Supplementary Information:
Single molecule magnetoresistance with combined
antiferromagnetic and ferromagnetic electrodes
Alexei Bagrets,∗,†,‡ Stefan Schmaus,¶,§,@ Ali Jaafar,k Detlef Kramczynski,¶ Toyo
Kazu Yamada,¶,⊥ Mébarek Alouani,k Wulf Wulfhekel,¶,§ and Ferdinand Evers‡,#
Steinbuch Centre for Computing, Karlsruhe Institute of Technology, 76344
Eggenstein-Leopoldshafen, Germany, Institute of Nanotechnology, Karlsruhe Institute ofTechnology, 76344 Eggenstein-Leopoldshafen, Germany, Physikalisches Institut, Karlsruhe
Institute of Technology, 76131 Karlsruhe, Germany, DFG-Center for Functional Nanostructures,
Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany, Institut de Physique et Chimie desMatériaux de Strasbourg (IPCMS), UMR 7504 CNRS-ULP, 67034 Strasbourg, France, Graduate
School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan, and Institut
für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe,
Germany
E-mail: Alexej.Bagrets@kit.edu∗ To whom correspondence should be addressed† Steinbuch Centre for Computing, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany‡ Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany¶

Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany§ DFG-Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germanyk Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), UMR 7504 CNRS-ULP, 67034 Strasbourg,

France⊥ Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan# Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany@ Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany1

I. Atomic structure of H2Pc on Mn/Fe(001)
A. Methodology
To identify an adsorption geometry of H2 Pc molecule on Mn/Fe(001) film, we have carried out
electronic structure calculations based on density functional theory using a pseudopotential method
as implemented in the SIESTA code. 1 A local spin density approximation (LSDA) to the exchange
and correlation energy has been employed using the parametrization of Perdew and Zunger. 2 To
further refine the calculation of the molecule-substrate interaction, the generalized gradient approximation 3 (GGA) was merged with the Grimme’s correction scheme 4 to account for van der
Waals interactions. Both systems, Mn/Fe(001) substrate and H2 Pc/Mn/Fe(001), were modeled using periodic supercell structure with each cell separated from its neighbors by a 15Å vacuum gap
to ensure a minimal interaction between repeated images. The Brillouin-zone was meshed by a
Monkhorst-Pack 5 grid with 4 × 4 × 1 k-points. The standard Troullier-Martins 6 pseudopotentials
are adopted and expressed in the Kleinman-Bylander 7 factorization. The double-ζ atomic orbitals
have been used as the basis sets with an equivalent plane-wave cutoff of 500 Ry to represent the
charge density.

B. Structural properties of Mn/Fe(001) films
First, we have examined the optimal growth of Mn layers on a Fe(001) surface. In fact, bulk Mn
can be stable only in simple bcc or fcc crystal structures by alloying or epitaxial growth at room
temperature. 8 Concerning the epitaxial growth, Mn layers grow on Fe(001) in the bct structure 9,10
with an in-plane lattice constant a equals to the interatomic distance of the substrate’s surface layer.
In the present work, the Mn/Fe(001) substrate is modeled by 3 monolayers (ML) of Mn deposited on three layers of bcc Fe(001) (see Suppl. Fig. 1). A simulation cell contains 294 atoms,
with 49 atoms in each layer. A calculated optimal distance between the Mn layers and the Fe(001)substrate is about 3 Å in the out-of-plane and 2.858 Å in the in-plane direction. This structure canbe regarded rather as a body centered tetragonal bct with c/a ∼ 1.05, which is in agreement with2

Suppl. Fig. 1: Three monolayers of Mn deposited on Fe(001).
that found by Krüger et al. 10
In order to determine an adsorption geometry of the H2 Pc on Mn/Fe(001) substrates, we havechecked four high-symmetry positions, i.e., the center and top positions where the H2 atoms of the
H2 Pc molecule are placed either in the center of the square or on top of Mn atom of the Mn/Fe(001)substrate, and the two equivalent bridge positions (see Suppl. Fig. 2).

C. Adsorption geometries of H2 Pc on Mn/Fe(001)Concerning the stability of H2 Pc on Mn/Fe(001), we found that the center and the top positions(see Suppl. Fig. 3) are the most stable and the optimal distance between the molecule and thesubstrate is 2.1 Å within the LSDA. Computed relative energies of the optimized structures ofH2 Pc adsorbed on Mn/Fe(001) are listed in Suppl. Table 1 for each of the adsorption sites. The
total energy as a function of the distance between the molecule and the substrate is displayed in
Suppl. Fig. 3. The figure shows that the difference between the total energy of top and center
adsorption sites at 2.1 Å is small. Indeed, both curves are lower in energy compared to that of
the bridge position. Switching to GGA and Grimme’s correction scheme for vdW interactions 4
reduced further the molecule-surface distance to 1.93 Å but the top position remains the mostfavorable.

3

Suppl. Table 1: Calculated relative energy ∆E (eV), within the LSDA functional, for different
adsorption geometries. The energy for the most stable position is set to zero.
∆E(eV)

top
0.0

center
0.06

bridge3.1

Suppl. Fig. 2: Adsorption geometry of H2 Pc on Mn/Fe(001) surface.

-2858

-0.5

top position / GGA+VdW
center position / GGA+VdW-1

Etot (eV)∆Ε (eV)bridgecenter
top

-2862

-1.5

-2
1.5

-2860

2

2.5

-2864

1.6

3

1.8

2

2.2

2.4

2.6

molecule-surface distance (Å)

Distance (Å)

Suppl. Fig. 3: Energy vs the distance between H2 Pc and Mn/Fe(001) substrate for different adsorption geometries. The left panel represents the LSDA results and the right panel those within
the GGA + vdW Grimme’s correction scheme.

4II. Binding of H2Pc to the Fe STM tip
In this section we discuss a possible binding mechanism between the H2 Pc and the Fe coated STMtip. As shown in Fig. 1 of the paper, STM tips are simulated by bcc (001) atomic clusters of Fe,
containing either 14 atoms (“sharp” tip) or 13 atoms (“flat” tip). Since only one phenyl ring of themolecule is found in close proximity with the tip, it is essentially enough to consider binding of abenzene molecule to the Fe atomic cluster. We assume that such binding could be realized via theoverlap between the highly directional d orbitals of the low-coordinated Fe atoms of the tip withthe carbon pz (out-of-plane) orbitals. In the case of “sharp” tip, we consider that Fe apex atom isbound to a single C atom (Suppl. Fig. 4a, inset). In the case of “flat” Fe tip, four out of six C atomsof the benzene ring are facing the corresponding Fe atoms of the cluster ensuring effective overlap
between orbitals (inset of Suppl. Fig. 5a).
To estimate a binding distance D of the benzene ring to the Fe cluster(s), we have performed
ground state energy calculations considering D as the only relevant parameter and keeping fixed allother interatomic distances. We have employed modern full-electron electronic structure code FHIaims, 11 which is based on the numerical atom-centered basis sets. The PBE exchange correlation
functional and the “tier1” basis set (of the split-valence plus polarization quality) have been used.
Furthermore, van der Waals contribution to the ground state energy has been accounted for within
the Tkatchenko-Scheffler model, 12 which relies on the interatomic dispersion coefficients derived
from electron density.
Our results for the binding energy, Ebinding = Emol−tip − Emol − Etip , are shown in Suppl. Figs. 4
and 5. Indeed, we observe that a benzene molecule binds to the Fe clusters. In the case of “sharp”
tip, a binding energy is around 0.75 eV at the optimal distance of 4.04 Å. Note that van der Waals
forces contribute up to ≈ 50% to the bond energy. In the case of “flat” tip, because of the larger
number of C atoms involved, the binding energy is sufficiently larger, around 2 eV, allowing forthe smaller molecule-to-tip distance of 3.78 Å. As follows from Supp. Fig. 5, this bond may bequantified as predominately covalent, since 70% of the binding energy is already given by the PBE
functional, which does not account for the dispersion van der Waals interactions.
5Suppl. Fig. 4: (a) Binding energy of the benzene molecule to the apex atom of the Fe cluster with
14 atoms (exact atomic geometry is given in the inset). Red and blue curves show, respectively,
full binding energy (including dispersion vdW forces) and a contribution to the bond energy due
to a covalent overlap between Fe and C orbitals. (b) A hybrid molecular orbital of the H2 Pc boundto the Fe cluster, which illustrates a directional covalent-like character of the bond.

Suppl. Fig. 5: The same as in Supp. Fig. 4 but for the case of Fe cluster with 13 atoms.
To further support our statements, we present in Suppl. Figs. 4b and 5b selected hybrid wave
functions of the H2 Pc bound to the Fe atomic clusters. Wave functions plots correspond to hybird states in the majority spin channel placed approx. 4 eV below the Fermi level. Both hybrid
molecular orbitals show significant overlap between formely delocalized π orbitals of the phenyl
ring with those Fe d like orbitals that point towards C atoms. Such a covalent-like hybridization
distorts the perfect conjugation of the involved side phenyl ring of the H2 Pc.

6

III. Electronic structure of Fe(001)/H2Pc/Mn/Fe(001) junctions
A. TURBOMOLE
Methodology
Density functional theory (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 13 AITRANSS (abbrev. stands for ab initio
transport simulations) interfaced to the quantum chemistry package TURBOMOLE. 14 An approach,which we follow here, is quite similar to that chosen in our previous work. 15 Two slightly different
atomic configurations of the “extended molecule” used to simulate a bottle-neck of molecular junctions are shown in Figs. 1a and 1b (see text of the paper): H2 Pc is bound to the two bcc(001)-likeclusters, with 13 (or 14) and 28 atoms, representing an Fe tip and a Mn surface, respectively. As argued in the previous section, in the case of a “flat” tip geometry (Fig. 1a), four Fe atoms are boundto four C atoms of the molecule’s side group, while in the case of a “sharp” tip geometry (Fig. 1b),
an Fe apex atom forms a bond to only one C atom. Furthermore, the geometry of H2 Pc molecule,
initially placed at top position on the bcc Mn cluster, was later on fixed by bending along the
low-energy vibrational eigenmode (ω = 15.5 meV). This choice was motivated by earlier experiments, as discussed previously. 15,16 The GGA (BP86 functional 17 ) and a contracted Gaussian-type
split-valence basis set with polarization functions (SVP) 18 were used for calculations.
First, a closed-shell (nonmagnetic) solution was found for the “extended molecule” comprising either 1304 electrons (case of a “flat” Fe tip, Fig. 1a) or 1330 electrons (case of a “sharp”
Fe tip, Fig. 1b). To account for infinite reservoirs with spin-polarized electrons, spin-dependentihsub/tip
sub/tip′(x, x ) = λ + σ ∆ex− iγ δ (x − x′ ), were ascribed to(σ = ±1/2) local self-energies, Σσ
sub/tip

the outermost boundaries of the simulation clusters. Here, a parameter |∆ex

| = 1.43 eV ac-

counts for exchange splitting of the d-states of the Fe surface at the bottom of the d band. 19 (Atthis point we imply that a few atomic layers thick Mn film is deposited on the Fe substrate, which is
sub/tip

an experimental situation.) A freedom to choose a sign of ∆ex7

independently for the "substrate"and "STM tip" clusters allowed us to achieve two solutions with a parallel (P) and antiparallel (AP)alignment of the magnetizations of the Fe tip and the Mn surface.
We have applied the NEGF to evaluate the charge- and spin-density matrices in the presenceof open boundaries, respecting charge neutrality within the “extended molecule”. In an iterative
scheme, the density matrices computed by AITRANSS module are returned to TURBOMOLE to finda modified set of Kohn-Sham orbitals, with a cycle to be repeated unless the self-consistent solution
is reached. For a given value γ ( = 1.36 eV in present calculations) of the level broadening, thecontribution λ to the real part of the self-energy is defined by imposing the condition that the charge
on the outermost surfaces of the simulation cluster approaches the bulk value. An initial guess forthe charge- and spin-density matrices has been prepared in such a way that Mn spins within the"substrate" cluster reflect antiferromagnetic (AF) ordering of magnetizations between the surfaceand next-to-the-surface atomic layers. We have insured that AF ordering is also preserved whenself-consistency is reached.

Electronic structure of Fe tip and Mn substrate.
One can deduce from Suppl. Fig. 6 that within our approach a desired solution reflecting magnetic
ordering within the Fe tip and the Mn surface is indeed achieved. Namely, the density of statesat the Fe tip is spin-polarized (here we consider the case of a “sharp” STM tip, Fig. 1b of the paper), with the majority spin band being almost occupied and the minority spin band being centeredaround the Fermi level. Based on the Löwdin population analysis, we found out magnetic momentsof 2.52µB at the Fe apex atom of the tip and 2.87µB at four next-to-the-apex atoms. These values
are slightly larger that the bulk magnetic moment of bcc-Fe (≈ 2.2µB ) due to a lower coordination number. Electronic states at the Mn surface are even stronger spin-polarized with exchange
splitting ≃ 4 eV being roughly twice as large as compared to Fe. According to our calculations,
Mn surface atoms have (Löwdin) magnetic moments around 4.1µB . This implies that an electronic
configuration of Mn is close to 3d 6 4s1 where one s electron (per atom) is redistributed among
the two spin bands. Due to the AF ordering, negative (and smaller) magnetic moments, around−3.0µB , have been found within the next-to-the-surface atomic plane of Mn.
8

-5 -4
12

-3 -2

-1

0

2

3

Fe tip: majority
Fe tip: minority
Fe apex: majority (x4)
Fe apex: minority (x4)8Local density of states [1/eV]

1

4
0
4
8
60

Mn surface: majority
Mn surface: minority

40
20
0
20
40
60
-5 -4

-3 -2

-1

0

1

2

3

E - EF [eV]Suppl. Fig. 6: Local density of states at the Fe tip (apex and four neighboring atoms are distinguished) and at the Mn (001) surface atomic layer (sum over 16 atoms). The case of parallelalignment of spins in the Fe tip and the Mn surface is shown.
Spin-selective hybridization of electronic states at H2 Pc.
To provide further arguments in support of our discussion (cf. text of the paper) on the formationof spin-polarized states at H2 Pc and on-resonance LUMO transport, we present in Suppl. Figs. 7
and 8 the local density of states (LDoS) at H2 Pc and its projection on frontier molecular orbitals, ahighest occupied molecular orbital (HOMO) and a lowest unoccupied molecular orbital (LUMO)
doublet. We observe that LDoS at the vicinity of the Fermi level is dominated by LUMOs implying
a charge transfer (around 1.2e) from Mn surface to H2 Pc. In case of weak hybridization to the metalstates, LUMO orbitals show up as sharp resonances. This is realized for the majority (α ) channel inthe case of a “flat” tip geometry and P alignment of Fe tip and Mn-surface magnetizations (Suppl.
Fig. 7a), as well as for the majority (α ) spins in the case of a “sharp” tip geometry, both for P and
AP alignment of magnetizations (Suppl. Fig. 8a,c). In contrast, for the minority (β ) channel, due
to a substantial hybridization to the minority spin Mn states, LUMO orbitals exhibit much broader
structures (quasi-bands) in the LDoS with long tails spreading above the Fermi level (see Suppl.
9

P configuration

AP configuration
H
52Pc, α channel

Local density of states at H2Pc [1/eV]

5

(a)
4
3

3

2

2

1

1

0

0

-2

-1

0

1

2

-2

-1

0

1

2

H
52Pc, β channel

5
4

(c)

α HOMO
4 LUMOαα LUMO+1

β HOMO
4 LUMOββ LUMO+1

(b)

3

(d)

3

2

2

1

1

0

0

-2

-1

0

1

2

-2

E - EF [eV]

-1

0

1

2

E - EF [eV]Suppl. Fig. 7: A case of the "flat" Fe tip: shown is the spin-dependent local density of states(LDoS) at H2 Pc molecule, and contributions to it due to HOMO (orange color) and a LUMO
doublet (violet and magenta colors). Left column of plots refers to the parallel (P) alignmentof magnetizations of the Fe tip and the Mn surface, right column refers to the antiparallel (AP)alignment.

P configuration

AP configuration
H
52Pc, α channel

Local density of states at H2Pc [1/eV]

5

(a)
4
3

3

2

2

1

1

0

0

-2

-1

0

1

2

-1

0

1

β HOMO
4 LUMOββ LUMO+1

(b)

3

2

(d)

3

2

2

1

1

0

-2

H
52Pc, β channel

5
4

(c)

α HOMO
4 LUMOαα LUMO+1

-2

-1

0

1

2

E - EF [eV]

0

-2

-1

0

1

2

E - EF [eV]Suppl. Fig. 8: The same as in Suppl. Fig. 7 but for the case of H2 Pc molecule attached to a “sharp”
Fe tip.

10

Figs. 7b,d and 8b,d). As we stressed in the text of the paper, peculiarities in the spin-dependent
LDoS at H2 Pc molecule are transferred to the energy-dependent transmission function, which
therefore acquires a dependence on spin and gives rise to a magnetoresistance effect. Finally,
we mention that a significant charge transfer to the LUMO doublet (slightly larger than one electron per spin channel) is partially compensated by the leakage of charge from occupied molecularlevels.

B. SIESTA/SMEAGOL
MethodWe have also performed complementary studies of electronic structure of a H2 Pc/Mn/Fe(001) system employing SIESTA 1 and SMEAGOL 20 codes. These codes are based on a pseudopotential
method and numerically localized pseudoatomic orbitals forming a basis set for the valence electrons. For the exchange and correlation potential, the LSDA was used as parametrized by Perdew
and Zunger 2 for non-metallic and metallic systems. The standard Troullier-Martins 6 pseudopotentials were adopted and expressed in the Kleinman-Bylander 7 factorization. In our calculations,
we used double-ζ atomic orbitals as the basis set with an equivalent plane-wave cutoff of 500 Ry
to represent the charge density. For the structural optimizations, a conjugate gradient method was
employed, with a force at each atom converged below 0.04 eV/Å.

Results
Before examining electronic properties of a H2 Pc molecule deposited on a Mn/Fe(001), we havechecked electronic structure of the isolated H2 Pc. The resulting density of states (DoS) is shownin Suppl. Fig. 9 plotted vs the Fermi level, EF , of the Mn/Fe(001) substrate. The H2 Pc molecule ischaracterized by energetically isolated HOMO and LUMO levels located at −0.55 eV and 0.87 eV
below and above EF , respectively, with the HOMO-LUMO gap about ∼ 1.42 eV. We observe thatthe quasi-degenerate LUMO is projected both on C and N atoms, while the HOMO does not havea weight on nitrogens, in agreement with our previous calculations. 15
1140

DOS (states/eV)

N (8 atoms)
C (32 atoms)
Total~ 1.42 eV30

20~ 1.42 eV

10

0
-6

~ 2.46 eV

-4

-2

0
2
E - EF (eV)46Suppl. Fig. 9: Density of states (DoS) of isolated H2 Pc plotted vs the Fermi level of Mn/Fe(001)substrate.
Further, on Suppl. Fig. 10, we compare DoS of the first and second Mn layer of the substratealone and with that calculated when the H2 Pc is deposited at the center position on a Mn surface.
The H2 Pc has negligible effect on Mn DoS, which clearly confirms an antifferomagnetic ordering
between neighboring atomic planes. The observed exchange splitting is, however, larger than thatfound within a quantum chemistry based method (cf. Suppl. Fig. 6). This can be attributed todifferent exchange-correlation functionals (LSDA vs GGA) and basis sets used and points out toa known sensitivity in the prediction of a position of the localized d bands of transition metals on
employed methodologies.
We now focus on the effect of Mn/Fe(001) substrate on the electronic structure of H2 Pc molecule. For that, we show in Suppl. Fig. 11 DoS projected at various atoms of H2 Pc, namely, the twocentral H atoms, and both N and C atoms which are nearest neighbors to the central H atoms. For
the majority spin states (upper plot), we observe a gap of ∼ 1.5 eV between HOMO and LUMO
resonances, with the LUMO peak placed just above the Fermi level and the HOMO peak positioned∼ 1.2 eV below EF . In the minority spin channel (lower plot), the LUMO orbital is much stronger
hybridized with the substrate and develops a broader structure around EF which spreads down
to −1.0 eV. The HOMO resonance is shifted to approx. −2.0 eV. The picture resembles a close
similarity to that shown on Suppl. Figs. 7 and 8, and implies a charge transfer from the H2 Pc on
the Mn surface, in a full agreement with our previous discussion.
12DOS (states/eV)

200

Mn/Fe(001)First layer of Mn

0
H2Pc/Mn/Fe(001)

(a)
-200
-12
200

-8

-4

0

4
Mn/Fe(001)Second layer of Mn

DOS (states/eV)

8

0
H2Pc/Mn/Fe(001)

(b)
-200
-12

-8

-4
0
E - EF (eV)48Suppl. Fig. 10: Density of states at the surface (a) and at the next-to-the-surface (b) atomic layersof a bcc Mn film for the two systems: Mn/Fe(001) and H2 Pc/Mn/Fe(001).

PDOS (states/eV)

PDOS (states/eV)

0.5

spin_up~1.4 eVN
C
H~1.6 eV

(a)

0
-4
-2
0.5
spin_down

0

2

4

(b)

~1.05 eV ~0.65 eV~1.05 eV ~0.8 eV

0
-4

-2

0
E - EF (eV)24Suppl. Fig. 11: Partial density of states (PDoS) of H2 Pc deposited on Mn/Fe(001) projected on N
and C atoms, which are nearest neighbors to the central H atoms of the molecule.

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