Table Of ContentAsymmetric angular dependence of spin-transfer torques in CoFe/Mg-B-O/CoFe
magnetic tunnel junctions
Ling Tang,∗ Zhi-Jun Xu,† Xian-Jun Zuo, and Ze-Jin Yang‡
Department of Applied Physics, College of Science,
Zhejiang University of Technology, Hangzhou 310023, China
Qing-He Gao
6 College of Science, Northeastern University, Shenyang 110004, China
1 Information Engineering College, Liaoning University of Traditional Chinese Medicine, Shenyang 110847, China
0
2 Rong-Feng Linghu§
n School of Physics and Electronics Sciences, Guizhou Education University, Guiyang 550018, China
a
J Yun-Dong Guo¶
0 College of Engineering and Technology, Neijiang Normal University, Neijiang 641112, China
3 (Dated: February 2, 2016)
] Usingafirst-principlesnoncollinearwave-function-matchingmethod,westudiedthespin-transfer
l
l torques (STTs) in CoFe/Mg-B-O/CoFe(001) magnetic tunnel junctions (MTJs), where three dif-
a
ferent types of B-doped MgO in the spacer are considered, including B atoms replacing Mg atoms
h
(Mg3BO4), B atoms replacing O atoms (Mg4BO3), and B atoms occupying interstitial positions
-
s (Mg4BO4)in MgO.A strong asymmetric angulardependenceof STTcan beobtained bothin bal-
e listic CoFe/Mg3BO4 and CoFe/Mg4BO4 based MTJs, whereas a nearly symmetric STT curve is
m observed in the junctions based on CoFe/Mg4BO3. Furthermore, the asymmetry of the angular
. dependenceofSTTcanbesuppressedsignificantlybythedisorderofBdistribution. Suchskewness
t
a of STTs in the CoFe/Mg-B-O/CoFe MTJs could be attributed to the interfacial resonance states
m inducedbytheBdiffusion intoMgO spacer. The presentinvestigation demonstratesthefeasibility
of effectively enhancing microwave output power in MgO based spin torque oscillator (STO) by
-
d dopingthe B atoms into MgO spacer.
n
PACSnumbers:
o
c
[
I. INTRODUCTION Fe/MgO/Fe MTJ with only 3 layers of MgO as spacer,
2 according to the calculated results of strong asymmetric
v
angular dependence of STTs. However, the situation in
6 The current-induced spin-transfer torque (STT) can
CoFeB/MgO MTJs, which is widely employed as STO
8 be used to drive a steady magnetization precession,1–3
devices,ismorecomplicatedthanthatinFe/MgOMTJs
2
whichhasattractedmuchattentionforapplicationssuch
7 asnanometer-sizedspintorqueoscillator(STO),4,5where due to the introductionofB atoms. Therefore,the ques-
0 tion about what kind of influence on the angular depen-
a microwave signal with tunable frequency and narrow
. dence of STT by introducing B atoms into CoFe/MgO
1 linewidthcanbegeneratedbyadirectcurrent(DC).Re-
0 centlyIkedaet al. 6 foundthatthe CoFeB/MgO/CoFeB and whether the introduction of B is beneficial to pro-
6 duce high power of microwave emission are still unclear
magnetic tunnel junctions (MTJs) with interfacial per-
1 yet.
pendicular magnetic anisotropy (PMA) is a excellent
:
v candidate for STO devices. Inspired by this develop-
In addition, some experimental results indicate that
i
X ment, the STT induced microwave oscillator based on the amorphous CoFeB electrodes near the interface in
CoFeB/MgOMTJs,inwhichtheBatomsareintroduced
r CoFeB/MgOMTJscrystallizedintoorderedbodycenter
a during the fabrication of junctions, have been inves- cubic (bcc) CoFe crystal after annealing process. 15–18
tigated intensively by several experimental researchers.
Meanwhile, the B atoms are pushed out of the CoFeB
7–10
electrodesandthendiffusedintotheMgOlayersforming
However,generatingahighemissionpowerinSTOde- Mg-B-Ospacer.19–23 However,theexactdistributionand
viceswithoutexternalmagneticfieldstillremainsagreat position of B atoms in Mg-B-O spacer are still unclear
challenge so far. Rippard et al. 11 pointed out that the up to now. Thus several possible structures of B-doped
output power of STO is closely related to the angular Mg-B-O spacer have been proposed and investigated.
dependence of STT, namely the larger asymmetry pa- Stewart24 suggestedthatthe B atomsdiffusedinto MgO
rameter Λ,12,13 which is proportional to the skewness of layer forming kotoite Mg B O . Bai et al.25 studied
3 2 6
STT, the higher output power of STO devices will be thetransportpropertiesofCoFe/kotoite/CoFeMTJand
achieved. Based on such conclusion of STT induced os- concludedthatthesymmetryreductionisresponsiblefor
cillation, Jia et al.14 predicted a large emission power in the lower tunneling magnetoresistance (TMR). In ad-
2
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Calculation
103 Experiment, Ref. 33
Experiment, Ref. 34
) 2
2 m 10
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0
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-1
10
#:%6()*+0 !4,"4#5 %0 !"#$ %0 !4,"4#5 %0()*+ 3 4 5 6 7 8 9
’ !4,"4#5 % ’ ./0123/+ Thickness of MgO (Layer)
FIG. 2: (color online). The MgO thickness dependence of
resistance-area (RA) in CoFe/MgO/CoFe(001) MTJs. The
9
black squares are ourcalculated results of ballistic junctions.
& TheredandgreentrianglesareexperimentalvaluesfromRef.
3 -
() *+ ! " , 3B9B;<5A>6/? 33 and 34, respectively.
FIG.1: (coloronline). Theatomicstructuresofsupercellsfor
threeprototypesofCoFe/Mg-B-O/CoFe(001)MTJs. Herewe II. COMPUTATIONAL METHOD
consider three types of dopant in spacer: (a) B substituting
for Mg (Mg3BO4), (b) B substituting for O (Mg4BO3), and
(c) B occupying the interstitial position (Mg4BO4) in MgO, The stuttgart tight-binding linearized muffin-tin-
respectively. The views of Mg-B-O spacer along the trans- orbital atomic sphere approximation (TB-LMTO-ASA)
port direction (z axis) are also displayed on the right of fig- program31 is used to obtain the effective single-electron
ure. The3layers (3L) undopedMgO in themiddleof spacer potential of CoFe/Mg-B-O/CoFe(001) MTJs. A super-
is introduced to avoid the possible coupling between two fer- cell including 11 monolayers (MLs) of ordered bcc CoFe
romagnetic electrodes which might be intermediated by the
and a spacer partially filled with B-doped MgO is used
magnetic B atoms.
forsuchself-consistentcalculation. Toinvestigatethein-
fluence of B diffusion, three types of B-doped MgO are
considered, where B atoms substitute for Mg, O atoms
and occupy the interstitial position of MgO. The corre-
spondingformulasofthreeB-dopedMgOcanbe written
dition, the electronic structures of bulk B-doped MgO
with different configurations have been studied26,27 but as Mg3BO4, Mg4BO3 and Mg4BO4, respectively, where
the dopant concentration is 25%.
the properties of STTs in corresponding CoFe/Mg-B-O
basedMTJsarestillunknownyet. Sothepurposeofthis Fig. 1 shows the atomic structures of supercells for
paper is to investigate which configuration of CoFe/Mg- threeprototypesofCoFe/Mg-B-O/CoFe(001)MTJscon-
B-O is most efficient for high microwave output power sideredin ourcalculations,where the B-dopedMgOlay-
from the viewpoint of the STT. ers locate at the interfacial region near the electrodes
andtheundopedMgOlayersareinthemiddleofspacer.
In this work, we calculate the STT of CoFe/Mg- Here the introduction of middle undoped MgO layers
B-O/CoFe(001) MTJs by noncollinear scattering wave- is in order to decouple the possible interaction between
function matching method in combination with first- pinnedlayer(therightCoFelead)andfreelayer(the left
principles calculations.28–30 Here the B atoms are as- CoFe lead) in CoFe/Mg-B-O/CoFe MTJs. Such interac-
sumed to diffuse into the MgO layers forming Mg-B-O tionmightbe intermediatedby the magnetic B atoms in
spacer and three possible types of B-doped (25%) MgO B-doped MgO [see shaded part in Fig. 3(b) for details].
are considered, i.e., (1) B replacing Mg (Mg BO ), (2) Moreover,theCoFeleadwithorderedbccphaseandCo-
3 4
B replacing O (Mg BO ), and (3) B occupying the in- terminalinterfaceareusedinourcalculations,wherethe
4 3
terstitial position (Mg BO ) in MgO, respectively. Our Co-O distance at the interface is 2.16 ˚A.32 The in-plane
4 4
calculated results show that a significantly asymmetric lattice constant of supercell is a = b = 5.68 ˚A, whereas
angular dependence of STT could be obtained in ballis- the distance between adjacent Co and Fe layer is equal
ticCoFe/Mg BO andCoFe/Mg BO basedMTJs,both to that of bulk CoFe (1.42 ˚A). The crystal lattice of B-
3 4 4 4
ofwhichareable to resultinthe largemicrowaveoutput doped MgO as well as undoped MgO can be matched
power. with CoFe lead in (001) direction by rotating 45 degree
3
(a) CoFe-MgO(9L)-CoFe
23 (a) Mg3BO4 eV)b 4 Ty
ell) ---32101 -9 T (10 --0242 CoFe MgO Tx CoFe
DOS (states/eV/c ---3210123 (b) Mg4BO3 -3 T (10eV)b-0000....1012(bC) oCFoeFe-MgO(3L)-CoFeMg O CoFe
23 (c) Mg4BO4 -0.2
01 V)b (c) CoFe-Mg3BO4(3L)-MgO( 3L)-Mg3BO4(3L)-CoFe
--21 -3 0e 0.1
-3 T (1 0.0
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 -0.1 CoFe Mg3BO4 MgO Mg3BO4 CoFe
Energy (eV)
V)b (d) CoFe-Mg4BO3(3L)-MgO( 3L)-Mg4BO3(3L)-CoFe
FIG. 3: (color online). The total DOS (solid) for bulk (a) e 2
Mg3BO4, (b) Mg4BO3, and (c) Mg4BO4, respectively. It -3 0 1
showsthatallthreebulkB-dopedMgOcrystalsexhibitmetal- T (1 -01
lic state. The projected DOS (shaded) on impurity B atoms -2 CoFe Mg4BO3 MgO Mg4BO3 CoFe
arealsoplottedin(a)-(c),whichindicatesthatatFermilevel
thecouplingbetweenBandthehostMgOismuchweakerfor (e) CoFe-Mg4BO4(5L)-MgO( 3L)-Mg4BO4(5L)-CoFe
Mg4BO3 than that for theother twotypesof B-dopedMgO. V)b 4
-3 0e 02
1
around (001) axis and compressing lattice slightly. T ( --42 CoFe Mg4BO4 MgO Mg4BO4 CoFe
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8
With the rigid potential approximation, the STT
can be calculated by the noncollinear scattering wave- Position (nm)
functioninTB-LMTO-ASAbasis,wheretheeffectivepo-
FIG.4: (color online). Thelayerresolved in-planeSTTs (Tx
tentials for each atomic spheres are rotated by different
anglesrelativetoglobalquantizationaxisinspinspace.28 and Ty) of MTJs at unit bias with and without B diffusion
fortherelativeangleof90degreebetweentwoleads. Itshows
In addition, those angles are according to the direction thatthetorquesmainly distributearoundtheCoFe/Mg-B-O
of magnetization on each atomic spheres. In the present interfaceexceptforthecaseofCoFe/Mg4BO3basedMTJ.As
CoFe/Mg-B-O/CoFeMTJs,the directionsof magnetiza- showninfigure(d),theSTTsexertalmosttotallyonBatoms
tionfortherightCoFeleadandmagneticBatomsatthe close to MgO/Mg4BO3 interface, which could be attributed
right side of spacer are all align with y axis. For the left to the large magnetic moments and the evanescent states on
CoFeleadandmagneticBatomsattheleftsideofspacer, ferromagnetic impurity B atoms.
themagnetizationsarerotatedthesamerelativeangleto
y axis within x-y plane (in-plane). So the transport di-
rection is along the z axis (out-of-plane). In addition, a the experimental value33 of 3.01 Ωµm2.
240×240 k-point mesh is used in full two-dimensional
(2D) Brillouin zone (BZ) to evaluate the in-plane STTs
(T and T ). The out-of-plane torque (T ) is excluded III. RESULTS AND DISCUSSION
x y z
inthis workdue to it needs morek points to ensurecon-
vergence, which is beyond our computational capability. Firstly, the density of state (DOS) for three types of
In order to compare the present transport calcula- bulk B-doped (25%) MgO crystals are calculated. Un-
tion with experiment, the resistance-area (RA) prod- like the initial undoped MgO, all of the three B-doped
ucts in ballistic undoped CoFe/MgO/CoFe(001) MTJs MgO crystals exhibit metallic state, as shown in Fig. 3.
are evaluated in this work. Fig. 2 demonstrates the cal- ThepresentcalculationsalsoshowthatthebulkMg BO
3 4
culated RA dependence on the thickness of MgO spacer. is paramagnetic. Meanwhile, the B atoms in Mg BO
4 3
The measuredRAvaluesfromexperiments33,34 (redand have large nonzero magnetic moments (∼ 2.0µ ), con-
B
green triangles) are also plotted in Fig. 2. The present sistingwiththepreviousfirst-principlescalculations.26,35
calculations show that the RA product decreases expo- The magnetic moment of B in Mg BO is relative small
4 4
nentially with reducing the thickness of MgO spacer. (∼ 0.15µ ) in comparison with that of ordered CoFe
B
Moreover,forMTJwith5 MgOlayers(∼ 1nmthick)as lead (µ ∼1.7µ , µ ∼2.7µ ). Moreover, the shaded
Co B Fe B
spacer the calculated RA is 4.44 Ωµm2 that is close to parts in Fig. 3 display the projectedDOS onimpurity B
4
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! " # $% $& $’ ’ $ ( &" &) &% ’ $ ( &" &) &% ’ $ ( &" &) &%
()%*+# ,+%" 56)78%38)’ 56)7&%8&)’ 56&78%98&’
FIG. 5: (color online). The angular dependence of total in-plane STTs in CoFe/MgO and CoFe/Mg-B-O based MTJs
with different spacers labeled in the titles of the figures. The red solid lines are the fitted Slonczewski’s formulas with
asymmetry parameter Λ. As shown in figure (c) and (g), a strong asymmetry of angular dependence of STT is obtained
in CoFe/Mg3BO4(3L)/MgO(3L)/Mg3BO4(3L)/CoFe and CoFe/Mg4BO4(5L)/MgO(3L)/Mg4BO4(5L)/CoFe junctions respec-
tively. Such asymmetry of STTs could be attributed to the existence of interfacial resonance states induced by B atoms in
Mg-B-O spacer.
atoms. Clearly,a significantcoupling between the impu- on all atoms (including magnetic B atoms) at the right
rityBandMgOatomsatFermilevelappearsinMg BO half of MTJ.
3 4
and Mg BO , whereas such coupling is much smaller in
4 4 Fig. 5 gives the angular resolved total in-plane STTs
Mg BO . As a result, this difference of projected DOS
4 3 for CoFe/MgOandCoFe/Mg-B-ObasedMTJs with dif-
should be responsible for the different STT characters
ferent spacers. The highly asymmetric anglular depen-
among the three types of CoFe/Mg-B-O/CoFeMTJs.
dence of STTs in CoFe/Mg BO and CoFe/Mg BO
3 4 4 4
based MTJs are clearly shown in Fig. 5(c) and
Fig. 4 presents the calculated layer resolved in-plane
(g). Their corresponding atomic structures are pre-
STTs of MTJs atunit bias with [Fig.4(c)-(e)] andwith-
sented in Fig. 1(a) and (c) respectively. Further-
out [Fig. 4(a) and (b)] B diffusion for the relative an-
more, the respective fitted Slonczewski parameters are
gle of 90 degree between two leads. Here the calcula-
Λ(CoFe/Mg BO ) ≈ 3.6 and Λ(CoFe/Mg BO ) ≈ 4.2,
tions show that the torques emerge mainly on Co or Fe 3 4 4 4
which suggests that the doping of B into MgO spacer
atoms near the CoFe/Mg-B-O interface, similar to the
first-principlescalculationsinFe/MgOsystem.14,36How- of CoFe/MgO MTJs may be benefit to improve out-
put power of high-frequency generation. Meanwhile,
ever,inCoFe/Mg BO basedMTJtheSTTsonBatoms
4 3
as shown in Fig. 5(f), the angular dependence of STT
whichisclosetoMgO/Mg BO interfacearemuchlarger
4 3
is a symmetric sine function for the CoFe/Mg BO
than that on Co or Fe atoms [see Fig. 4(d)]. This be- 4 3
based MTJ whose structure is shown in Fig. 1(b).
havior is partially due to the large magnetic moments
on those B atoms (∼2.0µ ) and the metallic state of B- This STT curve is similar with the case of undoped
B CoFe/MgO/CoFe MTJ with 9 layers (9L) MgO [see
dopedMgO,whichmaketheB-dopedMgOlayerbecome
Fig. 5(b)], which indicates that the B atoms substitut-
a interfacialpart of ferromagnetic electrodes of MTJ. So
ing O atoms in MgO spacer is not an effective way to
thespincurrentwillbeabsorbedinthisregionleadingto
get skewed STT. In addition, the previous study on for-
angular momentum transfer torques. Furthermore, the
mation energy27 observe that the B atom is favored to
evanescent state in ferromagnetic impurity B could also
occupy the position of Mg atom in MgO, namely, the
contributeto the STT,whichis responsibleforthe rapid
MTJ based on CoFe/Mg BO should be the most likely
vanishing of the torque awayfromB atoms. Inaddition, 3 4
formed. Therefore, we demonstrate that the asymme-
when the bias is applied on CoFe/Mg BO based MTJ,
4 3
try parameter Λ, which dominates the output power of
althoughthetorquesexertalmosttotallyonBatoms,the
high-frequency generation, could be increased after B
magnetizationofCoFeleadcouldstillbeswitchedbycur-
moving into MgO spacer in the fabrication procedure of
rent owing to the possible exchange interaction between
CoFe/Mg-B-O/CoFeMTJ.
B and CoFe lead. Therefore, the total in-plane STT cal-
culatedinthisworkmeansthesumofthein-planeSTTs TounderstandtheangularasymmetryofSTT,wealso
5
(a) parallel config uration (majority) (b) parallel configuration (minority)
1.0 1.1 CoFe-Mg3BO4(3L)-MgO(3L)-Mg3BO4(3L)-CoFe
0.9 1.0 1.2
0.7 0.9 CoFe-Mg4BO4(5L)-MgO(3L)-Mg4BO4(5L)-CoFe
0.6 0.7 1.0 =1.4
0.5 0.6
0.4 0.4
0.2 0.3 0.8
x
0.1 0.1 Ma
0 0 T 0.6
/
(c) anti-parallel configuration (majority)(d) total in-plan e STT for single k|| state T
point 0.4
1.2
0.28 resonant point
0.25 1.0
resonant point 0.21 0.8 0.2 B atoms distribute randomly in
00..1148 0.6 T/TMax 0.0 Mg3BO4(Mg4BO4) layers
0.11 0.4
0.07
0.04 0.2 0 30 60 9 0 120 150 180
0 0.0
0 30 60 90 120 150 180 Angle (deg)
Angle (deg)
FIG. 6: (color online). kk dependence of transmit- FIG. 7: (color online). The angular dependence of total in-
tance for (a) majority, (b) minority of parallel configu- planeSTTsfordisorderedCoFe/Mg3BO4andCoFe/Mg4BO4
ration, and (c) majority of anti-parallel configuration for basedMTJswithBatomsdistributingrandomlyinMg3BO4
CoFe/Mg3BO4(3L)/MgO(3L)/Mg3BO4(3L)/CoFe junction. and Mg4BO4 layers respectively. The green solid lines is
Figure (d) presents the angular dependence of STTs for Γ the fitted Slonczewski’s formula with asymmetry parameter
and one of theresonant point highlighted byan arrow in fig- Λ = 1.4. The results indicate that the disorder of B atoms
ure (c). The angular dependence of STT is very skewed for distribution could effectively restore the angular dependence
this resonant kk state, as shown in figure (d). of STT to symmetric sine function.
calculate the STT of CoFe/MgO(3L)/CoFe MTJ with 3 duetothe effectivebarrierthicknessisfailedtodecouple
layers MgO spacer, as shown in Fig. 5(a). Obviously, its the interfacial states here.
STT curve is highly asymmetric, similar to the results To reveal interfacial resonances in
ofFe/MgO(3L)/Fe MTJ.14 So far, it is believedthat the more detail, in Fig. 6(a)-(c) we present
asymmetriccharacterofSTTinFe/MgOMTJswiththin the k dependence of transmittance for
k
barrierareoriginatedfromthemultiplescatteringcaused CoFe/Mg BO (3L)/MgO(3L)/Mg BO (3L)/CoFe
3 4 3 4
by the interfacial resonance states. Considering the B- with parallel (P) and anti-parallel (AP) magnetic
dopedMgO layersin spacerbehaveas conductivemetal, configuration. It can be seen clearly that the hot-spots
theeffectivetunnelingbarrierthicknessinCoFe/Mg-B-O of conductance owing to interfacial resonance states
MTJs are therefore decreased in comparison to the case appear within 2D BZ for both P and AP configuration.
of undoped CoFe/MgO MTJs. As a result, the interfa- Moreover, the results show that the k states with
k
cial states at Mg3BO4(Mg4BO3, Mg4BO4)/MgO inter- resonant tunneling for majority and minority of P
face can resonate once the effective barrier thickness is configurationare nearly in the same positions within 2D
small enough. BZ. Meanwhile, the resonant points of AP configuration
As we well know, the interfacial resonance state can are also contributed almost by these k states. Here
k
be exponentially suppressed when the barrier thick- we find that the angular dependence of STT is quite
ness is increasing. In the MTJs with the structures different between the resonant state and non-resonant
shown in Fig. 1(a)-(c), the barrier thickness is de- state. Take Fig. 6(d) as an example, it gives the angular
termined by the number of layers of middle undoped dependence of STT for one of this resonant tunneling
MgO. Therefore we further calculated the STTs of k states which is highlighted by an arrow in Fig. 6(c).
k
CoFe/Mg BO (3L)/MgO(5L)/Mg BO (3L)/CoFe junc- Such angular dependence of STT is very skewed for
3 4 3 4
tion which has 5 layers of undoped MgO in the mid- this resonant tunneling state, as shown in Fig. 6(d).
dle of spacer. As shown in Fig. 5(d), the obtained an- On the other hand, to compare the case of resonant
gular dependence of STT recovers to a symmetric sine state, we calculate the STT of Γ point also plotted in
function, consisting with the fact of exponentially sup- Fig.6(d)andfoundthattheSTTcurveissymmetricsine
pressed behavior. Similarly, when we insert 5 layers of function. Because the interface transparency dominates
undoped MgO in the middle of CoFe/Mg BO based the magnitude of STT,37 the resonant point within 2D
4 4
MTJ,theangulardependenceofSTTforsuchjunctionof BZ contributes mainly to the torque of MTJ due to
CoFe/Mg BO (5L)/MgO(5L)/Mg BO (5L)/CoFe also its large conductance. As a result, the very skew STT
4 4 4 4
becomesmoresymmetric[seeFig.5(h)]despitetheasym- curve could be obtained when the significant interfacial
metry parameteris stilllargerthan1(Λ≈1.7),whichis resonance emerges in MTJ.
6
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34%51 *61%, %&’() *+)’, 01!2&’#3&!%
FIG.8: (coloronline). Theangulardependenceoftotalin-planeSTTsforseveralconfigurationsofCoFe/Mg3BO4 basedMTJs,
whose atomic structures are plotted in the insets. The red solid lines are the fitted Slonczewski’s formulas with asymmetry
parameter Λ. As shown in figure (a)-(c), the angular dependent of STTs are still highly asymmetric for the MTJs with B
atoms diffusion intotheentireregion of spacer. Duetothenatureof metallic state at Fermilevelin Mg3BO4 spacer, thehigh
spin polarization of CoFe lead is responsible for the skewness of STT, similar with the case of spin valve with half-metallic
ferromagnetic electrodes.
However,unlikethecaseofCoFe/Mg BO basedMTJ, is plotted in Fig. 1(b) and calculate the STT of
3 4
the angular dependence of STT of CoFe/Mg BO based CoFe/Mg BO (3L)/MgO(2L)/Mg BO (3L)/CoFe junc-
4 3 4 3 4 3
MTJ whose structure is shown in Fig. 1(b) is still sym- tion, which has only 2 layers undoped MgO in the mid-
metric, as shown in Fig. 5(f). Here we argue that the dle of spacer. Note that this kind of MTJ is no longer
interfacial resonance is greatly weaker in CoFe/Mg BO a symmetric junction, i.e., the interface between right
4 3
based MTJ than that in CoFe/Mg BO based MTJ, al- lead and spacer is Co-Mg instead of Co-O. As expected,
3 4
though both MTJs all have 3 layers undoped MgO in the STT curve indeed starts to become skew at the
the middle of spacer. For the MTJs with the struc- case of only 2 layers middle undoped MgO, as shown
tures plotted in Fig. 1(a) and (b), the interfacial reso- in Fig. 5(e). Hence, the present results suggest that
nance states mainly come from the states on B atoms at the resonance behavior of interfacial states also occur in
the MgO/Mg BO or MgO/Mg BO interface. There- the CoFe/Mg BO based MTJ, although it is relatively
3 4 4 3 4 3
fore, the strength of corresponding interfacial resonance weaker than that of CoFe/Mg BO based MTJ.
3 4
is proportional generally to the coupling between such Moreover, the calculated TMR ratio also reflects the
interfacial B atoms and the undoped MgO layers in the existence of interfacial resonance states in CoFe/Mg-B-
middleofspacer. Furthermore,fromFig.3(a)-(c)onecan O MTJs. As presented in Fig. 5, the B atoms diffusion
infer that at Fermi level the orbital admixture between into the MgO spacer will decrease TMR ratio compared
the B and MgO is relative weaker for Mg4BO3 crystal. to the case of undoped CoFe/MgO MTJs. In addition,
Therefore, the coupling between B atoms and the mid- withthethicknessofmiddleundopedMgOlayerincreas-
dle undoped MgO atoms in CoFe/Mg4BO3 based MTJ ing, the TMR ratio will recover to a larger value. Such
is certainly weaker. Accordingly, the corresponding in- behaviors of TMR ratio can be attributed to the reduc-
terfacialresonancewillbemuchmoredifficulttobebuilt tion of effective tunneling barrier thickness due to the
comparedtothecaseofCoFe/Mg3BO4basedMTJunder metallic proprieties of B-doped MgO layer. Therefore,
the same thickness of middle undoped MgO layers. when the barrier thickness is cut downto very thin (∼ 3
With the thickness of middle undoped MgO layers layers),theemergenceofinterfacialresonancewillreduce
decreasing, the interfacial resonance in CoFe/Mg BO the TMR ratio, similar to the case of Fe/MgO MTJ. 38
4 3
based MTJ can be restored. To confirm the exis- Next, we investigate how the random distribution of
tence of interfacial resonance state in CoFe/Mg BO B atoms influences the skewness of STTs in CoFe/Mg-
4 3
based MTJ, we will remove one layer of undoped B-O MTJs. Here we consider the CoFe/Mg BO and
3 4
MgO in the middle of the MTJ whose structure CoFe/Mg BO based MTJs with the structures shown
4 4
7
in Fig. 1(a) and (c) respectively. In order to simu- middleregionofspacerarealsoinvestigated. Asshownin
late the random distribution, the 3×3 lateral supercell Fig.8(f), the maximumvalue ofangulardependentSTT
without distortion is constructed. The B atoms ran- occurs around 90 degree corresponding to Slonczewski’s
domly substitute for Mg atoms in Mg BO layers of formula with Λ=1. This result shows that the STT be-
3 4
CoFe/Mg BO based MTJ. Likewise, the B atoms also havior originated from interfacial resonance states is ab-
3 4
randomly occupy the interstitial positions in Mg BO sentinthedopantformofBatomslocatingatthemiddle
4 4
layersofCoFe/Mg BO basedMTJ.Inthepresenttrans- regionofspacer. As shownin the insetofFig. 8(f), from
4 4
port calculations the frozen potential model is used, the structure ofthis kindofMTJone caninfer that here
namely the potential of disordered 3×3 lateral super- the middle B-doped MgO layers could’t couple the two
cell is constructed by randomly distributing the self- CoFe/MgO interfacial states and the distance between
consistent atomic sphere potential of B and Mg atoms twoCoFe/MgOinterfaceistoolargetosetupinterfacial
which are obtained from the case of ordered supercell. resonance efficiently. In other words, the B atoms resid-
In Fig. 7, the results show that the angular dependence ing in the region near CoFe lead is crucial to reduce the
STT of CoFe/Mg BO based MTJ recovers to symmet- distance between two interfacial states and obtain the
3 4
ric (Λ = 1) when B atoms distribute randomly. Simi- skew STT curve in such MTJ with 1.4 nm thick spacer.
larly,thedegreeofsymmetryforSTTcurveindisordered This conclusioncouldguildthe experimentalresearchers
CoFe/Mg BO basedMTJislargerthanthatinordered to tune the B atoms occupancy accurately and thus in-
4 4
MTJ, although it is still a skew curve with Λ ≈ 1.4. crease the experimental output power of STO.
According to the above results, the disorder of B atoms
distribution will destroy the interfacial resonance states,
which is the origin of asymmetric angular dependence of IV. SUMMARY
STT. Obviously, to improve the output power of STO
based on CoFe/Mg-B-O MTJs, the B atoms need to be In summary, the angular dependence of spin-transfer
crystallizedinto a orderedlattice in Mg-B-Ospacer dur- torques in different configurations of CoFe/Mg-B-
ing the preparation of junctions. O/CoFemagnetictunneljunctionsarestudiedbyafirst-
To date, it is known that the B atoms have diffused principles noncollinear wave-function-matching method.
into the MgO spacer but where and how these B atoms It is believed that the B atoms have diffused into MgO
exactly distribute are still unclear yet. Thus we further spacer after annealing process, and therefore three types
demonstrate the angular dependence STTs for several of B-doped (25%) MgO are considered here, (1) B sub-
different configurations of CoFe/Mg3BO4 based MTJs, stituting for Mg (Mg3BO4), (2) B substituting for O
in which the thickness of spacer is about 1.4 nm. (Mg BO ), and (c) B occupying an interstitial position
4 3
Firstly,theMTJswithBatomsdiffusionintotheentire (Mg BO ) in MgO. A strong asymmetric angular de-
4 4
region of spacer are considered. As shown in Fig. 8(a), pendence of STT with large asymmetry parameter Λ
for CoFe/Mg3BO4(7L)/CoFe we found that the STT is could be obtained both in ballistic CoFe/Mg3BO4 and
significantly asymmetric with Λ ≈ 2.2. When the thick- CoFe/Mg BO based MTJs respectively. However, the
4 4
ness of spacer is increasing, as shown in Fig. 8(b), the skewness of STT can be suppressed by the disorder of
angular dependence STT of CoFe/Mg3BO4(9L)/CoFe is B distribution in MgO spacer. Moreover, a relatively
stillasymmetric. Due to Mg3BO4 behavesas conductive symmetric angular dependence of STT is observed in
metal,thewholesystemthereforecouldbeviewedasthe CoFe/Mg BO based MTJ. These phenomenons could
4 3
metallic multilayersspin valve. Thus,similar to the case be attributed to the interfacial resonance states induced
of spin valve with half-metallic ferromagneticlead,37 the byBdiffusionintoMgOspacer. Ourcalculationsdemon-
high spin polarizationof CoFe leadis responsible for the stratethattheBatomsdiffusionintoMgOspacerinbal-
skewness of STT. In addition, this phenomenon is also listic CoFe/Mg-B-O/CoFeMTJs is beneficialto produce
found in CoFe/MgO(1L)/Mg3BO4(5L)/MgO(1L)/CoFe, high microwave output power in spin transfer oscillator.
in which the corresponding angular dependence of STT Acknowledgements The authors are grateful to
is very skew with Λ≈4.0, as shown in Fig. 8(c). Prof. Ke Xia, Dr. Shuai Wang, and Dr. Yuan Xu
Secondly, the CoFe/Mg3BO4 based MTJs with B for their preliminary works. We are also grateful to
atoms only diffusion into the edge of spacer near the left Dr. Anton Starikov for the TB-MTO code based upon
and right CoFe leads are considered. As expected, the sparse matrix techniques. This work is supported by
calculationsshowthattheangulardependenceofSTT is the Natural Science Foundation of China (Grant No:
asymmetric(Λ≈1.7)fortheMTJwith3layersundoped 11304279, 11364007), the Natural Science Foundation
middle MgO [see Fig. 8(d) for details]. Meanwhile, the of Zhejiang Province, China (Grant No: LY13A040004,
STT curve is symmetric for the MTJ with 5 layers un- LY16A040013),the China PostdoctoralScience Founda-
doped middle MgO [see also Fig. 8(e) for details], which tion(GrantNo. 2012M520666),theScienceandTechnol-
suggests that the interfacial states on Mg3BO4/MgO ogy Foundation from Ministry of Education of Liaoning
could’t efficiently resonate at such large distance (∼ 1 Province (Grant No: L2015333), and the Science and
nm). Technology Foundation from Guizhou Province (Grant
Finally, the MTJ with the B atoms distributing in the No: J [2013]2242).
8
∗ Electronic address: [email protected] Phys. Lett.95, 032506 (2009).
† Electronic address: [email protected] 20 Y. Lu, B. Lepine, G. Jezequel, S. Ababou, M. Alnot, J.
‡ Electronic address: [email protected] Lambert, A. Renard, M. Mullet, C. Deranlot, H. Jaffres,
§ Electronic address: [email protected] F. Petroff, and J.-M. George, J. Appl. Phys. 108, 043703
¶ Electronic address: [email protected] (2010).
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