arXiv:0804.2557v5 [cond-mat.mes-hall] 24 Feb 2009
Single-band tight-binding parameters for Fe-MgO-Fe magnetic heterostructures
Tehseen Z. Raza
School of Electrical and Computer Engineering and NSF Network for
Computational Nanotechnology, Purdue University, West Lafayette, IN 47907
School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853
We present a computationally efficient transferable single-band tight-binding model (SBTB) for
spin polarized transport in heterostructures with an effort to capture the band structure effects.
As an example, we apply it to study transport through Fe-MgO-Fe(100) magnetic tunnel junction
devices. We propose a novel approach to extract suitable tight-binding parameters for a material by
using the energy resolved transmission as the benchmark, which inherently has the bandstructure
effects over the two dimensional transverse Brillouin zone. The SBTB parameters for each of the four
symmetry bands for bcc Fe(100) are first proposed which are complemented with the transferable
tight-binding parameters for the MgO tunnel barrier for the ∆1 and ∆5 bands. The non-equilibrium
Green’s function formalism is then used to calculate the transport. Features like I-V characteristics,
voltage dependence and the barrier width dependence of the tunnel magnetoresistance ratio are
captured quantitatively and the trends match well with the ones observed by ab initio methods.
PACS numbers: 72.25.-b, 85.75.-d, 75.47.-m, 75.47.Jn, 85.35.-p
Transport across multilayered heterostructures is a
problem of great interest both for its intrinsic physics
as well as its device applications . Very often each of
the component materials has been studied extensively on
its own, but it is difficult to make use of this knowledge
because various studies employ different models and it is
difficult to combine their results. As a result, the only vi-
able approach is to start anew for each heterostructure.
The objective of this paper is to present a scheme for
extracting suitable single-band tight-binding (SBTB) pa-
rameters for each of the component materials, thus trans-
lating the results of earlier studies all into one common
SBTB platform which can then be used in a standard
non-equilibrium Green’s function (NEGF) based model
for quantum transport. We illustrate our approach with
an example of great current interest, namely an Fe-MgO-
Fe magnetic tunnel junction (MTJ) device. We use the
principles described in this paper to obtain the SBTB
parameters for bcc Fe(100) from the extended H¨ uckel
parameters  and those for MgO from ab initio mod-
els [3, 4, 5]. Using these SBTB parameters, extracted
from different sources, in an NEGF model for transport
we obtain I-V characteristics, voltage dependence of tun-
nel magnetoresistance (TMR) ratios and barrier width
dependence of TMR in good agreement with published
first-principles results for the same structure.
Ab initio modeling of materials is at an advanced stage
. Coupled with the quantum transport, these models
have been successfully applied to nanoscale systems and
heterostructures. However, such methods are resource
intensive, and simplified models that capture the essen-
tial physics due to the underlying electronic structure
effects are desirable. Since the seminal work of study-
ing material properties using tight binding parameters
(ab initio) J
FIG. 1: Total current densities for the parallel and the anti-
parallel configurations and the tunnel magneto resistance ra-
tio (TMR) for a 4-layer (top) and 12-layer (bottom) device.
SBTB transferable parameters are optimized for the MgO
tunnel barrier to match the current levels from the ab initio
calculations [3, 4, 5]. The bias dependence of TMR is also cap-
tured well within this simple single-band tight-binding model.
by Slater and Koster , there has been a motivation
to develop computationally efficient yet accurate models
to capture the underlying physical mechanisms and the
bandstructure effects. Such simple methods may or may
not capture all the intricate details present in the more
sophisticated models, e.g. ab initio, semi-empirical tight-
binding [8, 9] and empirical tight-binding methods, but
they do provide a platform for large scale calculations.
The simplest method currently available in this context
is an effective mass model. Although very successful for
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a two-dimensional electron and hole gas on a Si(001) −
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Atom to Transistor
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