First-principles investigation of the very
large perpendicular magnetic anisotropy
at Fe | MgO and Co | MgO interfaces
Item Type Article
Authors Yang, H. X.; Chshiev, M.; Dieny, B.; Lee, J. H.; Manchon, Aurelien;
Shin, K. H.
Citation First-principles investigation of the very large perpendicular
magnetic anisotropy at Fe | MgO and Co | MgO interfaces 2011, 84
(5) Physical Review B
Eprint version Publisher's Version/PDF
DOI 10.1103/PhysRevB.84.054401
Publisher American Physical Society (APS)
Journal Physical Review B
Rights Archived with thanks to Physical Review B
Download date 10/08/2022 07:02:40
Link to Item http://hdl.handle.net/10754/553019
PHYSICAL REVIEW B 84, 054401 (2011)
First-principles investigation of the very large perpendicular magnetic anisotropy at Fe|MgO
and Co|MgO interfaces
H. X. Yang, M. Chshiev,
*
and B. Dieny
SPINTEC, UMR CEA/CNRS/UJF-Grenoble 1/Grenoble-INP, INAC, Grenoble, F-38054, France
J. H. Lee
SPINTEC, UMR CEA/CNRS/UJF-Grenoble 1/Grenoble-INP, INAC, Grenoble, F-38054, France, and Korea Institute of Science and
Technology, Seoul 136-791, Korea
A. Manchon
SPINTEC, UMR CEA/CNRS/UJF-Grenoble 1/Grenoble-INP, INAC, Grenoble, F-38054, France, and King Abdullah University of Science
and Technology, Thuwal 23955-6900, Saudi Arabia
K. H. Shin
Korea Institute of Science and Technology, Seoul 136-791, Korea
(Received 21 February 2011; revised manuscript received 22 April 2011; published 1 August 2011)
The perpendicular magnetic anisotropy (PMA) arising at the interface between ferromagnetic transition metals
and metallic oxides was investigated via first-principles calculations. In this work very large values of PMA,
upto3erg/cm
2
,atFe|MgO interfaces are reported, in agreement with recent experiments. The origin of
PMA is attributed to overlap between O-p
z
and transition metal d
z
2
orbitals hybridized with d
xz(yz)
orbitals with
stronger spin-orbit coupling-induced splitting around the Fermi level for perpendicular magnetization orientation.
Furthermore, it is shown that the PMA value weakens in the case of over- or underoxidation due to the fact that
oxygen p
z
and transition metal d
z
2
orbital overlap is strongly affected by disorder, in agreement with experimental
observations in magnetic tunnel junctions.
DOI: 10.1103/PhysRevB.84.054401 PACS number(s): 75.30.Gw, 72.25.−b, 73.40.Rw, 75.70.Cn
I. INTRODUCTION
Spin-orbit i nteraction (SOI) plays a major role in a wide
class of physical phenomena from both fundamental and
applications points of view.
1
For instance, it is at the heart
of basic magnetic phenomena such as magnetocrystalline
anisotropy,
2
the Rashba effect,
3,4
and magnetization damping.
Controlling SOI strength at the interface between ferromag-
netic (FM) and nonmagnetic layers represents an outstand-
ing challenge for advancement of transport and magnetic
properties of spintronic magnetic devices, such as perpen-
dicular magnetic tunnel junctions
5–10
(p-MTJs) and tunneling
anisotropic magnetoresistive (TAMR) systems.
11,12
Recently,
electric field control of interfacial magnetic anisotropy has
attracted much attention as well.
13,14
Traditionally, interfaces
between magnetic and heavy nonmagnetic transition metals
such as Co|Pt,
15
Co|Pd,
16,17
and Co|Au
18
have been used to
obtain perpendicular magnetic anisotropy (PMA). It has been
shown that the onset of PMA at these interfaces is related
to an increase in the orbital momentum of Co
18
due to the
strong hybridization between the 3d orbitals of the transition
metal and the 5d orbitals of heavy metal.
15
This hybridization
enhances the energy splitting between the Co 3d
z
2
and the
Co 3d
x
2
−y
2
orbitals and induces a charge transfer between the
two layers.
19–21
As a result, the combination between SOI and
hybridization-induced charge transfer leads to PMA. Thus, the
presence of a heavy nonmagnetic layer (Pt, Pd, Au, W, Mo)
was believed to be essential to obtain large PMA.
However, Monso et al. have shown that PMA could
be observed also at Co(Fe)|MOx interfaces (M = Ta, Mg,
Al, Ru, etc.)
22,23
despite the weak SOI at the interface.
Surprisingly large PMA values, up to 1 to 2 erg/cm
2
,have
been reported, which are comparable or even larger than the
PMA observed at Co|Pt or Co|Pd interfaces.
24,25
This result
is quite general and has been observed in both crystalline
(MgO) and amorphous (AlOx) barriers, using both natural
or plasma oxidation.
26,27
The PMA could be dramatically
improved under annealing,
10,28,29
and x-ray photoemission
spectroscopy has demonstrated that the PMA could be cor-
related without ambiguity with the presence of oxygen atoms
at the interface.
26,27
In fact, a correlation between PMA and
oxidation conditions has been demonstrated for a wide range of
FM|MOx including those based on Co
x
Fe
1−x
, thus indicating
that the phenomenon is quite general at interfaces between
magnetic transition metals and oxygen-terminated oxides.
These observations led the authors to postulate that, despite the
weak SOI of the elements (Fe, Co, Al, O), oxidation conditions
play an essential role in PMA, as they do for TMR
30
or inter-
layer exchange coupling.
31
Recent experiments reported large
PMA values of 1.3 erg/cm
2
at CoFeB|MgO structures.
32,33
Furthermore, it has been demonstrated experimentally that
there is a strong correlation between PMA and TMR maximum
values obtained at the same optimal oxidation and annealing
conditions.
34
In this article, we report first-principles investigations of
the PMA and the effect of interfacial oxidation conditions
on the PMA at Fe|MgO(100) structures. The latter can be
viewed as a model system for FM|MOx interfaces involving
bcc electrodes including Co
x
Fe
1−x
alloys. In agreement with
experiments, it is demonstrated that despite the weak SOI, the
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YANG, CHSHIEV, DIENY, LEE, MANCHON, AND SHIN PHYSICAL REVIEW B 84, 054401 (2011)
bonding between the Fe-3d and the O-2p orbitals can give rise
to PMA even stronger than that of Co|Pt interfaces. The largest
PMA value is obtained for ideal interfaces, while it is reduced
for the case of over- or underoxidized interfaces. In addition,
it is found that the FM|MgO PMA strength decreases when Fe
is replaced by Co, consistent with the recent report that PMA
values decrease in Co
x
Fe
1−x
|MgO as the Co concentration
increases.
35
II. METHODOLOGY
For ab initio calculations, the Vienna ab initio simulation
package (
VASP)
36
was used with the generalized gradient
approximation
37
and projector augmented wave potentials.
38
Calculations were performed in three steps. First, calculations
were performed for both unrelaxed and relaxed structrures. In
the case of relaxed structures, full structural relaxation in shape
and volume was performed until the forces become lower
than 0.001 eV/
˚
A for determining the most stable interfacial
geometries. Next, the Kohn-Sham equations were solved with
no SOI taken into account to determine the charge distribution
of the system ground state. Finally, the spin-orbit coupling was
included and the total energy of the system was determined
as a function of the orientation of the magnetic moments.
A19× 19 × 3 K-point mesh was used in our calculations,
with the energy cutoff equal to 520 eV. Three structures were
considered, as shown in Fig. 1(a) a “pure” (O-terminated)
interface, (b) an overoxidized interface (with O inserted at
the interfacial magnetic layer), and (c) an underoxidized
(Mg-terminated) interface. The relaxed structures have been
reported in our previous work.
31
We point out that the situation
of a “pure” interface is the most stable one, as observed
in annealing experiments.
28,29
The most stable location for
the oxygen atoms is on top of metal ions due to the strong
overlap between Fe-3d and O-2p orbitals. Correlatively, it
is interesting t o note that this structural configuration also
yields the spin filtering phenomenon based on Bloch state
(a)
(b)
(c)
FIG. 1. (Color online) Schematics of the calculated crystalline
structures for (a) pure, (b) overoxidized, and (c) underoxidized
geometries. Fe, Mg, and O are represented by blue, green, and red
balls, respectively.
FIG. 2. (Color online) Angular dependence of the magnetic
energy, where θ is the angle between the magnetization direction
and the normal to the interface plane.
symmetry leading to high TMR values.
39,40
Furthermore, the
strong hybridization significantly modifies the band structure,
giving rise to a high interfacial crystal field.
19
III. RESULTS AND DISCUSSION
In Fig. 2, we present the calculated energy per unit cell as
a function of the angle θ between magnetization orientation
and normal to the plane for the pure unrelaxed Fe|MgO
interface. The dependence is well fitted by the conventional
uniaxial anisotropy expression E
A
= K
0
+ K
2
sin
2
θ, where
K
2
= 0.7meV/atom ( K
2
= 1.36 erg/cm
2
). Interestingly, the
perpendicular surface anisotropy in this case is stronger than
that of Co|Pt,
24,25
in agreement with recent experiments.
32
The
calculated anisotropy value is further enhanced for relaxed
structures as reported in Table I, reaching the very l arge
value of almost 3 erg/cm
2
for the structure with three MgO
monolayers shown in Fig. 1(a). It is interesting to note that
the PMA is not strongly affected when the MgO thickness is
increased up to 11 monolayers, giving the calculated value
of 3.15 erg/cm
2
, which provides a good agreement with
recent experiments.
41
The PMA for relaxed Fe|MgO s tructures
weakens in the presence of interfacial disorder and becomes
equal to 2.27 and 0.93 erg/cm
2
for under- and overoxidized
cases, respectively (see Table I), indicating that the oxidation
TABLE I. PMA value (erg/cm
2
) and magnetic moment m [μ
B
per Fe(Co) atom] for different layers of Fe(Co) in Fe(Co)|MgO
magnetic tunnel junctions under different oxidation conditions.
Fe|MgO Co|MgO:
Pure Underoxidized Overoxidized pure
PMA 2.93 2.27 0.98 0.38
m (μ
B
)
Interfacial 2.73 2.14 3.33 1.67
Sublayer 2.54 2.41 2.70 1.84
Bulk 2.56 2.55 2.61 1.60
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FIRST-PRINCIPLES INVESTIGATION OF THE VERY ... PHYSICAL REVIEW B 84, 054401 (2011)
conditions play a critical role in PMA as they do for both
TMR
30
and interlayer exchange coupling.
31
Upon replacing
Fe with Co, the PMA value decreases down to 0.38 erg/cm
2
,
which agrees with report by Yakata et al. that Fe-rich FeCoB
top free layers in Co
60
Fe
20
B
20
|MgO| (Co
x
Fe
1−x
)
80
B
20
MTJs
exhibit larger PMA than their Co-rich counterparts.
35
Further-
more, the tendency for PMA to decrease with oxygen excess
or deficit along the metal/oxide interface is consistent with the
experimental observations of PMA dependence on annealing
temperature and oxidation conditions.
10,34
It was reported
that at higher annealing temperatures, PMA increases due to
interfacial quality improvement.
10
Furthermore, upon varying
the oxidation or annealing conditions, it was observed that the
PMA reaches a maximum value for the same conditions under
which the TMR ratio is also maximized, indicating that ideal
interfaces are also crucial for PMA observation.
34
In Table I we also report the evolution of interfacial Fe
magnetic atomic moments as a function of distance from the
interface. One can see that, compared to the pure case, the
moments are enhanced or weakened for over- or underoxidized
interfaces, respectively.
Let us now proceed with the explanation of the
physical origin of the results obtained from first principles on
the effect of oxidation conditions on PMA. To understand the
PMA origin at Fe|MgO interfaces, we performed a detailed
analysis of the impact of SOI on electronic bands with
out-of-plane (d
z
2
, d
xz
, d
yz
) and in-plane (d
x
2
−y
2
, d
xy
) Fe-3d
and O-p
z
orbital character.
We start from the analysis for pure interfaces represented
in Fig. 1(a).InFig.3, we show bands around the Fermi
FIG. 3. (Color online) Spin-orbit coupling effects on wave func-
tion character at the
¯
point of interfacial Fe d and neighbor oxygen p
z
orbitals for the pure Fe|MgO interface shown in Fig. 1(a). The three
subcolumns in each column show the band levels for out-of-plane
(left) and in-plane (right) orientations of magnetization as well as for
the case with no spin-orbit interaction included (middle). Numbers are
the percentage of orbital character components within Wigner-Seitz
spheres around interfacial atoms.
level E
F
at the
¯
point with the orbital and interfacial
atom projected wave function character for out-of-plane (left
subcolumns) and in-plane (right subcolumns) orientation of
the magnetization as well as in the absence of spin-orbit
coupling (middle subcolumns). Let us concentrate on band
levels in the immediate vicinity of the Fermi level. When no
SOI is included (middle subcolumns), there are several double-
degenerated band levels with d
xz
and d
yz
character, which
represent the minority Bloch states with
5
(p
x
,p
y
,d
xz
,d
yz
)
symmetry. At the same time, there is a band level resulting
from hybridization between Fe-d
z
2
and O-p
z
orbitals, which
is a signature of the majority Bloch state with
1
(s,p
z
,d
z
2
)
symmetry for Fe and MgO which is at the heart of the
spin filtering phenomenon causing enhanced TMR values in
MgO-based MTJs.
39
When SOI is switched on, the picture
is strongly modified. First, one can clearly see that the
degeneracy is lifted for energy levels with a d
xz,yz
orbital
character. Second, these levels become hybridized with Fe d
z
2
,
resulting in the appearance of additional levels of both d
z
2
and
d
xz,yz
orbital character, represented by numbers showing the
percentage of the corresponding orbital character components
within Wigner-Seitz spheres (see Fig. 3). In particular, for
the out-of-plane magnetization orientation (left subcolumns),
the additional d
z
2
levels, with 5%, 2%, and 44%, originate
from the d
xz,yz
orbital character due to SOI. For the same
reason, the additional d
xz,yz
band, with 8%, comes from the
d
z
2
orbital. Furthermore, since the Fe-d
z
2
orbital has already
been hybridized with O-p
z
being a part of the
1
Bloch
state, additional energy levels with O-p
z
character also appear
when SOI is switched on. This entire mechanism can be
seen as spin-orbit-induced mixing between majority
1
and
minority
5
Bloch states, which, by the way, may affect the
amplitude of predicted high TMR ratios in MTJs.
42
Finally,
the hybridized band levels with d
z
2
, d
xz
, d
yz
, and p
z
character
are lower in energy, with a larger splitting for an out-of-plane
magnetization orientation compared to the in-plane one, as
clearly shown in the left and right subcolumns in Fig. 3,
respectively. Thus, the lift of degeneracy of d
xz
and d
yz
orbitals, combined with the hybridizations between Fe-d
xz,yz
and d
z
2
, as well as the hybridization between Fe-d
z
2
and O- p
z
orbitals, is at the origin of PMA for pure Fe|MgO interfaces.
This result shows that the out-of-plane components of d
xz,yz
orbitals play a crucial role for PMA, similarly to Co|Pd
interfaces.
43
Next, we proceed with the same analysis for under- and
overoxidized Fe|MgO interfaces represented in Figs. 1(b) and
1(c), respectively. As shown in Fig. 4 for the case with an
additional oxygen located at the Fe|MgO interface [Fig. 1(b)],
spin orbit coupling again lifts the degeneracy for states with
d
xz,yz
, causing stronger splitting and a deeper level position
for the out-of-plane orientation of magnetization compared to
the in-plane one. However, the number of mixed states with
both Fe-d
z
2
and O-p
z
orbitals is reduced due to the local charge
redistribution induced by additional oxygen atoms.
30
Since d
z
2
and p
z
orbital hybridization, which is one of the main causes
of PMA, is not split, the anisotropy is significantly reduced.
A different picture occurs in the case of the underoxidized
Fe|MgO interface represented in Fig. 1(c). As shown in Fig. 5,
the Fe-d
z
2
and O-p
z
components around the Fermi level are
now absent. As a result, the degeneracy lift induced by SOI
054401-3
YANG, CHSHIEV, DIENY, LEE, MANCHON, AND SHIN PHYSICAL REVIEW B 84, 054401 (2011)
FIG. 4. (Color online) The same as Fig. 3, for an overoxidized
Fe|MgO interface.
for states with d
xz,yz
character is now solely responsible for
the PMA. Since the splitting of these d
xz,yz
orbitals is still
relatively strong and higher for the out-of-plane magneti-
zation orientation compared to the in-plane one, anisotropy
values are higher compared to the overoxidized case but
lower compared to ideal Fe|MgO interfaces. Thus, the PMA
reaches its maximum for ideal interfaces. To understand the
correlation between PMA and TMR, in Fig. 6 we have
plotted the wave function character of the
1
Bloch state
as a function of the position across the supercells used for
PMA calculations. One can clearly see that the
1
decay
rate is strongly enhanced in the case of the overoxidized
FIG. 5. (Color online) The same as Fig. 3, for an underoxidized
Fe|MgO interface.
FIG. 6. (Color online)
1
Bloch state character at the point
around the Fermi level as a function of layer number in the pure
and overoxidized Fe|MgO interfaces shown in Figs. 1(a) and 1(b),
respectively. The
1
Bloch state is absent around the Fermi level in
the underoxidized case shown in Fig. 1(c).
interface compared to the ideal one.
44
There is no
1
band around the Fermi level for the underoxidized case as
demonstrated above. This explains why both PMA and TMR
reach their maximum values in a correlated way as observed
experimentally,
34
this maximum being reached for ideal
interfaces.
IV. CONCLUSION
In conclusion, we have presented ab initio studies of PMA
at Fe|MgO interfaces as a function of the oxygen content
along the interface. PMA values are higher in the case of pure
interfaces, in agreement with recent experimental studies,
32,34
and may reach up to 3 erg/cm
2
for relaxed interfaces. The
origin of the large PMA is ascribed to a combination of
several factors: the degeneracy lift of out-of-plane 3d orbitals,
hybridizations between
1
(d
z
2
) and
5
-like (d
xz
and d
yz
)3d
orbitals induced by SOI, and hybridizations between Fe-3d
and O-2p orbitals at the interface between the transition
metal and the insulator. The PMA amplitude decreases in
the case of over- or underoxidized interfaces, in agreement
with recent experiments .
10,34
This is due to the impact of
splitting(disappearance) of
1
-like hybridized states around
the Fermi level in the presence(absence) of an additional
oxygen atom. In addition, the PMA value is lower in the case of
aCo|MgO interface, which agrees with experimental findings
that Fe-rich Co
x
Fe
1−x
B|MgO structures have larger PMA than
their Co-rich counterparts.
35
ACKNOWLEDGMENTS
We thank L. Nistor, B. Rodmacq, A. Fert, H. Jaffres,
O. Mryasov, A. Schuhl, and W. H. Butler for fruitful dis-
cussions. This work was supported by the Chair of Excellence
Program of the Nanosciences Foundation in Grenoble, France,
the ERC Advanced Grant Hymagine, and the KRCF DRC
program.
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