Vacancy-induced ferromagnetism in ZnO probed by spin-polarized positronannihilation spectroscopy
Masaki Maekawa, Hiroshi Abe, Atsumi Miyashita, Seiji Sakai, Shunya Yamamoto, and Atsuo Kawasuso

Citation: Appl. Phys. Lett. 110, 172402 (2017); doi: 10.1063/1.4979696
View online: http://dx.doi.org/10.1063/1.4979696
View Table of Contents: http://aip.scitation.org/toc/apl/110/17
Published by the American Institute of Physics

APPLIED PHYSICS LETTERS 110, 172402 (2017)

Vacancy-induced ferromagnetism in ZnO probed by spin-polarized positronannihilation spectroscopy
Masaki Maekawa, Hiroshi Abe, Atsumi Miyashita, Seiji Sakai, Shunya Yamamoto,and Atsuo Kawasuso
Quantum Beam Science Research Directorate, National Institutes for Quantum and Radiological Scienceand Technology, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan(Received 8 December 2016; accepted 18 March 2017; published online 25 April 2017)
We investigated the ferromagnetism of ZnO induced by oxygen implantation by using spin-polarized
positron annihilation spectroscopy together with magnetization measurements. The magnetization
measurements showed the appearance of ferromagnetism after oxygen implantation and its disappearance during post-implantation annealing at temperatures above 573 K. The Doppler broadening ofannihilation radiation (DBAR) spectrum showed asymmetry upon field reversal after oxygen implantation. The obtained differential DBAR spectrum between positive and negative magnetic fields was
well-explained with a theoretical calculation considering zinc vacancies. The disappearance of the
field-reversal asymmetry of the DBAR spectrum as a result of annealing agreed with the observationsof ferromagnetism by magnetization measurements. These results suggest the radiation-induced zincvacancies to be the source of the observed ferromagnetism of ZnO. Published by AIP Publishing.
[http://dx.doi.org/10.1063/1.4979696]

Discovery of ferromagnetic behavior of a hafnium oxide(HfO2) thin film in 2004 made an impact, showing that ferromagnetism could be induced by lattice defects even without
intentional doping with ferromagnetic elements.1 Many subsequent investigations demonstrated that such “d0 ferromagnetism”
is a common feature of metal oxides. Zinc oxide (ZnO),
which is a wide-bandgap semiconductor, is one of such metaloxides that shows d0 ferromagnetism.2 From the coexistenceof macroscopic ferromagnetism observed by magnetization
measurements and lattice defects detected by X-ray diffraction,3 Hall effect measurement,4 electron microscopy,5 photoluminescence spectroscopy,6–8 X-ray absorption spectroscopy,9,10
and positron annihilation spectroscopy,11–13 the latticedefects are thought to cause the ferromagnetism. Based on
the ab initio studies, it has been proposed that zinc vacancies
are the likely candidate.14–21 The previous positron annihilation
studies supported this theoretical prediction. Moreover, zincvacancies and ferromagnetism have been observed to coexist.
This observation, however, is only a circumstantial evidence
for zinc vacancy-induced ferromagnetism. To directly determine
whether zinc vacancies cause ferromagnetism, the magnetic
moments of zinc vacancies need to be detected. To do this,spin-polarized positron annihilation spectroscopy (SP-PAS)
could be a uniquely powerful method.
The probability of a positron–electron pair annihilation
depends on the total spin (S). For S ¼ 0, a positron–electron
pair immediately annihilates and produces two gamma rays.
For S ¼ 1, most of the electron-positron pairs that do annihilate produce three gamma rays.22 Because the probability ofsuch three-gamma annihilation is only 1/1115 that of twogamma annihilation, positrons and electrons with antiparallel
spins tend to end up pairing, resulting in S ¼ 0 and twogamma annihilation. Thus, if both positrons and electrons
are spin-polarized, then two-gamma annihilation characteristics, such as the annihilation lifetime, Doppler broadening ofannihilation radiation (DBAR), and angular correlation of0003-6951/2017/110(17)/172402/5/$30.00

annihilation radiation (ACAR), change upon spin reversal andso excess electron spin can be detected. To date, SP-PAS
based on ACAR has been used for studying spin-polarized
electronic states of ferromagnets. Recently, we demonstrated
that the DBAR method and lifetime measurements can also be
used for the same purpose.23–26 Considering that positrons are
preferentially trapped at vacancy defects, magnetic moments
associated with vacancy defects may be detected by using the
SP-PAS method.27 In this study, we applied the DBAR-based
SP-PAS method to the issue of vacancy-induced ferromagnetism in ZnO.
The samples tested were commercial (Optostar Ltd.)hydrothermally grown ZnO single crystals with the dimensions of 10  10  0.5 mm. To remove residual defects introduced during the crystal growth, all the samples wereannealed at 1473 K for 2 h in air.28 Then, the samples were
subjected to X-ray diffraction measurements. The width of the
2h-x rocking curve was reduced from 0.011 for the unannealed
sample to 0.0032 for the annealed sample, indicating improvements in the crystallinity, although native defects would not be
removed completely by this heat treatment. Oxygen ions withan energy of 100 keV were implanted into the samples toachieve doses of 1012 Oþ/cm2 to 1017 Oþ/cm2 (flux: 1 lA) atroom temperature. The depth of ion implantation was estimatedto be 100 nm by using the Stopping and Range of Ions in Matter(SRIM) code.29 After oxygen implantation, the samples were
subjected to isochronal annealing below 1473 K for 1 h in air.
Magnetization (M-H) curves were acquired by thesuperconducting quantum interference device measurements
at 100 K. Figure 1(a) shows a schematic of the positron beam
apparatus used here. Longitudinally spin-polarized positrons
each with a polarization Pþ of 27% and energy of 6 keVwere injected into the samples cooled to 15 K. The positron
implantation profile is found to overlap the SRIM-predictedvacancy profile (Fig. 1(b)) due to oxygen implantation. Theenergy spread of the slow positron beam is 1%,30 and

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Maekawa et al.

FIG. 1. (a) Schematic of the positron annihilation measurement system.
Longitudinally spin-polarized positrons were injected into the sample
mounted on the cold stage (15 K) between the electromagnet pole pieces(60.91 T). Annihilation gamma rays (511 keV) were detected by a Ge
detector. (b) Calculated depth distributions of vacancies and positrons. (c)and (d) Schematic representation of the principle of the DBAR-based
SP-PAS method. Electron spins are ferromagnetically aligned in the magnetic field. When positron and electron spins are parallel* (antiparallel),two-gamma annihilation is prohibited (permitted). Consequently, the shapeof the DBAR spectrum undergoes a field reversal, as is also visualized in
the MDB spectrum, which shows the difference between the positive andnegative fields. *More strictly, S ¼ 1 and mS ¼ 61, where mS is the magnetic quantum number.

hence the influence on the positron implantation profile isalmost negligible. The DBAR measurements were taken inmagnetic fields of 60.91 T using a Ge detector with an energy
resolution of 1.9 keV at 1.33 MeV.31,32 The energy Doppler
shift from 511 keV (¼m0c2, where m0 is the electron rest massand c is the speed of light) corresponds to an electron momentum of p ¼ 3.92  103 m0c per 1 keV. More than 3  106
events were accumulated in each spectrum. Backgrounds arising from random coincidence and Compton scattering weresubtracted by applying a numerical method.33 Here, the difference between the DBAR spectrum of the positive field andthat of the negative field, Nþ(p)  N(p), is called the ‘magnetic Doppler broadening (MDB)’ spectrum. A positive (resp.
negative) field is defined by the positron polarization and themagnetic field direction being parallel (resp. antiparallel).
Figures 1(c) and 1(d) schematically explain the principle ofthis method. If electron spins at vacancies are made to alignparallel or antiparallel to positron spins by changing the field
direction, then the probability of a two-gamma annihilation ofAppl. Phys. Lett. 110, 172402 (2017)

positrons with unpaired electrons occurring would be changed.
Consequently, the shape of the DBAR spectrum in one field
direction may be different from that in the opposite field direction, as easily observed in the MDB spectrum. To evaluate
vacancy defects, S and W parameters were also calculatedwith the energy window of 510.2–511.8 keV and 514.8–
517.4 keV. All the S and W parameters were normalized tothat of the unimplanted sample.
To interpret the experimental MDB data, a theoretical
calculation was carried out assuming appropriate defectmodels. The details of the theoretical framework and the calculation were described elsewhere.26 The electron wave
functions were obtained by carrying out an ABINIT computation34 with the projector-augmented-wave method.35 For
Zn and O atoms, the valence electron configurations were
3s23p63d104s2 and 2s22p4, respectively. For the defect structures, the supercell included 32 Zn and 32 O atoms. The lattice constants were fixed to a ¼ 3.25 Å and c ¼ 5.21 Å.36 In
the calculation of defect structures, only the gamma point
was considered. The lattice relaxations around defects wereconsidered based on the molecular dynamics simulation
implemented in the ABINIT code. The cut-off energy of theplane-wave basis set was 60 Ry. The core electron wave
function was represented by the Slater function parameterized by Clementi and Roetti.37 A self-consistent positronwave function was calculated based on two-component density functional theory in order to minimize the energy functional. The Boronski–Nieminen enhancement factor was
adopted.38 The DBAR spectrum was obtained by doubleintegrating the momentum density with a Gaussian convolution having a full width at half-maximum of 1.9 keV.
Figure 2(a) shows M-H curves obtained before and after
ion implantation. Although weak (background) magnetization

FIG. 2. (a) Irradiation dose dependence and (b) post-annealing temperaturedependence of M-H curves for the oxygen-implanted ZnO single crystals
measured at a temperature of 100 K. The implantation dose for the annealing
behavior experiments was 5  1016 Oþ/cm2. The annealing duration at eachtemperature was 1 h.

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Maekawa et al.

is seen before implantation, an increase in magnetization to alevel exceeding the background level is found to be inducedby oxygen implantation. The magnetization increase withincreasing ion dose appears to saturate above 5  1016 Oþ/
cm2. The background magnetization in the unimplanted statearises from the whole region of the sample (which was
0.5 mm thick). This might be due to residual impurities, suchas iron, whereas the magnetization induced by oxygen
implantation results from the shallow ion depth (200 nm).
Hence, the net magnetization induced by oxygen implantation should be much greater than that in the unimplanted
state. Figure 2(b) shows how annealing influenced the M-Hcurve obtained for the sample implanted with a dose of
5  1016 Oþ/cm2. After annealing at 573 K, the magnetization is reduced to almost the same level as for the unimplanted state. These results suggest that the ferromagnetism
is induced in the ZnO by oxygen implantation and that some
defects are the source. The disappearance of magnetization
by post-implantation annealing may have been related to therecovery of the defects. The magnetization decreased to 80%
from 100 K to room temperature. This suggests that theCurie temperature is higher than room temperature.
Figure 3 shows the S-W plot for the various annealing
temperatures together with theoretical values.39 The inset
shows S parameters for the unimplanted and as-implanted
states as a function of positron incident energy. After theoxygen implantation, S parameters increase at 5 keV < E< 15 keV. This S-E profile matches the calculated distributions of vacancies in Fig. 1(b). All subsequent measurements
were performed at the energy of 6 keV. (S, W) ¼ (1, 1) corresponds to the unimplanted and bulk states in experiment andcalculation. The calculated S and W parameters for thenearest-neighbor divacancy (VZnVO) and zinc vacancy (VZn)
are on distinguishable two lines from the bulk state. The
experimental S and W parameters are located nearby those
calculated for zinc vacancy in the as-implanted state andshifted towards the calculated values for divacancy after

FIG. 3. S-W plot obtained for the oxygen implanted sample at various annealing temperatures. Filled circles show the experiments. Open circles are thecalculated values for zinc vacancy (VZn) and nearest-neighbor divacancy(VZnVO). The inset shows S parameters for unimplanted and as-implanted
state as a function of positron incident energy.

Appl. Phys. Lett. 110, 172402 (2017)

673 K annealing. At higher annealing temperature, S and W
parameters move to the bulk state. These suggest that zincvacancies disappear around 673 K leaving divacancies (andpresumably also higher order vacancy clusters) that areannealed out above 873 K. This behavior is in good agreementwith the previous electron beam experiment.40 This annealing
temperature of zinc vacancies agrees with that of magnetization by superconducting quantum interference device(SQUID). As shown below, the MDB measurements provide
further evidence for the zinc vacancy-induced ferromagnetism.
Figure 4(a) shows the MDB spectra at different ion
doses. The MDB spectrum of the unimplanted sample isnearly flat. But, after oxygen implantation, the amplitude
increase with ion dose tends to saturate above 5  1016 Oþ/
cm2. Figure 4(b) shows the annealing behavior of the MDB
spectrum obtained for the sample implanted with a dose of
5  1016 Oþ/cm2. The MDB spectrum becomes nearly flat
for the annealing carried out at 673 K. The effects of doseand annealing on the MDB spectrum are found to be very
similar to their effects on the M-H curve (Fig. 2). A previous
study showed positrons to be nearly fully trapped at zincvacancies in oxygen-implanted ZnO,41 and other studies
showed the contribution of oxygen vacancies to be verysmall.42,43 The change of the DBAR spectrum itself upon
oxygen implantation (characterized by the so-called S
parameter) indicates the positrons to be trapped by zincvacancies in the current samples as well. The solid lines
shown in Fig. 4(a) (for 5  1016 Oþ/cm2 and 1.8  1017 Oþ/cm2) are theoretical MDB spectra calculated by assuming
an electrically neutral zinc vacancy. (The amplitudes here
were adjusted by a factor of 0.42 and 0.2 to be comparable to

FIG. 4. (a) The irradiation dose dependence and (b) the post-annealing temperature dependence of the magnetic Doppler broadening (MDB) spectrum[Nþ(p)  N(p)] in an external magnetic fields of 60.91 T at 15 K. The
solid lines in the 5  1016 Oþ/cm2 and 1.8  1017 Oþ/cm2 panels are MDB
spectra calculated using the ABINIT code, which adjusts amplitudes to levels comparable with the experiments. The implantation dose used for theannealing behavior experiments was 5  1016 Oþ/cm2. The annealing duration at each temperature was 1 h.

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Maekawa et al.

the corresponding experiments.) The MDB spectra calculated for an oxygen vacancy and nearest-neighbor divacancy
are completely flat. An electrically neutral zinc vacancy is ina high spin state with S ¼ 1, and hence it possesses a magnetic moment of 2.0 lB (lB: the Bohr magneton).19 Such ahigh spin state is not available for an oxygen vacancy or anearest-neighbor divacancy. At zinc vacancies, positrons are
preferentially annihilated together with oxygen 2p electrons.
Due to the momenta of oxygen 2p electrons being higher
than those of outer-shell electrons of zinc atoms, the intensity of the MDB spectrum becomes negative at around p ¼ 0
m0c and positive at around 67 m0c, as shown in Fig. 4(a). A
similar shape was observed for the MDB spectrum of iron,which results from its 3d electrons.23 This similarity resultsfrom the similar radial distributions of oxygen 2p electrons
and iron 3d electrons.18,19
After zinc vacancies disappear, some secondary defects
may be generated. However, the above results show that such
defects induce no ferromagnetism. It is reported that ferromagnetism may be induced thorough the interaction between
oxygen vacancies and Mn impurities.44 Considering the factthat positrons are rarely trapped by the oxygen vacancies,42,43
the present results are hardly attributed to such oxygen
vacancy-related defect complexes. Enhancement of the ferromagnetism in Co-doped ZnO by the mediation of Zn-related
vacancies is theoretically predicted.45 However, the crystal
used in this study is not intentionally doped with Co. Even
though zinc vacancies couple with impurities, the agreement
between experimental MDB spectrum and that calculated forzinc vacancies suggests that those impurities are not located atthe vicinity of zinc vacancies.
As shown above, both the magnetization and the amplitude of the MDB spectrum appear to saturate above 5  1016
Oþ/cm2. This observation suggests that the number of zincvacancies is high enough to induce magnetic interactions
between these vacancies. Considering that the amplitudesof the experimentally determined MDB spectra were 20% 40% of those of the corresponding theoretical ones, theeffective magnetization per zinc vacancy is estimated to be
0.4–0.8 lB. (The estimation of effective magnetization per
zinc vacancy from the M-H measurements is somewhat problematic because of uncertainty in estimating the number ofzinc vacancies.) Since the zinc vacancies have acceptor levelsin the lower half of the band gap and the Fermi levels of thepresent samples are located in the mid-gap, the charge state ofzinc vacancies is probably the mixture of neutral and single
negative. The reduced magnetization per zinc vacancy (lessthan 2.0 lB) may have resulted from the elimination of thehigh spin state due to the occupation of the acceptor levels
with additional electrons having antiparallel spins.
In conclusion, by using SP-PAS, we have obtained
direct evidence for Zn vacancies being responsible for the
ferromagnetism in oxygen-implanted ZnO. There are manykinds of materials, including oxides,46,47 nitrides,48 carbides,49 and graphite,50 which are anticipated to exhibit d0
ferromagnetism. SP-PAS should be a useful tool for confirming whether d0 ferromagnetism is induced by vacancies.
Considering the low carrier density and high vacancy density
after irradiation, one possible reason of magnetic couplingmight be the electron hopping among vacancies.

Appl. Phys. Lett. 110, 172402 (2017)

This work was financially supported by JSPS KAKENHI
under Grant Nos. 24310072 and 15K14135.
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