Effect of Native Defects and Co Doping on

Ferromagnetism in HfO2: First-Principles Calculations

CHONG HAN, SHI-SHEN YAN, XUE-LING LIN, SHU-JUN HU, MING-WEN ZHAO,

XIN-XIN YAO, YAN-XUE CHEN, GUO-LEI LIU, LIANG-MO MEI

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan,Shandong, 250100, People’s Republic of China

Received 9 October 2009; Revised 31 August 2010; Accepted 14 October 2010DOI 10.1002/jcc.21711

Published online 16 December 2010 in Wiley Online Library (wileyonlinelibrary.com).

Abstract: First-principles calculations of undoped HfO2 and cobalt-doped HfO2 have been carried out to study the

magnetic properties of the dielectric material. In contrast to previous reports, it was found that the native defects in

HfO2 could not induce strong ferromagnetism. However, the cobalt substituting hafnium is the most stable defect

under oxidation condition, and the ferromagnetic (FM) coupling between the cobalt substitutions is favorable in vari-

ous configurations. We found that the FM coupling is mediated by the threefold-coordinated oxygen atoms in mono-

clinic HfO2 and could be further enhanced in electron-rich condition.

q 2010 Wiley Periodicals, Inc. J Comput Chem 32: 1298–1302, 2011

Key words: magnetic semiconductor; hafnium oxide; ferromagnetism; electronic structure; first-principles calcula-

tions

Introduction

The high-k dielectric oxide HfO2 has been widely studied in

recent years because of its promising application to replace SiO2

as the next generation gate dielectric material in semiconductor

technology. The possibility of making the dielectric material fer-

romagnetic (FM) could substantially broaden its application in

the field of spintronics. Since the first report of unexpected fer-

romagnetism for HfO2 thin films,1 much attention has been

attracted to find out the origin of the d0 ferromagnetism in such

wide-band gap high-dielectric constant material. Different lattice

defects are considered as the likely source of the magnetism,2

such as the oxygen vacancies generated by the annealing treat-

ments,3,4 the isolated hafnium vacancies in the low symmetry

monoclinic HfO2,5 or O:2p orbital polarized by the nonmagnetic

elements, which substitute hafnium.6 Although considerable

effort has been devoted to clarify how the isolated defects pro-

vide localized magnetic moment,2,5,6 few studies on the mag-

netic coupling between the defects have been reported, which

are essential for the ferromagnetism in these materials.

Meanwhile, some reports have questioned such unexpected

ferromagnetism in HfO2. Abraham et al.7 attributed the ferro-

magnetism to the contamination of stainless-steel tweezers. In

addition, numerous sources of pollution in the samples could

induce the same magnitude of the observed tiny FM signals.8

Recently, a first-principles study pointed out that native point

defects are unlikely to cause ferromagnetism in HfO2.9 The con-

trary results make such issue much complicated, and the reliabil-

ity of the magnetism in undoped HfO2 is still suspectable.

Another approach to achieve the ferromagnetism is doping

transition metal atoms in HfO2. Room temperature ferromagnet-

ism has been observed in cobalt-doped HfO2.10–12 However, all

the ferromagnetism is due to the cobalt clusters or other defects

in these materials, i.e., it is extrinsic. To date, no theoretical

investigations have been reported to verify the intrinsic ferro-

magnetism in transition metal-doped HfO2.

In this article, we perform first-principles calculations to

study the cobalt-doped HfO2. It was found that the cobalt substi-

tuting hafnium is the most stable defect in oxidation condition.

FM coupling is favorable in substitution configurations, where

the nearest-neighbor cobalt substitution with FM spin ordering is

the most stable configuration. The ferromagnetism is mediated

by the threefold-coordinated oxygen atoms in monoclinic HfO2

and could be enhanced in electron-rich condition. Without the

transition metal dopants, the native defects in HfO2 cannot

induce strong ferromagnetism comparable with the experimental

findings.

Correspondence to: S.-S Yan; e-mail: shishenyan@sdu.edu.cn.

Contract/grant sponsor: National Basic Research Program of China; con-

tract/grant number: 2007CB924903

Contract/grant sponsor: NSF; contract/grant number: 10974120

q 2010 Wiley Periodicals, Inc.

Computational Details

The monoclinic structure of HfO2 was selected in the present

studies, which is the stable phase at room temperature.13 The

calculations for a 96-atom supercell of HfO2 (Fig. 1) were car-

ried out by using a plane-wave basis set and ultrasoft pseudopo-

tentials (RRKJUS form) as implemented in the QUANTUM_E-

SPRESSO program.14 The valence charge configurations of Hf,

O, and Co are 5d26s2, 2s22p4, and 3d74s2, respectively. The

wave functions were expanded by plane waves up to a cutoff

energy of 50 Ry. Exchange correlation functional was treated by

the local density approximation (LDA).15 The Brillouin zone

integrations were carried out with the special 2 3 2 3 2 Mon-

khorst–Pack k-points mesh, which is accurate enough for this

supercell. All the calculations of the defect configurations are

performed by fixing the theoretical lattice constants of host

HfO2, and freeing all the atomic coordinates of the ions. Atomic

positions were optimized until the atomic forces were smaller

than 1023 Ry/Bohr. The lattice constants are listed in Table 1 in

comparison with previous theoretical16 and experimental17

results. Figure 2(a) gives the density of states (DOS) of the host

HfO2. Although the calculated band gap of the host HfO2 is

3.8 eV, which is smaller than the experimental value of 5.7 eV,

the occupied defect states are all localized in the theoretical gap.

Therefore, the calculated results are scarcely affected by the

band gap limitation of LDA scheme. The charged defects have

been realized by using a compensating jellium background.

Calculated Results and Discussion

We first investigated the thermodynamic stability of various

defects and impurities, which may induce the localized magnetic

moment, such as the oxygen vacancy, the hafnium vacancy, the

cobalt substitution, and the cobalt interstitial. The formation

energy Ef determines the concentration c of the defect (or impu-

rity) in the semiconductor, through the expression

c ¼ Nsites expð�Ef=kBTÞ (1)

where Nsites is the number of sites where the defect can be incor-

porated, kB is the Boltzmann constant, and T is the temperature

in Kelvin. In thermodynamic equilibrium and in the same

growth conditions, the defects with low formation energy will

occur in high concentrations.

The formation energy of a neutral defect (or impurity) X is

defined as follows18:

Ef ½X0� ¼ Etot½X0� � Etot½HFO2; bulk� �X

i

nili; (2)

where Etot[HfO2, bulk] and Etot[X0] are the total energies of the

supercells with and without the defect(or impurity), ni indicatesthe number of atoms of type i (host atoms or impurity atoms)

that have been added to (ni [ 0) or removed from (ni \ 0) the

Figure 1. The 2 3 2 3 2 supercell of monoclinic HfO2 consisting

of 96 atoms. The big gray balls are hafnium atoms, and the small

red balls are oxygen atoms.

Table 1. The Structural Parameters of Monoclinic HfO2.

Properties This work Other theory16 Experiment17

a (A) 4.93 5.22 5.12

b/a 1.025 1.013 1.010

c/a 1.028 1.025 1.035

b (8) 99.6 99.7 99.2

Figure 2. The density of states of (a) HfO2 host, (b) a supercell

with a hafnium vacancy, (c) a supercell with a cobalt substitution,

and (d) a supercell with two hafnium vacancies. The blue lines

denote the projected DOS of the O3:2p states and the red lines, the

Co:3d states. The vertical lines denote the Fermi energy. The pro-

jected DOS and total DOS are not shown on the same intensity

scale.

1299Effect of Native Defects and Co Doping on Ferromagnetism in HfO2

Journal of Computational Chemistry DOI 10.1002/jcc

supercell when the defect (or impurity) is created, and the li isthe corresponding chemical potential of these species, which

depend on the experimental growth conditions. In extreme oxi-

dation conditions (oxygen rich), the chemical potential of one

oxygen atom is subject to an upper bound given by the energy

of O in an O2 molecule lmaxO ¼ 1

2l½O2� and which results in the

lower limit on lHf and lCo.

lHf ¼ Etot½HfO2� � l½O2�; (3)

lCo ¼ Etot½CoO� � 1

2l½O2�: (4)

Here, l[O2] is energy of a O2 molecule, Etot[HfO2] and Etot

[CoO] are the energies of HfO2 and CoO bulk, respectively. In

extreme reduction conditions (oxygen deficient), lHf is subject

to an upper bound given by the energy of Hf in bulk phase (lHf5 lHf[bulk]), and the relationship lCo is also applicable. Corre-

spondingly, the upper limit on lHf results in a lower limit on lO

lO ¼ 1

2Etot½HfO2� � lHf ; (5)

The formation energies are shown in Table 2. These results

about native defects are quantitatively consistent with those of

previous report,9 and the calculation results about cobalt impu-

rity in HfO2 are first reported. There are two kinds of oxygen

atoms in the monoclinic HfO2: threefold-coordinated oxygens

(O3) and fourfold-coordinated oxygens (O4), which are con-

nected to three Hf atoms and four Hf atoms, respectively. Obvi-

ously, neither the O3 vacancy nor the O4 vacancy could induce

magnetic moment. Therefore, the oxygen vacancy makes no

contribution to the magnetism. The absence of hafnium can

induce a magnetic moment by the outward shifts and the spin

polarizations of the three O3 atoms around the vacancy site (see

Fig. 2b), which is in good agreement with Pemmaraju’s results.5

However, the formation energy of the hafnium vacancy is

always high in any conditions, suggesting that its equilibrium

concentration is very low. Additionally, when two hafnium

vacancies couple with each other, the displacements of the O

atoms around the vacancy site are greatly counteracted, and the

spin polarization in O3 atoms vanishes (see Fig. 2d). This indi-

cates that the hafnium vacancies could not ferromagnetically

couple together.

In contrast to the native point defects, substituting Hf by Co

is a good approach to induce ferromagnetism in HfO2. First, the

formation energy of cobalt substituting hafnium is much lower

than the others under the oxidation condition (Table 2), which is

also beneficial to the stability of the monoclinic structure.19 In

addition, the Co substitution can induce localized magnetic

moment arising from the Co:3d electrons. As shown in Figure

2c, the Co:3d states are hybridized with the 2p states of the O3

atoms around the Fermi energy. In contrast to the hafnium va-

cancy, the Co substitution attracts the surrounding O3 atoms,

and thus enhances the overlap between the Co:3d and O3:2p

states. In such crystal field, the Co:3d energy bands split into

two parts: (i) the low energy zone in the valence band, which

consists of the indirect overlap between the partial Co:3d orbit

and the O3:2p orbit; (ii) the direct overlap part along the Co��O

bond, which is repulsed to the high-energy zone in the energy

gap. The exchange splitting is relatively smaller than the crystal

field splitting, and the O3:2p states are also spin polarized

because of the magnetic coupling with the Co:3d electrons. The

Fermi energy is located in the valence band and just crosses the

Table 2. The Formation Energy and the Magnetic Moment of Different

Defects in Oxidation and Reduction Conditions, respectively, such as O3

Vacancy (VO3), O4 Vacancy (VO4), Hafnium Vacancy (VHf), Cobalt

Interstitial (Co-int), and Cobalt Substitution (Co-sub).

Defect types

Formation energy (eV)

Magnetic moment (lB)Oxidation Reduction

VO3 7.858 0.815 0.0

VO4 7.796 0.754 0.0

VHf 5.057 19.142 3.3

Co-int 5.777 3.226 1.0

Co-sub 20.466 11.068 1.0

Table 3. The Total Energies and Magnetic Moments of Different Configurations.

Configuration

number

Distance between

two Co atoms before

relaxing (A) EFM (meV)

EAFM

(meV)

EFM 2 EAFM

(meV)

Magnetic moment

in FM state (lBper unit cell)

1 3.210 0.00 141.64 2141.64 2.00

2 3.284 40.08 112.46 272.38 2.00

3 3.809 233.34 292.11 258.78 2.00

4 4.381 382.32 409.26 226.94 2.00

5 4.933 877.98 881.24 23.27 5.91

6 5.055 431.57 474.70 243.13 2.00

7 5.072 160.28 172.93 212.65 2.00

8 5.564 917.43 832.94 84.49 5.77

9 5.712 467.90 957.02 2489.12 2.00

10 6.459 342.05 348.44 26.39 2.00

11 7.161 484.63 497.15 212.52 2.00

12 8.202 435.52 440.28 24.76 2.00

1300 Han et al. • Vol. 32, No. 7 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

spin down states, which leads to a low spin state of cobalt atom.

On the other hand, the DOS of the O4 atoms are less influenced

by the Co substitution and nonspin polarized.

As CoHf is the most stable magnetic defects in HfO2, we

focus on the configurations with two CoHf in a 96-atom mono-

clinic supercell, corresponding to the doping concentration of

6.25%. Because of the low lattice symmetry, 12 configurations

can be constructed, and we denote them according to the dis-

tance between the two Co substitutions. The total energies and

magnetic moments of different configurations are shown in Ta-

ble 3. The FM coupling state of the nearest-neighbor Co atoms,

i.e., the configuration 1, is the ground state in energy. The FM

states are energetically more favorable than the corresponding

antiferromagnetic (AFM) states for all configurations except the

configuration 8. Our results indicate the possibility of intrinsic

ferromagnetism in Co-doped HfO2. Nevertheless, only the FM

state of configurations 1 and 9 is much stable than the AFM

one, which predicts the low Curie temperature.

Figures 3a–3d show the DOS of some selected configurations

of the Co-doped HfO2. It was found that the O3 atoms play the

key role in mediating the magnetic exchange interactions. In the

configuration 1 (Fig. 3a), the Co substitutions are connected

with two O3 atoms, and the parallel spin ordering of Co:3d and

O3:2p states results in a FM coupling between the Co atoms

(Fig. 4a). In the configuration 9 (Figure 3b), two O3:2p states

overlap along the Co��Co direction (highlight by ellipse in Fig.

4b), which mediates a relatively strong FM interaction. In con-

figuration 8 (Fig. 3c), however, all the Co��O3 bonds are dis-

tributed approximately perpendicular to the Co��Co direction.

Therefore, the O3 atoms could not couple together (Fig. 4c), and

the spin-parallel state of the Co atoms shows a higher energy

than the spin-antiparallel state. However, the spin-antiparallel

state can also induce the net magnetic moment of 3.65 lB, asshown in Figures 3d and 4d, which could be regarded as a ferri-

magnetic state. In other configurations, the orientation of the dis-

tribution of the O3 atoms is unobvious. Therefore, the energy

differences between the spin parallel and antiparallel ordering

are small, which indicates a weak exchange interaction in these

configurations.

Next, we study the stability of the ground state configuration

1 in charged conditions. We found that the FM coupling could

be further enhanced significantly in electron-rich condition,

whereas it is slightly weakened in hole-rich condition, as shown

in Table 4. As the DOS around the Fermi energy is fully polar-

ized, the charge state could only influence the occupation of mi-

nority spin state. The DOS of hole-rich system (Fig. 5a) is simi-

lar to that of the electronic neutral system (Fig. 5b) except for

the lower Fermi energy, whereas in electron-rich system the

Fermi energy is lifted (Fig. 5c). As the FM interaction is medi-

Figure 3. The density of states of configurations (a) 1, (b) 9, and

(c) 8 of the Co-doped HfO2 in spin parallel ordering and (d) 8 in

spin antiparallel ordering. The blue lines denote the projected DOS

of the O3:2p states and the red lines, the Co:3d states. The vertical

lines denote the Fermi energy. The arrows highlight feature for

which we give the spin density pictures in Figure 4. The projected

DOS and total DOS are not shown on the same intensity scale.

Figure 4. The yellow surfaces indicate the spin density distribution

for the states marked by arrows in Figure 3, respectively. The O3

atoms connecting to Co atoms are marked by small circles.

Table 4. The Energy Differences and Magnetic Moments of

Configuration 1 in Charged Conditions.

Charge state EFM 2 EAFM (meV)

Magnetic moment

in FM state

(lB per unit cell)

Hole rich 2122.64 2.73

Neutral 2141.53 2.00

Electron rich 2583.32 4.95

1301Effect of Native Defects and Co Doping on Ferromagnetism in HfO2

Journal of Computational Chemistry DOI 10.1002/jcc

ated by the minority spin state of Co:3d and O:2p orbits, the

FM interaction could be enhanced in electron-rich condition.

Conclusions

In conclusion, our first-principles studies show that neither the

oxygen vacancies nor the hafnium vacancies could induce the

intrinsic d0 ferromagnetism in undoped monoclinic HfO2. Ferro-

magnetism of HfO2 could be induced by substituting cobalt for

hafnium atoms, which is the most stable defect under oxidation

conditions. The FM interaction is mediated by the minority

states of the threefold-coordinated oxygen atoms between the

cobalt substitutions, and therefore it could be enhanced under

electron-rich condition.

References

1. Venkatesan, M.; Fitzgerald, C. B.; Coey, J. M. D. Nature 2004, 430,

630.

2. Coey, J. M. D.; Venkatesan, M.; Stamenov, P.; Fitzgerald, C. B.;

Dorneles, L. S. Phys Rev B 2005, 72, 024450.

3. Hong, N. H.; Poirot, N.; Sakai, J. Appl Phys Lett 2006, 89, 042503.

4. Hong, N. H.; Sakai, J.; Poirot, N.; Brize, V. Phys Rev B 2006, 73,

132404.

5. Pemmaraju, C. D.; Sanvito, S. Phys Rev Lett 2005, 94, 217205.

6. Weng, H.; Dong, J. Phys Rev B 2006, 73, 132410.

7. Abraham, D. W.; Frank, M. M.; Guha, S. Appl Phys Lett 2005, 87,

252502.

8. Hadacek, N.; Nosov, A.; Ranno, L.; Strobel, P.; Galera, R-M.

J Phys: Condens Matter 2007, 19, 486206.

9. Zheng, J. X.; Ceder, G.; Maxisch, T.; Chim, W. K.; Choi, W. K.

Phys Rev B 2007, 75, 104112.

10. Rao, M. S. R.; Kundaliya, D. C.; Ogale, S. B.; Fu, L. F.; Welz, S.

J.; Browning, N. D.; Zaitsev, V.; Varughese, B.; Cardoso, C. A.;

Curtin, A.; Dhar, S.; Shinde, S. R.; Venkatesan, T.; Lofland, S. E.;

Schwarz, S. A. Appl Phys Lett 2006, 88, 142505.

11. Chang, Y. H.; Soo, Y. L.; Lee, W. C.; Huang, M. L.; Lee, Y. J.;

Weng, S. C.; Sun, W. H.; Hong, M.; Kwo, J.; Lee, S. F.; Ablett, J.

M.; Kao, C.-C. Appl Phys Lett 2007, 91, 082504.

12. Soo, Y. L.; Weng, S. C.; Sun, W. H.; Chang, S. L.; Lee, W. C.;

Chang, Y. S.; Kwo, J.; Hong, M.; Ablett, J. M.; Kao, C.-C.; Liu, D.

G.; Lee, J. F. Phys Rev B 2007, 76, 132404.

13. Foster, A. S.; Lopez Gejo, F.; Shluger, A. L.; Nieminen, R. M. Phys

Rev B 2002, 65, 174117.

14. Giannozzi, P.; et al., J Phys: Condens Matter 2009, 21, 395502.

http://www.quantum-espresso.org.

15. Perdew, J. P.; Zunger, A. Phys Rev B 1981, 23, 5048.

16. Kang, J.; Lee, E.-C.; Chang, K. J. Phys Rev B 2003, 68, 054106.

17. Wang, J.; Li, H. P.; Stevens, R. J Mater Sci 1992, 27, 5397.

18. Van de Walle, C. G.; Neugebauer, J. J Appl Phys 2004, 95, 3851.

19. Lee, C.-K.; Cho, E.; Lee, H.-S.; Hwang, C. S.; Han, S. Phys Rev B

2008, 78, 012102.

Figure 5. The DOS of configuration 1 in (a) hole-rich, (b) neutral,

and (c) electron-rich conditions. The red lines denote the projected

DOS of the Co:3d states. The vertical lines denote the Fermi energy.

The projected DOS and total DOS are not shown on the same inten-

sity scale. [Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

1302 Han et al. • Vol. 32, No. 7 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc