Table Of ContentVer21
Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares
R. Koch, O. Waldmann, and P. Mu¨ller
Physikalisches Institut III, Universit¨at Erlangen-Nu¨rnberg, D-91058 Erlangen, Germany
U. Reimann and R. W. Saalfrank
Institut fu¨r Organische Chemie, Universit¨at Erlangen-Nu¨rnberg, D-91054 Erlangen, Germany
(Dated: February 2, 2008)
3
0 We investigated the magnetic properties of two isostructural Ni(II) metal complexes [Ni4Lb8] and
0 [Ni4Lc8]. In each molecule the four Ni(II) centers form almost perfect regular squares. Magnetic
2
coupling and anisotropy of single crystals were examined by magnetization measurements and in
n particularbyhigh-fieldtorquemagnetometryatlowtemperatures. Thedatawereanalyzedinterms
a ofaneffectivespinHamiltonianappropriateforNi(II)centers. Forbothcompounds,wefoundaweak
J intramolecular ferromagnetic coupling of thefour Ni(II)spins and sizable single-ion anisotropies of
1 the easy-axis type. The coupling strengths are roughly identical for both compounds, whereas the
2 zero-field-splitting parameters are significantly different. Possible reasons for this observation are
discussed.
]
l PACSnumbers: 33.15.Kr,71.70.-d,75.10.Jm,75.30.Et,
e
-
r
t
s I. INTRODUCTION
. TABLEI: Comparison of selected distances and bondingan-
at glesofthecoordinationsphereforthecompounds[Ni4Lb8]and
m Modern inorganic chemistry provides arrangements of [Ni4Lc8]. Consideringthenickelcentersattheupperrightcor-
magnetic metal ions in highly symmetric geometries, nersin Figs.1(b)and1(c),respectively,theNatomsoftheir
-
d wherethemetalcentersareseparatedbyorganicligands. coordinationsphereswerenumberedclockwisefromN1toN5
n Compounds with a topologically simple arrangement of starting with oxygen/sulfur.
co their metal centers like grids and rings have been inves- [Ni4Lb8] [Ni4Lc8]
[ tigated extensively. [1, 2, 3, 4, 5, 6] Due to their high Ni - O/S 2.032(2) ˚A 2.051(3) ˚A
symmetry it is possible to experimentally determine the Ni - N1 2.081(3) ˚A 2.073(4) ˚A
1 magnetic parameters of large and rather complex sys- Ni - N2 2.076(3) ˚A 2.072(4) ˚A
v tems. As intermolecular effects are negligible in these Ni - N3 2.111(3) ˚A 2.074(4) ˚A
3
systems, they actually form perfect models to explore Ni - N4 2.065(3) ˚A 2.112(4) ˚A
7
3 finite size spin systems. [7] In a number of cases, sev- Ni - N5 2.062(3) ˚A 2.070(4) ˚A
1 eralrelatedspeciesofacompoundclassareavailable,al-
◦ ◦
0 lowing to observe correlations between crystallographic O/S - Ni- N1 88.44(11) 86.98(15)
◦ ◦
3 structure and magnetic properties. [6, 8] Investigation N1 - Ni - N2 79.02(13) 78.04(17)
◦ ◦
0 of such correlations is of key help for understanding e.g. N2 - Ni - N3 94.62(12) 98.04(12)
◦ ◦
/ N3 - Ni - N4 79.26(11) 79.20(15)
at coupling mechanisms in detail. [9] N4 - Ni - N5 90.28(12) ◦ 92.46(15) ◦
m Recently, the highly symmetric Ni(II) square [Ni4Lb8] N5 - Ni - O/S 83.24(11) ◦ 83.30(14) ◦
with Lb = C5H4N-CON-CN4-C2H5 attracted consider-
-
able interest. [10, 11] Preliminary magnetic studies of
d
n powder samples revealed a sizeable ferromagnetic cou-
perimental methods like SQUID magnetometry, EPR
o pling of the four Ni(II) metal centers within a molecule.
c This system is thus one of the very rare examples of a and torque magnetometry are possible. Torque magne-
v: ferromagnetic Ni(II) complex. A second species, [Ni4Lc8] tometry has been proven to be a very valuable tool in
Xi with Lc = C5H4N-CSN-CN4-C2H5, could be also syn- this field. [2, 5, 6]
thesized. [11, 12] The two ligands used differ only at
r one position, i.e the oxygen in Lb is replaced by a sul-
a
fur in Lc. Interestingly, the two Ni4 squaresare not only II. EXPERIMENTAL
isostructural. Theirmagneticallyrelevantgeometricaldi-
mensions actually differ by less than 3.5%. This leads to A. Preparation and Crystal Structures
a new situation: Differences in magnetic properties stem
predominatelyfromdifferentelectronicpropertiesofoxy- The tetranuclear Ni(II) cluster [Ni4Lb8] · 4CH2Cl2
gen and sulfur and not from geometrical distinctions. It with Lb = C5H4N-CON-CN4-C2H5 was prepared as de-
isthe purposeofthis worktoinvestigatethe magnetism, scribed in Ref. 10. The isostructural compound [Ni4Lc8]
especiallythe magneticcouplingandanisotropy,ofthese · 4CH2Cl2 with Lc = C5H4N-CSN-CN4-C2H5 was syn-
two compounds in detail. thesized with a method analogous to that used for the
When focusing on anisotropic properties, several ex- [Ni4Lb8] complex. [12] The two ligands Lb and Lc are
2
(a) ligands (b) Ni Lb (c) Ni Lc
4 8 4 8
N
H
Lb = N N
N
O N
N
N
H
Lc = N N
N
S N
N
FIG. 1: (a) Sketch of both ligands Lb and Lc. (b) Structural representation of [Ni4Lb8] and (c) [Ni4Lc8] (view along the
crystallo graphic S4-axis, H atoms omitted).
sketchedinFig.1. Theyonlydifferbyoneposition: The interactions. As the two molecules are almost struc-
C=O group in Lb is replaced by a C=S group in Lc. turallyidentical,thepotentiallydifferentmagneticprop-
ThecrystalstructuresweredeterminedbyX-raystruc- ertiesof[Ni4Lb8]and[Ni4Lc8]shouldbecontrolledpredom-
ture analysisof single crystals. [10, 12] Both compounds inantly by the different electronic properties of oxygen
crystallize in the space group I4(1)/a. They exhibit and sulfur.
crystallographic S4 molecular symmetry with the four
nickel centers forming almost regular squares (Fig. 1).
The molecular S4 symmetry axes are perpendicular to B. Magnetization Measurements
the planes of the molecules defined by the Ni centers,
and necessarily coincide with the magnetic z-axes of the For magnetization measurements, a single crystal was
molecules. The shapeofthe crystalsisquadraticbipyra- selected by light microscopy in the mother liquor. To
midal. The molecular magnetic z-axes are thus parallel avoiddecomposition,the crystalwastransferreddirectly
to the S4 symmetry axis of the crystals. from the solution into Apiezon grease and mounted on
The eight ligands in a molecule coordinate the nickel a plastic straw. The weight of the crystals was typi-
centers in two different ways (Fig. 1). A set of four cally100µg. Thebackgroundsignalofgreaseandsample
ligands links two nickel centers each and builds up the holder was negligible comparedto the signalof the crys-
[Ni4L4]4+ square-like cores. The second set of four lig- tals. Magnetic moment was measured with a MPMS-7
ands coordinates the nickel centers at the corners of the SQUID magnetometer from Quantum Design. The tem-
square cores. Each nickel center is surrounded by six perature range was 1.8- 300K, the maximum magnetic
donor atoms, five N and one O for [Ni4Lb8] and five N field 5.5T. The measurements were performed for mag-
and one S for [Ni4Lc8], respectively, forming slightly dis- neticfieldsparallelandperpendiculartothez-axisofthe
torted octahedral coordination spheres. crystal. Due to the quadratic bipyramidal shape of the
Althoughthesulfurdonorsaresignificantlylargerthan single crystals, none of the crystal planes is parallel to
the oxygen donors, the structures of the two complexes the magnetic z-axis. Therefore, a proper orientation of
areremarkablysimilar. Thisisevidentfromacarefulin- the sample on the sample holder was difficult. The ori-
◦
spection of Figs. 1(b) and 1(c). The most notable struc- entation accuracy was about 10 . Two samples of each
tural difference arises for the CN4-C2H5 groups of the compound were investigated.
corner-ligands. Their orientations differ slightly in the
two compounds. This is plausible since these groups are
not coordinated to nickel centers. C. Magnetic Torque Measurements
However, the geometry of the nickel coordination
sphere as well as the structure of the ligand linking two Torque measurements of single crystal samples were
nickel ions are almost not affected by the replacement performed with an appropriately designed silicon can-
of oxygen with sulfur (Table I). The Ni-Ni next neigh- tilever torque sensor which will be described in detail in
bor distance is 5.567(5)˚A for [Ni4Lb8] and 5.560(5)˚A for the next chapter. As for magnetizationmeasurements, a
[Ni4Lc8]. Several further distances and bond angles are crystalwasselectedfromthemotherliquor,immediately
listed in Table I for both compounds. covered with grease, and mounted on the torque sensor.
These structural elements are most relevant for the Thetypicalsampleweightwaslessthan10µg,butcould
magnetic properties, i.e. ligand-field and superexchange be determined only within an error of 50% due to the
3
z B thedeviceinFig.2). Finally,thecantileverwasgluedon
Q x
z the quartz substrate.
sample
Thetorqueofthesamplecausesadeflectionofthecan-
tilever which is detected by a change of the capacitance
y 0.3mm ∆C. For readout, the two capacitors were connected
Dd silicon
Au to a ratio transformer forming an ac bridge. With this
setup a sensitivity of ∆C/C0 =10−7 is readilyobtained.
8mm [13,14]C0 denotesthezero-fieldcapacitance(1pF).The
properties of the cantilever torquemeter can be mod-
FIG. 2: Sketch of the silicon torquemeter described in sec- eled as follows: The deflection is ∆d = (3/2)τ/(D L ),
c c
tionIII. Thetypicalorientationofaquadraticbipyramidially
where D is the spring constantandL the length ofthe
c c
shapedcrystalsampleanditsz-axisareshown. Foradjusting
cantilever. The change of the capacitance is given by
the angle Θ, the device could be rotated in-situ around the
magnetic y-axis. ∆C/C0 ≈ ∆d/d0(1+∆d/d0), where d0 denotes the dis-
tanceofthecapacitorplates. Thisrelationshowsnonlin-
earbehavior. However,forallmeasurementspresentedin
thisworknonlinearitywaslessthan2%andcouldbene-
unknown amount of grease coveringthe crystals. There-
fore, the number of molecules in a crystal, X, is known glected. With U0 being a characteristic of the ac bridge,
only roughly and a calibration of the torque signal was its output voltage can be expressed as U =U0(∆C/C0).
Altogether,oneobtainsU =Kτ(1+αKτ)withthe cali-
notfeasible. Thetorquemeterwasmountedonarotating
brationconstantKandthenonlinearityα. Ifrequired,K
plate which allowed an in-situ orientation of the crystal
◦ andαmaybeobtainedfromanexplicitcalibrationwhich
with an accuracy of 0.3 . The sample was mounted on
can be done quite easily in many ways. [14, 15, 16] As
the sensor with its z-axis perpendicular to the rotation
we were not able to determine the weight of the samples
axis,asindicatedinFig.2. Thepositioningaccuracywas
◦ accurately, calibration of the device was not necessary.
better than 3 , which is much better than for the mag-
netization measurements. Figure 2 defines the angle Θ
between magnetic field and magnetic z-axis of the crys-
tal. Thetorquemeterprovidesaresolutionof10−11Nm. IV. THEORY
Itwasinsertedintoa15/17Tsuperconductingcryomag-
net system. The temperature wasadjusted by a variable The appropriate Hamiltonian for molecular spin clus-
temperatureinsert. Typically,torquemeasurementsver- ters consisting of Ni(II) centers is given by [7, 17]
susappliedmagneticfieldwereperformedat15different
◦
anglesΘinarangeof220 . Thelowesttemperaturewas
1.8K.For severalsamples, the low-fieldrange was inves- H =− J S ·S +
X ij i j
tigated in detail, i.e. at 60 different angles in a range of
i<j
◦
180 . 5 samples of each compound were investigated. S ·Dlig ·S +µ S ·g ·B (1)
X i i i BX i i
i i
III. SILICON CANTILEVER TORQUEMETER with S = 1 and the following standard terms: a
i
Heisenberg term modeling isotropic next-neighbor ex-
A schematic drawing of the cantilever device is pre- changeinteractions,azero-field-splitting(ZFS)termdue
sented in Fig. 2. The cantilever is mounted on a sub- to ligand-field interactions, and the Zeeman term. Due
strate of crystalline quartz glass. It is made from a very to the small coupling constants in [Ni4Lb8] and [Ni4Lc8],
pure crystallinesiliconwafer (resistivity>3kΩcm)with anisotropic and biquadratic coupling terms can be ne-
a (100)surfaceorientationandthickness of300µm. The glected. Dipole-dipole interactions are negligible due to
use of crystalline silicon guarantees excellent mechanical the large distances of the spin centers. Cross-coupling
aswellasnon-magneticalproperties. AsshowninFig.2, superexchange terms hardly exist as corresponding cou-
thesinglecrystalsiliconcantileverconsistsofpartsatthe plingpathsarenotpresent. DuetothemolecularS4sym-
original thickness of 300µm and strongly thinned parts. metry of the complexes, magnetic anisotropy is strictly
This has been achieved by different masks on the two uniaxial and a simplified Hamiltonian is obtained:
sidesofthe wafer. Themaskswereformedby1µmthick
SiO2layersgrownonbothsidesofthesiliconwaferwhich
were patterned by standard photolithography and etch- H =−J S ·S +D (S2 −2/3)+
X i j X i,z
ing with buffered fluorine acid. The silicon cantilever i<j i
itselfwasetchedby hotKOHto athicknessof10-30µm. µ g (S B +S B )+µ g S B . (2)
B xy x x y y B z z z
A 200nm gold layer was evaporated on the bottom side
of the cantilever. Together with gold pads structured on Thus, four magnetic parameters are sufficient to de-
the quartz substrate it forms a capacitorand a reference scribe the properties of the Ni4 squares correctly: the
capacitor (which is placed at the right hand section of coupling constant J, the ZFS parameter D and the two
4
5 7
a)
B || z J = 0.40(4) K 74°
4 D = -2.80(5) K 60°
K) g = 2.33(9) 6
-1T 3 Dg = 0.01(1) 46°
mB
A 5
N
( 2
T B z
c 32°
1 s)4
NiLb nit
4 8 u
0 b.
0 10 20 30 40 50 ar3
(
T (K) t
10 18°
b)
2
8 B || z NiLb
4 8
6 1
m)B
A 4°
N
( 4
0
m
0 3 6 9 12 15
B z
2 B (T)
0 FIG.4: Torquemeasurementsvs. magneticfieldofa[Ni4Lb8]
0 1 2 3 4 5 6 crystal sample at several angles Θ and T = 1.8K (circles).
B (T)
Thecurvesareshiftedforclarity. Thesolidlinesrepresentfits
usingHamiltonian eq.(2). Thearrows indicatetheinflection
FIG. 3: (a) Magnetic susceptibility times temperature vs. points of thecurves.
temperature and (b) magnetic moment vs. magnetic field at
T=1.8Kofa[Ni4Lb8]crystalfortwodifferent orientationsof
magnetic field. The solid lines represent best fits based on showedthatthelowtemperaturebehaviorofthemagne-
eq. (2).
tizationisverysensitivetoamisalignmentofthecrystal.
◦
Alreadyamisalignmentof5 ,whichiswellwithinexperi-
mentaluncertainty(seesectionIIB),leadstonotablydif-
g-factorsg andg . In the following we will use the pa-
xy z ferent parameters. Therefore, the results from the mag-
rameterizationg =q(2gx2y+gz2)/3and∆g =gz−gxyfor netization measurements will be regarded as guidelines
theg-factors. As wewillsee,J ≈0.9KandD ≈−2.5K. and will not be discussed further. Nevertheless, a trend
Thus neither the strong exchange limit (|D/J|≪1) nor isindicated: Thecouplingconstantsareroughlyidentical
the Ising limit (|D/J| ≫ 1) is valid. Therefore, a full in both compounds, whereas the ZFS parameters differ
matrix diagonalization has to be performed. Due to the significantly.
small dimension of the Hilbert space of 34 = 81, this
canbedoneonacommercialPC.Calculationtimecould
be reduced by a factor of 12 by taking into account a VI. TORQUE MAGNETOMETRY: RESULTS
C2ν spinpermutationalsymmetryofHamiltonianeq.(2). AND ANALYSIS
[18]
The torque measurements were analyzed by fitting
Hamiltonianeq.(2)tothedata. Asthetorquesignalwas
V. MAGNETIZATION MEASUREMENTS: uncalibrated,thenumberX ofmoleculesinasamplehad
RESULTS AND ANALYSIS to be considered also as a free parameter, in addition to
the parameters J, D, g, and ∆g. In our first attempt to
Magnetic susceptibility and magnetization curves for determine the magnetic parameters, we fitted the com-
[Ni4Lb8]withmagneticfieldparallelandperpendicularto pleteangulardependenceτ(B,Θ)ofasamplewithX,J,
the magnetic z-axis are shown in Fig. 3. Fits based on D and∆g varyingsimultaneously. g wasfixedtoreason-
eq.(2)revealedthefollowingparameters: J =0.40(4)K, ablevaluesbetween2.1and2.3. [7,19,20]Atypicaldata
D = −2.80(5)K, g = 2.33(9) and ∆g = 0.01(1) for setwithcorrespondingfitisshowninFig.4. Concerning
[Ni4Lb8] and J =0.40(4)K, D =−1.80(8)K, g =2.33(9) theparameterR= (τsim−τmeas)2/ τm2eas,whiches-
and ∆g = 0.01(1) for [Ni4Lc8]. It should be noted, that timates the qualityPof the least squarPe fits, we obtained
the given errors reflect statistical uncertainties only and excellent results. Unfortunately, this approach revealed
do not include systematical errors. Detailed simulations rather large variations of the parameters for different
5
1.50
TABLEII:Magneticparametersfortheexaminedmolecules. T= 2 K D = -3 K
D = -2.5 K
J (K) D (K) ∆ g
1.25 D = -2 K
[Ni4Lb8] 0.9(1) -2.7(1) 0.01(1)
[Ni4Lc8] 0.9(1) -2.0(1) 0.01(1)
T) 1.00 J=0.5K
(
Bip
samples. However, fixing one additional parameter be-
0.75
J=1K
sides g yielded stable fitting results. Thus, either J, D
or∆gshouldbedeterminedinadifferentway. Aswewill
show, this can be done without additional experimental 0.50
0 90 180 270 360
data. The improved strategy rests on the fact, that a fit
Q (°)
to the whole data set does not consider that the param-
eters affect individual parts of the torque curves selec-
FIG. 5: Calculated values for the inflection point Bip of
tively. Acarefulstudyofnumericalsimulationsbasedon
torquecurvesasfunctionofΘfordifferentparametersJ and
Hamiltonian eq. (2) provides valuable information con- D (g=2.2, ∆g=0 ).
cerning this topic.
Figure 3(b) shows that the magnetization curves sat-
urate at fields of about 5T. This is easily understood as a)2.5
calculationsshowthatthe groundstateis wellseparated NiLb
4 8
fromtheexitedstatesat5T(∆E>5K).Thetorquemea- 2.0 T= 4 K
surementsexhibitsimilarsaturation(Fig.4). Inthisfield
regime, the torque curves are featureless and the magni-
T) 1.5
tudeiscontrolledbyX,∆g,andD simultaneously. Here (
the curves are over parameterized. Bip
T= 2 K
For a detailed examination of the low-field part, it is 1.0
useful to analyze the behavior of the inflection points
B (Θ) of the torque curves. In this way, the parameter
ip 0.5
X is eliminated as the value of B (Θ) is independent of -90 -45 0 45 90 135 180
ip
the magnitude of the curves. Figure 4 shows that the Q (°)
inflection points vary slightly with Θ. The calculated b) 1.1
angular dependence of Bip for different values of J and NiLc
D is presented in Fig. 5. It turns out that the offset 1.0 4 8
of the oscillation is shifted downwards with increasing J
0.9
(andg,notshownhere). Ontheotherhand,the offsetis
not influenced by D and, as further simulations showed, T)
(
by ∆g. In contrast, the amplitude of the oscillation is Bip 0.8
controlled by D exclusively. So it is possible to extract
the values of D and J (for given g) from analyzing the 0.7 T= 2 K
inflection points of the measured torque curves. As g
should be between 2.1 and 2.3, J may be obtained with 0.6
0 45 90 135 180 225 270
an accuracy of 10%.
Q°
For two samples of every compound, we determined
Bip(Θ)frommeasurementsat60differentangles. Fitting FIG. 6: Bip vs. angle Θ of measured torque curves for (a)
this data (Fig. 6) revealed D and J very precisely. To [Ni4Lb8]and(b)[Ni4Lc8]. Solidlinesrepresentfitsusingeq.(2).
obtain the remaining parameter ∆g, the whole torque For [Ni4Lb8], data sets for two temperatures have been used
data set τ(B, Θ) was fitted with D and g fixed. As J simultaneously in theanalysis.
was not fixed in this procedure, it could be determined
againandcomparedto the value extractedfromB (Θ).
ip
This provided prove for the consistency of our analysis. mined here. We ascribe this to structural changes of the
The parameters for the two compounds are summarized clusterresultingfromlossofCH2Cl2moleculesupondry-
in Table II. ing of crystals. This effect has been observed for other
molecules, which decompose rapidly under exposure to
air, too. [6, 16] The different values for J obtained from
VII. DISCUSSION single crystal SQUID measurements as compared to the
torqueresultsisexplainedbymisalignmenterrorsasdis-
The value ofJ observedforpowdersamples of[Ni4Lb8] cussed in section V.
inRef.10isalmostafactoroftwolargerthanthatdeter- Within the error ranges, the value of ∆g is consistent
6
ent for [Ni4Lb8] and [Ni4Lc8], as demonstrated by the ob-
served different values for D. Thus, one would expect
path 1
that also the coupling constants are clearly different, in
N
contrastto experimentalobservation. This suggeststhat
C O
the magnetic coupling is predominantly controlled by
N Ni2 path 2. But then, an antiferromagnetic coupling should
be expected which generally dominates if the overlap is
Ni1 C N
non-zero. [21] Obviously, the ferromagnetic coupling in
N N [Ni4Lb8] and [Ni4Lc8] is the result of a subtle balance be-
path 2 tweenferromagneticandantiferromagneticcontributions
N
which is not easily reconciled with present knowledge.
FIG.7: Sketchoftheligand Lb8 bridgingtwonickelions, the VIII. CONCLUSION
free metal orbitals of the two linked Ni centers, and the two
obvious coupling paths. The two Ni4 compounds studied in this work are of
interest for three reasons: (i) Ferromagnetic coupling
in molecular spin systems is rather rare. Concerning
withpredictionsofligand-fieldtheory: From∆g =2D/λ polynuclear Ni complexes, only few systems are known
and λ = −250K appropriate for Ni(II) centers [19] one to date. [22](ii) The high crystallographicsymmetry re-
obtains ∆g=0.02. duces the number of magnetic parameters significantly,
The above analysis demonstrated that the coupling allowingveryaccuratedeterminationofthemagneticpa-
constants are identical within experimental accuracy in rameters. (iii)Twospecieswithminimalgeometricaldif-
bothcompounds,whereasthe ZFSparametersdiffer sig- ferences of one system facilitates an isolation of possible
nificantly. The geometry of the Ni coordination spheres links betweenligand-fieldsplitting ormagnetic coupling,
are essentially identical for the two complexes. Thus, respectively, and electro-structural properties.
different values ofD shouldbe ascribedto different elec-
We showed that J and D can be determined very ac-
tronic environments of the Ni centers. In particular, the
curately by torque magnetometry in combination with
different donor capabilities of oxygen and sulfur should
sophisticated analysis also for systems where J and D
clearly affect the ligand-fields and thus the ZFS parame-
are on the same order of magnitude. This extends re-
ters.
cent applications of torque magnetometry to molecular
The results for J are more puzzling. The special ge-
nanomagnets. [2, 5, 6]
ometrical arrangement of the two coordination pockets
The differences of the anisotropy parameter D have
leads to an othogonality of the metal orbitals. To point
been ascribed to local differences in the electronic envi-
thisout,Fig.7showsasketchoftheligandLblinkingtwo
ronment of the Ni centers. For the coupling constant J
Ni centers and the relevant metal orbitals (hypothetical
some mechanisms have been suggested but no final ex-
orbitalsofafreeNiatom). Themagneticorbitalsshould
planation could be given. Ab-initio calculations would
extend along the coupling path between neighboring Ni
be of great help to provide comprehensive explanations
ions as indicated by the gray background in Fig. 7. The
for the origin and the strength of the coupling. [23]
coupling path actually may be split in two sub-paths,
path 1 along the Ni-N-C-O-Ni chain and path 2 along
theNi-N-C-N-Nichain. Thissuggestsanexplanationfor
Acknowledgments
the observedferromagnetic couplings: When path 1 and
path 2 contribute equally to the magnetic coupling, the
overlap of the magnetic orbitals will be zero for parity We would like to thank Andreas Richter for help in
reasons. Then, magnetic coupling would be ferromag- the lab and Jochen Thomas for silicon handling. Fur-
netic since an antiferromagnetic contribution, which is thermorewethankStefanSchrommandStephanRother
proportional to the overlap, cancels out. [21] forvaluablediscussions. Thisworkwassupportedbythe
However, path 1 of the coupling path is quite differ- Deutsche Forschungsgemeinschaft.
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