Magnetism of two-dimensional defects in Pd: stacking faults, twin boundaries and surfaces

0.34 MB·English

by  Simone S. Alexandre

Magnetism of two-dimensional defects in Pd:
stacking faults, twin boundaries and surfaces
Simone S. Alexandre and Eduardo Anglada
Departamento de F´isica de la Materia Condensada,
Universidad Aut´onoma de Madrid, 28049 Madrid, Spain.
6
0 Jos´e M. Soler and F´elix Yndurain∗
0 Departamento de F´isica de la Materia Condensada,
2 Universidad Aut´onoma de Madrid, 28049 Madrid, Spain, and
n Instituto de Ciencia de Materiales Nicol´as Cabrera,
a Universidad Aut´onoma de Madrid, 28049 Madrid, Spain.
J (Dated: February 6, 2008)

0
Careful first-principles density functional calculations reveal the importance of hexagonal versus
3
cubic stacking of closed packed planes of Pd as far as local magnetic properties are concerned. We

find that, contrary to the stable face centered cubic phase, which is paramagnetic, the hexagonal
]
i close-packed phase of Pd is ferromagnetic with a magnetic moment of 0.35 µB/atom. Our results
c
showthattwo-dimensionaldefectswithlocalhcpstacking,liketwinboundariesandstackingfaults,
s
- in the otherwise fcc Pd structure, increase the magnetic susceptibility. The (111) surface also
l increasesthemagneticsusceptibilityanditbecomesferromagneticincombinationwithanindividual
r
t stackingfaultortwinboundaryclosetoit. Onthecontrary,wefindthatthe(100)surfacedecreases
m
the tendency to ferromagnetism. The results are consistent with the magnetic moment recently
. observed in small Pd nanoparticles, with a large surface area and a high concentration of two-
t
a dimensional stacking defects.
m
PACSnumbers: 73.22.-f,75.75.+a,75.50.Cc
-
d
n
o I. INTRODUCTION two-dimensionaldefects in face centeredcubic (fcc) met-
c alsaswellasindiamondandwurtzite-structuresemicon-
[ ductors. Their abundance is partly due to their low en-
Despite their narrow d-bands and high densities of
1 states (DOS) atthe Fermilevel, which favormagnetism, ergyofformation,sincethey preservethe localgeometry
v and close packing. Their importance in the mechanical
there are only three ferromagnetic transition metals in
8 properties, like hardness and brittleness are recognized
nature. Palladiumisparamagneticinitsstablefccstruc-
5 sincemanyyears. Recently,theroleplayedbythestack-
6 ture, but with a very high magnetic susceptibility. Sev-
ing of (111) layers has been emphasized in connection
1 eralcalculationshave shownthat its Fermi levellies just
with magnetic orientationand magnetic ordering of thin
0 abovealargepeakintheDOS,atthetopofthed-bands.
6 The DOS atthe Fermi-level,of ∼1.1 states per spin, eV layers and superlattices of magnetic metals10,11,12. The
0 and atom (Chen et al.1 and references therein) is almost growth of Co on top of the Cu(111) surface has been
/ extensively studied experimentally, and the correlation
t high enough, but not quite so, to fulfill the Stoner crite-
a between stacking pattern and magnetic properties has
rion for itinerant magnetism, since the Stoner exchange
m parameter is ∼ 0.73 eV2,3. The calculations have also been reasonably well established.
- At this stage it seems worth studying the effect of
shown that Pd, in its fcc crystal structure, becomes fer-
d
the stacking sequences and of the surfaces on the elec-
n romagnetic by increasing the lattice constant by just a
o few percent4. All these results have stressed the subtle tronic and magnetic properties of Pd. With these ideas
in mind, we have calculated total energies and magnetic
c balance of magnetism in Pd.
: moments of Pd in both the fcc and hexagonal close-
v Therefore,wesuggestthatvariationsintheatomicar-
packed(hcp) phases,as wellasinsurfacesandneartwo-
i rangementcaninduce changesin the density of states at
X dimensional stacking defects like intrinsic and extrinsic
the Fermi level that, in turn, can induce magnetism. In
r stacking faults, and twin boundaries.
a this direction, it has been proposed that monatomic Pd
nanowires are ferromagnetic, either in their energetic5,6
or thermodynamic7 equilibrium length. Also, recent ex-
perimental results8 indicate that fcc Pd nanoparticles II. METHODOLOGY
with stacking faults and twin boundaries present ferro-
magnetism. Other experiments9 on small Pd nanoparti- All our calculations are performed within density
clesalsoindicatetheexistenceofahysteresisloopwhich, functional theory13 (DFT), using either the local den-
in this case,is interpretedas due to a nonzero magnetic sity approximation14 (LDA) or the generalized gradi-
moment at the surface atoms. ent approximation15 (GGA) to exchange and correla-
Stacking faults and twin boundaries are very common tion. Most of the calculations were obtained with the
2
SIESTA16,17 method, which uses a basis of numerical
atomic orbitals18 andseparable19 normconservingpseu- )B0.5 fcc Bulk
dopotentials20 with partial core corrections21. To gen- nt (0.4 35LDA (a) 35 (b) GGA
erate the pseudopotentials and basis orbitals, we use a me V)30 V)30
Pledadcsotnofigbuertatetirontra4nds9f5esr1a,bisliintyceawnde bhuavlke pchroepckeertdietshtahtaint Mo0.3 y (me122505 y (me122505
the ground state configuration 4d105s0. After several etic 0.2 Energ1005 Energ1005
tests we have found satisfactory the standard double-ζ gn -5 -5
basis with polarization orbitals (DZP) which has been Ma0.1 Ma-g0.n8et-i0c. 4Mo0m.0en0t. 4( B0).8 Ma-g0.n8eti-0c. 4Mo0m.0en0t. 4( B0).8
used throughout this work. The convergence of other
precisionparameterswascarefullychecked. Therangeof 0.0
3.0 3.2 3.4 3.6 3.8 4.0 3.2 3.4 3.6 3.8 4.0
the atomic basis orbitals was obtained using an energy
Lattice Constant (¯) Lattice Constant (¯)
shift17 of 50 meV. The real space integration grid had a
cut-off of 500 Ryd, while around 9000 k points/atom−1 FIG. 1: Magnetic moment versus lattice constant for fcc Pd
obtainedwiththeSIESTAcodeandtheLDAandGGAfunc-
were used in the Brillouin zone sampling. To accelerate
tionals. The insets indicate the variation of the total energy
the selfconsistency convergence, a broadening of the en-
with magnetic moment at thecorresponding equilibrium lat-
ergylevelswasperformedusingthemethodofMethfessel
tice constants, indicated by arrows.
and Paxton22 which is very suitable for systems with a
large variation of the density of states at the vicinity of
the Fermi level. twootherDFTmethods: thepseudopotentialplanewave
It is necessary to mention that most of the energy dif- code VASP23 andthe all-electronaugmentedplane wave
ferences between paramagnetic and ferromagnetic solu- methodWIEN24,bothwiththesameGGAfunctional15.
tionsinPdstructuresareextremelysmall,whatrequires Previous GGA calculations by Singh and Ashkenazi25,
a very high convergence in all precision parameters and using a different functional, also found a lattice constant
tolerances, and specially in the number of k points. It largerthantheexperimentalone,butdidnotaddressthe
must be recognized,however,that the basic DFT uncer- subtle ferromagnetic-paramagnetic transition with suffi-
taintyisprobablylargerthanthoseenergydifferences,so cient detail.
thatitisnotreallypossibletodeterminereliablywhether Ontheotherhand,withintheLDAwefindaparamag-
a particular defect or structure is para or ferromagnetic. netic groundstate and a lattice constant of 3.89˚A, both
Still, we think thatit is possible to find reliablythe rela- inagreementwiththe experimentalvaluesandwithpre-
tive tendency towardsmagnetism of different structures. vious LDA calculations of Moruzzi and Marcus4. These
In particular, E(M) curves, of total energy versus total results suggest that the GGA is not necessarily more re-
magneticmoment, provideanexcellenttooltostudy the liabletostudymagnetisminPd. Infact,itisnotfeasible
tendency to magnetism in different systems: indepen- to study the possible existence of magnetic defects in fcc
dently ofwhether thesystems areparaorferromagnetic, Pdwhenthebulkresultisalreadyferromagnetic. There-
one may determine if a defect or a surface has a smaller fore,wehavechosenthespin-dependentLDAtoperform
or a larger tendency to magnetism than the bulk, de- mostoftheremainingcalculationsinthiswork,although
pending on which of the two E(M) curves is higher. In GGA results have been obtained also as a check in some
addition, the selfconsistent convergengy is considerably cases.
faster at constant magnetic moment, so that it is possi- Themagneticsusceptibilityχofthemagneticmoment
ble to determine reliably (for a givenfunctional) relative M to an external magnetic field H is
energies as small as a fraction of an meV.
∂M ∂2E −1
χ= =
(cid:18)∂H(cid:19) (cid:18)∂M2(cid:19)
H=0 M=0
III. BULK CRYSTALS
Thus, the flatness ofthe E(M) curve in Figure 1 implies
averylargesusceptibility,evenwithintheLDA.Tocom-
Thefirstmandatorysystemtobeconsideredistheper- parewiththeothertransitionmetalsinthesamecolumn
fectbulkcrystalinitsexperimentally-stablefccphase. In of the Periodic Table we have calculatedthe variationof
principle,the GGAfunctionalgoesbeyondthe LDAand energywithmagneticmomentforNiandPt. Theresults
it is generally considered to be more accurate and reli- are shown in Figure 2. We immediately observe a clear
able. However, in the case of Pd, we find that the GGA ferromagnetic and paramagnetic behavior of Ni and Pt
givesalatticeconstantof3.99˚A,2.5%largerthanexperi- respectively, while Pd, as indicated above, is paramag-
ment, and a ferromagneticgroundstate with a magnetic netic but very close to the ferromagnetic transition.
moment of 0.4µ /atom and an energy 4.5 meV/atom Inordertostudy howmagnetismdepends onthe local
B
below the paramagnetic phase (Figure 1). Since this geometry and stacking of atoms, we have first consid-
energy difference is very small, and to discard that the ered the hcp structure as compared to the fcc one. It is
ferromagnetic phase is favoured by the pseudopotential knownthatthebreakingofthecubicsymmetryinstack-
or basis set used, we have reproduced6 this result using ing faults, while keeping the number of nearest-neighbor
3
2.0
fcc bulk
n) hcp bulk
pi
S
60 V 1.5
eV) 50 a) m e
Energy (m 123400000 Ni- fcc f states (1/ato1.0
o
60 y
50 b) nsit0.5
V) 40 Pd-fcc De
e
m 30
y ( 20 0.0-7 -6 -5 -4 -3 -2 -1 0 1 2
erg 10 Energy (eV)
n
E 0
60 FIG. 3: Calculated electronic densities of states of Pd in

50 c) the paramagnetic phase (i.e. forcing equal spin up and spin
)
V 40 Pt-fcc downpopulations) inthefccandhcpcrystalstructures. The
e
m 30 vertical line indicates theFermi level.
(
y 20
g
ner 10 I×D(EF)=0.84 for fcc and I×D(EF)=1.05 for hcp.
E 0
Wehavethencalculatedthetotalenergyandthemag-
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
netic order in the hcp phase in the LDA. The results
Magnetic Moment (m )
B are shown in Figure 4. We immediately observe that,
contrary to what happens in the fcc structure, there is
a non zero magnetic moment of 0.35 µ /atom at the
B
equilibriuminteratomicseparationforthe hcpstructure,
d=2.76 ˚A. Like in the fcc phase, the system is close to
FIG.2: Totalenergyversusmagneticmomentforthreetran- a magnetic-nonmagnetic transition but, in this case, in
sition metals in the same column of the Periodoc Table, cal- theferromagneticside,withtheferromagnetichcpphase
culated in the LDA. Note the flatness of the Pd curve, re- approximately1.7 meV lower in energy than the param-
sponsible of thelarge magnetic susceptibility of this metal. agneticone. Thetransitionfromparatoferromagnetism,
asafunctionofthelatticeconstant,isabrupt,likeinthe
fcc case, although we cannot assess with enough confi-
dence whether it is first or second order4,27.
atomsandtheirbondlengthsandangles,inducesarear-
Finally, the hcp structure is 4.0 meV higher in energy
rangement of the d energy bands that can even give rise
to localized electronic states26. The DOS of hcp and fcc than the fcc. This ordering is in agreement with experi-
ment,andwereproduceitalsowiththeGGA,butitisin
structures, in the paramagnetic phase, shown in Figure
contradictionwiththecalculationsofHugerandOsuch28
3,werecalculatedforthesamenearestneighbordistance
of 2.76 ˚A and the ideal ratio c/a = (8/3)1/2 for the hcp that reported an hcp structure lower in energy, but also
ferromagnetic.
structure, since we obtain that both structures are sta-
ble at this distance, with the hcp c/a ratio only 0.75%
largerthantheidealvalue. Severalpointsareworthmen-
tioning: (i) The d bandwidth is almost identical in both IV. BULK DEFECTS
structures because they have identical nearest-neighbor
configurations. (ii) The shapes of the DOS are very dif- Hexagonal(111)closedpackedplanes of atoms can be
ferent, as a consequence of the breaking of the cubic stacked in different ways, giving rise to different struc-
symmetry: in fcc the second-nearest-neighbor atoms are tures. Ifwelabelthethreepossiblepositionsoftheatoms
staggered whereas in hcp they are eclipsed and the lack asA,BandC,thefccstackingis...ABCABC... andthat
of cubic symmetry inhibits the t −e splitting of the of hcp is ...ABABAB...29, where the layers with hexag-
2g g
d bands. (iii) The DOS at the Fermi level is larger in onal symmetry are undelined. Different defects can be
hcp than in fcc (1.43 versus 1.15 states per atom per eV generatedinthefccstructure: Theintrinsicandextrinsic
and per spin). This implies that Pd in the hcp struc- stacking faults have two hexagonal layers, with stacking
ture satisfies the Stoner condition for ferromagnetism: sequences ...ABCACABC... and ...ABCACBCABC...
with a Stoner exchange parameter I=0.73 eV2,3, we get respectively. The twin boundary has a single hexagonal
4

0.030
a)
0.025 fcc 0.3
100
) (a) cubic
V 0.020 80
(e V) 0.2 hex
m 0.015 me 60
gy per ato 00..000150 Energy ( 24000 000...301--ABCACABCACABCA CABCACABCACABC
r
Ene 0.000 -0.M9-a0g.n6e-t0ic.3 m0o.0m0en.3t (0m .6)0.9 ) (b)
B B 0.2
-0.005 m(
2.72 2.76 B2o.8n0d le n2g.8t4h (Å)2.88 2.92 2.96 ent 0.1
m
0.046 o 0.0
M --ABCACABCABCACABCABCACABCABCA--
b) hcp 20 c 0.3
V)0.044 15 neti 0.2 (c)
e g
atom (0.042 y (meV)105 Ma 0.1
er erg 0.0
y p En 0 0.3--ABCACABCABCABCACABCABCABCACA--
erg0.040 -5 (d)
En -0.6-0.4-0.20.00.20.40.6 0.2
Magnetic moment (m )
B
0.038 0.1
2.72 2.76 2.80 2.84 2.88 2.92 2.96
Bond length (Å)
0.0
ABCABCACABCABCABCABCACABCABC--

FIG.4: Calculatedtotalenergyfor(a)fccand(b)hcpPdasa FIG. 5: Local magnetic moment in supercells of different
functionofthenearestneighbordistance. Thearrowsindicate thickness,containingasingleintrinsicstackingfault between
the minimum (equilibrium) nearest-neighbor distance. The fcc layers, calculated with theLDA.
insets at (a) and (b) show the total energy versus magnetic
moment for the fcc and hcp structures respectively. In these
cases theenergy origin is at thecorresponding minima.
behaviourisduetoanoscillatorycomponentofthemag-
netic coupling between the neighbouring stacking faults,
like that observed in superstructures of magnetic slabs
layer with ...ABCACBA... stacking.
sandwichedbetweennonmagneticmetals31. Althoughwe
Previous model calculations26 at stacking faults of havenot been able to stabilize any antiferromagneticso-
transition metals indicate an important perturbation of lution in double-size supercells, this may be due to the
the local densities of states from that of the perfect fcc size limitations andto the difficulties ofconvergence. As
lattice. Thepresenceofahexagonalstackingoflayersin- expected, the magnetic moments are smaller in fcc than
duceslocalizedelectronicstates26,30 andanenhancement in hcp layers, but they are nevertheless far from negligi-
of the DOS at the top of the valence band. These calcu- ble. Theinterplaybetweenthemagnetismofthehexago-
lations suggest possible variations of the magnetic prop- nallayersandtheparamagnetismofthecubicones,both
erties around the extended defect. We have performed close to a paramagnetic to ferromagnetic transition, is
calculations of several packing sequences, in supercells verysubtle. Whatisimportantisthatthehexagonallay-
containingvariousnumbersoffcclayers,tostudytowhat ershaveatendencytobecomemagneticandtheyinduce
extentdifferentlocalconfigurationscangiverisetomag- magneticmomentsattheatomsinthecubiclayers. This
netic moments. The results of the calculations, both in isduefirst,tothelargemagneticsusceptibilityinfccPd,
the perfect crystals and in the defects, are independent where the hexagonal layers act as magnetic impurities.
(within less than 1%) of the initial input moment. And second, because of the two-dimensional character
Most of the calculated supercells have a finite mag- of the defects, any magnetic perturbation decays very
neticmomentandsomeareshowninFigure5. However, slowly with distance, like in a pseudo one-dimensional
its variation with the supercell thickness is rather com- metal. In other words, there is a long-range RKKY-like
plex and nonmonotonic. We suspect that this complex interaction between the hcp layers through the interme-
5
diate fcc ones. (111)orientations,aftercarefullyrelaxingtheirgeomme-
Given the size limitations of our calculated supercells, try. The results of the calculated total energy versus
andthenonmonotonicmagneticmomentwithincreasing magnetic moment are shown in Figure 7 for the largest
supercell thickness, it is not possible to conclude con- calculated thickness. This general tendency is consis-
fidently whether isolated planar defects in fcc Pd have
a finite magnetic moment, within the LDA. However,
Fig. 6 clearly shows that all the hexagonal defects have
a larger tendency to magnetism than the bulk fcc lat-
tice, as indicated by their respective E(M) curves. This 6
is hardly surprising, given the ferromagnetic character
) fcc bulk
of hcp Pd. On the other hand, all the supercells are of V
e slab (100)
m
4
( slab (111)
m
o
t
6 er a2
p
y
) fcc bulk g
V r
e twin boundary ne
(m4 stacking-fault E0
m
o
t -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
a
per 2 Magnetic moment per atom ( B)
y
g
r
ne FIG. 7: Total energy within the LDA versus magnetic mo-
E0
mentofbulkfccPdandof9-layerslabswithsurfacesoriented
in the (100) and (111) directions. The energy at M = 0 has
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 been shifted to a common value.
Magnetic moment per atom ( )
B
tently obtained for sufficiently thick slabs, but the thik-
nessdependenceofthetotalmagneticmoment,shownin
FIG. 6: Total energy as a function of the magnetic moment Fig. 8 is not monotonic, as in the bulk supercells.
fordifferentstwodimensionaldefectsofPd,withlocalhexag-
onal symmetry,compared tothebulkfcclattice. Theenergy
at M = 0 has been shifted to a common value. The defects
areseparatedby6fcclayerslikeinFigure5(b). Thestacking
faultcurvehasaminimumof-0.2meVatM ≃0.09µB/atom, 0.5
in agreement with Figure 5b, which is not noticeable at the
figure scale. slab(111)
)
B slab(100)
m( 0.4
course strongly magnetic within the GGA, with a larger nt
e
tendency to magnetism (lower E(M) curve) than the m
o
bulk fcc crystal. Therefore, it is perfectly possible that m 0.3
anisolatedstackingfault infcc Pdis indeed magnetic in c
nature. neti
g
a 0.2
m
m
u
V. SURFACES m
xi 0.1
a
M
Recentexperimentalresults9 onPdnanoparticleshave
beeninterpretedasmagnetismat(100)surfaces. Inprin- 0
0 1 2 3 4 5 6 7 8 9 10
ciple, surface magnetism is plausible in general because
Number of layers
the lower coordination of surface atoms favors narrower
bands and larger densities of states. In practice, how-
ever,surface relaxationand reconstructionmay contract
the surface bond lengths and more than compensate for FIG.8: Largest local magneticmoment,asafunctionofthe
the lower coordination. We have then calculated the numberof layers, in slabs with surfaces oriented in the(100)
and (111) directions.
electronic structure of finite Pd slabs in the (100) and
6
We observe in Fig. 7 that the minimun energy is at
zeromagneticmomentandthereforethetwosurfacesare
paramagnetic. Moreover, the E(M) curve of the (100)
surfaceis higherthanthatofthe bulk, showingthatthis
0.3
surface is less prone to magnetism than the bulk. On a) E=-2.5 meV
0.2
the other hand, the (111) surface, although also param-
agnetic within the LDA, has a larger susceptibility than 0.1
the bulk, what makes plausible that it may be magnetic 0.0
-- A C A B C A B C A
in nature.
0.3
We have found that bulk planar defects, as well as b) E=-9.9 meV
0.2
(111)surfaces,havealargertendencytomagnetismthan )B
0.1
the bulk Pd crystal, which is itself on the verge of ferro-
magnetism. Since both surfaces and defects are in high nt ( 0.0-- A B A B C A B C A --
e
concentrations in nanoparticles, and both have in fact m 0.3
been proposed independently 8,9 as responsible of the Mo 0.2 c) E=-4.5 meV
osebnsseervteodcmonasgidneerticthmeiormcoemntbionfedtheeffseecpt.arTtiocleths,isitenmda,kwees tic 0.1
ne 0.0
havecalculatedthe geometry,energy,andmagnetism,of g -- A B C B C A B C A --
a
planar defects close to a (111) surface. We use a slab in M 0.3
which the opposite surface is “magnetically passivated” 0.2 d) E=-11.1 meV

byimposingashortdistancebetweenthefirsttwoatomic
0.1
planes, what inmediately kills their local magnetic mo-
0.0
nent. In this way, we ensure that the possible magnetic -- A B C A C A B C A --
momentoftheslabisduetothecombinationofthestack- 0.3
ing fault and a single surface (in fact, this structure pe- 0.2 e) E=-14.9 meV

nalizes and sets a lower limit for the appearence of mag- 0.1 ¤dead layers¤
netism). Still, asshowninFigure9,we findaclearmag-
0.0
netic moment in all the cases considered. This tendency C A C B C A B C A --
isfurtherdemonstratedbytheirE(M)curves,presented
in Figure 10 for two cases, which show unambiguously
FIG. 9: Local magnetic moments for diferents stackings of
their magnetic character. Furthermore, the total energy
hexagonal and cubic planes in a slab of 9 layers. (a) Twin
of all the slabs is lower than that of the defects in the
boundary. (b),(c),and(d)Intrinsicstackingfaults, withthe
bulk, plus that of the unfaulted slab, implying that the
hcp layers in differents positions. (e) Extrinsic staking fault.
surfaceatractsthedefectsandthattheyshouldtherefore
Squares and hexagons represent cubic and hexagonal layers,
be expected to appear together in nanoparticles, due to respectively. The distance between the two rightmost layers
thehighconcentrationofstackingfaultsandtothesmall was fixed to a small value, in order to kill their tendency
space between surfaces. Notice that the extrinsic stack- to magnetism and thus to simulate the bulk. The energies
ingfaultismorestablethantheintrinsiconebothatthe reported are the difference between the total energy of the
surface and at the bulk. slab,minusthoseofthedefectinthebulkandoftheunfaulted
slab. The formation energies in the bulk are 33.9, 74.7 and
73.0 meV forthetwin boundary,intrinsicstackingfault, and
extrinsic stacking fault, respectively.
VI. CONCLUSIONS
Our main conclusions can be summarized as follows: surface is paramagnetic, with a lower susceptibility than
(i) The GGAfunctionalgivesanincorrectferromagnetic the bulk crystal. (v) The (111) surface is paramagnetic
ground state for the fcc Pd crystal. Accordingly, all the in the LDA, but it has a larger susceptibility than the
defects studied are also magnetic within the GGA but, bulk crystal, and it might be magnetic in nature. (vi)
obviously, this does not imply that they are magnetic Hexagonal planar defects are atracted towards a (111)
in nature. On the contrary, the simpler LDA gives the surface, and they become clearly magnetic when close
correctlatticeconstantandparamagneticstate. (ii)The enough.
hcp phase is ferromagnetic, within both the LDA and Therefore, (100) surfaces are not good candidates as
GGA. In the LDA, it has an energy 1.7 meV lower than the origin of magnetism in Pd nanoparticles, as they
the hcp paramagnetic state and 4.0 meV above the fcc had been proposed9. In contrast, planar stacking de-
phase. (iii) We cannot determine whether an isolated fects,(111)surfaces,andspeciallyacombinationofboth,
stackingfaultismagneticintheLDA,butitcertainlyhas are plausible candidates to present permanent magnetic
a larger magnetic susceptibility than the perfect crystal, moments and to be responsible for the magnetism ob-
and might be magnetic in nature, given the uncertainty served in Pd nanoparticles. Thus, our results are con-
between the different functionals. (iv) The free (100) sistent with experiments in small Pd clusters of average
7
particlesexhibitsingleandmultipletwinningboundaries.
Inaddition,thesmallnessofthespontaneousmagnetiza-
0.2 tionseemstoindicatethatonlyasmallfractionofatoms
a)
0.0 hold a permanent magnetic moment and contribute to
-0.2 ferromagnetism. Other experimental results9 on small
V) -0.4 Pdparticles havealso showntheir ferromagneticcharac-
me -0.6 ter. Besides,ferromagnetismcanalsotakeplaceinother
y ( -0.8 non ideal structures like nanowires5.
erg -1.0 Intrinsic
En -1.2 stacking fault Magnetic anomalies observed experimentally in differ-
-1.4 ent Ni32 and Co12 stacking can be interpreted along the
-1.6 lines described in this work. The fact that stacking-
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
0.2 faults in Pd display non negligible magnetic moments,

0.0 b) not present in bulk fcc crystal, opens new lines of re-
-0.2 search. The appearance of magnetism in nominal fcc
V) -0.4 samples should be revisited in view of our results, since
e -0.6 sofarthepossibilityofmagnetismaroundstackingfaults
m
y ( -0.8 has been overlooked. Also, layer growth of Pd on top of
Energ --11..20 Extrinsic ndouncemanaginnetteircesstuinbgstrmaategsn,etinicclpuhdeinngomPednoiltosgelyf,inmcaoynpnreoc--
stacking fault
-1.4 tion with the stacking structure which, in turn, depends
-1.6 onthe methodusedforgrowth. The study ofthe depen-
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
dence of the magnetic properties of Pd grown Ag(111)
Magnetic moment (m )
and Pd/Ag multilayers on the stacking sequences is un-
B
der way and will be reported elsewhere.
Acknowledgments
FIG. 10: Calculated total energy, as a function of the mag-
neticmoment,fortwodifferenttwo-dimentional defectsclose
to a (111) surface (shown in Figure 9 (c) and (e)). WewouldliketothankA.Hernando,whobroughtour
attention to this problem, to O´. Paz for his assistance
in the technical part of this work, and to M. Mattesini
diameter 2.4 nm, which are reported to display sponta- for his help in the plane wave basis calculations. Work
neousmagnetization8. High-resolutiontransmissionelec- supported Spain’s Ministery of Science through grants
tronmicroscopyhasshownthatahighpercentageofthe BFM2002-10510-Eand BFM2003-03372.
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