We examine electron transport through a single-molecule magnet Mn12 bridged
between Au electrodes using the first-principles method. We find crucial
features which were inaccessible in model Hamiltonian studies: spin filtering
and a strong dependence of charge distribution on local environments. The spin
filtering remains robust with different molecular geometries and interfaces,
and strong electron correlations, while the charge distribution over the Mn12
strongly depends on them. We point out a qualitative difference between locally
charged and free-electron charged Mn12

Barraza-Lopez, Salvador

Ferrer, Jaime

Garcia-Suarez, Victor

Park, Kyungwha

English

arXiv

Salvador Barraza-Lopez

Kyungwha Park

Víctor García-Suárez

Jaime Ferrer

Crossref

First-Principles Study of Electron Transport through the Single-Molecule Magnet
                    
                      
                        Mn

Barraza López, Salvador

García Suárez, Víctor Manuel

Ferrer Rodríguez, Jaime

Repositorio Institucional de la Universidad de Oviedo

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First-principles study of electron transport through the
single-molecule magnet Mn12
Salvador Barraza-Lopez1 ∗, Kyungwha Park1, V´ıctor Garc´ıa-Sua´rez2, and Jaime Ferrer3
1Department of Physics, Virginia Polytechnic
Institute and State University. Blacksburg VA, 24061
2Department of Physics, Lancaster University,
Lancaster, LA1 4YB, United Kingdom
3Departamento de Fisica, Universidad de Oviedo, 33007 Oviedo, Spain
(Dated: September 21, 2009)
Abstract
We examine electron transport through a single-molecule magnet Mn12 bridged between Au
electrodes using the first-principles method. We find crucial features which were inaccessible in
model Hamiltonian studies: spin filtering and a strong dependence of charge distribution on local
environments. The spin filtering remains robust with different molecular geometries and interfaces,
and strong electron correlations, while the charge distribution over the Mn12 strongly depends on
them. We point out a qualitative difference between locally charged and free-electron charged
Mn12.
PACS numbers: 85.65.+h, 75.50.Xx, 85.75.-d, 73.23.Hk
∗ Present address: School of Physics, Georgia Institute of Technology, Atlanta, GA 30332
1
In the past two decades, electron transport through quantum dots has been studied
in single-electron transistors as an effort to manipulate single electrons at a time. [1, 2,
3] Semiconducting quantum dots were typically used because of easy manipulation of the
number of electrons inside the dots, by varying gate voltages.
Recently, several experiments [4, 5, 6, 7] on electron transport through a single-molecule
magnet (SMM) Mn12 were reported in transistor set-ups or scanning tunneling microscope
(STM) measurements. SMMs differ from magnetic clusters or quantum dots in the sense that
transition metal ions in SMMs are interacting with each other via super-exchange through
ligands, and that there is large magnetic anisotropy caused by spin-orbit coupling within
each SMM. Thus, the degeneracy in different magnetic states for a given spin multiplet
of SMMs is lifted even in the absence of external magnetic field. The main questions in
these transport studies are whether the electronic and magnetic properties of SMMs would
survive in low-dimensional structures and how the magnetic degrees of freedom interplay
with the electronic degrees of freedom. The challenges in these types of experiments are, so
far, to maintain stable molecular structures [8], to determine orientations of SMMs relative
to surfaces, and to characterize interfaces.
Our previous first-principles studies [9, 10, 11] showed that SMMs are weakly coupled to
Au surfaces and electrodes. Thus, transport through SMMs belongs to a Coulomb block-
ade regime. In most theoretical studies on transport through SMMs, one treated SMMs
as quantum dots and relied on many-body model Hamiltonians with unknown parameter
values.[12, 13, 14, 15, 16, 17] However, in contrast to quantum dots, the magnetic properties
of SMMs are delicately balanced by interactions among transition metal ions. Thus, caution
needs to be exercised in interpretation of experimental data to construct effective model
Hamiltonians.
In this paper, we simulate semi-infinite electrodes and different molecular geometries and
interfaces, and investigate transport properties through a SMM Mn12 bridged between Au
electrodes, using the non-equilibrium Green’s function method in conjunction with spin-
polarized density-functional theory (DFT). Our calculations provide crucial microscopic
information such as a spin-filtering effect and a strong dependence of charge distribution
over the Mn12 on local environments. This information was unattainable in the theoretical
studies solely based on model Hamiltonians with unknown parameter values, and could qual-
itatively change transport properties through SMMs. Mn12 molecules used in the transport
2
FIG. 1: (Color online) Scattering region for (a) geometry 1 consisting of Mn12 attached to Au
layers via S atoms and alkane chains (distance between the electrodes d= 25.7 A˚), and for (b)
geometry 2 consisting of Mn12, four S atoms, and Au layers (d=14.5 A˚). The transport direction
is along the horizontal axis, z axis. Semi-infinite Au electrodes are considered in calculations (not
shown). On the right hand side the positions of the Mn ions are marked for each geometry. For
geometry 1 the dashed lines indicate the alkane chains. For geometry 2 the solid and dashed blocks
represent the areas where the four S atoms are attached through bonding to the C atoms.
experiments [4, 7] were bulky due to large ligands, and so the distances between the Mn12
molecule and the electrodes (or the lengths of linker molecules) for our molecular geometries
are comparable to or much shorter than those in the experiments. We emphasize the effects
of interfaces and molecular geometries on the charge distribution and the coupling constant
between a SMM and electrodes. To take into account strong electron correlations in transi-
tion metal ions, we included a Hubbard-like U term in our previous calculations.[10, 11]
We consider two molecular geometries for a SMM Mn12 bridged between Au(111) elec-
trodes as shown in Figs. 1 (a) and (b): (i) geometry 1 where the magnetic easy axis of Mn12
is perpendicular to the transport direction and Mn12 is attached to the electrodes via alkane
chains and S atoms. (ii) geometry 2 where the easy axis of Mn12 is parallel to the transport
direction and Mn12 is attached to the electrodes via four S atoms. The linker molecules
are used to chemically bind the Mn12 to the electrodes, and play a role of energy barriers
whose heights depend on their lengths and types of chemical bonding. The Au electrodes are
3
FIG. 2: (Color online) Spin-polarized density of states (DOS) projected onto Mn d orbitals (a) for
geometry 1 and (b) for geometry 2: majority spin (black), minority spin (red with symbol). Refer
to Fig. 1 for numbering of the Mn ions. Insets: zoom-in of the majority DOS onto Mn(5), Mn(9),
Mn(8), and Mn(12).
treated as semi-infinite and the scattering region contains a few Au layers, linker molecules,
and Mn12, as shown in Fig. 1. Our calculations are performed using SMEAGOL [18, 19], a
quantum transport code interfaced with DFT SIESTA program [20]. Generalized-gradient
approximation (GGA) [21] is used for exchange-correlation potential in spin-polarized DFT
formalism. When spin-orbit coupling is included self-consistently for an isolated neutral
Mn12 molecule, magnetic anisotropy barrier is computed to be 65.3 K using VASP[22] and
66.4 K using SIESTA,[19] which agrees well with experimental data.[23] Gate voltages and
interactions with phonons are not considered in this study. Further details of the method
and assumptions for this work and brief discussion on the transport for geometry 1 were
presented in Ref.[11].
The spin-polarized densities of states (DOS) of the scattering region projected onto all
Mn d orbitals for geometries 1 and 2 are shown relative to the Fermi level, Ef , in Figs. 2(a)
and (b). In the DOS for both geometries a bin size of 0.5 meV and Gaussian broadening
of 1 meV are used. The minority-spin DOS become negligible in the energy window (-1.6,
0.42 eV) and (-1.5, 0.3 eV) relative to Ef for geometries 1 and 2, respectively. Thus, for
both geometries only the majority-spin orbitals contribute to the densities near Ef . Further
discussion of the DOS for geometry 1 is followed by that for geometry 2.
For geometry 1 the fourfold symmetry of Mn12 is broken due to the linker molecules so
that the degeneracy in the molecular orbitals is lifted. As shown in Fig. 2(a), the projected
4
densities of states (PDOS) for Mn(5) and Mn(9) completely differ from those for Mn(7) and
Mn(11), although the four Mn sites are equivalent according to the fourfold symmetry. The
individual molecular orbitals are clearly identifiable due to the larger distance between the
Mn12 and the electrodes (or longer linker molecules) compared to those in geometry 2. The
coupling (or broadening) of the orbitals to the electrodes near Ef is of the order of 1 meV
or less. The lowest unoccupied molecular orbital (LUMO) is located slightly above Ef and
the highest occupied molecular orbital (HOMO) is placed 0.29 eV below Ef [Fig. 2(a)]. The
LUMO is mainly from two of the Mn ions in the outer ring, Mn(5) and Mn(9), while the
HOMO is from Mn(8) and Mn(12).
For geometry 2 the shorter distance between the Mn12 and the electrodes allows the
molecular orbitals to substantially broaden, which makes the individual orbitals unidentifi-
able [Compare the insets of Figs. 2 (a) and (b)]. That distance for geometry 2 is about a
half of that for geometry 1, but the increase in the coupling constant for geometry 2 is much
greater than a factor of 2 due to the exponential decay of the coupling with the distance
for a given chemical bonding. The group of peaks near Ef is formed by broadening of the
LUMO, which arises from coupling of all of the Mn ions to the electrodes, in contrast to the
case of geometry 1. The HOMO broadens due to coupling of Mn(6), Mn(8), Mn(10), and
Mn(12) to the electrodes. In geometry 2 the fourfold symmetry of an isolated Mn12 is, to
some extent, preserved, because the linker molecules are attached in a fourfold symmetric
fashion. The coupling constant between the Mn12 and electrodes near Ef is of the order of
10 meV [insets of Fig. 2(b)].
We compute a spin-polarized transmission coefficient T (E) for geometry 1 and our result
at zero bias is shown in Fig. 3(a). The majority-spin LUMO is responsible for the resonant
tunneling near Ef . The widths of the T (E) peaks, in general, depend on broadening of the
orbitals, phonon populations, and defects. In our case, since we did not include defects or
interactions with phonons, the widths depend on the broadening only. The weak coupling
leads to the widths of the T (E) peaks ranging from 0.01 to 1 meV [Fig. 3(b)]. The minority-
spin contribution to T (E) appears only 0.42 eV above Ef and 1.6 eV below Ef . This agrees
with the locations of the orbitals in the PDOS [Fig. 2(a)]. For geometry 1 there is a one-
to-one mapping between the T (E) peaks and the orbitals. The spatially resolved density
of states integrated over (-0.23, 0.06 eV) relative to Ef (Fig. 4) clearly corroborates that
minority-spin electrons cannot tunnel through the Mn12 at low bias voltages. Using the same
5
0 0.04 0.081e-06
1e-05
0.0001
0.001
0.01
0.1
1
majority Vb=0
0 0.02 0.04 0.06 0.08
Vb (V)
Tr
an
sm
iss
io
n
10C
ur
re
nt
 (n
A)
20
30
40
50
60
E - Ef (eV)
(b)
(c)
FIG. 3: (Color online) (a) Spin-polarized transmission coefficient at zero bias, (b) zoom-in of the
majority-spin transmission at zero bias [(a)], and (c) computed current I vs bias voltage Vb for
geometry 1.
FIG. 4: (Color online) Majority-spin and minority-spin density of states integrated between -0.23
and 0.06 eV relative to the Fermi level with isosurface criterion of 2 e/nm3 for geometry 1.
analogy, we expect that for geometry 2 only the majority-spin orbitals would contribute to
T (E) near Ef , and that the T (E) peaks would be wider due to the broadening of the orbitals.
As shown in Fig. 3(c), for geometry 1 our computed current as a function of bias voltage Vb
is of the order of tens of nA when Vb < 0.1 V. For a given positive Vb, the chemical potential
of the left (right) electrode increases (decreases) by eVb/2. We find that for 0 < Vb < 0.1 V,
T (E) is shited upward compared to the zero-bias T (E) without changing the main features.
This shift is caused by the polarization of the Mn12 with Vb and the amount of the shift is
proportional to Vb. Then the area of T (E) integrated over E starts to saturate above 0.02 V,
which results in the saturation in the current-voltage dependence [Fig. 3(c)].
To compare with experiment, additional electron correlations within the Mn ions that are
6
N=1N=0
HOMO
LUMO
lower energy higher energyground state S=10
FIG. 5: Spin non-degenerate molecular orbitals of neutral Mn12 (N = 0) in the ground state
(S = 10) and of singly-charged Mn12 (N = 1) in the ground state and an excited state, obtained
from DFT. In each state, four majority-spin (two minority-spin) orbitals are shown on the left
(right).
absent in standard DFT must be considered. Beyond DFT, the U term was included in our
calculation of the electronic structure of an isolated Mn12 molecule [10] using VASP. It was
found that the majority-spin HOMO-LUMO gap increased to 1.1 eV and that the majority-
spin LUMO was shifted upward by 0.12 eV. The minority-spin LUMO was, however, still
0.12 eV above the majority-spin LUMO. Thus, when an extra electron is added to the
Mn12, the majority-spin orbitals are still well separated from the minority-spin orbitals.
Consequently, only majority-spin electrons can be tunneled through the Mn12 at low bias
voltages (below 0.5 eV). Thus, we conclude that the spin-filtering effect remains robust with
different molecular geometries and interfaces, and strong electron correlations.
Henceforth, we discuss a subtle but important issue in the transport through SMM Mn12.
The computed charging energy of an isolated Mn12 is 3.8 eV and thus the Mn12 can be only
singly charged at low bias voltages. Due to the nature of less-than-half-filled d orbitals, the
Mn d orbitals in the Mn12 are not spin-degenerate. If an extra electron is added to Mn12,
the ground state would be achieved when the added electron has majority spin (Fig. 5).
This is the origin of the spin-filtering effect in the transport through Mn12. However, this
argument must not be straightforwardly interpreted that the ground-state spin of [Mn12]
1−,
is S = 10+1/2 = 21/2. This is true only if the ground-state spin of [Mn12]
1− has a collinear
configuration or if the extra charge is distributed over several Mn sites instead of being
localized at one Mn site.
When conduction electrons are added to the Mn12 from the electrodes, our DFT calcu-
7
lations with collinear spin configurations support that the electrons will be distributed over
more than one Mn site. The specific distribution of the electrons over the Mn sites depends
on the way the Mn12 molecule is attached to the electrodes. For geometry 1 the electrons
will be mainly distributed over the Mn(5) and Mn(9) sites, while for geometry 2 they will be
distributed over all of the Mn sites [Figs. 2(a) and (b)]. Our noncollinear DFT calculations
on [Mn12]
1− (using SIESTA) reveal that the collinear spin configuration with S = 21/2 has
the lowest energy.
Some transport studies based on model Hamiltonians,[4, 13, 16] assumed that a singly
charged Mn12 molecule has the ground-state spin of S = 19/2, by referring to experiments
[24, 25] performed on locally charged Mn12 molecules. In these experiments, extra electrons
were added to the magnetic core of the Mn12, by inserting cations (or electron donors) close
to one or two of the Mn ions. Since a bulk form of Mn12 molecules is an insulator, the added
electrons would be localized to the Mn sites closest to the cations. The experiments showed
that the total spin for [Mn12]
−1 was S = 19/2, and that one of the Mn ions in the outer
ring changed its valence from 3+ (S = 2) to 2+ (S = 5/2). In contrast to typical quantum
dots, the total spin of Mn12 is maintained through delicate balance among interactions
between the different Mn ions. We perform noncollinear calculations on Mn11Fe (one of
the Mn ions in the outer ring is replaced by Fe in the Mn12 geometry) in order to mimic a
singly locally charged Mn12. Using UMn=4 eV [10] and UFe=6 eV in VASP, we find that the
collinear spin configuration with 2S = 19 has 100 meV higher energy than the collinear spin
configuration with 2S = 21. The latter has 5.8 meV higher energy than the noncollinear
spin configuration (2S = 18.71) in which the magnetic moment vector of the Fe3+ (S = 5/2)
ion is tilted by 62◦ from the moment vectors of the eleven Mn ions mostly aligned along with
the z axis. Additional noncollinear calculations on the Mn11Fe with U = 0 also supports
that the collinear spin configuration with 2S = 21 is not the ground state for the singly
locally charged Mn12. Thus, the spin-filtering effect and single-electron picture (Fig. 5) are
compatible with the experimental findings [24, 25].
In summary, we have investigated transport properties through a Mn12 molecule bridged
between Au(111) electrodes using the non-equilibrium Green’s function method and spin-
polarized DFT. We found that the Mn12 functioned as a spin filter in a low bias regime (below
0.5 eV). The spin-filter effect persisted with different molecular geometries and interfaces
and strong electron correlations, while the distribution of conduction electrons over the Mn12
8
strongly depended on them. Conduction electrons from the electrodes would be distributed
over several Mn sites rather than being localized at one Mn site. There is no contradiction
between the spin-filtering effect and the experimental observation on S = 19/2 for the singly
locally charged Mn12 molecules.
K.P. was supported by NSF DMR-0804665, the Jeffress Memorial Trust Funds, and NCSA
under DMR060009N. J.F. was supported by MEC FIS2006-12117. The authors are grateful
to W. Wernsdorfer for discussions.
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10


First-principles study of electron transport through the single-molecule magnet Mn12

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First-principles study of electron transport through the single-molecule
  magnet Mn12

First-principles study of electron transport through the single-molecule magnet Mn12

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