SUPPLEMENTARY INFORMATION
doi: 10.1038/nnano.2011.11

Giant magnetoresistance through a single molecule
S. Schmaus, A. Bagrets, Y. Nahas, T. K. Yamada, A. Bork, M. Bowen, E. Beaurepaire, F. Evers, and W. Wulfhekel

GEOMETRY OPTIMIZATION

We used the quantum chemistry package TURBOMOLE [1] to ﬁnd the atomic structure of the molecular junctions.
We performed standard geometry optimization for H2 Pc on the Cu(111) surface, represented by a cluster of 65 atoms.
The use of Co(111)-clusters for structure optimization is impaired by the very large number of energetically almost
degenerate spin multiplets. The gradient corrected approximation (GGA [2, 3]) density functional theory (DFT)energy was amended by empirical corrections [4] to account for dispersive van der Waals interactions between themolecule and the surface. Our analysis suggests that hydrogen phthalocyanine (H2 Pc ) prefers the ”bridge” position(see main text, Figure 3a) with a binding energy −8.17 eV, relative to the ”hollow” site position (binding energy−8.06 eV) and ”atop” site position (binding energy −7.45 eV), which is consistent with earlier ﬁndings [5, 6].
ELECTRONIC STRUCTURE AND TRANSPORT CALCULATIONS THROUGH H2 PC.

DFT based electronic structure and transport calculations through H2 Pc molecular junctions were performed within
the non-equilibrium Green’s function (NEGF) approach as implemented in a homemade simulation code [7] interfaced
to the quantum chemistry package TURBOMOLE [1]. The atomic conﬁguration of the ”extended molecule” used tosimulate the bottle-neck of the molecular junction is shown in Suppl. Fig. 1a (”contact” regime): H2 Pc is boundto the two Co(111) clusters with 51 and 19 atoms that represent the Co surface and the Co tip of the scanningtunneling microscope (STM), respectively. To establish this conﬁguration, a free H2 Pc molecule was bent along thelowest-energy vibrational eigenmode that agrees with the experimental geometry. A similar atomic conﬁguration
with H2 Pc bound to the surface only was used for transport simulations in the tunneling regime. The GGA (BP86functional [2, 3]) and a contracted Gaussian-type split-valence basis set with polarization functions (SVP) [8] wereused for calculations.
First, a closed-shell (nonmagnetic) solution for the ”extended molecule” comprising 2156 electrons was found.
To account for inﬁnite reservoirs with spin-polarized electrons, the spin-dependent (σ = ±1/2) local self-energies,surface/tip(x, x ) = [λ + σ∆ex − iγ] δ(x − x ), were ascribed to the outermost boundaries of the simulation clusterΣσ(dark gray atoms at Suppl. Fig. 1a). Here, a parameter ∆ex = 1.6 eV accounts for the exchange splitting of the bulk
Co d-states [9]. The freedom to choose the sign of ∆ex independently for the ”surface” and ”STM-tip” clusters allows
us to assemble two solutions with a parallel and antiparallel alignment of the electrodes’ magnetizations.
We apply the NEGF to evaluate the charge- and spin-density matrices in the presence of open boundaries, insuring
a charge neutrality within the ”extended molecule”. The density matrices are returned to TURBOMOLE to ﬁnd amodiﬁed set of Kohn-Sham orbitals, with a cycle to be repeated unless the self-consistent solution is reached. Fora given value γ ( = 1.36 eV in present calculations) of the level broadening, the contribution λ to the real part ofthe self-energy was deﬁned by imposing the condition of spurious charge accumulation to be absent at the cluster’sboundaries. Further details of the computational approach will be published elsewhere.
As an example, details of electronic structure for the molecular junction in the case of a parallel alignment ofmagnetizations are presented in Suppl. Fig. 1c,d. We have ascertained that, in our study, the electronic structure ofthe Co surface is properly reproduced. In particular, the electronic states at the Co-surface are spin-polarized withan exchange splitting ≈ 1.8 eV (Suppl. Fig. 1d), giving rise to an average magnetic moment ≈ 1.65µB per a surface
Co atom, in agreement with previously reported calculations [10].
Inspecting the H2 Pc local density of states (DOS) (see Suppl. Fig. 1c), we ascribe the majority spin resonanceabove the Fermi level (EF ) to the quasi-degenerate lowest unoccupied molecular orbital (LUMO), which is weighed
signiﬁcantly by nitrogen atoms (cf. Suppl. Fig. 1b). In contrast, no density is seen on nitrogen sites for the majority
spin highest occupied molecular orbital (HOMO) resonance positioned at ∼ 1.2 eV below EF (Suppl. Fig. 1b).
Furthermore, the minority spin H2 Pc LUMO level evolves into a broad peak due to a hybridization with the minority
spin Co states, with a density near EF that signiﬁcantly exceeds that of majority spin electrons. It is the asymmetry
in the LUMO level broadenings, i.e. Γmin > Γmaj , that gives rise to the magnetoresistance eﬀect (see main text for
further details).

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supplementary information

doi: 10.1038/nnano.2011.112

self-energy  isascribed tocluster's boundaries

u2g

Local DOS [states/eV]c 10H2Pc

LUMO

HOMO

1N, majority spin
H2Pc, majority spin

0.1
0.1

Local DOS [states/eV]

dN, minority spin
H2Pc, minority spin

110-53g-4-3-2-10E - EF [eV]123Co, majority spin

Co(111) surface4037 atoms

200Co, minority spin

2040-5-4-3-2-10E - EF [eV]123Suppl. Fig. 1: (a) Atomic cluster representing the bottle-neck of the H2 Pc molecular junction, as used for the electronicstructure and transport calculations. The outermost boundaries of the Co cluster (dark gray) are subject to the absorbing
boundary conditions modeled by the self-energy Σσ . (b) Frontier molecular orbitals of H2 Pc (D2h symmetry): an Au HOMO
and a quasi-degenerate LUMO doublet, B2g and B3g . (c) and (d): spin-polarized local density of states of the H2 Pc moleculeand Co(111) surface, respectively.

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supplementary information

doi: 10.1038/nnano.2011.11

3ab30022d I/dV [arb. units]

Current in Contact [nA]200-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

100
0-100-200-300-100-50050

100

Voltage [mV]

Energy [eV]Suppl. Fig. 2: (a) d2 I / dV 2 curve for Pc [11] taken in the tunneling regime. One observes an excitation located at around20 meV. The insets shows the d2 I / dV 2 map taken at these energies. The dip-peak structure is clearly constrained to the sidegroups of the molecule, visualized in the inset of (b) showing the diﬀerence of the two images. (b) I(V ) conductance curves
measured in the contact regime, when the molecules bridge the tunnel gap. At 20 mV the noise of the curve strongly increases,
indicating that the soft vibron of the molecule is excited.

SOFT VIBRON EXCITATION

We calculated the junction’s geometry before and after contact. These two geometries correspond to two local
minima in the energy landscape separated by an energy barrier. The transition between these two states is expected
to follow the lowest energy path between the two states. Thus, the transition is related to the softest vibration mode of
the molecule agreeing with the geometry. As shown in our previous work [11], the lowest-lying vibron of the molecule
is at around 20 meV (see Suppl. Fig. 2a). Spatially resolved inelastic tunneling spectroscopy is also consistent withthe theoretical observation, namely, that the excitation is located on the sidegroups of the molecule, indicated by a
dip and peak in the spectroscopy data of the two insets of Suppl. Fig. 2a. To extract the spatial distribution of thevibron, the diﬀerence signal was taken, resulting in bright spots on the four sidegroups (inset Suppl. Fig. 2b). This
soft vibron is not only responsible for forming the contact but also for breaking it. When taking the I(V ) in thecontact geometry (see Suppl. Fig. 2b), one notices a strong increase of the current noise when exceeding the excitationthreshold of 20 mV (dashed lines). This is an additional reason to acquire the giant magneto-resistance (GMR) data
at voltages below 20 mV so as to reduce the current noise.
TRANSPORT MEASUREMENTS ACROSS MAGNETIC PHTHALOCYANINE MOLECULESWe also carried out GMR measurements across Co-Phthalocyanine molecules on Co thin ﬁlms with Co coated tips.
In contract to the case of H2 Pc molecules, we were not successful to observe any GMR eﬀect. This may be due to twoeﬀects. First, the magnetic molecules posses a local spin on the molecule that can cause substantial spin scatteringof the transport electrons destroying the spin polarization of the current. Second, if the Co molecular site is coupledferromagnetically to both the substrate and tip as observed [12, 13] for related interfaces, it may be diﬃcult to achievea simple antiparallel alignment. In this case, a tunneling regime across two Co/CoPc interfaces that are decoupledby additional CoPc monolayers [14] or by vacuum [5] appears more promising.

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doi: 10.1038/nnano.2011.11

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