Prospect for room temperature tunneling anisotropic magnetoresistance effect: density of states anisotropies in CoPt systems

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by  A. B. Shick

Prospect for room temperature tunneling anisotropic magnetoresistance effect:
density of states anisotropies in CoPt systems
A. B. Shick,1 F. Ma´ca,1 J. Maˇsek,1 and T. Jungwirth2,3
1Institute of Physics ASCR, Na Slovance 2, 182 21 Praha 8, Czech Republic
2Institute of Physics ASCR, Cukrovarnick´a 10, 162 53 Praha 6, Czech Republic
3School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, UK
6
0 Tunneling anisotropic magnetoresistance (TAMR) effect, discovered recently in (Ga,Mn)As fer-
0
romagnetic semiconductors, arises from spin-orbit coupling and reflects thedependenceof the tun-
2
neling density of states in a ferromagnetic layer on orientation of the magnetic moment. Based on

n abinitiorelativistic calculationsoftheanisotropyinthedensityofstateswepredictsizableTAMR
a effects in room-temperature metallic ferromagnets. This opens prospect for new spintronic devices
J with a simpler geometry as these do not require antiferromagnetically coupled contacts on either

4 side of the tunnel junction. We focus on several model systems ranging from simple hcp-Co to
more complex ferromagnetic structures with enhanced spin-orbit coupling, namely bulk and thin

] film L1 -CoPt ordered alloys and a monatomic-Co chain at a Pt surface step edge. Reliability of
0
i
c the predicted density of states anisotropies is confirmed by comparing quantitatively our ab initio
s results for the magnetocrystalline anisotropies in these systems with experimental data.
-
l
r PACSnumbers: 85.75.Mm,75.50.Cc
t
m
t. Theareaofcondensedmatterresearchthataimsatex- tween the TAMR in the tunneling nanoconstriction and
a
ploiting synergies of magnetic and semiconducting prop- normal anisotropic magnetoresistance in the ferromag-
m
erties in solid state systems has served as an important netic lead. Since the lattereffectalsooriginatesfromSO
- test bed for understanding basic physics and discovering couplingandhasbeenobservedinmanymetallicsystems
d
new applications in spintronics [1, 2]. The anomalous the work suggests that the TAMR has been overlooked
n
o Hall effect and the tunneling anisotropic magnetoresis- in conventional room temperature ferromagnets. To ex-
c tance (TAMR) studies are two examples of the research plore this possibility we follow a theoretical strategy ap-
[ that provided main motivation for the work presented plied previously to (Ga,Mn)As TAMR devices which is

1 here. The former study demonstrated [3, 4, 5, 6, 7] based on calculating tunneling density of states (DOS)
v that a successful theory of the anomalous Hall effect anisotropies in the ferromagnet with respect to the ori-
1 in (Ga,Mn)As ferromagnetic semiconductors, based on entation of the magnetic moment and which assumes a
7 spin-orbit (SO) coupling effects present in the band proportionalitybetween the DOS andtunneling conduc-
0 structure of Bloch states, can be directly applied to tance anisotropies.
1
conventional metallic ferromagnets such as Fe, and de- Thepaperisorganizedasfollows: Westartwithasim-
0
6 scribe quantitatively this fundamental transport coeffi- ple hcp-Co crystal as a bench mark material and then
0 cient. The TAMR effect [8] is an offspring of attempts addtothecomplexitiesofthestudiedstructuresinorder
/ to develop hybrid metal/semiconductor spin-valve de- to enhance SO coupling related effects. The next sys-
t
a vices which revealed that a spin-valve-like response can tem we explore is bulk L1 -CoPt alloy [11, 12]. Here Co
0
m be achieved without the seemingly fundamental switch- produces large exchange splitting resulting in the Curie
- ing sequence between parallel and antiparallel magneti- temperature of 750 K while the heavy elements of Pt
d zationsintwoferromagneticcontactswithdifferentcoer- substantially increase the strength of SO coupling in the
n
civities. Instead,asingleferromagneticmaterialwithSO band structure of the alloy. Effects of reduced dimen-
o
interaction is sufficient for realizing the sensing or mem- sionalityareexploredinathinL1 -CoPtfilmand,reach-
c 0
: ory functionality through TAMR whose phenomenology ing the ultimate nanoscale regime, in the monatomic-Co
v
isevenricherthanthatofconventionalgiantmagnetore- chain at Pt surface step edge [13, 14, 15]. An important
i
X sistance or tunneling magnetoresistance effects. For ex- part of the presented work is a simultaneous analysis of
r ample, both lower and higher resistance states can be magnetocrystallineanisotropiesinthestudiedstructures.
a obtained at saturation depending on the external mag- Giventhepredictivenatureofourtheoreticalconclusions
netic field orientation, i.e., the TAMR device can act as fortunnelingDOSanisotropies,calculationsofaphysical
asensoroftheabsolutedirectionoftheexternalfield[9]. quantity originating from the same SO coupled ab initio
The TAMR was discoveredin a (Ga,Mn)As/AlO /Au bandstructureanddirectlycomparabletoexistingexper-
x
stack [8] and confirmed by subsequent experiments in imentaldataisparticularlyvaluable. Magnetocrystalline
(Ga,Mn)As based vertical [9] and planar [10] tunnel de- anisotropies, and the derived magnetization reversals in
vices. Theformerexperimentunderlinedtheimportance external magnetic fields, are also important characteris-
of high quality interfaces and barrier materials for the tics that define functionality of a TAMR device.
magnitudeoftheeffect. Thelithographicallydefinedpla- We use the relativistic versionof the full-potential lin-
nar nanodevice allowed to demonstrate a direct link be- earizedaugmentedplane-wavemethod(FP-LAPW)[16],
2
in which SO coupling is included in a self-consistent isknowntohaveastrongMAEwiththeeasy-axisaligned
second-variational procedure [17]. The conventional perpendiculartoalternatingCoandPtmetallayers[11].
(von Barth-Hedin) local spin-density approximation is Thelargeanisotropyresultsfrombrokencubicsymmetry
adopted,whichisexpectedtobevalidforitinerantmetal- in this layered alloy and from the presence of heavy ele-
lic systems. The magnetic force theorem [18] is used to mentsofPt,asexplainedabove. Ourpreviousrelativistic
evaluatetheDOSanisotropyandthemagnetocrystalline FP-LAPWcalculations[12] yield the MAE of1.03 meV,
anisotropy energy (MAE): starting from self-consistent in a very good agreement with experimental data [11].
chargeandspindensitiescalculatedforthemagneticmo- DOS anisotropy calculations performed here follow the
ment M aligned along one of principal axes, the M samenumericalproceduresas inRef. [12]. Starting from
S S
is rotated and a single energy band calculation is per- self-consistent calculations for M aligned along the z-
S
formed for the new orientation of M . The DOS and [001]axis,we rotateM tothe x-[110]directionandcal-
S S
magnetocrystalline anisotropies result from SO coupling culate the corresponding DOS. 952 k-points in the irre-
induced changes in the band eigenvalues. Importantly, ducible part of BZ (3584 k-points in full BZ) are used
the same set of k-points has to be used for the integra- in these numerical simulations. As expected, both the
tion overthe Brillouinzone (BZ) for accurateevaluation N anisotropy of 1.8% and N anisotropy of 4.6% (see
I T
of the DOS anisotropy and of the MAE. Furthermore, Tab.1 andFig.1)inthis mixedcrystalaresubstantially
in order to increase the accuracy in DOS evaluation, the larger than their hcp-Co counterparts.
smoothFourierinterpolationschemeofPickettetal. [19]
is used together with linear tetrahedron method [20]. hcp-Co M~S kxaxis M~S kz axis
We start by investigating the possibility of TAMR in NI 1.999 2.004
elemental transitional metal ferromagnets. Bulk hcp- NT 6.780 6.696
Co is a theoretically well understood uniaxial ferromag- L10-CoPt-bulk M~S kxaxis M~S kz axis
net with the MAE of 60 µeV per unit cell and the NI 2.091 2.055
easy axis of magnetization along the z-[0001] crystallo- NT 10.709 11.205
graphic direction [21]. To evaluate the DOS anisotropy, L10-CoPt-film M~S kxaxis M~S kz axis
we first performed the self-consistent FP-LAPW calcu- NI 13.310 12.745
lation of the band structure of hcp-Co using experimen- N↑ + N↓ = Ntot N↑ + N↓ = Ntot
I I I I I I
tal lattice constant values and fixing MS along the z- Pt-Surface 0.489+0.485=0.974 0.385+0.480=0.865
[0001] axis. The DOS anisotropy is obtained by rotat- Co-subsurface 0.231+1.637=1.868 0.187+1.615=1.802
ing M from the z-[0001] axis to the in-plane x-[1000]
S
axis. 1200 k-points were used for the BZ integration. TABLEI:DOSinhcp-CoandL10 CoPt: TotalintegralDOS
TheintegralDOSsatthe FermienergyforMS alongthe NI (1/eV)andtunnelingDOSNT (eV(a.u.)2)DOSatEF for
x-[1000] axis, NI(x), and z-[0001] axis, NI(z), are given M~s k x and z axes. For L10-CoPt film we show also layer-
in Tab. 1. Corresponding DOS anisotropy defined as, and spin- projected DOS. The k-space convergence achieved
in the numerical calculations, using the smooth Fourier in-
|N (x)−N (z)|/min(N (x),N (z)) is plotted in Fig. 1
I I I I
(see black bars). The integralDOS anisotropy∼0.3% is terpolation scheme [19], gives error-bars < 1% for NI(x) in
relatively weak, similar to the weak magnetocrystalline hcp-Co,<2.5%forNT inhcp-Co,and<0.5%forNI(x)and
NT in L10 CoPt.
anisotropy, which is a result of a small value of SO
coupling in elemental 3d-metals. Assuming high crys-
So far we have demonstrated prospects of room tem-
talline quality of an hcp-Co based TAMR device with a
perature TAMR and confirmed expected trends in the
large degree of in-plane momentum conservation during
TAMR with increasing strength of SO coupling in well
the tunneling we can improve our estimate of the effect
understood conventional ferromagnets. In these bulk
by considering the tunneling DOS at the Fermi energy
systems, ab initio relativistic calculations are known to
[22], NT =1/ΩBZ RBZd3kvz2(EF)δ(E(~k)−EF), where provide accurate description of their properties, includ-
vz = ∂E(~k)/∂kz is the group velocity component along ing the subtle, SO coupling related magnetocrystalline
the tunneling z-direction and EF is the Fermi energy. anisotropy. The two model systems discussed in the fol-
The corresponding anisotropy (see blue bar in Fig. 1) is lowing paragraphs allow us to take a different view at
a factor of 4 larger than the anisotropy in NI which is the DOS anisotropy which might be more closely re-
a trend seen previously in the (Ga,Mn)As [8]. The 1.3 lated to the TAMR in real tunneling structures and, in
% anisotropy in NT suggests a measurable, albeit weak, the latter case, explores metallic TAMR in the ultimate
TAMR effect even with a simple hcp-Co. nanoscale limit. Ferromagnetic electrodes in magnetic
A natural recipe for enhancing the TAMR effect is by tunnel junctions are grown in thin films in which sur-
using ordered mixed crystals of magnetic 3d and non- faces/interfaces effects are known to play an important
magnetic5dtransitionmetals. Inthesesystemsthemag- role. To analyze these effects in our context we evalu-
netic atoms can produce large exchange fields polarizing ate DOS anisotropies of a free standing L1 -CoPt film
0
theneighboringheavyelementswithstrongSOcoupling. consisting of 5 Co and 6 Pt layers with the same inter-
Pt is particularly favorablebecause of its large magnetic layer distances as in the bulk. 400 k-points in the two-
susceptibility. HereweconsidertheL1 -CoPtalloywhich dimensional BZ were used in the numerical calculations.
0
3
The resulting N anisotropy of the film is more than a is modeled by 3 rows ofPt, one Co row,and two rowsof
I
factorof2largerthaninthebulkL1 -CoPt. Assuminga empty Pt sites. Vacuum was modeled by the equivalent
0
vacuumtunnelbarrierandrealizingthattunnelingtrans- of two empty Pt layers. All interatomic distances in the
port characteristics are dominated by properties of elec- y−z-plane were relaxed using scalar-relativistic atomic
tronic states near the barrier, we can use the calculated forces [24]. This represents an important improvement
DOSspatially resolvedto individuallayersto make are- over previous calculations [14, 15] which assumed values
fined estimate of the TAMR effect in the L1 -CoPt film. for pure Pt.
0
ThepartialDOScorrespondingtosurfacePtandsubsur-
faceComonolayersarelistedinTab1. Theanisotropyin
5
the DOSofthe surfacePtlayeris closeto13%. We note relaxed A−step
thattheMAEpertwo-dimensionalunitcellisaboutfac- eV) 4 relaxed B−step z
m
torof5 largerthanthe anisotropyper three-dimensional y ( 3 −x θ φ
g
unit cell in the bulk L10-CoPt. Recalling that our CoPt ner y
E 2
film has 5 Co and 6 Pt layersthe MAE in the two struc- y
p
o
tures are very similar. Since Curie temperatures in the otr 1
s
fitilhlamirn(afi∼nlmd7bL5u01l0kK-CL)o1tP0h-teCisomPaatggcnoaoentdicaclatsnuodnbindeealetxejupfneoccrttoeiodbnsteobrvabisneegdsitmohne- stalline ani −10 Step Edge Model
y
TAMR effect at room temperature. ocr −2
et
n
ag −3
M
−4
18 hcp - Co L1 - CoPt L1 - CoPt Co −90 −70 −50 −30 −10 10 30 50 70 90
0 0 φ (degrees)
16 bulk bulk film chain
%)14 FIG. 2: Monatomic-Co chain: MAE as a function of the
y (12 magnetization angle φ. Solid lines are fits to the numeri-
p
sotro10 c[3a.l53p0oin−ts [14..144754co−s2(2φ.8−012c8o◦s)2](φeV−(5B2◦-s)t]epeV) .(AL-setfetp)inasentd:
ni 8
a schematic crystal structure, used to represent the Co chain
OS 6 at thePt(111) surface B-step edge. Right inset: polar angles
D
4 φ and θ.
2
0 The self-consistent relativistic FP-LAPW calculations
were performed for magnetization aligned along the z-
FIG. 1: Bulk systems: integral (filled bars)
axis, using 180 k-points in a quasi-2D BZ. The MAE is
and tunneling (half-filled bars) DOS anisotropy,
shown in Fig. 2. As already described in Ref. [14], the
|N (x) − N (z)|/min(N (x),N (z)). L1 -
I(T) I(T) I(T) I(T) 0
CoPt thin film: integral (filled bar) and Pt-surface step-edge removes any high-symmetry directions in the
(half-filled bar) DOS anisotropy. Monoatomic Co chain: y−z-plane. Theeasyaxisistiltedfromthez-axistowards
◦ ◦
|NI(x) − NI(z)|/min(NI(x),NI(z)) for A-step (filled bar) thePtstepedgeby52 forthe A-stepandby28 forthe
and|NI(x)−NI(y)|/min(NI(x),NI(y))forB-step(half-filled B-step, in good agreement with the experimentally ob-
bar). served [13] angle of 43◦. The total energy difference be-
tween states with the magnetization along the hard and
Recently, Gambardella et al. [13] reported ferro- easy axes is ≈ 2.8 meV/Co (A-step) and 4.5 meV/Co
magnetism below 15 K in monatomic-Co chains at the (B-step); the experimental value of ∼ 2 meV/Co was
Pt(997) surface step edge. While this system is unlikely obtained from magnetic reversal measurements at tem-
to lead to room temperature spintronic applications, it perature 45 K. Higher experimental MAE and therefore
providesauniqueopportunitytostudyboththeoretically even better quantitative agreementbetween our calcula-
and experimentally magnetic and transport anisotropies tions and experiment is expected at temperatures below
in monatomic ferromagnetic chains. The experiments the ferromagnetic transition temperature in this system.
[13] revealed an unexpectedly strong MAE (∼ 2.0±0.2
meV/Coatom)withtheeasymagnetizationaxisdirected The energy differences between states with M along
S
◦
along a peculiar angle of 43 towards the Pt step edge the x-axis (along the Co-chain) or y-axis (in-plane, per-
and normal to the Co chain. pendicular to the chain), and the z-axis (out-of-plane,
We analyzedthe experiment by consideringtwo possi- perpendiculartothe chain)areshowninTab.II.Forthe
ble Pt(111) surface step edge geometries, the h100i mi- A-step, the MAE is relatively weak in the y −z-plane,
crofacetedA-stepandtheh111imicrofacetedB-step[23]. and it becomes very strong when M is rotated towards
S
IntheleftinsetofFig.2weshowmodelsupercellsforthe the x-axis. Forthe B-step,the MAE isstrongeriny−z-
B-stepwhichconsistofasub-subsurfaceandasubsurface plane,andbecomesweakerforx−z-plane. Furthermore,
Ptlayerbuiltof6rowsofPtatoms,whilethesurfacestep wecanevaluatethemagneticanisotropyconstantsbyfit-
4
M~S kxaxis M~S ky axis M~S kz axis EF forthe twoMS directions. Weobtained25bandsfor
A-step: Ex,y − Ez 8.54 -0.571 MS alongthe z-axisand26 bands forMS parallelto the
NI(EF) 26.225 24.963 24.719 x-axis. The corresponding 4% effect is consistent with
B-step: Ex,y − Ez -0.190 2.639 the estimate based on the calculated DOS anisotropies.
NI(EF) 24.731 29.313 26.606 FortheB-step,the changeinNI fordifferentmagnetiza-
Anisotropy constants K1 K2 K3 tionorientationsisparticularlylargeforMS alongthex-
relaxedA-step -1.99 2.28 1.16 andy-axes. ThecorrespondingDOSanisotropyis18.5%.
relaxedB-step -0.63 -0.71 -2.00
Toconclude, ourtheoreticalresults forDOSandmag-
unrelaxedA-step (Ref. [14]) -1.70 -0.12 -1.34
netocrystalline anisotropies in CoPt structures, based
unrelaxedB-step (Ref. [15]) -0.16 -1.06 -4.81
for both quantities on the same ab initio relativistic
band structures and in the latter one agreeing quanti-
TABLE II:The MAE and DOS in monatomic-Co chain: To-
tatively with available experimental data, suggest siz-
talenergydifferencesEx−Ez,Ey−Ez (meV),integralDOS
able TAMR effects in these metal ferromagnets. While
(NI(EF), 1/eV) for M~s kx, y and z axes, and magnetocrys- the anisotropies in the ferromagnetic material make the
talline anisotropy constants (meV).
TAMR possible, the magnitude of the effect can be very
sensitive to parameters of the entire tunnel device, most
notably of the geometry and crystalline quality of the
ting our results to the total energy angular dependence
tunnel junction, as demonstrated in (Ga,Mn)As based
[15], [K cos2θ+K (1−cos2θ)cos2φ+K sin2θsinφ],
1 2 3
devices [9, 10]. The integral DOS anisotropies calcu-
whereK aretheuniaxialanisotropyconstants,andθ
1,2,3
lated here for the CoPt systems are larger than their
and φ are conventionalpolar angles. The calculated val-
(Ga,Mn)As counterparts.
ues of the anisotropyconstants are shownin Tab. II and
compared with previous results assuming no structural
We acknowledge fruitful discussions with B.L. Gal-
relaxation [14, 15]. The Co-chain anisotropy constants,
lagher, C. Gould, B. Gurney, K. Ito, S. Maat, A.H.
∼2meV/Co,setarecord,exceedingthebulkandsurface
MacDonald, E. Marinero, L.W. Molenkamp, P.M. Op-
anisotropies for the conventional transitional metal ma-
peneer, W.E. Pickett, J. Sinova, and J. Wunderlich,
terials. Similarly, the anisotropy in N is large. For the
I and support from Grant Agency of the Czech Repub-
A-step, e.g., we obtained a (6.1 %) anisotropy in the in-
lic under Grant No. 202/05/0575, by Academy of Sci-
tegralDOS,indicatingasizableTAMReffect. Notethat
ences of the Czech Republic under Institutional Support
fortheone-dimensionalchainwecanmakeanalternative
No. AV0Z10100521,by the Ministry of Education of the
estimateofthemagnitudeoftheTAMRbasedonthecal-
CzechRepublicCenterforFundamentalResearchLC510,
culateddifferencebetweenthenumberofenergybandsat
and by the UK EPSRC under Grant GR/S81407/01.
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