The epsilon Fe2O3 phase of iron oxide has been studied to understand the spin structure and the magnetocrystalline anisotropy in the bulk and in thin films of  -Fe2O3 and Co-doped  -Fe2O3. The preferential magnetization direction in the nanoparticles of  -Fe2O3 is along the a-axis [M. Gich et al., Chem. Mater. 18, 3889 (2006)]. Compared to the bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in the Co-free films and to 0.7 eV in the film with partial Co substitution. The easy magnetization direction of the bulk and Co-free  -Fe2O3 is along the c-axis, but it switches to the a-axis on Co substitution. All three systems exhibit in-plane anisotropies associated with the orthorhombic crystal structure of the oxide

Ahamed, Imran

Kashyap, Arti

Pathak, Rohilt

English

DigitalCommons@University of Nebraska

University of Nebraska - LincolnDigitalCommons@University of Nebraska - LincolnFaculty Publications from Nebraska Center forMaterials and NanoscienceMaterials and Nanoscience, Nebraska Center for(NCMN)12-28-2017Magnetocrystalline anisotropy of "-Fe2O3Imran AhamedIndian Institute of TechnologyRohilt PathakUniversity of Nebraska - LincolnArti KashyapIndian Institute of Technology, arti@iitmandi.ac.inFollow this and additional works at: http://digitalcommons.unl.edu/cmrafacpubPart of the Atomic, Molecular and Optical Physics Commons, Condensed Matter PhysicsCommons, Engineering Physics Commons, and the Other Physics CommonsThis Article is brought to you for free and open access by the Materials and Nanoscience, Nebraska Center for (NCMN) atDigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications from Nebraska Center for Materials andNanoscience by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln.Ahamed, Imran; Pathak, Rohilt; and Kashyap, Arti, "Magnetocrystalline anisotropy of "-Fe2O3" (2017). Faculty Publications fromNebraska Center for Materials and Nanoscience. 130.http://digitalcommons.unl.edu/cmrafacpub/130AIP ADVANCES 8, 055815 (2018)Magnetocrystalline anisotropy of ε-Fe2O3Imran Ahamed,1 Rohit Pathak,1 Ralph Skomski,2 and Arti Kashyap1,a1School of Basic Sciences, Indian Institute of Technology, Mandi 175001, HP, India2Nebraska Center for Materials and Nanoscience and Department of Physics and Astronomy,University of Nebraska, Lincoln, Nebraska 68588, USA(Presented 9 November 2017; received 2 October 2017; accepted 3 November 2017;published online 28 December 2017)The epsilon Fe2O3 phase of iron oxide has been studied to understand the spin struc-ture and the magnetocrystalline anisotropy in the bulk and in thin films of ε-Fe2O3 andCo-doped ε-Fe2O3. The preferential magnetization direction in the nanoparticles ofε-Fe2O3 is along the a-axis [M. Gich et al., Chem. Mater. 18, 3889 (2006)]. Com-pared to the bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in theCo-free films and to 0.7 eV in the film with partial Co substitution. The easy magne-tization direction of the bulk and Co-free ε-Fe2O3 is along the c-axis, but it switchesto the a-axis on Co substitution. All three systems exhibit in-plane anisotropiesassociated with the orthorhombic crystal structure of the oxide. © 2017 Author(s).All article content, except where otherwise noted, is licensed under a CreativeCommons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/1.5007659I. INTRODUCTIONThe metastable oxide ε-Fe2O3, a rare polymorph of Fe2O3, has recently attracted interest as amaterial for photoelectrochemistry and as the only magnetoelectric Fe2O3 phase.1 The oxide was firstidentified by Forestier and Guiot-Guillain in 1934 but has actually been an ingredient of Tenmokuglaze on Chinese pottery for about a thousand years.2 This rare phase of Fe2O3 is orthorhombicand has the space-group Pna21.1 Figure 1 shows the bulk crystal structure of ε-Fe2O3. The unitcell contains 8 formula units of Fe2O3, thus having a total of 40 atoms. The experimental latticeparameters are a = 5.095 Å, b = 8.789 Å and c = 9.437 Å.3The interatomic exchange coupling is A-type antiferromagnetic, characterized by the spin direc-tions (β, α, α, β) for the (FeA, FeB, FeC, FeD) atoms. FeA and FeB are coordinated by distortedoctahedrals, FeC exhibits a regular octahedral coordination, and FeD is tetrahedrally coordinated.Since the four Fe atoms are nonequivalent, the spin structure is ferrimagnetic, with a magnetizationof about 0.1 T and a Curie temperature of 510 K. However, it is only partially clear whether the spinstructure is collinear or noncollinear.1,3,4 Recent in-field Mo¨ssbauer experiments5 indicate collinearferrimagnetism.Coercivities Hc as high as 20 kOe [2 T] have been reported for ε-Fe2O3 nanoparticles,4 butthese high coercivities may reflect the small spontaneous magnetization Ms rather than a particularlyhigh anisotropy constant K1,6 since Hc ∼ 2K1/Ms. The coercivity of 20 kOe of nanoparticles ofε-Fe2O3 is reduced to an in-plane coercivity of 8 kOe7 in epitaxially stabilized (001) thin films onSrTiO3 (111). Tanskanen et al.8 reported coercivity of 1.6 kOe for thin films grown by atomic layerdeposition. Namai et al.9 enhanced the coercivity of ε-Fe2O3 nanomagnets by the substitution ofrhodium. To understand the coercive behavior of ε-Fe2O3, it is necessary to explain and describe themagnetocrystalline anisotropy of the oxide.In this paper, we use ab-initio calculations to investigate the spin structure and magneticanisotropy of bulk and thin-film ε-Fe2O3. Concerning the magnetic anisotropy, we reproducethe experimental findings and address the important point that orthorhombic crystals have twoaArti Kashyap. mailto:arti@iitmandi.ac.in2158-3226/2018/8(5)/055815/5 8, 055815-1 © Author(s) 2017      055815-2 Ahamed et al. AIP Advances 8, 055815 (2018)FIG. 1. Bulk crystal structure of ε-Fe2O3.lowest-order anisotropy constants, namely K1 and K1 ′.10 Finally, we outline the effects of Co substi-tution, which enhances the anisotropy by creating more than half-filled 3d shells, and of the surfacecontribution to the magnetic anisotropy of ε-Fe2O3.II. METHODWe have used the Vienna ab-initio simulation package (VASP),11–13 employing the generalizedgradient approximation (GGA),14 a Hubbard U,15 and a projector-augmented wave (PAW)13 potential.The magnetocrystalline anisotropy (Sect. III. C) was determined by evaluating the total energiesfor magnetization directions parallel to the x-, y-, and z-directions, using spin-orbit coupling asimplemented in VASP by Kresse and Lebacq. An energy cutoff of 530 eV was used for representingthe electronic wave functions.Aside from bulk ε-Fe2O3 (Fig. 1), we have investigated the thin-film structures shown in Fig. 2.The films of thickness 10.18 Å were constructed as supercells along the z-direction and a vacuum ofFIG. 2. Investigated thin-films structures: (a) ε-Fe2O3 thin film in the a-b plane (x-y plane), and (b) Co-substituted oxide.(Red, orange, and blue colors are used to indicate O, Fe, and Co, respectively.)055815-3 Ahamed et al. AIP Advances 8, 055815 (2018)20 Å inserted between the periodic images of the film to avoid interaction effects. The Co-substitutedthin film was obtained by just replacing one of the two FeD atoms by a Co atom in the top layer.The optimized lattice parameters for bulk are a = 5.125 Å, b = 8.854 Å and c = 9.563 Å.III. RESULTS AND DISCUSSIONAmong the possible spin structures (β, α, α, β), (α, β, α, β), (α, α, β, β), and (α, α, α, α), theconfiguration (β, α, α, β) has the lowest calculated energy in both bulk ε-Fe2O3 and in the Co-freeand Co-substituted thins films. For this reason, the following subsections deal with (β, α, α, β) spinstructures exclusively.A. Bulk calculationsVolume optimization and ionic relaxation were performed for the bulk structure, and the elec-tronic structure was calculated using a k-point grid of 5 × 3 × 3. The U-J parameter used in thecalculations is 4 eV. This value corresponds to the U of hematite (α-Fe2O3), since no informationis available for ε-Fe2O3. Figure 3 shows the density of states for the bulk structure. The predictedband gap is 1.9 eV, in agreement with the ab-initio studies of Yoshikiyo et al.16 The magneticmoment of 0.143 µB per unit cell comes nearly exclusively from Fe atoms and indicates an A-typeantiferromagnetic ordering resulting in a ferrimagnetic ground state.B. Thin-film calculationsThe electronic structure of the thin films was calculated after volume optimization and completerelaxation, using a k-point grid of 5 × 3 × 1. The density of states of the thin film and Co-substitutedthin film is shown in Fig. 4.The ε-Fe2O3 thin film shows a band gap of 1.3 eV in the spin-down channel, whereas the spin-upchannel near the Fermi level is occupied by Fe surface states. For the Co-substituted thin film, thereare surface states due to the Co atoms, but the band gap of about 0.732 eV is same for both spinchannels.C. Magnetocrystalline anisotropyThe magnetocrystalline anisotropies of bulk and thin-film ε-Fe2O3 were calculated by includingthe spin-orbit coupling and evaluating the total magnetic energy as a function of the magnetiza-tion angle (Sect. II). The Brillouin-zone integration for the anisotropy calculations was performedFIG. 3. The total density of states of bulk ε-Fe2O3 with partial density of states of Fe 3d and O 2p states.055815-4 Ahamed et al. AIP Advances 8, 055815 (2018)FIG. 4. The total densities of states in (a) pristine and (b) Co-substituted thin films of ε-Fe2O3.TABLE I. The anisotropy constants K1 and K1′ for bulk ε-Fe2O3, thin-film ε-Fe2O3, and Co-substituted thin-film ε-Fe2O3.System Ex (eV) Ey (eV) Ez (eV) K1 (kJ/m3) K1′ (kJ/m3)Bulk ε-Fe2O3 –273.63460089 –273.63460877 –273.63461010 4.93 2.91Co-free thin film –293.26412576 –293.26415896 –293.26417920 2.36 3.88Co-substituted thin film –291.92083283 –291.92080945 –291.92080544 -0.47 -2.73using Monkhorst-Pack k-point meshes of 11 × 11 × 11 for the bulk and 11 × 11 × 1 for the thinfilms.Due to the orthorhombic crystal structure it is sufficient to evaluate the energy for the threeprincipal directions ex, ey, and ez along the a-, b-, and c-axes, respectively. The definition10,17EV=K1sin2θ + K1 ′sin2θ cos 2φ (1)yields K1 = (Ey – Ez)/V and K1 ′ = (Ex – Ey)/V. In these equations, V is the volume of the unit-cell andEx, Ey and Ez are the energies when the spins are aligned in the x-, y- and z-directions, respectively.The calculated bulk and thin-film energies are listed in Table I.Bulk ε-Fe2O3 behaves like a uniaxial easy-axis magnet (K1 > 0) with a preferred magne-tization direction in the z-direction and in-plane anisotropy (K1 ′ , 0), except that the in-planeanisotropy is very high (of second order), as contrasted to fourth-order in-plane anisotropy intetragonal structures and the sixth-order in-plane anisotropy in hexagonal and trigonal (rhom-bohedral) structures. The same situation is found for the Co-free thin films, except the respec-tive magnitudes of K1 is smaller and K1 ′ is larger than in the bulk. The Co addition yields aspin-reorientation transition, the easiest axis switching from the z-to the x-direction and rela-tively small ‘in-plane’ anisotropy in the y-z plane (b-c plane). The calculated anisotropies are allrelatively small (several kJ/m3), but the small magnetization and the orthorhombic crystal struc-ture helps to create high coercivity, because K1 ′ imposes additional restrictions on magnetizationrotations.IV. CONCLUSIONSIn summary, we have used the first-principle calculations to study the electronic structure ofthe bulk ε-Fe2O3 as well as cobalt-free and cobalt containing thin films of ε-Fe2O3. Compared tothe bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in the Co-free films andto 0.7 eV in the film with partial Co substitution. The easy magnetization direction of the bulk andCo-free ε-Fe2O3 is along the c-axis, but it switches to the a-axis on Co substitution. All three systemsexhibit substantial in-plane anisotropies associated with the orthorhombic crystal structure of theoxide.055815-5 Ahamed et al. AIP Advances 8, 055815 (2018)ACKNOWLEDGMENTSThis work is supported by Nano Mission, DST, India (I. A., R. P., A. K). RS acknowledges partialsupport by DOE BES (04ER46152).1 M. Gich, C. Frontera, A. Roig, E. Taboada, E. Molins, H. R. Rechenberg, J. D. Ardisson, W. A. A. Macedo, C. Ritter,V. Hardy, J. Sort, V. Skumryev, and J. Nogue´s, Chem. Mater. 18, 3889 (2006).2 C. Dejoie, P. Sciau, W. Li, L. Noe´, A. Mehta, K. Chen, H. Luo, M. Kunz, N. Tamura, and Z. Liu, Sci. Rep. 4, 4941 (2014).3 E. Tronc, C. Chane´ac, and J. P. Jolivet, J. Solid State Chem. 139, 93 (1998).4 R. Zboril, M. Mashlan, and D. Petridis, Chem. Mater. 14, 969 (2002).5 J. Tucek, S. Ohkoshi, and R. Zboril, Appl. Phys. Lett. 99, 253108 (2011).6 Y.-C. Tseng, N. M. Souza-Neto, D. Haskel, M. Gich, C. Frontera, A. Roig, M. van Veenendaal, and J. Nogue´s, Phys. Rev. B79, 094404 (2009).7 M. Gich, J. Gazquez, A. Roig, A. Crespi, J. Fontcuberta, J. C. Idrobo, S. J. Pennycook, M. Varela, V. Skumryev, andM. Varela, Appl. Phys. Lett. 96, 112508 (2010).8 A. Tanskanen, O. Mustonen, and M. Karppinen, APL Mater. 5, 056104 (2017).9 A. Namai, M. Yoshikiyo, K. Yamada, S. Sakurai, T. Goto, T. Yoshida, T. Miyazaki, M. Nakajima, T. Suemoto, H. Tokoro,and S. Ohkoshi, Nat. Commun. 3, ncomms2038 (2012).10 R. Skomski, Simple Models of Magnetism, Reprinted (Oxford Univ. Press, Oxford, 2009).11 G. Kresse and J. Furthmu¨ller, Comput. Mater. Sci. 6, 15 (1996).12 G. Kresse and J. Furthmu¨ller, Phys. Rev. B 54, 11169 (1996).13 G. Kresse and D. Joubert, Phys Rev B 59, 1758 (1999).14 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).15 J. Hubbard, Proc R Soc Lond A 276, 238 (1963).16 M. Yoshikiyo, K. Yamada, A. Namai, and S. Ohkoshi, J. Phys. Chem. C 116, 8688 (2012).17 R. Skomski, J. Phys. Condens. Matter 15, R841 (2003).

Magnetocrystalline anisotropy of  -Fe2O3

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Faculty Publications from Nebraska Center for
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Materials and Nanoscience, Nebraska Center for
(NCMN)
12-28-2017
Magnetocrystalline anisotropy of "-Fe2O3
Imran Ahamed
Indian Institute of Technology
Rohilt Pathak
University of Nebraska - Lincoln
Arti Kashyap
Indian Institute of Technology, arti@iitmandi.ac.in
Follow this and additional works at: http://digitalcommons.unl.edu/cmrafacpub
Part of the Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics
Commons, Engineering Physics Commons, and the Other Physics Commons
This Article is brought to you for free and open access by the Materials and Nanoscience, Nebraska Center for (NCMN) at
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications from Nebraska Center for Materials and
Nanoscience by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln.
Ahamed, Imran; Pathak, Rohilt; and Kashyap, Arti, "Magnetocrystalline anisotropy of "-Fe2O3" (2017). Faculty Publications from
Nebraska Center for Materials and Nanoscience. 130.
http://digitalcommons.unl.edu/cmrafacpub/130
AIP ADVANCES 8, 055815 (2018)
Magnetocrystalline anisotropy of ε-Fe2O3
Imran Ahamed,1 Rohit Pathak,1 Ralph Skomski,2 and Arti Kashyap1,a
1School of Basic Sciences, Indian Institute of Technology, Mandi 175001, HP, India
2Nebraska Center for Materials and Nanoscience and Department of Physics and Astronomy,
University of Nebraska, Lincoln, Nebraska 68588, USA
(Presented 9 November 2017; received 2 October 2017; accepted 3 November 2017;
published online 28 December 2017)
The epsilon Fe2O3 phase of iron oxide has been studied to understand the spin struc-
ture and the magnetocrystalline anisotropy in the bulk and in thin films of ε-Fe2O3 and
Co-doped ε-Fe2O3. The preferential magnetization direction in the nanoparticles of
ε-Fe2O3 is along the a-axis [M. Gich et al., Chem. Mater. 18, 3889 (2006)]. Com-
pared to the bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in the
Co-free films and to 0.7 eV in the film with partial Co substitution. The easy magne-
tization direction of the bulk and Co-free ε-Fe2O3 is along the c-axis, but it switches
to the a-axis on Co substitution. All three systems exhibit in-plane anisotropies
associated with the orthorhombic crystal structure of the oxide. © 2017 Author(s).
All article content, except where otherwise noted, is licensed under a Creative
Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.1063/1.5007659
I. INTRODUCTION
The metastable oxide ε-Fe2O3, a rare polymorph of Fe2O3, has recently attracted interest as a
material for photoelectrochemistry and as the only magnetoelectric Fe2O3 phase.1 The oxide was first
identified by Forestier and Guiot-Guillain in 1934 but has actually been an ingredient of Tenmoku
glaze on Chinese pottery for about a thousand years.2 This rare phase of Fe2O3 is orthorhombic
and has the space-group Pna21.1 Figure 1 shows the bulk crystal structure of ε-Fe2O3. The unit
cell contains 8 formula units of Fe2O3, thus having a total of 40 atoms. The experimental lattice
parameters are a = 5.095 Å, b = 8.789 Å and c = 9.437 Å.3
The interatomic exchange coupling is A-type antiferromagnetic, characterized by the spin direc-
tions (β, α, α, β) for the (FeA, FeB, FeC, FeD) atoms. FeA and FeB are coordinated by distorted
octahedrals, FeC exhibits a regular octahedral coordination, and FeD is tetrahedrally coordinated.
Since the four Fe atoms are nonequivalent, the spin structure is ferrimagnetic, with a magnetization
of about 0.1 T and a Curie temperature of 510 K. However, it is only partially clear whether the spin
structure is collinear or noncollinear.1,3,4 Recent in-field Mo¨ssbauer experiments5 indicate collinear
ferrimagnetism.
Coercivities Hc as high as 20 kOe [2 T] have been reported for ε-Fe2O3 nanoparticles,4 but
these high coercivities may reflect the small spontaneous magnetization Ms rather than a particularly
high anisotropy constant K1,6 since Hc ∼ 2K1/Ms. The coercivity of 20 kOe of nanoparticles of
ε-Fe2O3 is reduced to an in-plane coercivity of 8 kOe7 in epitaxially stabilized (001) thin films on
SrTiO3 (111). Tanskanen et al.8 reported coercivity of 1.6 kOe for thin films grown by atomic layer
deposition. Namai et al.9 enhanced the coercivity of ε-Fe2O3 nanomagnets by the substitution of
rhodium. To understand the coercive behavior of ε-Fe2O3, it is necessary to explain and describe the
magnetocrystalline anisotropy of the oxide.
In this paper, we use ab-initio calculations to investigate the spin structure and magnetic
anisotropy of bulk and thin-film ε-Fe2O3. Concerning the magnetic anisotropy, we reproduce
the experimental findings and address the important point that orthorhombic crystals have two
aArti Kashyap. mailto:arti@iitmandi.ac.in
2158-3226/2018/8(5)/055815/5 8, 055815-1 © Author(s) 2017
 
 
 
 
 
 
055815-2 Ahamed et al. AIP Advances 8, 055815 (2018)
FIG. 1. Bulk crystal structure of ε-Fe2O3.
lowest-order anisotropy constants, namely K1 and K1 ′.10 Finally, we outline the effects of Co substi-
tution, which enhances the anisotropy by creating more than half-filled 3d shells, and of the surface
contribution to the magnetic anisotropy of ε-Fe2O3.
II. METHOD
We have used the Vienna ab-initio simulation package (VASP),11–13 employing the generalized
gradient approximation (GGA),14 a Hubbard U,15 and a projector-augmented wave (PAW)13 potential.
The magnetocrystalline anisotropy (Sect. III. C) was determined by evaluating the total energies
for magnetization directions parallel to the x-, y-, and z-directions, using spin-orbit coupling as
implemented in VASP by Kresse and Lebacq. An energy cutoff of 530 eV was used for representing
the electronic wave functions.
Aside from bulk ε-Fe2O3 (Fig. 1), we have investigated the thin-film structures shown in Fig. 2.
The films of thickness 10.18 Å were constructed as supercells along the z-direction and a vacuum of
FIG. 2. Investigated thin-films structures: (a) ε-Fe2O3 thin film in the a-b plane (x-y plane), and (b) Co-substituted oxide.
(Red, orange, and blue colors are used to indicate O, Fe, and Co, respectively.)
055815-3 Ahamed et al. AIP Advances 8, 055815 (2018)
20 Å inserted between the periodic images of the film to avoid interaction effects. The Co-substituted
thin film was obtained by just replacing one of the two FeD atoms by a Co atom in the top layer.
The optimized lattice parameters for bulk are a = 5.125 Å, b = 8.854 Å and c = 9.563 Å.
III. RESULTS AND DISCUSSION
Among the possible spin structures (β, α, α, β), (α, β, α, β), (α, α, β, β), and (α, α, α, α), the
configuration (β, α, α, β) has the lowest calculated energy in both bulk ε-Fe2O3 and in the Co-free
and Co-substituted thins films. For this reason, the following subsections deal with (β, α, α, β) spin
structures exclusively.
A. Bulk calculations
Volume optimization and ionic relaxation were performed for the bulk structure, and the elec-
tronic structure was calculated using a k-point grid of 5 × 3 × 3. The U-J parameter used in the
calculations is 4 eV. This value corresponds to the U of hematite (α-Fe2O3), since no information
is available for ε-Fe2O3. Figure 3 shows the density of states for the bulk structure. The predicted
band gap is 1.9 eV, in agreement with the ab-initio studies of Yoshikiyo et al.16 The magnetic
moment of 0.143 µB per unit cell comes nearly exclusively from Fe atoms and indicates an A-type
antiferromagnetic ordering resulting in a ferrimagnetic ground state.
B. Thin-film calculations
The electronic structure of the thin films was calculated after volume optimization and complete
relaxation, using a k-point grid of 5 × 3 × 1. The density of states of the thin film and Co-substituted
thin film is shown in Fig. 4.
The ε-Fe2O3 thin film shows a band gap of 1.3 eV in the spin-down channel, whereas the spin-up
channel near the Fermi level is occupied by Fe surface states. For the Co-substituted thin film, there
are surface states due to the Co atoms, but the band gap of about 0.732 eV is same for both spin
channels.
C. Magnetocrystalline anisotropy
The magnetocrystalline anisotropies of bulk and thin-film ε-Fe2O3 were calculated by including
the spin-orbit coupling and evaluating the total magnetic energy as a function of the magnetiza-
tion angle (Sect. II). The Brillouin-zone integration for the anisotropy calculations was performed
FIG. 3. The total density of states of bulk ε-Fe2O3 with partial density of states of Fe 3d and O 2p states.
055815-4 Ahamed et al. AIP Advances 8, 055815 (2018)
FIG. 4. The total densities of states in (a) pristine and (b) Co-substituted thin films of ε-Fe2O3.
TABLE I. The anisotropy constants K1 and K1′ for bulk ε-Fe2O3, thin-film ε-Fe2O3, and Co-substituted thin-film ε-Fe2O3.
System Ex (eV) Ey (eV) Ez (eV) K1 (kJ/m3) K1′ (kJ/m3)
Bulk ε-Fe2O3 –273.63460089 –273.63460877 –273.63461010 4.93 2.91
Co-free thin film –293.26412576 –293.26415896 –293.26417920 2.36 3.88
Co-substituted thin film –291.92083283 –291.92080945 –291.92080544 -0.47 -2.73
using Monkhorst-Pack k-point meshes of 11 × 11 × 11 for the bulk and 11 × 11 × 1 for the thin
films.
Due to the orthorhombic crystal structure it is sufficient to evaluate the energy for the three
principal directions ex, ey, and ez along the a-, b-, and c-axes, respectively. The definition10,17
E
V
=K1sin2θ + K1 ′sin2θ cos 2φ (1)
yields K1 = (Ey – Ez)/V and K1 ′ = (Ex – Ey)/V. In these equations, V is the volume of the unit-cell and
Ex, Ey and Ez are the energies when the spins are aligned in the x-, y- and z-directions, respectively.
The calculated bulk and thin-film energies are listed in Table I.
Bulk ε-Fe2O3 behaves like a uniaxial easy-axis magnet (K1 > 0) with a preferred magne-
tization direction in the z-direction and in-plane anisotropy (K1 ′ , 0), except that the in-plane
anisotropy is very high (of second order), as contrasted to fourth-order in-plane anisotropy in
tetragonal structures and the sixth-order in-plane anisotropy in hexagonal and trigonal (rhom-
bohedral) structures. The same situation is found for the Co-free thin films, except the respec-
tive magnitudes of K1 is smaller and K1 ′ is larger than in the bulk. The Co addition yields a
spin-reorientation transition, the easiest axis switching from the z-to the x-direction and rela-
tively small ‘in-plane’ anisotropy in the y-z plane (b-c plane). The calculated anisotropies are all
relatively small (several kJ/m3), but the small magnetization and the orthorhombic crystal struc-
ture helps to create high coercivity, because K1 ′ imposes additional restrictions on magnetization
rotations.
IV. CONCLUSIONS
In summary, we have used the first-principle calculations to study the electronic structure of
the bulk ε-Fe2O3 as well as cobalt-free and cobalt containing thin films of ε-Fe2O3. Compared to
the bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in the Co-free films and
to 0.7 eV in the film with partial Co substitution. The easy magnetization direction of the bulk and
Co-free ε-Fe2O3 is along the c-axis, but it switches to the a-axis on Co substitution. All three systems
exhibit substantial in-plane anisotropies associated with the orthorhombic crystal structure of the
oxide.
055815-5 Ahamed et al. AIP Advances 8, 055815 (2018)
ACKNOWLEDGMENTS
This work is supported by Nano Mission, DST, India (I. A., R. P., A. K). RS acknowledges partial
support by DOE BES (04ER46152).
1 M. Gich, C. Frontera, A. Roig, E. Taboada, E. Molins, H. R. Rechenberg, J. D. Ardisson, W. A. A. Macedo, C. Ritter,
V. Hardy, J. Sort, V. Skumryev, and J. Nogue´s, Chem. Mater. 18, 3889 (2006).
2 C. Dejoie, P. Sciau, W. Li, L. Noe´, A. Mehta, K. Chen, H. Luo, M. Kunz, N. Tamura, and Z. Liu, Sci. Rep. 4, 4941 (2014).
3 E. Tronc, C. Chane´ac, and J. P. Jolivet, J. Solid State Chem. 139, 93 (1998).
4 R. Zboril, M. Mashlan, and D. Petridis, Chem. Mater. 14, 969 (2002).
5 J. Tucek, S. Ohkoshi, and R. Zboril, Appl. Phys. Lett. 99, 253108 (2011).
6 Y.-C. Tseng, N. M. Souza-Neto, D. Haskel, M. Gich, C. Frontera, A. Roig, M. van Veenendaal, and J. Nogue´s, Phys. Rev. B
79, 094404 (2009).
7 M. Gich, J. Gazquez, A. Roig, A. Crespi, J. Fontcuberta, J. C. Idrobo, S. J. Pennycook, M. Varela, V. Skumryev, and
M. Varela, Appl. Phys. Lett. 96, 112508 (2010).
8 A. Tanskanen, O. Mustonen, and M. Karppinen, APL Mater. 5, 056104 (2017).
9 A. Namai, M. Yoshikiyo, K. Yamada, S. Sakurai, T. Goto, T. Yoshida, T. Miyazaki, M. Nakajima, T. Suemoto, H. Tokoro,
and S. Ohkoshi, Nat. Commun. 3, ncomms2038 (2012).
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Magnetocrystalline anisotropy of -Fe2O3

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