zn vacancy ferromagnetism in ZnS nanocrystals

Journal of Magnetism and Magnetic Materials 443 (2017) 9–12

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Research articles

Zn vacancy ferromagnetism in ZnS nanocrystals Vitaly Proshchenko, Yuri Dahnovsky ⇑ Department of Physics and Astronomy/3905, 1000 E. University Avenue, University of Wyoming, Laramie, WY 82071, USA

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 24 January 2017 Received in revised form 6 July 2017 Accepted 11 July 2017 Available online 13 July 2017

To explain three order of magnitude discrepancy between the experimental and calculated magnetic moments due to Zn vacancies in ZnS nanocrystals we study the effect of Zn vacancy distribution in a nanocrystal (NC). We consider small, intermediate, and large quantum dots. For the latter we employ the surface-bulk model. To study Zn vacancy distributions we choose aggregates and uniformly distributed gas in an NC core, on a surface, and both core + surface. From the investigation we find that the uniform distribution of vacancies on a surface is the most favorable configuration for quantum dots of all sizes. Then we investigate the detailed vacancy arrangement on an NC surface. We find that the most likely arrangement if the vacancies are placed along the diagonal of the unit cell square rather than along the square side. The former has the zero magnetic moment what explains the huge reduction in the total magnetization. The small nonvanishing magnetization is probably due to the presence of a small amount of Zn vacancies in the side configuration in a metastable state. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction In the grow ing field of spintronics [1,2] and biomedicine [3] the control of magnetization at room temperatures becomes of importance. Room temperature ferromagnetic ordering with the high 0

switching rate can be obtained in d ferromagnetics [4–16]. Zn vacancies in ZnS nanocrystals (NCs) can provide ferromagnetism at room temperatures. [11,12] As a bulk, Zn S is a crystal with hexagonal würzite [10,11,17–21] and zinc blende crystal structures. Doped by Mn impurities it can be used as a sensitizer in quantum dot solar cells [22]. The total magnetic moment in ZnS NCs was experimentally [10,11] and computationally [9–12,15,21] determined. The comprehensive review on first-principle theories of dilute magnetic semiconductors is presented in Ref. [17]. The density functional calculations revealed that the magnetic moment per unit cell is about three orders of magnitude higher than the experimental value. [10,11] To explain such a discrepancy the deeper understanding of the Zn vacancy ferromagnetism is necessary. One may believe that such a small magnetic moment is because of different orientations of magnetic moments from different nanocrystals.The averaging over the NC orientations significantly decreases the total magnetic moment. However this explanation has some difficulties due to a very small value of the residual magnetization in a zero magnetic field. [10,11] In a magnetic field the partial magnetic moments from Zn vacancies are aligned along the magnetic ⇑ Corresponding author. E-mail address: [email protected] (Y. Dahnovsky). http://dx.doi.org/10.1016/j.jmmm.2017.07.041 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.

field without the randomization. Hence these arguments have to be dismissed. The other hypothesis we would like to explore is based on different spatial distributions of Zn vacancies in a nanocrystal. As shown in Ref. [12] the total magnetic moment vanishes if the Zn vacancy concentration is extremely high indicating the importance of the choice of a vacancy configuration. Hence we expect that such high Zn vacancy concentration areas could exist in a nanocrystal decreasing the total NC magnetic moment. Thus the effect of mutual orientation of Zn vacancies on the magnetization motivates this research. 2. Computational details In this work we study different Zn vacancy configurations for small and large NCs. In the case of very small, Zn32 S32 , and medium, Zn82 S82 , nanocrystals we use the Gaussian09 codes [23] for electronic structure calculations. First we cut out spherical quantum dots from the ZnS würtzite crystal. Then we create vacancies removing Zn atoms in different configurations from the nanocrystals. Thus we have generated the following vacancy configurations: Zn31 S32 ; Zn30 S32 , and Zn78 S82 . We study the cases where Zn atoms have been removed from the core, the surface, and core + surface of a nanocrystal. Schematically the configuration with 2 vacancies is shown in Fig. 1. The obtained nanocrystals have been optimized with the B3LYP exchange-correlation functional and the LANL2dz basis set. For large size nanocrystals we use the surface-bulk (SB) model introduced in Refs. [11,12] The SB model that we discuss later, is schematically demonstrated in Fig. 2. This model assumes that the total magnetic moment consists of the two independent

10

V. Proshchenko, Y. Dahnovsky / Journal of Magnetism and Magnetic Materials 443 (2017) 9–12

Fig. 1. Schematic representation of the quantum dot with the two Zn vacancies.

QD core, (b) on a QD surface as a spot, and (c) with the uniformly distribution. The number of vacancies in a quantum dot determines a vacancy concentration. The configuration with the minimal total energy is considered to be the most probable. In a small quantum dot we investigate only one or two vacancies per quantum dot. In an intermediate size quantum dot we study four vacancies per nanocrystal. The calculations for small and intermediate quantum dots exhibit the similar properties. As shown in Table 1 the total energy difference, E ¼ Esurf  Ecore , gradually decreases with the number of vacancies. Esurf and Ecore represents the total energies of QDs with one one, two, andfour Zn vacancies placed on a QD surface and in a core, respectively. In these calculations we have studied the vacancy aggregations, i.e., the Zn vacancies are placed as the nearest neighbors. The energy analysis reveals that the aggregation of Zn vacancies placed in the middle (a core) of a quantum dot give the higher energy than on a QD surface, and therefore the core configurations are less likely. As follows from Table 1, the vacancies are located on the QD surface. The next step is to consider various surface distributions of the vacancies in Zn78 S82 nanocrystal. We have chosen the two configurations, the vacancies are aggregated or uniformly distributed over the surface. In addition we have also investigated an intermediate situation where the vacancies are located on a QD surface and in a core (aggregated in two surface layers) simultaneously. In Table 2 we present the results of the calculations for energy difference, DE ¼ Eaggreg  Euniform , where Eaggreg and Euniform are total energies of QDs with the surface QD vacancies in the aggregation and uniformly distributed configurations, respectively. The vacancy aggregations can be placed only in the first surface layer as a spot or two first surface layers that represent both surface and bulk configurations. From Table 2 we conclude that the uniformly distributed Zn vacancies located in the first surface layer describe the most likely vacancy configuration. For QDs with the larger sizes we cannot use the Gaussian codes because of the calculation time limitations. To overcome this problem we employ the surface-bulk (SB) model [11,12] to find the most likely configuration of Zn vacancies where we compute both magnetic moments and total energies. The schematic representation of the SB model is shown in Fig. 2 In this model the total QD magnetic moment and energy are presented in the following way:

MNC ¼ N S  mS þ NB  mB ;

ð1Þ

ENC ¼ N S  ES þ NB  EB ;

ð2Þ

Fig. 2. Schematic representation of the surface-bulk model for a quantum dot.

parts, which are the surface and core contributions. The model can be applied for medium and large quantum dots (QDs) and nonorods with the accuracy of about 10%. [12] For the surface and bulk electronic structure calculations we employ the VASP software package [24–27]. The Pedrew-Burke-Ernzerhof (PBE) exchange– correlation functional [28,29] within the generalized gradient approximation (GGA) and the projector-augmented plane-wave (PAW) pseudopotential [30,31] with the cutoff energy of 400 eV are employed for all calculations. The C -centered k-point grid has been generated from the Monkhorst–Pack scheme [32]. We conduct the electronic structure calculations of the würtzite ZnS surfaces with different number of layers. 3. Results and discussions For small and intermediate NC sizes we study Zn vacancy configurations by using the Gaussian software [23]. As mentioned before we choose the following quantum dots, Zn32 S32 and Zn82 S82 . To find a proper vacancy configuration we follow the strategy where one, two, and four vacancies have been placed (a) in a

where mS (ES ) and mB (EB ) are surface and bulk magnetic moments (total energies) per unit cell. NS and N B are surface and bulk unit cell numbers, respectively. From the N S and NB numbers and volumes of surface and bulk unit cells, V S and V B , we can find an NC volume and therefore evaluate an NC size, DNC defined by Eq. 3.

V NC ¼ NS  V S þ NV  V B :

ð3Þ

For the quantum dot volume, V NC ¼ pD3 =6 (here D is a QD

diameter) and for the nanowire volume, V NC ¼ pD2 L=4 (here D and L are a nanowire diameter and length, respectively) [11,12]. In all SB calculations we consider the NCs of the same size where the vacancies are located on the NC surface. For the energy

Table 1 Total energy difference, DE ¼ Esurf  Ecore , for small and intermediate quantum dots with different number of vacancies. Esurf and Ecore are total energies of QDs with one one, two, and four Zn vacancies placed on the QD surface and in the core, respectively. QD size

DE/QD (eV)

Zn31 S32 Zn30 S32 Zn78 S82

0.26 2.28 4.08

11

V. Proshchenko, Y. Dahnovsky / Journal of Magnetism and Magnetic Materials 443 (2017) 9–12 Table 2 Total energy difference, DE ¼ Eaggreg  Euniform , for intermediate quantum dots with four Zn vacancies. Eaggreg and Euniform are total energies of QDs with the surface QD vacancies in the aggregation and uniformly distributed configurations, respectively. In the second row the aggregation is placed in two surface layers. Zn78 S82

DE/QD (eV)

Surface aggregation (one layer) Surface aggregation (two layers) Surface uniform distribution (one layer)

0.54 3.26 0.00

differences the contribution from the bulk is the same and therefore is excluded from the consequent calculations. We study the distribution of Zn vacancies on a QD surface in the framework of the following three models presented in Figs. 3–5. In the Fig. 3 we schematically demonstrate (a) aggregated and (b) uniform Zn vacancy distributions. For these two distributions we have calculated total energies to find which distribution has the lower energy. The results of the total energy calculations are presented in Table 3 where the unit cell consists of the sixteen elementary unit cells. For the calculations we have chosen 25% concentration of Zn vacancies. From the energy analysis we conclude that the uniform distribution is more favorable rather than the aggregation state. This conclusion is consistent with the Gaussian calculations (see Table 2). As soon as the favorable distribution of Zn vacancies is found, we would like to verify whether the vacancies are uniformly distributed in one or two surface layers as depicted in Fig. 4. The results of the calculations are given in Table 4. For these calculations the unit cell consists of sixteen elementary unit cells for each layer (in total there are thirty-two elementary unit cells). The vacancy concentration is 25%. Despite the small energy differences between these two cases, the single layer vacancy distribution is more favorable that the vacancy distribution in two layers. This result is also consistent with the Gaussian calculations for small and intermediate quantum dots. For more accurate calculations we study five layers where the middle layer represents a QD core (bulk) as shown in Fig. 5. For this system we consider three different Zn vacancy configurations with the same 20% vacancy concentration. In configuration (a) the Zn vacancies are uniformly distributed only over the external layers. In configuration (b) the vacancies are located in both middle layer (bulk) and two external layers. The configuration (c) describes the vacancy distribution where two surface layers are populated. In all three cases we have studied two different Zn vacancy configurations depicted in Fig. 6. In configuration 1 the vacancies are placed as the closet neighbors along the square side and in configuration 2 the vacancies are located along the square diagonal. From Table 5 we conclude that configuration 2 where the vacancies are distributed only over the surface monolayer is the most favorable. The next favorable configuration is configuration 1 in the external monolayer. All other cases are too far by energy

Fig. 4. Schematic representation of the Zn vacancy distributions at a surface (a) mono and (b) double layers.

Fig. 5. Schematic representation of the Zn vacancy distributions at (a) a surface monolayer, (b) surface + bulk layers, and (c) surface doublelayer.

Table 3 Total energies per unit cell for surface monolayer with aggregation and uniform distribution of Zn vacancies as shown in Fig. 3. Surface (one layer)

Etot /unit cell (eV)

Aggregation Uniform distribution

90.88 91.44

Table 4 Total energies per unit cell for one and two surface layers depicted in Fig. 4. Vacancy occupation

Etot /unit cell (eV)

One layer Two layers

184.60 184.45

Fig. 6. Two different Zn vacancy configurations: two vacancies are placed along the square (1) side and (2) along the square diagonal.

Fig. 3. Schematic representation of the (a) aggregation and (b) uniform Zn vacancy distributions on the surface monolayer.

and the most unfavorable. Configuration 2 (the vacancies are along the square diagonal) provides the zero magnetization that vanishes the total magnetic moment. To explain the experimental data where the magnetic moment is small but nonvanishing we have to assume that there are some configurations with the non-zero magnetization in a metastable state. We suggest that these config-

12

V. Proshchenko, Y. Dahnovsky / Journal of Magnetism and Magnetic Materials 443 (2017) 9–12

Table 5 Total energies and magnetic moments per unit cell for different Zn vacancy distributions and configurations shown in Figs. 5 and 6, respectively. Vacancy occupation

Etot /unit cell (eV)

M tot /unit cell (lB )

Distribution (a) (Fig. 5a) Configuration 1 Configuration 2

119.365 120.459

1.55 0.00

Distribution (b) (Fig. 5b) Configuration 1 Configuration 2

115.954 115.949

3.27 3.37

Distribution (c) (Fig. 5c) Configuration 1 Configuration 2

114.924 114.445

4.64 6.44

urations are likely to be configurations 1 (the next lowest in energy configuration) where the Zn vacancies are arranged along the square side.

4. Conclusions In this work we have studied how a ZnS NC magnetization depends on Zn vacancy configurations in order to explain the three orders of magnitude discrepancy between the experimental and computational values. From the Gaussian and solid state (VASP) calculations we conclude that the vacancies are uniformly distributed over the surface monolayer rather than to be located in the NC core or occupy two surface layers. We have found that the vacancy aggregates are less favorable than the uniform distribution of the vacancies. The Zn vacancies with the 20% concentration can be in two different configurations, 1 and 2 (see Fig. 6). Configuration 1 stands for the side arrangement of the Zn vacancies and configuration 2 corresponds to the diagonal alignment. From the calculations it follows (see Table 5) that configuration 2 with the zero magnetization is the most favorable. This can explain the dramatic discrepancy between the theory and experiment. However the experimental magnetic moment is small but nonvanishing. To understand why such a finite non-zero magnetic moment takes place we have to suggest that there are some residual metastable states with configuration 1 in small concentrations. The origin of these metastable states is probably determined by the NC synthesis. Acknowledgments This work was supported by a grant (No. DEFG02-10ER46728) from the Department of Energy to the University of Wyoming and the University of Wyoming School of Energy Resources through its Graduate Assistantship program. References [1] A. Zunger, S. Lany, H. Raebiger, The quest for dilute ferromagnetism in semiconductors: Guides and misguides by theory, Physics 3 (2010) 53. [2] R. Beaulae, P.L. Arecher, S.T. Ochsenbein, D.R. Gamelein, Mn2þ -Doped CdSe quantum dots: new inorganic materials for spin-electronics and spinphotonics, Adv. Func. Mater. 18 (2008) 3873. [3] M.O. Aviles, S.T. Ebner, H. Chen, A.J. Rosengart, M.D. Kaminski, J.A. Ritter, Theoretical analysis of a transdermal ferromagnetic implant for retention of magnetic drug carrier particles, J. Magn. Mater. 293 (2005) 605. [4] M. Venkatesan, C.B. Fitzgerald, J.M.D. Coey, Unexpected magnetism in a dielectric oxide, Nature 430 (2004) 630.

[5] A. Sundaresan, R. Bhargavi, N. Rangarajan, U. Siddesh, C.N.R. Rao, Ferromagnetism as a universal feature of nanoparticles of the otherwise nonmagnetic oxide, Phys. Rev. B 74 (2006) 161306(R). [6] N.H. Hong, J. Sakai, N. Poirot, V. Brize, Room-temperature ferromagnetism observed in undoped semiconducting and insulating oxide thin films, Phys. Rev. B 73 (2006) 132404. [7] H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, J.Y. Lin, Y.P. Feng, J. Ding, L.H. Van, J.H. Yin, Room-temperature ferromagnetism in carbon-doped ZnO, Phys. Rev. Lett. 99 (2007) 127201. 0 [8] D. Gao, G. Yang, J. Zhang, Z. Zhu, M. Si, D. Xue, d ferromagnetism in undoped sphalerite ZnS nanoparticles, Appl. Phys. Lett. 99 (2011) 052502. 0 [9] Z. Zhang, U. Schwingenschlogl, I.S. Roqan, Possible mechanism for d ferromagnetism mediated by intrinsic defects, RSC Adv. 4 (2015) 50759. [10] G. Zhu, S. Zhang, Z. Xu, J. Ma, X. Shen, Ultrathin ZnS single crystal nanowires: controlled synthesis and room-temperature ferromagnetism properties, J. Am. Chem. Soc. 133 (2011) 15605. 0 [11] V. Proshchenko, S. Horoz, J. Tang, Yu. Dahnovsky, Room temperature d ferromagnetism in ZnS nanocrystals, J. Appl. Phys. 119 (2016) 223901. 0 [12] V. Proshchenko, A. Karanovich, Yu. Dahnovsky, Surface-bulk modelfor d ferromagentism in ZnS quantum dots, J. Phys. Chem. C 120 (2016) 11253. [13] W.-Z. Xiao, L.-L. Wang, Q.-Y. Rong, G. Xiao, B. Meng, Magnetism in undoped ZnS studied from density functional theory, J. Appl. Phys. 115 (2014) 213905. [14] C. Madhu, A. Sundaresan, C.N.R. Rao, Room-temperature ferromagnetism in undoped GaN and CdS semiconductor nanoparticles, Phys. Rev. B 77 (2008) 201306(R). [15] A. Shan, W. Liu, R. Wang, C. Chen, Magnetism in undoped ZnS nanotetrapods, Phys. Chem. Chem. Phys. 15 (2013) 2405. 0 [16] V. Proshchenko, Yu. Dahnovsky, Weak d ferromagnetism: Zn vacancy condensation in ZnS nanocrystals, J. Phys.: Condens. Matter 29 (2017) 025803. [17] K. Sato, L. Bergqvist, J. Kudrnovsky, P.H. Dederichs, O. Eriksson, I. Turek, G. Bouzerar, V.A. Dinh, T. Fukushima, H. Kizaki, R. Zeller, First-principle theory of delute magnetic semiconductors, Rev. Mod. Phys. 82 (2010) 1633. [18] S. Fang, Y. Bando, U.K. Gautam, T.Y. Zhai, H.B. Zeng, X.J. Xu, M.Y. Liao, D. Golberg, ZnO and ZnS nanostructures: ultraviolet-light emitters, lasers, and sensors, Crit. Rev. Solid State Mater. Sci. 34 (2009) 190. [19] W. Liu, N. Wang, R.M. Wang, S. Kumar, G.S. Duesberg, H.Z. Zhang, K. Sun, Atomresolved evidence of anisotropic growth in ZnS nanotetrapods, Nano Lett. 11 (2011) 2983. [20] Y.P. Zhang, W. Liu, R.M. Wang, From ZnS nanoparticles, nanobelts, to nanotetrapods: the ethylenediamine modulated anisotropic growth of ZnS nanostructure, Nanoscale 4 (2012) 2394. [21] K. Sato, H. Katayama-Yoshida, Ab initio study on the magnetism in ZnO-, ZnS-, ZnSe- and ZnTe- based diluted magnetic semiconductors, Phys. Stat. Sol. (b) 229 (2002) 673. [22] S. Horoz, Q. Dai, F.S. Maloney, B. Yakami, J.M. Pikal, X. Zhang, J. Wang, W. Wang, J. Tang, Absorption induced by Mn doping of ZnS for Improved sensitized quantum-dot solar cells, Phys. Rev. Appl. 3 (2015) 024011. [23] Gaussian 09, Revision E.01, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K. N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, and D.J. Fox, Gaussian Inc, Wallingford CT, 2009. [24] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558. [25] G. Kresse, J. Hafner, Ab initio molecular-dynamics simulation of the liquidmetal, amorphous-semiconductor transition in germanium, Phys. Rev. B 49 (1994) 14251. [26] G. Kresse, J. Furthmüller, Efficiency of Ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6 (1996) 15. [27] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169. [28] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78 (1997) 1396. [30] P.E. Blochl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953. [31] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758. [32] H.R. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188.