Is magnetoresistance in excess of 1,000 % possible in Ni point contacts?

1 MB·English

by  A. R. Rocha

Is magnetoresistance in excess of 1,000 % possible in Ni point contacts?
A. R. Rocha, T. Archer and S. Sanvito∗
School of Physics, Trinity College, Dublin 2, IRELAND
(Dated: February 6, 2008)
Electronictransportinnickelmagneticpointcontactsisinvestigatedwithacombinationofdensity
7 functional theory and the non-equilibrium Green functions method. In particular we address the
0 possibility of huge ballistic magnetoresistance in impurity-free point contacts and the effects of
0 oxygen impurities. On-site corrections over the local spin density approximation (LSDA) for the
2 exchange and correlation potential, namely the LDA+U method, are applied in order to account

n for low-coordination and strong correlations. We show that impurity-free point contacts present
a magnetoresistance never in excess of 50%. This value can raise up to about 450 % in the case of
J oxygen contamination. These results suggest that magnetoresistance in excess of 1,000 % can not

2 havesolely electronic origin.
2
PACSnumbers: 73.63.-b,75.75.+a,72.25.-b

]
i
c
s I. INTRODUCTION not completely resolved. On the one hand, it has been
- argued that magnetic field-induced mechanical effects
l
r can produce large magnetoresistance (MR). In fact, ei-
Since the discovery of the giant magnetoresistance
mt (GMR) in magnetic multilayers1,2 there has been an in- ther magnetostriction,12,13 dipole-dipole interactions14
and magnetically induced stress relief15 may cause the
. creasing interest in the electronic transport properties
t compression of the nano-contact once a magnetic field
a of magnetic materials. Besides establishing the ground
m for the manufacture of the present generation of mag- is applied. This enlarges the cross section of the MPC
andconsequentlytheresistanceofthejunctiondecreases.
- neticdatastoragedevices,GMRhasalsoprovidedanew
d paradigmwhereby the electron spin as well as its charge On the other hand, there is also evidence that mechan-
n can be used for electronic applications.3 ical effects alone are not able to account for whole MR.
o SpecificallyGarc´ıaet. al. haveshownthatthebehaviour
The GMR effect is the overall change in the electrical
c
of MPCs does not comply with mechanical changes, in
[ resistance of a magnetic device when an external mag-
particular with magnetostriction10. Hence the question
netic field is applied and it is associated to a change in
1 on whether or not electronic only effects are sufficient to
the internal magnetic structure of the device. For in-
v explain LBMR and HBMR remains.
2 stance,whenthe magneticmomentsofthe twomagnetic
1 layers forming a spin valve are aligned parallel to each Recently Garc´ıa et al.16 have proposed that the pres-
5 other from their zero-fieldantiparallelalignment, the re- enceofimpurities,inparticularoxygen,mightberelated
1 sistance across the junction drops. This is the principle toHBMR(exceeding1,000%). Thisisaninterestinghy-
0 behind the present generation of read-heads for hard- pothesisthatconcernsnotonlyexperimentsconductedin
7
drives. However, in order to reach storage densities of air but also those in ultra high vacuum conditions, since
0
the order of Terabit/in2 a substantial down-scaling of the samples usually become contaminated after only a
/
t the read/writedevicesis needed. Onepossibleavenueto couple of hours.17 Importantly at these extremely small
a
m this goal is offered by magnetic point contacts (MPCs), dimensions even a single impurity might have a large ef-
with typicalcross sections approachingthe atomic scale. fect on the current flowing through the device. In par-
-
d Inthesetheelectroncoherencelengthisgreaterthanthe ticular, it is also well know that Ni is extremely reactive
n size of the point contact and the electronic transport is to oxygen and that bulk NiO is an insulator. Assuming
o ballistic. that the insulating state of NiO persists in some form
c The experimental landscape for magnetic point con- down to the atomic scale, then an oxygen contaminated
:
v tact transport is rather rich and controversial. Viret et Nipointcontactcanbehaveasanatomicscaletunnelling
Xi al. have performed mechanically controlled break junc- junction and perhaps sustain LBMR or even HBMR.
tion experiments in cryogenic vacuum and shown that Large MR in ballistic tunnelling junctions are not un-
r
a the ballistic magnetoresistance (BMR) in a one-atom- commoninbulkjunctionsgrownepitaxially18,19 andval-
thick MPC can reach up to 40 % ,4 in good agreement ues in excess of 300%have been demonstrated. Interest-
withtheory.5Otherexperimentsusingslightlylargercon- ingly theoretical calculations have shown that the con-
strictions and performed in air showed large ballistic ductance is highly resonant in the two-dimensional Bril-
magnetoresistance (LBMR) ratios reaching up to 300 % louin zone orthogonal to the transport direction.20,21 In
.6,7,8,9 Finally claims of a huge ballistic magnetoresis- particular, minority spins present high conductance in
tance (HBMR) effect have been recently made with val- smallregionsawayfromtheΓpointandlowconductance
ues up to a few thousand percent.10,11 everywhereelse. Onemaythenspeculatethatsuchreso-
To date there is a long-standing debate around the nantconditionmaybe further exploitedinquasi-1Dsys-
origin of the LBMR and HBMR in MPCs, which is tem, where the transversal Brillouin zone collapses into
2
a single point. formedpreviouslybyYingetal.,36 whosuccessfullymod-
Numerical simulations have an important role to play eledaconstrictedjunctionusingamean-fieldHeisenberg
in addressing these issues. In particular it is necessary model.
to determine with a high degree of accuracy the under- A self-consistent procedure based on the non-
lying electronic structure of the MPC and from that to equilibrium Green function has been developed30,34 for
calculate the electronic transport. This can be achieved calculating both G(E) and the charge density ρ. Once
by using density functional theory (DFT)22 in its Kohn- convergence has been achieved the energy- and bias-
Sham form23 and the non-equilibrium Green function dependent transmission coefficients for each spin com-
(NEGF) formalism.24,25 However, for 3d transition met- ponent can be calculated by using
als in presence of oxygen it is crucial to choose correctly
the exchange and correlation (XC) potential, since this T(E,V)σ =Tr ΓLGΓRG† . (2)
(cid:2) (cid:3)
can significantly change the transport properties of the
device.26,27 Most notably, transition metal oxides are with Γ (E) = i Σ −Σ† . Finally, the spin po-
L/R h L/R L/Ri
poorly described by the local spin density approxima-
larisedconductance is simply proportionalto T(E) eval-
tion (LSDA) and corrections are needed. A particularly
uated at the Fermi level E
useful one is offered by the LDA+U scheme,28,29 where F
the LSDA functional is replaced by an Hubbard-like en- e2
ergyforthoseatomicorbitalsforwhichstrongcorrelation G= T↑(EF)+T↓(EF) . (3)
h (cid:2) (cid:3)
cannot be neglected (the 3d shell in this case).
This paper is organised as follows. In the next sec- We model the magnetoresistance in the MPC using
tion we describe the method used to calculate the mag- the typical spin-valve scheme, i.e. we assume that in the
netoresistance as well as the two point contact arrange- absence of an external magnetic field, the magnetisation
ments investigated in our calculations. In section III we vectors of the two leads are opposite to each other in an
present our results for the electronic transport proper- antiparallel alignment (AA). Therefore, for zero field a
tiesofimpurity-freeMPCsusingtheLSDAandLDA+U sharp domain wall is formed inside the MPC.37 When a
functionals. In section IV we discuss the role of oxygen magnetic field is applied, the magnetic moments of the
impurities and finally we draw our conclusions. leads align in the field parallel to each other (PA) and
the domain wall is eliminated from the junction. The
low-bias“optimistic”magnetoresistanceratioR can
GMR
II. METHOD then be calculated by using the conductances of the AA
(GAA) and the PA (GPA)
Transport calculations are performed with
Smeagol30,31 our electronic transport code, which R = GPA−GAA . (4)
uses a combination of DFT22,23 and NEGF method24,25 GMR GAA
to accurate predict the I-V characteristics of nano-scale
Our simulations are performed for atomic size point
devices. Smeagol is based on the DFT code SIESTA,32
contacts, this arrangement was initially proposed by
whichprovidesthe Kohn-ShamHamiltonianoverabasis Viret et al..4 The structure of a Ni break junction close
set of numerical atomic orbitals.
to the rupture pointis modelledby twoNipyramidsori-
We ideally divide the device under investigation into
ented along the [001] direction. These are formed from
three distinct regions,33 namely a left and a right semi- fcc bulk Ni, with a lattice constant equal to 3.46˚A and
infinite electrode and a central scattering region where
they sandwich one extra nickel atom in such a way that
thepotentialdrops.30 InthecaseofMPCsthescattering
a three atom-long Ni chain bridges the two Ni surfaces
region consists of the atoms pictured in either Fig.1 or
(see figure 1). The whole simulation cell consists of 56
Fig.2. The main quantity in our transport calculation
nickelatomsandthebasissetcomprisesofdouble-ζ (DZ)
is the retarded Green function of the central scattering
orbitals for the 4s, 4p and 3d orbitals, an additional po-
region evaluated at an energy E, larisationorbital is included for the 4s.32 The real space
gridisgivenbyanequivalentplanewavecut-offof500Ry
Gσ(E)= lim[(E+iη)S−Hσ−Σσ(E)−Σσ (E)] ,
η→0 L R and we use 64 complex energy points for integrating the
(1) charge density.30 Finally we use periodic boundary con-
where Hσ is the Kohn-Sham Hamiltonian23 for spin σ ditions in the transverse direction and we sample over 8
(σ =↑,↓), S is the overlap matrix, Σσ (Σσ) are the self- k-points in the 2D Brillouin zone.
L R
energys for the left and right lead respectively. The self Before the transport calculations are carried out we
energy contains information about the electronic struc- perform conjugate gradient structure relaxation of the
ture of the semi-infinite electrode as well as the coupling MPCs geometry. The two left-most and the two right-
to the scattering region.25,30,31,34 Here we consider the most atomic planes in the unit cell are kept fixed at the
two-spin fluid approximation,35 whereby the two spin Ni fcc bulk positions, while the middle atoms are free to
components of the current add in parallel. In this par- relax. Oncetherelaxationofaparticulararrangementis
ticularcasethisapproachisjustifiedbycalculationsper- completedwethenincreasetheseparationdbetweenthe
3
III. IMPURITY-FREE MPCs
A. LSDA calculations
We start our analysis by looking at impurity-free
MPCs. The projecteddensity ofstates (PDOS)canpro-
vide some initial insight into the character of the elec-
tronic states lying close to the Fermi level. In Fig.3 we
present the density of states projected onto the s and d
orbitals of the entire MPC and on those of the atoms in
the tip.
Figure 1: (Color online) Ball and stick diagram of a nickel
pointcontactformedbytwopyramidaltipsjoinedbyasingle
Ni atom. The eleven atoms included in the red box corre-
spondtothetipatoms(threeatomsformingtheatomicchain
and four atoms on either side forming the apexes). d is the
distance between thetwo outermost planes.
two outermost planes (see figure 1) and another relax-
ationisperformed. Thuswefindtheenergyminimumas
a function of d. The final distance between the plane of
atomsformingtheapexandthefirstatomineachsideof
the chain is 1.60 ˚A and the inter-atomic distance within
the chain itself is 2.24 ˚A. Finally the distance between
the plane of the apex andthe first neighbouringplane of
bulk atoms is 1.76 ˚A.
Figure 2: (Color online) Ball and stick representation of the
Figure3: (Coloronline)PDOSforimpurity-freeMPC:a)en-
relaxedatomicarrangementofanickelpointcontactwithone
tiresimulation cell, b)11atomsinthecentralregion (apexes
oxygen atom brigding the gap between the two tips. Color
plusatomicchain),c)apexatoms,d)the3Niatomsforming
code: grey (blue) Ni; black (red) O.
themonoatomic chain.
We also consider the possibility of oxygen impurities First we note that the DOS of the entire MPC is sim-
in the MPC, by replacing the middle nickel atom of the ilar to the one of the apexes and resembles that of bulk
single-atom chain by an oxygen atom (figure 2). In this nickel.38 In contrast the PDOS for the three-atom chain
case we perform structural relaxation to find the most (Fig. 3d)showstheeffectsoflow-coordination,sinceitis
energetically favourable arrangement of the device. For muchsharperthanthatofthe restofthe MPC.We then
this calculation we use, in addition to the basis set of expect peaks in the transmission coefficients. These are
Ni, a double-ζ polarised basis for s and p orbitals of O. presented in Figure 4 for both the magnetic configura-
Atomic relaxationis performedfrom two different initial tions of the MPC. In the PA configuration we observe
geometries. The first has the oxygen atom placed along minority-dominated transmission with T↓(E ) ≈ 2.5.
F
the axis of the two pyramids, while in the second this is The majority spins contribute with about T↑(E ) ≈ 1
F
displaced perpendicularly to the axis as a continuation to givea totalconductanceatzero biasaround3.5 e2/h.
of the fcc lattice. We find the same energy minimum In the AA, albeit still dominant, the minority peak is
for both the arrangementswith the O atomin a straight largelysuppressedandT(E ) takesvalue similarto that
F
configuration. In the transport calculations the relaxed of the majority spin in the PA. In fact, we observe a
coordinates are always considered. plateau at T (E) ≈ 1 for E > E and both the spins.
F
4
This originates from the presence of nearly un-polarised
selectronswhosetransmissionisratherinsensitivetothe
magnetic configuration of the MPC. The resulting MR
ratio is approximately 20%.
3
a)
2
1
)
E
0
(
T
1
Majority
2 Minority
3
b)
2
1
)
E
0
(
T
1
2
3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
E-E [eV]
F
Figure 4: (Color online) Transmission coefficients as a func-
tion of energy for Ni point contacts formed by a single atom
chain: a)parallelandb)anti-parallelmagneticconfiguration. Figure 5: (Color online) Schematic representation of the
atomicorbitalsresponsiblefortheelectronicstructureofaNi
The presence of unpolarised s electrons sets a serious mono-atomic wire. The dx2−y2 and dxy orbitals are perpen-
limitation to the maximum MR achievable. As we have dicular to theaxis of thewire and therefore weakly coupled.
just shown s electrons contribute with about 2e2/h to
the conductance of both the AA and the PA. The re-
maining contribution originates from d electrons. This appear close to EF and may affect drastically the low-
is sensitive to the magnetic configuration, but it cannot bias electron transport. For this reason it is crucial to
exceed 5e2/h for each spin, since at most 5 d-bands can describe their position correctly, and therefore we need
cross E . This gives us an upper bound for the MR of to consider XC potentials beyond LSDA.
F
about250%. Inpracticehowever,delectronsarestrongly Unfortunately, most of the corrections tend to deteri-
backscatteredand they never contribute with more than orate the LSDA electronic structure of bulk Ni. In the
1.5 to the transmission coefficient. This indicates that caseofpointcontacts,the problemthenbecomesthatof
huge MR is hardly possible in impurity-free MPC. finding a good functional for the low connectivity apex
region which at the same time does not alter the elec-
tronic structure of the planes at the edges of the cell.
B. LDA+U Calculations The LDA+U method28,29 is particularly suited for this
purpose. The approximation consists in replacing the
Although useful and accurate in many situations, the LSDA XC energy with an on-site Hubbard-type energy,
LSDA severely underperforms for a variety of systems whichappliesonlyto thoseatomic shellsthatneedto be
where strong electron correlations are important. Bulk corrected (the d shell in this case). The LDA+U poten-
Ni does not figure in this class of materials and in fact tial depends on two parameters, the Coulomb repulsion
its electronic properties are extremely well described by U andtheexchangeJ. Theseareassociatedtotheircor-
the LSDA.38 However the same cannot be said of Ni in responding atomic counterparts, although in a solid the
atomic-size chains, where the localisation of the 3d or- atomicvaluesmightbeseverelycorrectedbylocalscreen-
bitals can be enhanced by the low coordination. ing. WecanthusconsiderU andJ non-vanishingonlyin
In figure 5 we present a schematic diagram of the 3d the region of the point contact where the Ni atoms have
orbitals of a transition metal mono-atomic wire aligned low coordination (the apexes and the tip).
alongthez direction. Whilethedz2,dyz anddxz orbitals In order to understand the effect of the LDA+U on
are parallel to the chain and overlap considerably (note the electronic structure of the MPCs and to extract re-
that in this arrangement symmetry forbids s-d hybridi- alistic values for U andJ, we havefirst performedband-
sation for all the 3d orbitals except for dz2). The dxy structure calculations for an infinite one-dimensional
and dx2−y2 are perpendicular to the chain and remain nickel chain (lattice spacing 2.24 ˚A). For these calcu-
localised. The key point is that, in contrast to noble lations we have used the LSDA, LDA+U with various
metals,17,30 the localised d orbitals in transition metals choices of U and J and the atomic self-interaction cor-
5
rected (ASIC) LSDA method.40 ASIC is a fully ab ini- andforthe differentspins arepresentedinfigure7,little
tio scheme, which corrects for the atomic part of the difference is observed when the transmission coefficients
LSDA self-interaction and it is proved to perform ex- are calculated with LSDA (see Fig.4). In the PA case
tremely well for a broad range of materials including the transmissionforthe majorityspinsareclosetounity
transition metal monoxides. Recently it was also used forawide rangeofenergies,indicatinglesshybridization
betweensanddorbitals,whiletheminorityspinstillhas
a) b) c) a peak of T ≈ 2.5 at EF. In general the main difference
4 with the LSDA results is that now the transmission for
energybelowE isreducedandthepeaksarebroadened.
F
This is the result of the downshift of the d orbitals due
2 to the on-site U correction.
) AlsothetransmissionfortheAAissimilartothatcal-
V
e culated with LSDA, except for a general reduction of T.
(F 0 This is now rather close to unity at the Fermi energy for
E
boththe spin configurations(note that since the domain
-
E wallis locatedbetweenthe secondandthirdatominthe
-2 chain, the two spin directions are not degenerate for the
AA).
-4 3
a)
2
Γ Γ Γ Γ Γ Γ
1
)
E
0
(
Figure6: (Coloronline)Bandstructuresofaone-dimensional T
1
nickel chain (lattice spacing 2.24 ˚A). a) LSDA, b) ASIC and Majority
c)LDA+U withU=6eVandJ=1eV.Thepanelstotheleft 2 Minority
(right) correspond to majority (minority) spins. 3
b)
2
fortransportcalculations26,27 withconsiderableimprove-
1
)
ments over LSDA. The bandstructure around the Fermi E
0
(
energy thus obtained are presented in figure 6. T
1
Generally speaking the 3d manifold splits into three
2
distinctbands,abroadhybrids-dz2 bandapproximately 3
8eVwideandtwodoublydegeneratesbandsrespectively -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
E-E [eV]
of dyz, dxz and dxy, dx2−y2 symmetry. The first of these F
degenerate bands is about 2.5 eV wide (it is located at
energiesbetween-3 eVand-0.5eVforthe LSDAmajor- Figure 7: (Color online) Transmission coefficients as a func-
ity spin band), which is a direct consequence of the fact tion of energy using LDA+U for Ni MPC. a) Parallel and b)
thatthed andd orbitalsarealignedalongthechain. anti-parallelalignmentsofthemagneticmomentsoftheelec-
yz xz
Incontrastthedxy,dx2−y2 bandis only0.5eVwide(be- trodes. ThevaluesofU andJ are6eVand1eVrespectively.
tween -1.5 eV and -1 eV for the majority spin of the
LSDA bands). The spin-split is of about 1 eV similarly The results of figure 7 can be understood by noting
to bulk Ni. The main effect introduced by the LDA+U thatthe MPC investigatedis essentiallyformedby alin-
andtheASICisthatthedxy,dx2−y2 bandareshiftedto- ear mono-atomic Ni chain sandwiched between two Ni
wards lower energies, thus moving them away from E . surfaces. Thetransmissioncoefficientthusreflectsclosely
F
Taking the ASIC bands as reference we have fixed the the bandstructure of the chain itself. Consider first the
CoulombandexchangeLDA+U parametersrespectively majorityspinsforthePA.ThelargeplateauinT↑(E)for
to U=6 eV and J=1 eV. Importantly we note that the E ≥EF is associated with the broad s-dz2 hybrid band.
s-dz2 band anti-crosses at around its band-centre and it This is the only one present in the bandstructure of the
isalwayspresentatthe Fermilevelregardlessofthespin Ni chain in that energy range. Below E the contribu-
F
orientation and the XC functional used. One can thus tion of the remaining d orbitals becomes important and
expects a large portion of the conductance through the T exceeds unity. Such a contribution is present at E
F
chain to be insensitive to the magnetic state. forthe minority spins,forwhich4 bandscrossthe Fermi
Wethenmovetothecalculationofthetransportprop- level. One thus expects the conductance of the minority
erties of the MPC of Fig. 1. Here we apply the LDA+U spins to reach up to 4e2/h. However scattering with the
corrections only to the three atoms forming the mono- pyramid-shapeelectrodesresultsinavalueofonlyabout
atomicchain. Testcalculationswherethecorrectionsare 2.5e2/h in the actual MPC.
extendedtotheapexesyieldessentiallythesameresults. Similarly the transmissionfor the antiparallelconfigu-
Thezero-biastransmissioncoefficientsforthePAandAA ration can also be related to the bands of Fig. 6. In this
6
1
case the MPC can be thought of as two Ni chains with
opposite magnetization direction, coupled to each other
through an atomically sharp domain wall. Therefore
electrons propagating in the majority (minority) band
] 0
across the first half of the chain, must propagate as mi- V
e
nority (majority) in the other half.34 Consequently the [
F
transmission is large at those energies where bands with E
- Ni s
the same orbital character appear for both spin direc- E -1 Ni dz2
Ni d , d
tions. The only band that satisfies this criterion for en- xz yz
ergiesaroundEF isthehybrids-dz2,whichexplainswhy NOi p dxy, dx2-y2
T(E )∼1 for the AA. In contrastthe remaining “pure” z
d baFnds are narrow and exchange split and contribute -2Γ A0 1 2 3O px, py 4
PDOS [ a. u. ]
little to the total transmission.
The GMR in this case is enhanced with respect to
thatcalculatedwith LSDA andcanreachup 60%. This Figure 8: (Color online) Band structures (left panel) and
projected density of states (right panel) for an infinite one-
is in agreement with calculations performed with differ-
entab initio methods5,41 and experiments foratomically dimensional NiO wire in the antiferromagnetic configuration
calculatedwiththeLSDA.Inthiscasethetwospinsub-bands
thinjunctions.4 However,thisvalueisstillfarfromthose
are degenerate.
observed in some of the experiments where the HBMR
is measured.10,11 The broad s-dz2 hybrid band is both
1
highly conductive and crosses the Fermi energy for the
two spin sub-bands. This makes it difficult to compare
ourabinitioresultswiththatclassofexperiments. More-
over it is also important to note that the dominant s
orbital character of the s-dz2 band makes such conduc- V] 0
tance channel rather robust against conformal changes e
[
of the point contact. In fact calculations with different
F
MPC geometries give rather similar results. Thus, one E Ni s
mustconcludethatimpurityfreeMPCscannotproduce E- -1 Ni dz2
Ni d , d
HBMR. xz yz
NextweconsiderthecaseofMPCscontaminatedwith Ni dx2-y2, dxy
O p
strongly electronegative impurities such as oxygen. Our O pz, p
x y
expectation is then to remove the contribution to the -2
conductance originating from the s orbitals. Γ A-4 -2PDOS0 [ a. u. ]2 4Γ A
k
Figure 9: (Color online) Band structures and projected den-
IV. OXYGENATED Ni MPCs sity of states for an infinite one-dimensional NiO wire in the
ferromagnetic configuration calculated with the LSDA. The
A. LSDA Calculations left (right) panels are for the minority (majority) spins.
FollowingthesuggestionsofGarciaetal.16weconsider
the effects of oxygen contamination in MPCs. We start 0.5 eV in the ferromagnetic configuration with the ma-
bycalculatingtheLSDAbandstructureofamono-atomic jority componentcompletely filled. Thus, if one assumes
NiO linear chain. In doing this we follow the same idea that the transport throughthe chain is completely dom-
ofthe previoussection,i.e. thatthe transportproperties inatedby sucha highly conducting band, then the ferro-
oftheMPCcanbeunderstoodfromtheelectronicstruc- magnetic one-dimensional NiO will effectively behave as
ture ofthe one dimensionalchainassociatedto the three a half-metal with a potentially large GMR. However in
atoms forming the narrowerpart of the constriction. theantiferromagneticconfigurationsuchbandsplitsinto
In this case the chain associated to the MPC of fig- two narrow bands respectively at the Fermi level and at
ure 2 is a NiO chain with a bond length of 1.8 ˚A. The about 0.6 eV below EF, precluding the possibility of a
bandstructure and the corresponding PDOS for the an- strong suppression of the current for the AA.
tiferromagnetic and ferromagnetic ground state are pre- With these results in hand we move on to calculating
sented respectively in figures 8 and 9. The LSDA total T(E)forthestructureshowninfigure2,theseresultsare
energies of these two configurations are identical, which shown in figure 10. The transmission coefficients at the
means that the chain is actually paramagnetic. Metal- E for the PA configuration are large for the minority
F
licity is found regardless of the magnetic state and it is and small for the majority spins (respectively 0.5 and
duetoahybrids-dz2 band. This bandreceivescontribu- 2.5), this is consistent with our discussion based on the
tionsfromtheOp orbitalsandhasaspin-splitofabout NiO chain. HoweverT(E )is ratherlargefor bothspins
z F
7
2
a)
2 Majority 1
Minority
1 0
)
E0 ] -1
( V
T
e -2
1 [

EF-3
2
-
E -4
3
b) -5
E)2 Ni s
T(1 -6 Ni dz2
0-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -7Γ NOA1i p- d4xz, dyz-2PDOS0 [ a. u. ]2 4Γ A
E-E [eV]
F
Figure11: (Coloronline)Bandstructuresandprojectedden-
Figure 10: (Color online) Zero-bias transmission coefficients sity of states for an infinite one-dimensional NiO wire in
ofoxygencontaminatedNipointcontactscalculatedwiththe theferromagneticconfigurationcalculated withtheLDA+U.
LSDA: a) parallel and b) anti-parallel alignments. In the The left (right) panels are for the minority (majority) spins.
PAthesolid (dashed)linerepresentsthemajority (minority) Thevalues of U and J are set to6 eV and 1 eV respectively.
spins, while thetwo spins are degenerate in theAA.
2 is considered the non-magnetic solution is no longer
inthe AA becauseofthe contributionfromthe Nis-dz2- found. The transmission coefficients calculated using
Op band. Thisgivesanoverallconductancelargerthan LDA+U areshowninfigure 12. The PAconfigurationis
z
thatofthePAandatinynegativeGMRofapproximately qualitatively similar to the LSDA result (see figure 10a)
-6 %. It therefore appears that oxygen impurities are however the transmission for minority spins is slightly
unable to explain HBMR. higher while that for majority is lower (T ∼ 0.2). The
This negative result however should be taken with majoritydstatesarelowerthanintheLSDAcaseandal-
some care. As mentioned in the introduction LSDA thoughthetransmissioncoefficientsatE arenon-zeroit
F
poorly reproduces the electronic structure of standard does resemble the half-metal behaviour observed in the
Mott-Hubbard insulators such as NiO. One may argue infinite chain. The residual conductance at E is then
F
that the same problem appears in these low dimensional attributed to direct tunnelling at the apexes, which is
oxidesandthereforeourresultsneedtobetestedagainst substantial for these small separations.
the LDA+U scheme. For the AA configuration the LDA+U results are in
stark contrast to the LSDA ones and in particular there
is a drastic reduction of the transmission at E . This
F
B. LDA+U calculations issomehowexpectedsince the contributionofthe s elec-
tronstothetransmissionhasbeenseverelyreduced. The
resulting magnetoresistancereaches a much higher value
As intheprevioussectionswebeginwiththe LDA+U
of 450 % in good agreement with results obtained with
calculationofaninfiniteNiOchain. Hereweconsiderthe
by using hybrid XC functionals.42
same values of U and J used for the case of the Ni-only
chains. The configuration presenting the lowest energy
turnsouttobenon-magnetic,43 althoughbothferromag-
netic and antiferromagnetic solutions can be stabilized. V. CONCLUSION
Interestingly several antiferromagnetic states, both con-
ductingandinsulating,havebeenobtainedwiththecon- In summary, we have investigated the possibility of
vergence being extremely sensitive to the initial orbital LBMR and HBMR in Ni point contacts using a combi-
occupation. nationofDFTandNEGFmethod. Inparticularwehave
Infigure11wepresentthebandstructurefortheferro- exploredthe dependence of the MR onthe XC function-
magneticconfiguration. Theseappearsignificantlydiffer- als used and the effects of oxygen contamination. For
entfromtheirLSDAcounterpart,sinceNiOisnowahalf- defect-free point contacts both LSDA and and LDA+U
metal. Moreoverthe s electrons are no longer present at calculationsagreeinsettinganupperboundtotheMRin
the Fermi level, which in contrastis characterizedby or- the range of 50 %. This rather small value is essentially
bitals orthogonal to the chain axis, namely the oxygen due to the high transmission associated to an unpolar-
px and py and the Ni dxz and dyz. ized s-dz2 band, which is always present at the Fermi
We then proceed with calculating the transport level. This is rather insensitive to conformal changes of
through the point contact. When the structure of figure the MPC and contributes 2 e2/h to the conductance re-
8
a) MR while LDA+U gives a positive MR of about 450 %.
2 Majority Since the well-known problem of LSDA of dealing with
Minority
1 transitionmetalmonoxides,webelievethatthe LDA+U
E) results are the most relevant. Importantly even in this
0
(
T case the MR is still much smaller than those measured
1 in experiments showing HBMR. The main point is that,
2 although strongly suppressed, there is still substantial
currentforthe AA, attributedto directtunnelling ofthe
2
b) apexes. Certainlylargeroxygenation,ortheformationof
)
E long NiO chains may suppress this leakagecurrent,how-
1
(
T everwebelievethathighlyoxygenatedconfigurationsare
0 rather unlikely. This leads us to conclude that HBMR
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
E-E [eV] may haveadditionaloriginsbesides electronic considera-
F
tions.
Figure 12: (Color online) Zero-bias transmission coefficients
ofoxygencontaminatedNipointcontactscalculatedwiththe
LDA+U: a) parallel and b) anti-parallel alignments. In the
PAthesolid (dashed)linerepresentsthemajority (minority) VI. ACKNOWLEDGMENTS
spins, while thetwo spins are degenerate in theAA.
We would like to thank Chaitanya Das Pemmaraju
gardless of the magnetic state of the device. for stimulating discussions. This work is supported
Incontrast,oxygenationcandrasticallychangethepic- by Science Foundation of Ireland under the grants
ture. InparticularOpstatescanhybridizewiththes-dz2 SFI02/IN1/I175 and SFI05/RFP/PHY0062. Computa-
bandshifting itawayfromE . However,inthis casethe tional resources have been provided by the HEA IITAC
F
results are strongly dependent on the exchange and cor- project managed by the Trinity Centre for High Perfor-
relation functional, with LSDA giving a small negative mance Computing and by ICHEC.
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