Is magnesium oxide magnetic?

Defect formation energy and electronic structures

As a first step toward understanding the magnetic properties and effects of hydrogen impurity atoms in MgO, we obtained the electronic structures and formation energies of intrinsic O and Mg vacancy defects as well as H impurity atoms. It was found in previous studies that when the aforementioned defects were present in MgO, they affected the magnetic properties of MgO17,24,41,42. Figure 1 shows relaxed atomic structural models for perfect bulk MgO (Fig. 1a) and the hydroxide salt Mg(OH)2 (Fig. 1b), which was used as a reference and to study the hydrogen formed in MgO compounds in nature. The relaxed atomic structure of the point defect form (such as VMg0, Hi+1, (Hi-VMg)&#;1 and HO+1), which focuses on nearest neighbor atoms, is also shown in Fig. 1c&#;f, respectively. The perfect bulk MgO has a rock salt structure with a lattice constant of 4.199 Å, while the hydroxide form Mg(OH)2 is hexagonal with lattice constants a&#;=&#;b&#;=&#;3.186 Å and c&#;=&#;4.782 Å; however, the Mg atoms in both structures are surrounded by six oxygen atoms in an octahedral configuration such that the Mg-O bond lengths in MgO and Mg(OH)2 are 2.099 Å and 2.115 Å, respectively. We found that the lowest energy atomic configuration of interstitial hydrogen in MgO (Fig. 1d) was quite similar to that of H formed in Mg(OH)2. The interstitial H was bonded to an oxygen atom and bent off-axis from the Mg-O bond direction with an O&#;H bond length of 0.988 Å, which is comparable with the O&#;H bond length of 0.972 Å seen for Mg(OH)2. For the VMg structure (Fig. 1b), the O anion moved away from the point defect; on the other hand, the Mg cation moved toward the point defect, causing the total volume of the cell around the point defect to decrease because Mg is larger than O. In the Hi case (Fig. 1d), the O nearest neighbor H atoms moved toward the H interstitial atom, whereas Mg moved outward from Hi because of the Coulomb repulsion between the cations, which increased the total volume of the cell. However, when the VMg and Hi form Hi-VMg complexes (Fig. 1e), the O anion still moves away from the VMg point defect, and Mg moves outward from Hi but less than in the previous single point defect cases because Coulombic repulsions were suppressed, resulting in a decrease in the total volume of the cell. Note that in calculations of defect cases, we found an approximate lattice constant by measuring the average Mg-to-Mg distance for atoms that surround the defect point (as shown in Fig. 1). The calculated lattice constants for VMg0, Hi+1, (Hi-VMg)0 and (Hi-VMg)&#;1 were 4.142, 4.422, 4.103, and 4.093 Å, respectively.

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Figure 1.

Relaxed atomic structural models of (a) free defect MgO bulk, (b) Mg(OH)2 bulk, (c) VMg0, (d) Hi+1, (e) (Hi-VMg)&#;1 and (f) HO+1.

Figure 2 shows the formation energies calculated under O-rich conditions for the oxygen vacancy (VO) (solid black line), magnesium vacancy (VMg) (solid red line), hydrogen impurity (Hi) (solid green line), hydrogen impurity formed with a Mg vacancy (Hi-VMg) (solid purple line), and hydrogen impurity substituted on oxygen vacancy complex (HO) (solid yellow line) plotted as a function of Fermi energy. The zero Fermi energy is relative to the valence band maximum level, while the maximum Fermi energy represents the conduction band minimum. The slope of each line indicated the change in the charge state of defect q (Eq. 1), and only the most stable charged states were shown.

Figure 2.

Formation energies of defects (solid lines) in MgO as a function of Fermi energy under O-rich growth conditions. Only the formation energy for the lowest energy charge state is shown. The range of Fermi energies is limited by the calculated band gap of bulk MgO, the zero Fermi energy is a relative value with the valence band maximum energy, and the maximum Fermi energy represents the conduction band minimum. The slopes of the plots reflect changes in the charge states of the defect, and the kinks in the plots correspond to the energies at which transition from one charge state to another takes place, as discussed in the text. The binding energy levels of the (Hi-VMg) complex and HO are plotted as a function of Fermi energy with dashed lines.

For the formation energies of native vacancies (Fig. 2), VO is a donor defect with the lowest formation energy at a Fermi energy below 3.5 eV (p-type growth condition), which can be stable with&#;+&#;2 charges and form with a negative formation energy at Fermi energies below 2.5 eV. VMg is the lowest formation energy at a Fermi energy above 3.5 eV (n-type growth condition) and forms with a negative value at a Fermi energy above 5 eV. VMg is a shallow acceptor with a defect transition level change from the charge state q&#;=&#;0 to the charge state q&#;=&#;&#; 2 (ɛ(0/&#; 2)) at a Fermi energy level of 4.7 eV. The relationship between the formation energy of a defect X of charge state q, EfXq, and its concentration CXq for a sample under thermal equilibrium is defined as CXq=Nsiteexp[-EfXq/kBT] 40, where Nsite is the number of equivalent possibilities with the same energies in which the defect can be incorporated (per unit volume), kB is Boltzmann&#;s constant, and T is the temperature. Therefore, the defects with the lowest formation energies are stable and likely to form at high concentrations. These results suggest that VO and VMg can occur in the Fermi energy range of the sample under O-rich growth conditions because both defects can be formed with highly negative formation energies. In addition, the defect concentration can be increased by increasing the temperature (T) of the sample. In general, the shift in Fermi energy due to doping is proportional to the temperature35. If a MgO sample is heated at high temperature, the Fermi level will shift to a high energy. Therefore, under heat treatment conditions, VMg is more likely to form than VO. When hydrogen (H) is doped into the MgO system, among several possible configurations studied for Hi, the interstitial structure shown in Fig. 1d turned out to have the lowest energy. The H impurity is likely to occupy interstitial sites close to an oxygen atom and act as a donor defect with&#;+&#;1 charge and formation energy lower than both VO and VMg. As a charged defect, it can be compensated by a native defect with the opposite charge. Potential compensating point acceptor defects include VMg. The formation energy of the Hi complex formed with VMg (Hi-VMg) was calculated (the atomic structure is shown in Fig. 1e), and Hi-VMg was stable for charge states 0 (Hi-VMg)0 and -1 (Hi-VMg)&#;1 (Fig. 2). Hi+1 can donate an electron to the available states of VMg charge state 0 (VMg0) and -2 (VMg-2), respectively. Hi-VMg is a shallow acceptor exhibiting a defect transition level change from charge state q&#;=&#;0 to charge state q&#;=&#;-1 at a Fermi energy level of 4.7 eV with a negative formation energy over the entire Fermi level range. This indicated that Hi-VMg is quite stable and can form at high concentrations. Therefore, VMg can be a compensating defect in H-doped MgO samples and form Hi-VMg. In the case of VO, hydrogen impurities can form defect complexes with VO by substitution at vacancy sites surrounded by Mg cations (the atomic structure is shown in Fig. 1f). The HO acts as a shallow donor, and it is stable only in charge state&#;+&#;1 (Fig. 2), meaning that the H acts as H&#;1 to react with VO in a stable charge state&#;+&#;2 (VO2+). Therefore, the H in HO behaves as a negative multicenter for defect structures, in agreement with Janotti et al.43. However, the formation energy of HO is relatively high and positive throughout the Fermi level range for O-rich conditions. To determine the stabilities of various defect complexes (i.e., Fig. 2), we obtained the defect binding energy, which may be defined as Ebind (A-B)&#;=&#;Ef (A-B) &#; (Ef (A)&#;+&#;Ef (B)), where Ef (A) and Ef (B) are the formation energies of defects A and B, respectively, and Ef (A-B) is the formation energy of the A&#;B complex44. The complex had a large negative binding energy and is more likely to form. In Fig. 2, we observe the lowest binding energy of &#; 2.45 eV (purple dashed line) for Hi-VMg and 1.97 eV (yellow dashed line) for the HO complex. The binding energy of Hi-VMg becomes negative at a high Fermi level (>&#;4.5 eV) close to the conduction band energy. This indicates that such complex defects are most stable and likely to form at a high concentration in that energy region. However, Hi-VMg is the dominant defect complex and has a lower binding energy than the HO complex under O-rich growth conditions. This indicates that Hi can interact strongly with VMg in MgO, which might cause suppression of the ferromagnetic properties of MgO, as reported in other experimental studies20,24.

To understand the origin of defect-induced magnetization in MgO, we calculated the density of states (DOS) for perfect MgO and Mg(OH)2 (Fig. 3), as well as for various defect types (Fig. 4). The valence was defined by the state below the Fermi level. According to the orbital-resolved projected DOS, the valence bands of both perfect MgO (Fig. 3a) and Mg(OH)2 (Fig. 3b) were dominated by O 2 s (red) and O 2p (violet) orbitals, whereas almost all Mg 3 s (green) and 3p (blue) orbitals contributed to the conduction band. The valence band maximum was occupied only by O 2p electrons. In comparison, the H 1 s orbitals (orange line in Fig. 3b) contributed to the upper (energy below &#; 5 eV) and lower valence bands (energy below &#; 20 eV for Mg(OH)2), and the H 1 s orbitals formed covalent bonds with both O 2 s and O 2p orbitals. We found that the DOS for perfect MgO and Mg(OH)2 were symmetrical over the entire energy range for both spin-up (white area) and spin-down (gray area) states, indicating that the sums of the magnetic moments or magnetizations of both MgO and Mg(OH)2 were zero, in good agreement with other published works12,22,23. In other words, neither MgO nor Mg(OH)2 have any unpaired electron states. Therefore, a magnetic moment cannot occur in pure MgO or Mg(OH)2.

Figure 3.

Total density of states and projected density of states for (a) MgO and (b) Mg(OH)2 with projected orbitals (s, p, and d orbitals) from each atom. The Fermi energy is shifted to zero and is indicated by the gray dashed line. The white and gray shaded areas represent spin-up and spin-down electronic densities of states, respectively.

Figure 4.

Total density of states for various defects in MgO with (a) neutral VMg0 with projected atomic orbitals, (b) singly charged VMg-1, (c) doubly charged VMg-2, (d) neutral Hi-VMg0 complex, (e) singly charge d(Hi-VMg)-1 and (f) singly charged Hi+1. The orange and gray shaded areas represent spin-up and spin-down electronic densities of states, respectively. The Fermi energy is shifted to zero and indicated by a black dash-dotted line.

The total magnetic moments and specific magnetizations of various defect types are summarized in Table 1. The magnetic moment due only to the spin of an electron is 1 Bohr Magneton (µB)&#;=&#;9.27&#;×&#;10&#;21 emu. To convert this into magnetization, which is the magnetic moment per gram (or the magnetic moment per unit volume), we used the magnetic moment per cubic cell and divided this moment by the cell volume to obtain the magnetization in units of emu/cm3. The specific magnetization (emu/g) was obtained by dividing the above magnetization by the MgO density (3.47 g/cm3). Our calculations showed that neutrally charged VMg0 and singly charged VMg-1 and VO+1 were responsible for the magnetic moment of MgO, which originates from the partially occupied valence band. Other defects, i.e., VMg-2, VO0, and VO+2, cannot induce magnetic moments in MgO. However, according to the formation energy, binding energy and magnetic moment results, oxygen vacancies can be ruled out under our conditions, as discussed above. In addition, there is VO+1, which is responsible for the magnetic moment, but VO+1 is not the charge defect with the lowest formation energy.

Table 1.

Total magnetic moments (M) in Bohr magnetons (µB) and the specific magnetization in emu/g within corresponding defects.

VMg0

VMg-1

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VMg-2

VO0

VO+1

VO+2

Hi+1

(Hi-VMg)0

(Hi-VMg)-1

(Hi-VMg)+1

HO0

HO+1

Figure 4a shows the total density of states for neutral VMg0, which creates the hole state in MgO. Spin splitting exists in the valence band, and the spin-down states (gray area) are partially occupied, which is the cause for formation of the magnetic moment of&#;~&#;2 µB. The projected atomic orbital DOS shows that the maximum valence is dominated by O 2p orbitals (solid violet line), which indicates that the magnetic moment is mainly induced by O 2p orbitals. In the same way, for VMg-1 (Fig. 4b), spin splitting also occurs in the valence band, and the spin-down states (gray area) are partially occupied; hence, VMg-1 also creates a magnetic moment (~&#;1 µB). In comparison, the spin-polarized electron orbitals of VMg-2 are symmetric. Therefore, VMg-2 cannot induce a magnetic moment (Fig. 4c). In other words, when removing Mg from MgO, the Mg-O bond is broken to form VMg0 or VMg-1, which lose two and one donor electrons. This mechanism induced the hole state from O 2p orbitals to compensate for the loss of electrons. However, VMg0 has the lowest formation energy and can induce a magnetic moment. Therefore, under our experimental conditions, VMg0 is the origin of the magnetism in MgO.

When we dope a donor H impurity into perfect MgO (Hi), the Hi defect creates unpaired states below the Fermi level and below the valence band (Fig. 4f) with H 1 s orbitals. This doping introduces a magnetic moment of 1μB (see Fig. 4f) because Hi contributes one 1 s electron to the valence band (Fig. 4f). Hence, when the H impurity atom forms a defect complex with VMg0 such as (Hi-VMg), the H donates an electron to the O 2p hole state in the valence band of MgO, which is created by VMg and fills the unpaired state, then the magnetic moments remain 1 and 0 for (Hi-VMg)0 and (Hi-VMg)-1, respectively (see the DOS in Fig. 4d,e). Based on our calculation results, the origin of the magnetic moment in MgO is largely an unpaired electron from a Mg vacancy, in agreement with other works12,21&#;24. Hydrogen impurities suppress the magnetic moment in magnetic MgO by donating electrons to unpaired electronic states. Therefore, hydrogen is the most significant cause of the reduced magnetic properties in ferromagnetic MgO, which might occur in aged MgO samples20,24. For example, magnetic MgO samples are treated in air or under hydrogen gas. In this work, the VMg in MgO was induced by thermal heating in a vacuum environment because VMg is easy to form at low energy, whereas H2 gas injection into the MgO samples at different pressures was used to represent hydrogen doping. The structural and magnetic properties of MgO will be presented and discussed in the Experimental Section.