Dramatic Drop of d0 Ferromagnetism with ZnO Nanocrystal Size in

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Dramatic Drop of d Ferromagnetism with ZnO Nanocrystal Size in Vacuum and Air Artem Pimachev, Vitaly Proshchenko, and Yuri Dahnovsky J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02990 • Publication Date (Web): 07 Aug 2017 Downloaded from http://pubs.acs.org on August 8, 2017

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The Journal of Physical Chemistry

Dramatic Drop of d0 Ferromagnetism with ZnO Nanocrystal Size in Vacuum and Air Artem Pimachev, Vitaly Proshchenko, and Yuri Dahnovsky∗ Department of Physics and Astronomy/3905 1000 E. University Avenue University of Wyoming Laramie, WY 82071 E-mail: [email protected]

Abstract The dramatic drop of about 2.5 orders of magnitude in the Zn vacancy magnetization with nanocrystal (NC) size was experimentally found in ZnO quantum dots in vacuum and air. We explain such an unusual behavior by the different contributions of spatial surface and core Zn vacancy configurations. With the increase of a NC size the core contribution to the total NC magnetization becomes more pronounced. Therefore the magnetization drop with NC size can be explained by the input of the core configuration, which has the lowest magnetic moment, 260 times lower than the magnetic moments of other surface or core configurations. In air the additional oxygen molecules on a NC surface can cause chemical reactions of dissociation along with the attachments of the NC oxygen atoms. Such configurations are different from those of the vacuum ones resulting in the different NC size dependence of the magnetic moment. The excellent agreement between the experiments and computations is reached.

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Introduction Magnetic nanomaterials with high Curie temperature (Tc ) are essential in the fast growing fields of nanomagnetism, spintronics, 1,2 and biomedicine. 3 The important class of magnetic nanomaterials is transition metal (TM) doped semiconductor nanocrystals, which simultaneously exhibit both a magnetic order and unusual optical properties. 4–23 The TM nanocrystals, however, can lead to the formation of hazardous free radicals that make them unsuitable in medicine. Different types of dopants can substantially change the value of a magnetic moment in metal-oxide nanocrystals. For example, in In2 O3 quantum dots (QDs) doped by Cr3+ impurities ferromagnetism is sensitive to QD crystal structure. Indeed, for the bccIn2 O3 nanocrystals the saturation magnetic moment is much greater than that of in rh- In2 O3 quantum dots. 24 As shown in Ref. 25 different types of TM impurities can enhance or suppress the ferromagnetism in In2 O3 or SnO2 quantum dots. The Fe3+ decreases the magnetization while Mn2+ significantly enhances the ferromagnetism. In addition the oxygen vacancies are able to influence the electron transport properties. In In2 O3 nanocrystals a 2D electron mobility can be increased because of the metal-insulator transition due to the presence of O-vacancies. 26 There is another type of ferromagnetic material with Tc much above the room temperature and with no TM doping. 27–34 Such nanocrystals exhibit d0 (d or f electrons are not involved) ferromagnetism associated with unpaired electron spins due to the intrinsic defects – vacancies. ZnO and ZnS nanocrystals, e.g., demonstrate d0 ferromagnetism. One of the most interesting materials that exhibits d0 ferromagnetism is a ZnS nanocrystal with Zn vacancies. It was found that the theoretically predicted magnetization in ZnS nanocrystals is much higher than the experimental value. 35,36 As discussed in Ref. 37 such a dramatic decrease in magnetization is possible due to the condensation of Zn vacancies into a droplet, i.e., the total magnetization essentially depends on the vacancies’ arrangements. Another attractive material with d0 ferromagnetism in ZnO. ZnO exists in the stable cubic zinc blende and hexagonal w¨ urzite crystal structures with the bulk wide bandgap of 3.37 eV. ZnO compounds are widely used in light emitting diodes, room temperature UV lasers, 2


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field-effect transistors, as well as sensitizers for solar cells. 38–40 d0 ferromagnetism in ZnO was intensively studied by many investigators. 28,41–55 In ZnO NCs Zhigang Li et al. 56 discovered the dramatic dependance of the magnetic moment on an NC size. Indeed the magnetization drops by 2-3 orders of magnitude with a nanocrystal size. Moreover, the samples become very sensitive to an oxygen rich environment that reduces the magnetization by approximatelyt five times compared to the similar experiment in vacuum. In this work we explain a size-dependence of the magnetization in vacuum and air. We employ the surface-bulk (SB) model 35,36 where we show that the magnetization drastically depends on Zn vacancy configurations.

Surface-bulk model For NC magnetic moment calculations we use the SB model introduced in Refs. 35,36 where the total magnetic moment, MN C , is defined as a sum of the surface and core contributions (see Fig.1). This mean that we consider a single domain picture where the surface and core magnetic moments are additive.

M N C = NS · m S + NB · m B ,

(1)

where mS and mB are the surface and bulk magnetic moments per unit cell. NS and NB are the surface and bulk unit cell numbers, respectively. From the NS and NB numbers and the volumes of surface and bulk unit cells, VS and VB , we can find an NC volume and therefore, evaluate an NC size, DN C defined by Eq. 2.

V N C = NS · V S + N V · V B =

3 πDN C . 6

(2)

The surface-bulk model is based on the thermodynamic approach where a large system in equilibrium can be subdivided into smaller but still statistically large subsystems in equilib-

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Figure 1: Schematic representation of the SB model for a nanocrystal. The dark and light blue colors depict the surface and core unit cells, respectively.

rium with each other. Each subsystem can be considered independently in thermodynamics. For extensive variables such as energy, volume, the number of particles, magnetic moment, dipole moment etc. the total variable can be presented a sum of the same variables but for smaller subsystems. It is apparent that this approach is thermodynamically exact for very large systems. Now we consider a large nanocrystal where we select only two subsystems – an NC surface and core. Obviously the surface contribution to the extensive variable, e.g., a magnetic moment, is infinitesimally small because of the a very small number of the surface atoms (unit cells). Now we would like to investigate smaller nanocrystals. In particular, we would like to check the limits of the thermodynamic approach. For very small nanocrystals the surface contribution can be substantial and comparable with the core contribution and therefore, cannot be neglected. The NC surface and core magnetic moments are calculated for the 2D and 3D ZnO crystal structures, respectively. Then the numbers of surface and core cells define a NC size. In this model we neglect the curvature of a NC surface layer and also the correlations between the surface and core electrons. This implies that the sur-

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face and core calculations are considered for the infinite 2D and 3D crystals, respectively. The accuracy of the model was verified in Ref., 35 which appeared to be about 10%. It is obvious that the SB model becomes more accurate for the nanorcystals of intermediate and large sizes (> 1 nm). The SB model allows for magnetic moment calculation of different concentrations and configurations of Zn vacancies on the surface and in the core.

Computational details The electronic-structure calculations of 2D and 3D ZnO crystals have been performed within the density functional theory (DFT) using the Vienna Ab Initio Simulation Package (VASP). 57,58 The Pedrew-Burke-Ernzerhof (PBE) exchange-correlation functional 59 within the generalized gradient approximation (GGA) and the projector-augmented plane-wave (PAW) pseudopotential 60 with the cutoff energy of 400 eV are employed for all calculations. The choice of the PBE correlation functional as it will be shown below, is also justified by the excellent agreement between the calculated and experimental values of magnetic moments. This functional was also employed for electronic structure calculations for ZnO crystals in Ref. 45 The Γ -centered k-point grid has been generated from the Monkhorst-Pack scheme. 61 In this work we conduct the electronic structure calculations of the zinc blende ZnO crystal, different (100) termination surfaces with and without Zn vacancies as shown in Fig. 2. The change of a unit cell volume in the presence of a vacancy is negligibly small compared to the SB model accuracy. The symmetry group was not fixed during the optimization process. To make a smooth transition from a surface to bulk, we use the scheme where the system contains three layers where the first two layers (we consider them as the surface layers) are optimized while the third layer representing the core, has the fixed bulk geometry. The conjugate gradient optimization method with 4 × 4 × 4 and 4 × 1 × 4 k-point meshes has been employed for the bulk and surface structure relaxation, respectively. For efficient magnetic moment calculations we choose a k-mesh, which provides us the most reliable and fast

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Figure 2: Schematic representation of two different surface terminations where (a) oxygen (termination 1) and (b) Zn (termination 2) atoms form the external monolayer.

computations.

Results and discussions To explain the dramatic drop in magnetization with a nanocrystal size we assume that an NC magnetic moment strongly depends on the contributions from different spatial Zn vacancy configurations whose magnetic moments vary by more than two orders of magnitude. For the numerical evaluation of the total NC magnetic moment we employ the SB model where the surface and core configurations are considered separately. For the surface part we have to introduce different types of the surface termination, which can provide very different contributions to the surface magnetization. Indeed, as shown in Fig. 2 we consider the two types of surface terminations where oxygen (termination 1 in Fig. 2(a)) or zinc (termination 2 in Fig. 2(b)) atoms form the external monolayer. Besides a size-dependence of the NC magnetization we also study the effect of air on the total magnetization, which exhibits the higher drop with an NC size. 56 According to Eqs. 1 and 2 the SB model has the core (bulk) contribution to the total magnetization, which depends on the different configurations of Zn vacancies. In Fig. 3 we present the two core configurations, core configuration 1 (CC1) and core configuration

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2 (CC2) where the two Zn vacancies are far apart (CC1) or adjacent (CC2). These two

Figure 3: Schematic representation of a supercell for the two different core vacancy configurations. The supercell contains 27 elementary unit cells. Core configuration 1 and 2 represent two different vacancy arrangements where the Zn vacancies are far apart and adjacent, respectively. configurations provide different magnetization values shown in Table 1. Table 1: Magnetic moments and energies for the different Zn vacancy core configurations with the Zn vacancy concentration of 7.4%. Core Configuration 1 Core Configuration 2

Magnetic moment 0.01 emu/g 2.61 emu/g

∆ Energy/unit cell 0.46 meV 0.00 meV

As follows from Table 1 despite the small value in the energy difference (lesser than the room temperature) the CC2 magnetization is 260 times higher than that of in CC1. Contrary to the two core vacancy configurations there are three different surface Zn vacancy configurations presented in Fig. 4. The magnetization for these configurations depends on the surface termination shown in Fig. 2. The result of the magnetic moment and energy calculations for all surface configurations in vacuum and air are presented in Table 2. From this table we find the dramatic drop in the magnetization depending on the surface configuration. Surface configuration 2 (SC2) in vacuum is the most favorable and has the lowest magnetization that is about 200 times lower than that of for SC1. SC3 provides 7



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Figure 4: Surface crystal structures for three different vacancy configurations without ((a), (c), and (e)) and with ((b), (d), and (f)) air oxygen molecules. Surface configuration 1, surface configuration 2, and surface configuration 3 represent three different cases where the oxygen atom is on the surface, Zn atom is on the surface with the diagonal vacancy arrangement, and Zn atom is on the surface with the side vacancy arrangement, respectively as shown in the profile pictures.The air oxygen molecules and the bods between them are shown in the blue color. For configuration 3 the oxygen molecule has a strong chemical bond while for configurations 1 and 2 the O2 dissociates in two oxygen atoms where the connection between them is shown by the blue dashed lines. The gray dashed lines indicate the former (before the air oxygen molecules adsorbed by the surface) bonds of the oxygen to zinc atoms.

Table 2: Comparison of the magnetic moments for the different surface Zn vacancies configurations with the Zn vacancy concentration of 7.4% in vacuum and air.

Surface Configuration 1 Surface Configuration 2 Surface Configuration 3

Air Surface Configuration 1 Air Surface Configuration 2 Air Surface Configuration 3

Vacuum Magnetic moment 7.65 emu/g 0.04 emu/g 1.94 emu/g Air Magnetic moment 4.26 emu/g 13.5 emu/g 1.00 emu/g

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∆ Energy/unit cell 0.28 eV 0.00 eV 20.0 meV ∆ Energy/unit cell 0.16 eV 0.19 eV 18.0 meV


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as much as 50 times higher magnetization value than that of SC2. We use these three configurations to explain the very high magnetization values for small nanocrystals where the total magnetic moments are mostly due to the surface contribution despite the large energy differences. If we study the same surface configurations in air (additional oxygen molecules are on the NC surface), air surface configuration 2 (ASC2) has the highest magnetic moment and the highest energy that makes it the least favorable. Surface configuration 3 (ASC3) has the lowest magnetic moment being the most likely configuration. As demonstrated in Fig. 4(f) the oxygen molecule does not dissociate and is attached to the surface oxygen and zinc atoms. However, as depicted in Figs. 4(b) and (d) the dissociation of the air oxygen molecules, nevertheless, takes place. In air surface configuration 1 (ASC1) besides the dissociation, the second chemical reaction also occurs. In latter reaction the two surface oxygen atoms move away from their zinc atoms to make the chemical bond with the air oxygen atoms as shown in Fig. 4(b). In Table 2 the energy differences between the air configurations are taken with respect to the SC2 energy in vacuum. In all vacuum surface configurations we have added the energy of oxygen molecules in a gas phase located far away from the surface to keep the same number of atoms as for the case where the oxygen molecules are adsorbed by an NC surface. The presence of the oxygen molecules in vacuum does not affect the magnetic properties of the ZnO surface with Zn vacancies. As soon as the surface terminations and core and surface configurations are described we are ready to explain the experimental size-dependencies of the NC magnetizations in vacuum and air. 56 The experimental and computed magnetizations for NCs of different sizes are shown in Fig. 5 as the blue and red curves in vacuum and air, respectively. The magnetization units (1 emu = 1 erg/G) are normalized per gram of a nanocrystal. The experimental dependencies are very different if the experiments are conducted in vacuum or air. The magnetization in air is smaller than in vacuum because the partial magnetizations determined by ASC1 and ASC3 are smaller than surface configurations in vacuum. In order to explain the experimental behaviors in the framework of the SB model we have made the

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Figure 5: NC size-dependence of the magnetization in vacuum (the blue curve) and air (the red curve), respectively.

plausible assumption assuming that the oxygen from air does not interact with the core. Therefore we calculate the total energy of ZnO surface and oxygen molecule for the three different surface configurations. We have compared the total energies for the NC surface with and without a bound oxygen molecule (or atoms). The presence of the oxygen molecules on the NC surface decreases the magnetization by several times depending on an NC size (see Fig. 5). To explain the experimental dependences depicted in Fig.5 we have analyzed the various Zn vacancy configurations presented in Table 3. First we consider a magnetization size-dependence in vacuum (the blue curve in Fig. 5). According to the SB model (see Eqs. 1 and 2) the contribution of the surface is higher than the core one because of a small size of the nanocrystal. For instance, for the NC with DN C = 3 nm the contribution of the surface is 80% vs. 20% of the core contribution. In this case as follows from Tables 1 and 2 the magnetic moment is the largest because the surface contribution dominates. With the increase of a NC size the core contributions become more

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important. For smaller NC sizes core configuration 2 (CC2) is more favorable than the CC1 contributions. The difference in magnetic moments for CC2 and CC1 is tremendous (see Table 1). The CC1 magnetic moment is 260 times smaller than for CC2. However the energy difference between these two configurations is minuscule. For the larger NC sizes the CC1 input dominates and therefore the magnetic moment decreases by several orders of magnitude explaining the experimental data. Second, we study a magnetization size-dependence in air where the presence of additional oxygen atoms on a NC surface takes place. The ratio between the surface and core contributions remains the same as in the vacuum determining the same NC size. From Fig. 5 (the red curve) we see the dependence of the magnetization similar to the that of in the vacuum. As shown in Table 3 the core vacancy configurations are the same in air and vacuum. Table 3: Magnetic moments for the various configurations and sizes of ZnO NCs prepared in the vacuum and air. D, nm 3 5 8 10 12 15 D, nm 3 5 8 10 12 15

Prepared in vacuum Configuration 0.80 SC1 + 0.20 CC2 0.48 SC3 + 0.52 CC2 0.30 SC3 + 0.70 CC1 0.24 SC3 + 0.76 CC1 0.20 SC3 + 0.80 CC1 0.16 SC3 + 0.84 CC1 Prepared in air Configuration 0.80 ASC1(Air) + 0.20 0.48 ASC3(Air) + 0.52 0.30 ASC3(Air) + 0.70 0.24 ASC3(Air) + 0.76 0.10 ASC3(Air) + 0.10 0.08 ASC3(Air) + 0.08

Magnetic moment 6.64 emu/g 2.29 emu/g 0.59 emu/g 0.47 emu/g 0.39 emu/g 0.31 emu/g

CC2 CC2 CC1 CC1 SC2 + 0.80 CC1 SC2 + 0.84 CC1

Magnetic moment 3.93 emu/g 1.84 emu/g 0.30 emu/g 0.24 emu/g 0.11 emu/g 0.09 emu/g

The surface configurations for all NC sizes have different magnetic moments with the similar surface Zn vacancy configurations but the two cases shown in Table 3. Indeed, the magnetizations for NCs with DN C = 12 nm and DN C = 15 nm in the air have the contributions from the spots where the air oxygen is missed, which can be considered as the surface Zn vacancy configurations in vacuum. Thus we assume that the NC surface is not uniformly covered by the air oxygen molecules. This assumption is a posteriori confirmed by 11



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the agreement between the experiment and calculations. As shown in Fig. 5 the agreement between the experimental and computed magnetizations is excellent.

Conclusions In this work we study the effect of different Zn vacancy spatial configurations on d0 ferromagnetism in ZnO nanocrystals. The experiments show the tremendous decrease in the magnetization with an NC size in vacuum and air. 56 We have been able to explain this phenomenon by the various inputs from the different Zn vacancy configurations in the framework of the surface-bulk model where the surface and bulk magnetic moments contribute independently. 35,36 We have found that the different spatial Zn vacancy configurations contribute to the surface and core magnetic moments with the large differences where, for example, the contribution from CC1 is about 260 times smaller than the CC2 input to the total magnetic moment (see Tables 1 and 2) despite these configurations are close in energy. As soon as the an NC size is increased the CC1 configuration dominates and therefore the total magnetic moment in vacuum becomes much smaller. In air the picture is similar but at the same time different in details (see Fig. 5). Indeed the presence of oxygen molecules on an NC surface creates different than in vacuum Zn vacancy configurations. We have found that the oxygen molecules on the surface can cause chemical reaction of the O2 dissociation with the simultaneous attachment of the oxygen atoms from the ZnO surface as shown in Fig. 4 and Table 3. In addition, for the larger NC sizes we have found that the oxygen coverage of the NC surface is not uniform, i.e., there are some surface areas where the additional oxygen molecules are not present. Such an assumption allows us to explain the experimental data on a magnetization in air. Thus the surface Zn vacancy configuration picture is substantially different from that of in vacuum. Such a difference is important for the total magnetic moment calculations.

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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.

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Dramatic Drop of d0 Ferromagnetism with ZnO Nanocrystal Size in

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