Prediction of the bias voltage dependent magnetic contrast in spin-polarized scanning tunneling microscopy

0.31 MB·English

by  Krisztián Palotás

Prediction of bias voltage dependent magnetic contrast from spin-polarized tunneling
spectroscopy
Krisztia´n Palot´as∗
Budapest University of Technology and Economics,
Department of Theoretical Physics, Budafoki u´t 8., H-1111 Budapest, Hungary
(Dated: July 18, 2012)
We propose a method to estimate the bias voltage dependent magnetic contrast observed on
constant current spin-polarized scanning tunnelingmicroscopy (SP-STM) images from single point
2 differential conductance(dI/dV)tunnelingspectra. Dependingon thenumberof single point mea-
1 surements,thebiaspositionsofmagneticcontrastreversalsandthemaximallyachievablemagnetic
0 contrast can be determined. We validate this proposal by simulating SP-STM images on a com-
2 plex magnetic surface by employing a recently developed approach based on atomic superposition.
Furthermore, we show evidence that the tip electronic structure has a major effect on the mag-
l
u netic contrast. Our theoretical prediction should inspire experimentalists to considerably reduce
J measurement efforts for determining thebias dependentmagnetic contrast on magnetic surfaces.

7
1 PACSnumbers: 72.25.Ba,68.37.Ef,71.15.-m,73.22.-f

]
i Achievingultrahighinformationdensityinacontrolled be obtained, and this effect was explained by chemically
c
s way on surfaces of materials [1, 2] is one of the ultimate modified STM tips [11].
- goals of magnetic research nowadays for the purpose of Distinguishing atoms with different magnetic proper-
l
r future data storage technological applications. This can ties on a complex magnetic surface can successfully be
t
m be established by the reduction of the size of magnetic performed by spin-polarized scanning tunneling spec-
informationstorageunitsgoingdowntothenanoscaleor troscopy (SP-STS) as well. For example this technique
.
at even to single atoms [3]. Reading and writing informa- has recently been used to read out information from
m tionroutinelyfromandto suchmagneticunits isa great an atomic scale all-spin-based logic device [12]. Here,
challenge. Spin-polarizedscanningtunneling microscopy through scanning the surface with a magnetic tip, the
-
d (SP-STM) [4], employing a magnetic tip, proved to be measured differential conductance (dI/dV) values vary
n extremely successful for studying magnetism on surfaces depending on the magnetic properties of the underly-
o
inhighspatialresolution. Recentexperimentaladvances ing surface atom. For such a spectroscopic detection of
c
using this technique allow the investigation of complex atomic magnetism, the contrast, that is the dI/dV dif-
[
magnetic structures (frustrated antiferromagnets, spin ference above individual atoms, should also be tunable

1 spirals, skyrmion lattices, etc.) [3, 5–7]. by changing the bias voltage [13].
v
Inthiswork,weproposeamethodtoestimatethebias
5 In the most routinely used constant current mode of
dependent magnetic contrast observed in constant cur-
9 SP-STM, the apparent height difference between differ-
9 ently magnetized surface atoms allows the discrimina- rent SP-STM experiments from single point differential
3 conductancetunnelingspectra. Thekeyquantityforthis
tion of the individual atomic magnetic properties and
. estimationisthemagneticcontributiontothedifferential
7 the mapping of the magnetic structure. This apparent
0 height difference is called magnetic contrast. Finding conductance, dIMAGN/dV, that can be obtained from
2 measuringtunneling spectra with oppositely magnetized
the maximal magnetic contrast for a given surface-tip
1 tips. Let us assume that one can measure differential
combinationiscrucialforamoreefficientmagneticmap-
: conductancesdIA/dV(z ,V)anddIA /dV(z ,V)atthe
v ping. Thiscanbedonebyusingmagnetictipswithlarge P 1 AP 1
i spin polarization, or, by choosing the appropriate bias same tip position above surface atom A at z1 tip-sample
X
distance, where P and AP denote parallel and antipar-
voltage. A very few works focused on the investigation
r alleltipmagnetizationdirections,respectively,compared
a of the bias dependent magnetic contrast so far. Among
toapredefineddirection. Fromthesetwomeasuredspec-
those, a magnetic contrast reversal has been reported in
tra,themagneticcontributiontothedifferentialconduc-
two different magnetic systems [8, 9], and the effect was
tance can be calculated as
related to the surface electronic structure rather than to
the effect of the tip. In another work, such contrast re-
dIA 1 dIA dIA
versalswereobservedduringthe scanningwiththe STM MAGN(z ,V)= P (z ,V) AP(z ,V) . (1)
1 1 1
tip at fixed bias, and this was identified to be due to dV 2(cid:20) dV − dV (cid:21)
the magnetic switching of the tip [10]. Moreover, un-
Using this quantity, the magnetic current can be deter-
der certain circumstances,a giantmagnetic contrastcan
mined at arbitrary V bias voltages via integration:
V dIA
IA (z ,V)= dV˜ MAGN(z ,V˜). (2)
∗Electronicaddress: [email protected] MAGN 1 Z dV˜ 1
0
2
Here,weassumedzerotemperature. Foragivensurface- Ifthe topographiccontrast∆zAB iszero,thenthe to-
TOPO
tip combination, by varying the upper integral limit V, tal contrast in Eq.(6) corresponds to the magnetic con-
we can determine the bias voltage, where the magnetic trast. Thishappens,e.g.,onsurfacesconsistingofchem-
current is zero. This corresponds to a magnetic contrast icallyequivalentbutmagneticallyinequivalentatoms. In
reversal on the constant current SP-STM image, as will this case ITOPO =ITAOPO =ITBOPO. In order to be able
be demonstrated later. This bias position can be found tocalculatethesofarunknowndecayκ (V),athirdpair
0
using magnetic tips having arbitrary magnetization di- of single point P and AP spectra is needed at a different
rection, however, the contrast can further be enhanced tip-sampledistance z , e.g.,aboveatomA. Since IA
2 TOPO
by setting the tip magnetization direction properly as can be calculated from the spectra according to Eq.(4)
discussedinRef. [13]. Thus,fromP andAP single point at both tip-sample distances, and the tip displacement
spectra measured at tip position (A,z ), the bias volt- z z can be measured in experiments, the decay can
1 2 1
−
age(s) can be determined, where a magnetic contrastre- be determined as
versal occurs.
lnIA (z ,V) lnIA (z ,V)
Similarlytothemagneticcurrent,thetopographiccur- κ (V)= TOPO 1 − TOPO 2 . (8)
0
rent can be calculated from the same single point P and 2(z2 z1)
−
AP spectra as
Thus, by measuring P and AP tunneling spectra in each
dIA 1 dIA dIA of the three well-defined tip positions above the surface:
TOPO P AP
(z ,V) = (z ,V)+ (z ,V) ,(3)
dV 1 2(cid:20) dV 1 dV 1 (cid:21) (A,z1),(A,z2),and(B,z1),thebiasdependentmagnetic
V dIA contrast between atom A and B at the tip-sample dis-
ITAOPO(z1,V) = Z0 dV˜ TdOV˜PO(z1,V˜), (4) tFarnocmezt1h,is∆fzuAnBc(tzio1n,Vt)h,ecabniabsepporseidtiioctnedcafonllobweinidgeEntqifi.(e6d),.
and the total current with P tip alignment is where the maximal magnetic contrast can be achieved.
Since the magnetic contrast is assumed to be exponen-
A A A
I (z ,V)=I (z ,V)+I (z ,V). (5)
1 TOPO 1 MAGN 1 tially decaying with respect to the tip-sample distance
The same procedure can be repeated above atom B, i.e. similarly to the corrugation amplitude of nonmagnetic
P and AP single point spectra have to be measured, and STM images, the identified bias position of the maximal
thecorrespondingcurrentscanbecalculatedsimilarlyto magnetic contrast should not change by recording SP-
atom A, e.g. IB(z ,V) denotes the total current with STMimagesatdifferentconstantcurrentconditions,i.e.
1
P tip alignment at the tip-sample distance z and bias at different tip-sample distances.
1
voltage V. By additionallyrecordingPandAP tunneling spectra
In an SP-STM image of a complex magnetic surface at the tip position (B,z2), ∆zAB(z2,V) can also be cal-
the magnetic modulation is superimposed on top of the culated. Thus, measured spectra at four well-defined tip
topographic image. Generalizing the relation between positions above the surface: (A,z1), (A,z2), (B,z1), and
constant current and constant height STM images re- (B,z2) are, in principle, sufficient for determining the
ported in Ref. [14] to SP-STMimages,we candefine the bias dependent magnetic contrast between atom A and
contrast between atoms A and B on the surface at the B at an arbitrary tip-sample distance z in the tunneling
tip-sample distance z and bias voltage V as regime:
1
∆zAB(z1,V) = ∆IAB(z1,V) ∆zAB(z,V)=[∆zAB(z1,V)]zz22−−zz1[∆zAB(z2,V)]zz2−−zz11.
−∂ITOPO/∂z(z1,V) (9)
IA(z ,V) IB(z ,V) Notethatsincetheabsolutetip-sampledistancesareun-
1 1
= − , (6)
2κ0(V)ITOPO(z1,V) known in experiments, the magnetic contrast can be de-
termined at distance z relative to z and z only.
1 2
where the average tip-sample distance has been gener-
In order to demonstrate the applicability of the pro-
alized to the topographic image, i.e. the constant cur-
posed procedure for estimating the bias dependent mag-
rent contour of the nonmagnetic part of the tunneling
netic contrast from single point tunneling spectroscopy
current, ITOPO. We also took advantage of the expo- data, we perform simulations on a sample surface with
nentially decaying character of the tunneling current,
noncollinear magnetic order. One monolayer (ML) Cr
ITOPO(z,V) = I0(V)e−2κ0(V)z. The contrast in Eq.(6) on Ag(111) is a prototype of frustrated hexagonal anti-
corresponds to the apparent height difference of atom A
ferromagnets [14]. Due to the geometrical frustration of
and B on a proper constant currentcontour, and can be
the antiferromagnetic exchange interactions between the
decomposed to topographic and magnetic parts,
Cr spin moments, its magnetic ground state is a non-
∆zAB(z1,V) = ∆zTAOBPO(z1,V)+∆zMABAGN(z1,V) collinear 120◦ N´eelstate [15]. Taking the spin-orbit cou-
IA (z ,V) IB (z ,V) pling into account, two N´eel states with opposite chiral-
= TOPO 1 − TOPO 1 ities can form, and one of them is energetically favored
2κ0(V)ITOPO(z1,V) [9].
IMAAGN(z1,V) IMBAGN(z1,V) We performed fully noncollinear electronic structure
+ − . (7)
2κ0(V)ITOPO(z1,V) calculationsontheCr/Ag(111)system,basedontheden-
3
sity functional theory (DFT) within the generalizedgra-
dientapproximation(GGA)andusingtheprojectoraug-
mentedwave(PAW)method,implementedintheVienna
ab initio simulation package (VASP) [16–20]. The com-
putational details are reported elsewhere [9]. We used
two tip models: one is an electronically flat, maximally
spin-polarized (PT = +1) ideal magnetic tip, and the
second is a blunt Ni tip, i.e. a Ni adatom placed above
the hollowpositionofa Ni(110)surface. Moredetails on
the chosen tip models can be found in Ref. [13].
Taking the calculated electronic structures, the dif-
ferential conductances can be obtained following Ref.
[21]. On the other hand, the magnetic current can di-
rectly be determined from the sample and the tip elec-
tronic structures at the tip apex position R above
TIP
the sample surfaceusing the atomsuperpositionmethod
[9, 14, 22, 23] based on the spin-polarized Tersoff- FIG. 1: (Color online) Simulated magnetic current,
Hamann model [15, 24, 25], assuming elastic tunneling: IMAGN(V), according to Eq.(10) z = 3.5 ˚Aabove each Cr
atom (Cr1, Cr2, Cr3) in the (√3 √3) magnetic unit cell
×
IMAGN(RTIP,V) (see left part of Figure 3), measured with an ideal electroni-
cally flat maximally spin-polarized tip (gray), or a model Ni
V
α S T tip (black). The tip magnetization direction is fixed parallel
dU m (E +eU)m (E eV +eU)
S F T F
∝ Z − totheCr1magneticmomentinFigure3. Theinsetshowsthe
0 Xα
region between 0 V and 1 V zoomed in. The sign change of
e−~2r2m(cid:16)φS+φ2T+eV−eU(cid:17)|RTIP−Rα|. (10) INMiAtiGpN,(rVes)poecctciuvreslya.tT0.h9e4seVcaonrrdes0p.7o4ndVtfoormtahgeniedteiaclcaonndtrtahset
×
reversals.
Here,the sumoverα includes asufficientnumberofsur-
faceatoms[13]withpositionR andprojectedmagnetic
α
densityofstates(magneticDOS),mα. Similarly,m de-
S T
notes the magnetic density of states projected onto the V, 1 V]. The indicated rectangular area is shown in the
tip apex atom. ES and ET are the Fermi energiesofthe inset of Figure 1. It is clearly seen that the sign change
F F
surface and the tip, respectively. Moreover, the expo- of IMAGN(V) occurs at 0.94 V and 0.74 V for the ideal
nential expression is the tunneling transmission assum- and the Ni tip, respectively. Although the reversal is, in
ingsphericaldecayoftheelectronwavefunctionsandan principle, due to the surface electronic structure [8, 9],
effectiverectangulartunnelbarrier,whereφS andφT are the tip plays a crucial role as well, since its electronic
the surface and tip electron workfunctions, respectively. structuremodifies the bias positionofthe reversal. Note
Theshapeoftheelectronorbitalsinvolvedinthetunnel- that the determination of the above bias positions does
ing[26]areneglected(independentorbitalapproximation not depend onwhether the tip is placedabove Cr1,Cr2,
[14]). or Cr3 atoms. Moreover, we find that the bias voltage
Figure 1 shows the simulated magnetic current, ofthe contrastreversalsisstable within 0.01Vplacing
±
IMAGN(V), according to Eq.(10) z = 3.5 ˚Aabove each the tip above other surface positions.
Cratom(Cr1,Cr2,Cr3)inthe(√3 √3)magneticunit Inorderto estimate the bias dependent magnetic con-
×
cellshownintheleftpartofFigure3,measuredwiththe trast, Eq.(6) has to be employed. The topographic
two considered tip models. For the negative bias range, current ITOPO can be calculated similarly to Eq.(10)
theintegrallimitsarereversedinordertoobtainpositive by replacing the magnetic DOS by the corresponding
total current values, and the magnetic current has been charge DOS of the sample and the tip [9]. The decay
calculated accordingly. The tip magnetization direction of ITOPO(z,V) can be calculated using Eq.(8). In the
is fixed parallel to the Cr1 magnetic moment. Due to simulations we determined κ0(V) from ITOPO(z,V) by
thefrustratedmagneticstructure,the Cr2andCr3mag- linearregressiontaking150z valuesintherange[0.01˚A,
netic moments have an angle of 120◦ with respect to the 7.95 ˚A] at each chosen bias voltage with 0.01 V steps in
tipmagnetizationdirection. Followingthis,themagnetic the [-2.5 V, 2.5 V] interval. Figure 2 shows the bias de-
currents measured above the Cr2 and Cr3 surface atoms pendent magnetic contrast between Cr1 and Cr3 atoms
are equal and their values are cos(120◦) = 0.5 times attwodifferenttip-sampledistancesusingbothtipmod-
−
the magnetic current above Cr1. Moreover, it is clearly els. The sign of the curves corresponds to the ones de-
demonstrated in Figure 1 that the magnetic properties noted by solid line in Figure 1, and the contrastreversal
of the tip affect the magnetic current considerably. isobtainedat∆zCr1−Cr3(z,V)=0. However,duetothe
The magnetic contrast is reversed at IMAGN(V) = 0. denominator of Eq.(6), we obtain qualitatively different
In order to find out the corresponding bias positions for curves compared to Figure 1. From the calculated func-
the twoconsideredtips,wehavetozoominthe region[0 tions,biasvoltagescanbeidentifiedinboththenegative
4
30
Eq.(6), Ideal tip, z=3.5 Å
Eq.(6), Ni tip, z=3.5 Å
Eq.(6), Ideal tip, z=4.5 Å
20
Eq.(6), Ni tip, z=4.5 Å
-1.40 V SP-STM image, Ideal tip
SP-STM image, Ni tip
10
m]
p
V) [ +1.31 V
∆z (z,Cr1-Cr3-100 FonIGth.e3:bi(aCsovloorltaognelinaen)dStihmeucloantesdideSrPe-dStTipM: iidmeaaglemsadgenpeetnicditnipg
-0.84 V (toprow),Nitip(bottomrow). Themagneticmomentofthe
tip apex atom is parallel to Cr1, and indicated by a vector
-20 (M ). The surface geometry of 1 ML Cr on Ag(111) and
TIP
itsgroundstatemagneticstructureareexplicitlyshown. The
Cr and Ag atoms are denoted by spheres colored by green
-30
-2 -1 0 1 2 (medium gray) and purple (dark gray), respectively, while
Bias Voltage [V]
the magnetic moments of individual Cr atoms are indicated
by (red) arrows. The (√3 √3) magnetic unit cell is drawn
FIG.2: (Coloronline)Thebiasdependentmagneticcontrast ×
by yellow (light gray) color, and the scanning area is shown
between Cr1 and Cr3 atoms ∆zCr1−Cr3(z,V) at two differ-
ent tip-sample distances, z = 3.5 ˚A(solid lines) and z = 4.5 bythe black-framed rectangle.
˚A(dash-dotted lines) calculated using Eq.(6) measured with
the ideal magnetic tip (gray) and the Ni tip (black). The lo-
calabsolutemaximaofthemagneticcontrastsandtheirbias respondingtothelocalabsolutemaximaofthe magnetic
valuesareexplicitly shown in boththenegativeand thepos- contrast in both the negative and positive ranges. The
itive bias ranges. Vertical dashed lines denote the contrast surfacegeometryisshownintheleftpartofthefigure,to-
reversals, see also Figure 1. For comparison, color dashed gether with the scanning area (black-framed rectangle),
lines show the apparent height difference between Cr1 and and the magnetic unit cell (yellow (light gray) framed
Cr3atomscalculatedfromconstantcurrentSP-STMimages,
rhombus). The tip magnetization direction is parallel to
see text for details.
the Cr1 magnetic moment. For the zero bias images a
temperature of 4.2 K has been considered following Ref.
[9], since there is no current at 0 K.
and positive bias ranges, where a local absolute maxi-
Wefindasimilartypeofmagneticcontrastat0Vand
mummagneticcontrastcanbeachieved. Ascanbeseen,
at the negative bias voltages for both tips, respectively,
these highly depend on the properties of the magnetic
i.e., for V <0, ∆zCr1−Cr3 >0 (Cr1 appears higher than
tip. In the studied bias interval localabsolute maximum
Cr2 and Cr3) for the ideal tip, and ∆zCr1−Cr3<0 (Cr1
contrastsareexpectedat-1.40Vand2.50Vforthemea-
appearslowerthanCr2andCr3)fortheNitip,similarly
surementwiththeidealtip,whereasthesebiasvaluesare
as reported in Figure 2. At the corresponding reversal
considerablymodifiedto-0.84Vand1.31Vbyusingthe
voltages, 0.94 V (ideal tip) and 0.74 V (Ni tip), all Cr
Ni tip. The maximum absolute contrasts are obtained
atoms appear to be of equal height on the SP-STM im-
at the corresponding negative bias values for both tips.
age. Here, the magnetic contrast is lost as IMAGN = 0.
Moreover, as can be seen, the change of the tip-sample
This corresponds to a qualitatively similar image of per-
distance does not modify the bias positions of the abso-
forming the STM measurement with a nonmagnetic tip
lutecontrastmaxima. Wetesteditforotherdistancesas
[9]. Thus, the magnetic current calculated at a single
well, and the bias positions were found within 0.02 V.
point above the surface was indeed able to find the cor-
±
Forcomparison,colordashedlinesinFigure2showthe rect bias position of the magnetic contrast reversal. At
apparent height difference between Cr1 and Cr3 atoms biases above the reversal voltage, the magnetic contrast
calculated from constant current SP-STM images. The isinverted. We illustratethis forthe imagecalculatedat
current contour was chosen in such a way that the ap- 2.50 V for the ideal tip, and at 1.31 V for the Ni tip.
parent height of the Cr1 atom is 3.5 ˚Aat all considered Inconclusion,weproposedaprocedurefordetermining
bias voltages. The agreement with the estimated mag- the bias dependent magnetic contrast from single point
neticcontrastusingEq.(6)isremarkable,particularlyfor differentialconductancetunnelingspectrameasuredwith
∆zCr1−Cr3 >0. There are some quantitative deviations oppositely magnetized tips. By performing simulations
if ∆zCr1−Cr3 is negative,but the overallqualitative bias basedonfirstprincipleselectronicstructurecalculations,
dependence is well reproduced by Eq.(6). we demonstrated that the obtained bias dependent con-
In order to better visualize the bias dependent con- trast corresponds well to the apparent height difference
trast, we simulated constant current SP-STM images. calculated from constant current SP-STM images. Our
Figure3showssuchimagesmeasuredwiththeidealmag- theoretical prediction should inspire experimentalists to
netictip(toprow)andtheNitip(bottomrow)at0V,at considerablyreducemeasurementeffortsfordetermining
the bias voltages corresponding to the contrast reversal the bias dependent magnetic contrast on magnetic sur-
(0.94Vand0.74V,respectively),andatthevoltagescor- faces.
5
The author thanks La´szl´o Szunyogh for useful com- of Sciences, and the New Sz´echenyi Plan of Hungary
ments onthe manuscript. Financialsupportofthe Mag- (Project ID: TA´MOP-4.2.2.B-10/1–2010-0009) is grate-
yaryFoundation,EEAandNorwayGrants,the Hungar- fully acknowledged. Furthermore, partial usage of the
ianScientificResearchFund(OTKAPD83353,K77771), computing facilities of the Wigner Research Center for
the Bolyai Research Grant of the Hungarian Academy Physics is kindly acknowledged.
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