Magnetic moments in atomic scale domain walls formed in nanoconstrictions and
nanowires are softened which affects dramatically the domain wall resistance.
We perform ab initio calculations of the electronic structure and conductance
of atomic-size Ni nanowires with domain walls only a few atomic lattice
constants wide. We show that the hybridization between noncollinear spin states
leads to a reduction of the magnetic moments in the domain wall. This magnetic
moment softening strongly enhances the domain wall resistance due to scattering
produced by the local perturbation of the electronic potential.Comment: 4 pages, 5 figure

E. Y. Tsymbal

G. G. Cabrera

J. D. Burton

L. Landau

L. Néel

L. N. Bulaevskĭ

N. Beer

O. N. Mryasov

R. F. Sabirianov

R. Haydock

S. S. Jaswal

S. A. Turzhevskii

V. A. Zhirnov

English

arXiv

We perform ab initio calculations of the electronic structure and conductance of atomic-size Ni nanowires with domain walls only a few atomic lattice constants wide. We show that the hybridization between noncollinear spin states leads to a reduction of the magnetic moments in the domain wall resulting in the enhancement of the domain wall resistance. Experimental studies of the magnetic moment softening may be feasible with modern techniques such as scanning tunneling spectroscopy

Burton, John D.

Sabirianov, Renat F.

Jaswal, Sitaram S.

Tsymbal, Evgeny Y

Mryasov, O. N.

UNL | Libraries

University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Evgeny Tsymbal Publications Research Papers in Physics and Astronomy 
8-2006 
Magnetic Moment Softening and Domain Wall Resistance in Ni 
Nanowires 
John D. Burton 
University of Nebraska-Lincoln, jburton2@unl.edu 
Renat F. Sabirianov 
University of Nebraska at Omaha, rsabirianov@mail.unomaha.edu 
Sitaram S. Jaswal 
University of Nebraska-Lincoln, sjaswal1@unl.edu 
Evgeny Y. Tsymbal 
University of Nebraska-Lincoln, tsymbal@unl.edu 
O. N. Mryasov 
Seagate Research, Pittsburgh, PA 
Follow this and additional works at: https://digitalcommons.unl.edu/physicstsymbal 
 Part of the Condensed Matter Physics Commons 
Burton, John D.; Sabirianov, Renat F.; Jaswal, Sitaram S.; Tsymbal, Evgeny Y.; and Mryasov, O. N., 
"Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires" (2006). Evgeny Tsymbal 
Publications. 4. 
https://digitalcommons.unl.edu/physicstsymbal/4 
This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Evgeny Tsymbal Publications 
by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires
J. D. Burton,1,3 R. F. Sabirianov,2,3 S. S. Jaswal,1,3 and E. Y. Tsymbal1,3,*
1Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111, USA
2Department of Physics, University of Nebraska, Omaha, Nebraska 68182-0266, USA
3Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588-0111, USA
O. N. Mryasov
Seagate Research, Pittsburgh, Pennsylvania 15222, USA
(Received 27 January 2006; published 18 August 2006)
We perform ab initio calculations of the electronic structure and conductance of atomic-size Ni
nanowires with domain walls only a few atomic lattice constants wide. We show that the hybridization
between noncollinear spin states leads to a reduction of the magnetic moments in the domain wall
resulting in the enhancement of the domain wall resistance. Experimental studies of the magnetic moment
softening may be feasible with modern techniques such as scanning tunneling spectroscopy.
DOI: 10.1103/PhysRevLett.97.077204 PACS numbers: 75.47.Jn, 72.25.Ba, 73.63.b, 75.75.+a
The study of domain walls (DWs) in bulk ferromagnetic
materials began in the early 20th century with contribu-
tions from Bloch [1], Landau and Lifshitz [2], and Ne´el [3].
In bulk 3d metal ferromagnets DWs are wide (100 nm)
on the scale of the lattice spacing due to the strong ex-
change interaction which tends to align neighboring re-
gions of magnetization, compared to anisotropic effects
which prefer the magnetization to lie along specific direc-
tions. With the recent interest in magnetic nanostructures it
has been shown that DWs can be quite thin due to the
enhanced effective anisotropy of constricted geometry in
nanowires and nanocontacts [4]. Extremely narrow DWs
with a width of the order of a lattice constant have recently
been observed in Fe nanowires grown on W [5] and Mo [6].
The DW width controls the DW resistance. The origin of
the DW resistance is known to be the mixing of up- and
down-spin electrons due to the mistracking of the elec-
tron’s spin in passing through the DW [7]. The narrower
DW width results in a larger angle between the magneti-
zation directions of successive atomic layers thereby low-
ering the electron transmission. In bulk ferromagnets DWs
do not affect appreciably the resistance because the DW
width is much larger than the Fermi wave length, and
hence electrons can follow adiabatically the slowly varying
magnetization direction within the DW. In magnetic nano-
constrictions, where a DW can be very narrow, the DW
resistance may be appreciable.
Experimental studies of such DWs are feasible due to
remarkable progress in experimental techniques, making
possible to synthesize and characterize structures at the
atomic scale. In particular, conducting nanowires can be
fabricated by breaking metal junctions [8], by pulling apart
two metal surfaces [9], or by electrodepositing on prepat-
terned electrodes [10]. Using these techniques an atomic
scale DW can be formed in magnetic nanowires and
studied by modern experimental techniques such as scan-
ning tunneling spectroscopy [11]. Electronic transport
across DWs exhibits interesting spin-dependent phe-
nomena recently reviewed by Marrows [12].
The theoretical description of the DW resistance so far
was based on either free-electron models [13] in which the
DW is represented by an appropriate potential profile or
first-principles calculations [14,15] in which the DW is
typically described by a spin-spiral structure. All these
models assume that the DW is rigid; i.e., they neglect
any spatial variation of the magnitude of the magnetic
moment across the DW. It is well established, however,
that the magnitude of the magnetic moments in itinerant
magnets can depend strongly on the orientation of the
neighboring moments [16]. This effect is relatively weak
in well localized ferromagnets like Fe, but can reduce and
even destroy the atomic magnetic moment of the itinerant
ferromagnets, like Ni.
The origin of this phenomenon is the hybridization
between noncollinear spin states. In the uniformly magne-
tized material with no spin-orbit coupling the minority-
and majority-spin bands are independent. However, in a
noncollinear state, such as a DW, this is no longer the case
and the two spin bands are hybridized. This spin mixing
leads to charge transfer and level broadening, which results
in the reduction of the overall exchange splitting between
majority- and minority-spin states on each atom, and hence
the atomic moments are reduced. In bulk DWs of any
ferromagnetic material, this effect is small due to the
slow variation of the direction of the magnetization. For
the atomic scale DWs, however, there is a large degree of
canting between neighboring magnetic moments. This
leads to a significant hybridization between spin states
which leads to a reduction, or softening, of the magnetic
moments within the constrained DW. The magnetic mo-
ment softening affects the DW resistance due to the local
perturbation in the electronic potential.
PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006
0031-9007=06=97(7)=077204(4) 077204-1 © 2006 The American Physical Society
We note that the spatial variation of the magnetization in
DWs has been suggested before, but only in the context of
finite temperature magnetic disorder of the (fixed magni-
tude) atomic magnetic moments in a DW [17]. The effect
of spatial variation of the magnetization on DW resistance
was addressed previously, but only within the diffusive
transport regime and a free-electron model [18].
In this Letter we illustrate the importance of magnetic
moment softening by performing ab initio calculations of
the electronic structure and ballistic conductance of atomic
scale DWs in Ni nanowires. We show that the magnetic
moments within DWs only a few lattice constants wide can
be significantly reduced compared to the magnetic mo-
ments in a uniformly magnetized wire due to the presence
of substantial hybridization between spin states. We find
that the magnetic moment softening strongly enhances the
DW resistance due to additional scattering resulting from
the local perturbation in the electronic potential.
Density functional calculations of the spin-dependent
electronic structure of atomic scale DWs in Ni nanowires
were performed using the tight-binding linear muffin-tin-
orbital method [19] in the atomic sphere approximation
and the local spin density approximation for the exchange-
correlation energy. We used the real space recursion
method [20] with a Beer-Pettifor terminator [21] to calcu-
late the local density of states (DOS). Ultrathin domain
walls were examined for two different freestanding Ni
wires based on the bulk fcc structure: (110) monatomic
chains and 5 4 wires (described below). All the struc-
tures used the lattice constant a  3:52 A of bulk fcc Ni.
In the calculations we constructed a central region con-
taining the DW, surrounded by two uniformly magnetized
leads aligned antiparallel relative to each other. The self-
consistent calculations were carried out for the central
region and a large enough portion of the surrounding leads
so that the outermost atoms of the self-consistent region
were similar to those in the remaining semi-infinite section
of the leads in the uniformly magnetized state. A DW was
modeled by a finite spin spiral with the relative angle
between neighboring atomic layers of magnetic moments
being 180=N  1, where N is the number of atomic
layers in the DW [22].
First, we consider an N  1 DW in a monatomic Ni wire
[Fig. 1(a)]. Figure 1 displays the results of our calculations
for the N  1 DW. The electronic potentials of the anti-
parallel magnetized lead sites were frozen, while on the
central five sites the electronic structure was calculated
self-consistently. We find a 16% reduction of the magnetic
moment on the central site and a 7% reduction on the two
neighboring sites. The reduction in the magnetic moment
on the central site is due to the hybridization with the
different spin states of the noncollinear neighbors, which
results in the reduction of the exchange splitting, as de-
scribed earlier. This fact is evident from Fig. 1(b), which
shows the local DOS for the uniformly magnetized mona-
tomic Ni wire and for the central atom of an N  1 DW.
The reduction in the moment of the nearest neighbors of
the central atom is only about half of that of the central
atom because they are noncollinear with only one of the
two neighbors. Also apparent in Fig. 1(b) is an overall
broadening of the DOS on the central site compared to
the uniformly magnetized state produced by the spin
mixing.
Figure 2 shows the magnetic moment profile for several
DW widths in the monatomic wire. The reduction in the
moment is strongly dependent on the width of the DW. For
N  0 and N  1 DWs, the effect of softening is the
largest owing to the fact that the degree of noncollinearity
is the largest in these two cases. As the width of the DW
increases the softening decreases because of the reduction
of the angle between the nearest neighbor magnetic
moments.
Figure 3(a) shows the 5 4wire which has five atoms in
one layer and four in the next layer resulting in three
nonequivalent sites, each indicated by a different color.
Although the average magnetic moment of the uniformly
magnetized 5 4 wire,   0:7B, is lower than that of
the monatomic wire,   1:1B, we find that in the pres-
ence of ultrathin DWs the spatial variation of the magne-
tization displays qualitatively similar behavior. Figure 3(b)
shows the magnetic moments found for three DW widths in
the 5 4 wire. The largest reduction in magnetic moment
is nearly 90% for the central site of the N  1 DW, and the
effect is still substantial for the N  5 DW where the
FIG. 1 (color online). (a) A monatomic wire with an N  1
DW. The arrows show the orientation and relative magnitude of
calculated magnetic moments. (b) DOS per atom of the uni-
formly magnetized monatomic wire (dashed curve) and the local
DOS (LDOS) at the center of an N  1 DW (solid curve).
PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006
077204-2
magnetic moment of the central layer is softened by about
10%. The effect is significantly larger in the 5 4 wire
than that in the monatomic chain due to the enhanced
hybridization reflecting an increase in the number of neigh-
boring atoms.
The magnetic moment softening affects dramatically the
conductance across DWs. We calculate the conductance of
the 5 4 Ni wire with an N  1 DW using the standard
technique described in detail in Ref. [15]. It should be
noted, however, that in Ref. [15] the Hamiltonian for the
DW region was built by simply rotating (in spin space) the
self-consistent potentials obtained for the uniformly mag-
netized wire. Here we derive the Hamiltonian from the
self-consistent potentials found in the presence of the
abrupt DW. For comparison we also calculate the conduc-
tance in the same way as Ref. [15], which allows us to
determine the contribution of magnetic moment softening
to the DW resistance.
Figure 4(a) shows the spin-resolved conductance, GFM,
of a uniformly magnetized 5 4 Ni wire as a function of
energy E. The conductance is quantized in steps of e2=h,
corresponding to the number of bands crossing the energy
E. The bands are seen in Fig. 4(b) as being bound by the
sharp peaks corresponding to the band edges. The conduc-
tance in the zero-bias limit is given by the value at the
Fermi energy, EF, located at the center of the narrow
minority band. For the 5 4 Ni wire it is 14e2=h.
Figure 4(c) displays the conductance through an N  1
DW, GDW. For a ‘‘rigid’’ DW (no softening of the magnetic
moments) the Hamiltonian is constructed from the self-
consistent potentials of the uniformly magnetized wire,
while for the ‘‘soft’’ DW we use the potentials that yield
reduced magnetic moments in the DW region, as seen in
Fig. 3. We find that the magnetic moment softening in the
DW leads to a reduction in the conductance at the Fermi
energy from 5:38e2=h to 3:21e2=h.
The origin of this phenomenon can be understood using
a simple tight-binding model of a monatomic chain with an
abrupt N  0 DW. We model the majority states by a wide
band, characterized by the (large) nearest neighbor hop-
FIG. 3 (color online). (a) The 5 4 nanowire showing the
three nonequivalent sites and an N  3 DW. Each arrow repre-
sents the magnitude and orientation of the average magnetic
moment of the plane with 5 atoms. (b) The self-consistent
magnetic moments for several DW widths. The color in the
plot corresponds to the site of the same color in (a).
FIG. 4. (a) Spin-resolved conductance GFM and (b) density of
states near the Fermi energy EF as a function of energy for the
uniformly magnetized 5 4 Ni wire. (c) Conductance of the
N  1 DW, GDW, as a function of energy for the rigid DW
(dashed curve) and for the soft DW (solid curve).
FIG. 2. Magnetic moments in the monatomic Ni wire as a
function of distance from the DW center for several DW widths.
The N  1 plot corresponds to Fig. 1(a).
PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006
077204-3
ping parameter tmaj, to emulate the wide band near the
Fermi energy [see Fig. 4(b)]. The minority states are
modeled by a narrow band with (small) hopping tmin, offset
from the center of the majority band by energy . To
model magnetic moment softening we assume that the
on-site energies of the two interface sites are shifted rela-
tive to the uniformly magnetized leads. Majority states are
shifted up by energy , and minority states are shifted
down by the same amount . This corresponds effectively
to a reduction of the local exchange splitting by 2 on the
two interface sites, and hence softening of the magnetic
moment. The parameters for our model are chosen as
follows: tmaj  1, tmin  0:05, and   1. The results of
the model are shown in Fig. 5. As is seen from Figs. 5(b)
and 5(c), the model predicts a drastic reduction in the
conductance as a result of magnetic moment softening.
The origin of this reduction is the local perturbation in
the electronic potential which leads to stronger scattering
of transport electrons by the DW. When the on-site ener-
gies of the interface atoms are shifted with respect to the
narrow minority band, which determines the energy win-
dow for conductance, these sites act as additional scatterers
that hinder conductance.
Scanning tunneling spectroscopy (STS) has been shown
to reveal differences in the electronic structure of domains
and DWs in Fe nanowires grown on W(110) surfaces [11].
It may be possible to use techniques such as STS to study
the changes in the electronic structure due to magnetic
moment softening in narrow DWs predicted here. We
hope, therefore, that our theoretical predictions will stimu-
late experimental studies of the electronic and transport
properties of atomic scale domain walls.
This work is supported by Seagate Research, the NSF
(Grants No. DMR-0203359 and No. MRSEC DMR-
0213808), and the Nebraska Research Initiative. The cal-
culations were performed using the Research Computing
Facility of the University of Nebraska-Lincoln.
*Electronic address: tsymbal@unl.edu
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[22] To justify this model for the DW structure we performed
self-consistent noncollinear calculations of the magnetic
moment directions for the N  7 DW in a 5 4 Ni wire.
We found that the converged magnetic structure represents
a DW which has magnetic moment orientations almost
identical to those assumed within our model with devia-
tions not larger than 2.
FIG. 5. Results of a simple tight-binding model. (a) DOS of the
uniformly magnetized state versus energy for majority- (wide
band) and minority- (narrow band) spin electrons. (b) Con-
ductance versus energy for a rigid DW (  0, dashed line)
and for a soft DW (  0:2, solid line). (c) Conductance vs  for
E  EF.
PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006
077204-4


Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Evgeny Tsymbal Publications Research Papers in Physics and Astronomy 8-2006 Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires John D. Burton University of Nebraska-Lincoln, jburton2@unl.edu Renat F. Sabirianov University of Nebraska at Omaha, rsabirianov@mail.unomaha.edu Sitaram S. Jaswal University of Nebraska-Lincoln, sjaswal1@unl.edu Evgeny Y. Tsymbal University of Nebraska-Lincoln, tsymbal@unl.edu O. N. Mryasov Seagate Research, Pittsburgh, PA Follow this and additional works at: https://digitalcommons.unl.edu/physicstsymbal  Part of the Condensed Matter Physics Commons Burton, John D.; Sabirianov, Renat F.; Jaswal, Sitaram S.; Tsymbal, Evgeny Y.; and Mryasov, O. N., "Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires" (2006). Evgeny Tsymbal Publications. 4. https://digitalcommons.unl.edu/physicstsymbal/4 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Evgeny Tsymbal Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Magnetic Moment Softening and Domain Wall Resistance in Ni NanowiresJ. D. Burton,1,3 R. F. Sabirianov,2,3 S. S. Jaswal,1,3 and E. Y. Tsymbal1,3,*1Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111, USA2Department of Physics, University of Nebraska, Omaha, Nebraska 68182-0266, USA3Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588-0111, USAO. N. MryasovSeagate Research, Pittsburgh, Pennsylvania 15222, USA(Received 27 January 2006; published 18 August 2006)We perform ab initio calculations of the electronic structure and conductance of atomic-size Ninanowires with domain walls only a few atomic lattice constants wide. We show that the hybridizationbetween noncollinear spin states leads to a reduction of the magnetic moments in the domain wallresulting in the enhancement of the domain wall resistance. Experimental studies of the magnetic momentsoftening may be feasible with modern techniques such as scanning tunneling spectroscopy.DOI: 10.1103/PhysRevLett.97.077204 PACS numbers: 75.47.Jn, 72.25.Ba, 73.63.b, 75.75.+aThe study of domain walls (DWs) in bulk ferromagneticmaterials began in the early 20th century with contribu-tions from Bloch [1], Landau and Lifshitz [2], and Ne´el [3].In bulk 3d metal ferromagnets DWs are wide (100 nm)on the scale of the lattice spacing due to the strong ex-change interaction which tends to align neighboring re-gions of magnetization, compared to anisotropic effectswhich prefer the magnetization to lie along specific direc-tions. With the recent interest in magnetic nanostructures ithas been shown that DWs can be quite thin due to theenhanced effective anisotropy of constricted geometry innanowires and nanocontacts [4]. Extremely narrow DWswith a width of the order of a lattice constant have recentlybeen observed in Fe nanowires grown on W [5] and Mo [6].The DW width controls the DW resistance. The origin ofthe DW resistance is known to be the mixing of up- anddown-spin electrons due to the mistracking of the elec-tron’s spin in passing through the DW [7]. The narrowerDW width results in a larger angle between the magneti-zation directions of successive atomic layers thereby low-ering the electron transmission. In bulk ferromagnets DWsdo not affect appreciably the resistance because the DWwidth is much larger than the Fermi wave length, andhence electrons can follow adiabatically the slowly varyingmagnetization direction within the DW. In magnetic nano-constrictions, where a DW can be very narrow, the DWresistance may be appreciable.Experimental studies of such DWs are feasible due toremarkable progress in experimental techniques, makingpossible to synthesize and characterize structures at theatomic scale. In particular, conducting nanowires can befabricated by breaking metal junctions [8], by pulling aparttwo metal surfaces [9], or by electrodepositing on prepat-terned electrodes [10]. Using these techniques an atomicscale DW can be formed in magnetic nanowires andstudied by modern experimental techniques such as scan-ning tunneling spectroscopy [11]. Electronic transportacross DWs exhibits interesting spin-dependent phe-nomena recently reviewed by Marrows [12].The theoretical description of the DW resistance so farwas based on either free-electron models [13] in which theDW is represented by an appropriate potential profile orfirst-principles calculations [14,15] in which the DW istypically described by a spin-spiral structure. All thesemodels assume that the DW is rigid; i.e., they neglectany spatial variation of the magnitude of the magneticmoment across the DW. It is well established, however,that the magnitude of the magnetic moments in itinerantmagnets can depend strongly on the orientation of theneighboring moments [16]. This effect is relatively weakin well localized ferromagnets like Fe, but can reduce andeven destroy the atomic magnetic moment of the itinerantferromagnets, like Ni.The origin of this phenomenon is the hybridizationbetween noncollinear spin states. In the uniformly magne-tized material with no spin-orbit coupling the minority-and majority-spin bands are independent. However, in anoncollinear state, such as a DW, this is no longer the caseand the two spin bands are hybridized. This spin mixingleads to charge transfer and level broadening, which resultsin the reduction of the overall exchange splitting betweenmajority- and minority-spin states on each atom, and hencethe atomic moments are reduced. In bulk DWs of anyferromagnetic material, this effect is small due to theslow variation of the direction of the magnetization. Forthe atomic scale DWs, however, there is a large degree ofcanting between neighboring magnetic moments. Thisleads to a significant hybridization between spin stateswhich leads to a reduction, or softening, of the magneticmoments within the constrained DW. The magnetic mo-ment softening affects the DW resistance due to the localperturbation in the electronic potential.PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 20060031-9007=06=97(7)=077204(4) 077204-1 © 2006 The American Physical SocietyWe note that the spatial variation of the magnetization inDWs has been suggested before, but only in the context offinite temperature magnetic disorder of the (fixed magni-tude) atomic magnetic moments in a DW [17]. The effectof spatial variation of the magnetization on DW resistancewas addressed previously, but only within the diffusivetransport regime and a free-electron model [18].In this Letter we illustrate the importance of magneticmoment softening by performing ab initio calculations ofthe electronic structure and ballistic conductance of atomicscale DWs in Ni nanowires. We show that the magneticmoments within DWs only a few lattice constants wide canbe significantly reduced compared to the magnetic mo-ments in a uniformly magnetized wire due to the presenceof substantial hybridization between spin states. We findthat the magnetic moment softening strongly enhances theDW resistance due to additional scattering resulting fromthe local perturbation in the electronic potential.Density functional calculations of the spin-dependentelectronic structure of atomic scale DWs in Ni nanowireswere performed using the tight-binding linear muffin-tin-orbital method [19] in the atomic sphere approximationand the local spin density approximation for the exchange-correlation energy. We used the real space recursionmethod [20] with a Beer-Pettifor terminator [21] to calcu-late the local density of states (DOS). Ultrathin domainwalls were examined for two different freestanding Niwires based on the bulk fcc structure: (110) monatomicchains and 5 4 wires (described below). All the struc-tures used the lattice constant a  3:52 A of bulk fcc Ni.In the calculations we constructed a central region con-taining the DW, surrounded by two uniformly magnetizedleads aligned antiparallel relative to each other. The self-consistent calculations were carried out for the centralregion and a large enough portion of the surrounding leadsso that the outermost atoms of the self-consistent regionwere similar to those in the remaining semi-infinite sectionof the leads in the uniformly magnetized state. A DW wasmodeled by a finite spin spiral with the relative anglebetween neighboring atomic layers of magnetic momentsbeing 180=N  1, where N is the number of atomiclayers in the DW [22].First, we consider an N  1 DW in a monatomic Ni wire[Fig. 1(a)]. Figure 1 displays the results of our calculationsfor the N  1 DW. The electronic potentials of the anti-parallel magnetized lead sites were frozen, while on thecentral five sites the electronic structure was calculatedself-consistently. We find a 16% reduction of the magneticmoment on the central site and a 7% reduction on the twoneighboring sites. The reduction in the magnetic momenton the central site is due to the hybridization with thedifferent spin states of the noncollinear neighbors, whichresults in the reduction of the exchange splitting, as de-scribed earlier. This fact is evident from Fig. 1(b), whichshows the local DOS for the uniformly magnetized mona-tomic Ni wire and for the central atom of an N  1 DW.The reduction in the moment of the nearest neighbors ofthe central atom is only about half of that of the centralatom because they are noncollinear with only one of thetwo neighbors. Also apparent in Fig. 1(b) is an overallbroadening of the DOS on the central site compared tothe uniformly magnetized state produced by the spinmixing.Figure 2 shows the magnetic moment profile for severalDW widths in the monatomic wire. The reduction in themoment is strongly dependent on the width of the DW. ForN  0 and N  1 DWs, the effect of softening is thelargest owing to the fact that the degree of noncollinearityis the largest in these two cases. As the width of the DWincreases the softening decreases because of the reductionof the angle between the nearest neighbor magneticmoments.Figure 3(a) shows the 5 4wire which has five atoms inone layer and four in the next layer resulting in threenonequivalent sites, each indicated by a different color.Although the average magnetic moment of the uniformlymagnetized 5 4 wire,   0:7B, is lower than that ofthe monatomic wire,   1:1B, we find that in the pres-ence of ultrathin DWs the spatial variation of the magne-tization displays qualitatively similar behavior. Figure 3(b)shows the magnetic moments found for three DW widths inthe 5 4 wire. The largest reduction in magnetic momentis nearly 90% for the central site of the N  1 DW, and theeffect is still substantial for the N  5 DW where theFIG. 1 (color online). (a) A monatomic wire with an N  1DW. The arrows show the orientation and relative magnitude ofcalculated magnetic moments. (b) DOS per atom of the uni-formly magnetized monatomic wire (dashed curve) and the localDOS (LDOS) at the center of an N  1 DW (solid curve).PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-2magnetic moment of the central layer is softened by about10%. The effect is significantly larger in the 5 4 wirethan that in the monatomic chain due to the enhancedhybridization reflecting an increase in the number of neigh-boring atoms.The magnetic moment softening affects dramatically theconductance across DWs. We calculate the conductance ofthe 5 4 Ni wire with an N  1 DW using the standardtechnique described in detail in Ref. [15]. It should benoted, however, that in Ref. [15] the Hamiltonian for theDW region was built by simply rotating (in spin space) theself-consistent potentials obtained for the uniformly mag-netized wire. Here we derive the Hamiltonian from theself-consistent potentials found in the presence of theabrupt DW. For comparison we also calculate the conduc-tance in the same way as Ref. [15], which allows us todetermine the contribution of magnetic moment softeningto the DW resistance.Figure 4(a) shows the spin-resolved conductance, GFM,of a uniformly magnetized 5 4 Ni wire as a function ofenergy E. The conductance is quantized in steps of e2=h,corresponding to the number of bands crossing the energyE. The bands are seen in Fig. 4(b) as being bound by thesharp peaks corresponding to the band edges. The conduc-tance in the zero-bias limit is given by the value at theFermi energy, EF, located at the center of the narrowminority band. For the 5 4 Ni wire it is 14e2=h.Figure 4(c) displays the conductance through an N  1DW, GDW. For a ‘‘rigid’’ DW (no softening of the magneticmoments) the Hamiltonian is constructed from the self-consistent potentials of the uniformly magnetized wire,while for the ‘‘soft’’ DW we use the potentials that yieldreduced magnetic moments in the DW region, as seen inFig. 3. We find that the magnetic moment softening in theDW leads to a reduction in the conductance at the Fermienergy from 5:38e2=h to 3:21e2=h.The origin of this phenomenon can be understood usinga simple tight-binding model of a monatomic chain with anabrupt N  0 DW. We model the majority states by a wideband, characterized by the (large) nearest neighbor hop-FIG. 3 (color online). (a) The 5 4 nanowire showing thethree nonequivalent sites and an N  3 DW. Each arrow repre-sents the magnitude and orientation of the average magneticmoment of the plane with 5 atoms. (b) The self-consistentmagnetic moments for several DW widths. The color in theplot corresponds to the site of the same color in (a).FIG. 4. (a) Spin-resolved conductance GFM and (b) density ofstates near the Fermi energy EF as a function of energy for theuniformly magnetized 5 4 Ni wire. (c) Conductance of theN  1 DW, GDW, as a function of energy for the rigid DW(dashed curve) and for the soft DW (solid curve).FIG. 2. Magnetic moments in the monatomic Ni wire as afunction of distance from the DW center for several DW widths.The N  1 plot corresponds to Fig. 1(a).PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-3ping parameter tmaj, to emulate the wide band near theFermi energy [see Fig. 4(b)]. The minority states aremodeled by a narrow band with (small) hopping tmin, offsetfrom the center of the majority band by energy . Tomodel magnetic moment softening we assume that theon-site energies of the two interface sites are shifted rela-tive to the uniformly magnetized leads. Majority states areshifted up by energy , and minority states are shifteddown by the same amount . This corresponds effectivelyto a reduction of the local exchange splitting by 2 on thetwo interface sites, and hence softening of the magneticmoment. The parameters for our model are chosen asfollows: tmaj  1, tmin  0:05, and   1. The results ofthe model are shown in Fig. 5. As is seen from Figs. 5(b)and 5(c), the model predicts a drastic reduction in theconductance as a result of magnetic moment softening.The origin of this reduction is the local perturbation inthe electronic potential which leads to stronger scatteringof transport electrons by the DW. When the on-site ener-gies of the interface atoms are shifted with respect to thenarrow minority band, which determines the energy win-dow for conductance, these sites act as additional scatterersthat hinder conductance.Scanning tunneling spectroscopy (STS) has been shownto reveal differences in the electronic structure of domainsand DWs in Fe nanowires grown on W(110) surfaces [11].It may be possible to use techniques such as STS to studythe changes in the electronic structure due to magneticmoment softening in narrow DWs predicted here. Wehope, therefore, that our theoretical predictions will stimu-late experimental studies of the electronic and transportproperties of atomic scale domain walls.This work is supported by Seagate Research, the NSF(Grants No. DMR-0203359 and No. MRSEC DMR-0213808), and the Nebraska Research Initiative. The cal-culations were performed using the Research ComputingFacility of the University of Nebraska-Lincoln.*Electronic address: tsymbal@unl.edu[1] F. Bloch, Z. Phys. 74, 295 (1932).[2] L. Landau and E. Lifshitz, Phys. Z. Sowjetunion 8, 153(1935).[3] L. Ne´el, J. Phys. Radium 17, 250 (1956).[4] P. Bruno, Phys. Rev. Lett. 83, 2425 (1999).[5] M. Pratzer et al., Phys. Rev. Lett. 87, 127201 (2001).[6] J. Prokop, A. Kukunin, and H. J. Elmers, Phys. Rev. Lett.95, 187202 (2005).[7] G. G. Cabrera and L. M. Falicov, Phys. Status Solidi (b)61, 539 (1974).[8] N. Agraı¨t, A. Levy Yeyati, and J. M. van Ruitenbeek,Phys. Rep. 377, 81 (2003).[9] V. Rodrigues, J. Bettini, P. C. Silva, and D. Ugarte, Phys.Rev. Lett. 91, 096801 (2003).[10] C. S. Yang, C. Zhang, J. Redepenning, and B. Doudin,Appl. Phys. Lett. 84, 2865 (2004).[11] M. Bode et al., Phys. Rev. Lett. 89, 237205 (2002).[12] C. H. Marrows, Adv. Phys. 54, 585 (2005).[13] H. Imamura, N. Kobayashi, S. Takahashi, and S. Mae-kawa, Phys. Rev. Lett. 84, 1003 (2000); L. R. Tagirov, B. P.Vodopyanov, and K. B. Efetov, Phys. Rev. B 65, 214419(2002); V. K. Dugaev, J. Berakdar, and J. Barnas, Phys.Rev. B 68, 104434 (2003); J. D. Burton et al., Appl. Phys.Lett. 85, 251 (2004).[14] J. B. A. N. van Hoof et al., Phys. Rev. B 59, 138 (1999);J. Kudrnovsky et al., Phys. Rev. B 62, 15 084 (2000);B. Yu. Yavorsky et al., Phys. Rev. B 66, 174422 (2002);J. Velev and W. H. Butler, Phys. Rev. B 69, 094425 (2004).[15] R. F. Sabirianov et al., Phys. Rev. B 72, 054443 (2005).[16] J. Hubbard, Phys. Rev. B 23, 5974 (1981); S. A.Turzhevskii, A. I. Likhtenshtein, and M. I. Katsnelson,Sov. Phys. Solid State 32, 1138 (1990); O. N. Mryasov,V. A. Gubanov, and A. I. Liechtenstein, Phys. Rev. B 45,12 330 (1992).[17] L. N. Bulaevsk and V. L. Ginzburg, Sov. Phys. JETP 18,530 (1964); V. A. Zhirnov, Zh. Eksp. Teor. Fiz. 35, 1175(1959) [Sov. Phys. JETP 8, 822 (1959)]; N. Kazantseva,R. Wieser, and U. Nowak, Phys. Rev. Lett. 94, 037206(2005).[18] R. P. van Gorkom, A. Brataas, and G. E. W. Bauer, Phys.Rev. Lett. 83, 4401 (1999).[19] O. K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, 2571(1984).[20] R. Haydock, in Solid State Physics (Academic Press,New York, 1980), Vol. 35, pp. 215–294.[21] N. Beer and D. G. Pettifor, in The Electronic Structure ofComplex Systems, edited by P. Phariseau and W. M.Temmerman, NATO ASI, Ser. B, Vol. 113 (Plenum,New York, 1984).[22] To justify this model for the DW structure we performedself-consistent noncollinear calculations of the magneticmoment directions for the N  7 DW in a 5 4 Ni wire.We found that the converged magnetic structure representsa DW which has magnetic moment orientations almostidentical to those assumed within our model with devia-tions not larger than 2.FIG. 5. Results of a simple tight-binding model. (a) DOS of theuniformly magnetized state versus energy for majority- (wideband) and minority- (narrow band) spin electrons. (b) Con-ductance versus energy for a rigid DW (  0, dashed line)and for a soft DW (  0:2, solid line). (c) Conductance vs  forE  EF.PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-4

Crossref

Burton, J. D.

Jaswal, Sitaram

Mryasov, Oleg N.

The University of Nebraska, Omaha

University of Nebraska at OmahaDigitalCommons@UNOPhysics Faculty Publications Department of Physics8-2006Magnetic Moment Softening and Domain WallResistance in Ni NanowiresJ. D. BurtonUniversity of Nebraska-Lincoln, jdburton1@gmail.comRenat F. SabirianovUniversity of Nebraska at Omaha, rsabirianov@unomaha.eduSitaram JaswalUniversity of Nebraska, sjaswal1@unl.eduEvgeny Y. TsymbalUniversity of Nebraska at Lincoln, tsymbal@unl.eduOleg N. MryasovSeagate Research, Pittsburgh, PA, omryasov@mint.ua.eduFollow this and additional works at: https://digitalcommons.unomaha.edu/physicsfacpubPart of the Physics CommonsThis Article is brought to you for free and open access by the Departmentof Physics at DigitalCommons@UNO. It has been accepted for inclusion inPhysics Faculty Publications by an authorized administrator ofDigitalCommons@UNO. For more information, please contactunodigitalcommons@unomaha.edu.Recommended CitationBurton, J. D.; Sabirianov, Renat F.; Jaswal, Sitaram; Tsymbal, Evgeny Y.; and Mryasov, Oleg N., "Magnetic Moment Softening andDomain Wall Resistance in Ni Nanowires" (2006). Physics Faculty Publications. 31.https://digitalcommons.unomaha.edu/physicsfacpub/31Magnetic Moment Softening and Domain Wall Resistance in Ni NanowiresJ. D. Burton,1,3 R. F. Sabirianov,2,3 S. S. Jaswal,1,3 and E. Y. Tsymbal1,3,*1Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111, USA2Department of Physics, University of Nebraska, Omaha, Nebraska 68182-0266, USA3Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588-0111, USAO. N. MryasovSeagate Research, Pittsburgh, Pennsylvania 15222, USA(Received 27 January 2006; published 18 August 2006)We perform ab initio calculations of the electronic structure and conductance of atomic-size Ninanowires with domain walls only a few atomic lattice constants wide. We show that the hybridizationbetween noncollinear spin states leads to a reduction of the magnetic moments in the domain wallresulting in the enhancement of the domain wall resistance. Experimental studies of the magnetic momentsoftening may be feasible with modern techniques such as scanning tunneling spectroscopy.DOI: 10.1103/PhysRevLett.97.077204 PACS numbers: 75.47.Jn, 72.25.Ba, 73.63.b, 75.75.+aThe study of domain walls (DWs) in bulk ferromagneticmaterials began in the early 20th century with contribu-tions from Bloch [1], Landau and Lifshitz [2], and Ne´el [3].In bulk 3d metal ferromagnets DWs are wide (100 nm)on the scale of the lattice spacing due to the strong ex-change interaction which tends to align neighboring re-gions of magnetization, compared to anisotropic effectswhich prefer the magnetization to lie along specific direc-tions. With the recent interest in magnetic nanostructures ithas been shown that DWs can be quite thin due to theenhanced effective anisotropy of constricted geometry innanowires and nanocontacts [4]. Extremely narrow DWswith a width of the order of a lattice constant have recentlybeen observed in Fe nanowires grown on W [5] and Mo [6].The DW width controls the DW resistance. The origin ofthe DW resistance is known to be the mixing of up- anddown-spin electrons due to the mistracking of the elec-tron’s spin in passing through the DW [7]. The narrowerDW width results in a larger angle between the magneti-zation directions of successive atomic layers thereby low-ering the electron transmission. In bulk ferromagnets DWsdo not affect appreciably the resistance because the DWwidth is much larger than the Fermi wave length, andhence electrons can follow adiabatically the slowly varyingmagnetization direction within the DW. In magnetic nano-constrictions, where a DW can be very narrow, the DWresistance may be appreciable.Experimental studies of such DWs are feasible due toremarkable progress in experimental techniques, makingpossible to synthesize and characterize structures at theatomic scale. In particular, conducting nanowires can befabricated by breaking metal junctions [8], by pulling aparttwo metal surfaces [9], or by electrodepositing on prepat-terned electrodes [10]. Using these techniques an atomicscale DW can be formed in magnetic nanowires andstudied by modern experimental techniques such as scan-ning tunneling spectroscopy [11]. Electronic transportacross DWs exhibits interesting spin-dependent phe-nomena recently reviewed by Marrows [12].The theoretical description of the DW resistance so farwas based on either free-electron models [13] in which theDW is represented by an appropriate potential profile orfirst-principles calculations [14,15] in which the DW istypically described by a spin-spiral structure. All thesemodels assume that the DW is rigid; i.e., they neglectany spatial variation of the magnitude of the magneticmoment across the DW. It is well established, however,that the magnitude of the magnetic moments in itinerantmagnets can depend strongly on the orientation of theneighboring moments [16]. This effect is relatively weakin well localized ferromagnets like Fe, but can reduce andeven destroy the atomic magnetic moment of the itinerantferromagnets, like Ni.The origin of this phenomenon is the hybridizationbetween noncollinear spin states. In the uniformly magne-tized material with no spin-orbit coupling the minority-and majority-spin bands are independent. However, in anoncollinear state, such as a DW, this is no longer the caseand the two spin bands are hybridized. This spin mixingleads to charge transfer and level broadening, which resultsin the reduction of the overall exchange splitting betweenmajority- and minority-spin states on each atom, and hencethe atomic moments are reduced. In bulk DWs of anyferromagnetic material, this effect is small due to theslow variation of the direction of the magnetization. Forthe atomic scale DWs, however, there is a large degree ofcanting between neighboring magnetic moments. Thisleads to a significant hybridization between spin stateswhich leads to a reduction, or softening, of the magneticmoments within the constrained DW. The magnetic mo-ment softening affects the DW resistance due to the localperturbation in the electronic potential.PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 20060031-9007=06=97(7)=077204(4) 077204-1 © 2006 The American Physical SocietyWe note that the spatial variation of the magnetization inDWs has been suggested before, but only in the context offinite temperature magnetic disorder of the (fixed magni-tude) atomic magnetic moments in a DW [17]. The effectof spatial variation of the magnetization on DW resistancewas addressed previously, but only within the diffusivetransport regime and a free-electron model [18].In this Letter we illustrate the importance of magneticmoment softening by performing ab initio calculations ofthe electronic structure and ballistic conductance of atomicscale DWs in Ni nanowires. We show that the magneticmoments within DWs only a few lattice constants wide canbe significantly reduced compared to the magnetic mo-ments in a uniformly magnetized wire due to the presenceof substantial hybridization between spin states. We findthat the magnetic moment softening strongly enhances theDW resistance due to additional scattering resulting fromthe local perturbation in the electronic potential.Density functional calculations of the spin-dependentelectronic structure of atomic scale DWs in Ni nanowireswere performed using the tight-binding linear muffin-tin-orbital method [19] in the atomic sphere approximationand the local spin density approximation for the exchange-correlation energy. We used the real space recursionmethod [20] with a Beer-Pettifor terminator [21] to calcu-late the local density of states (DOS). Ultrathin domainwalls were examined for two different freestanding Niwires based on the bulk fcc structure: (110) monatomicchains and 5 4 wires (described below). All the struc-tures used the lattice constant a  3:52 A of bulk fcc Ni.In the calculations we constructed a central region con-taining the DW, surrounded by two uniformly magnetizedleads aligned antiparallel relative to each other. The self-consistent calculations were carried out for the centralregion and a large enough portion of the surrounding leadsso that the outermost atoms of the self-consistent regionwere similar to those in the remaining semi-infinite sectionof the leads in the uniformly magnetized state. A DW wasmodeled by a finite spin spiral with the relative anglebetween neighboring atomic layers of magnetic momentsbeing 180=N  1, where N is the number of atomiclayers in the DW [22].First, we consider an N  1 DW in a monatomic Ni wire[Fig. 1(a)]. Figure 1 displays the results of our calculationsfor the N  1 DW. The electronic potentials of the anti-parallel magnetized lead sites were frozen, while on thecentral five sites the electronic structure was calculatedself-consistently. We find a 16% reduction of the magneticmoment on the central site and a 7% reduction on the twoneighboring sites. The reduction in the magnetic momenton the central site is due to the hybridization with thedifferent spin states of the noncollinear neighbors, whichresults in the reduction of the exchange splitting, as de-scribed earlier. This fact is evident from Fig. 1(b), whichshows the local DOS for the uniformly magnetized mona-tomic Ni wire and for the central atom of an N  1 DW.The reduction in the moment of the nearest neighbors ofthe central atom is only about half of that of the centralatom because they are noncollinear with only one of thetwo neighbors. Also apparent in Fig. 1(b) is an overallbroadening of the DOS on the central site compared tothe uniformly magnetized state produced by the spinmixing.Figure 2 shows the magnetic moment profile for severalDW widths in the monatomic wire. The reduction in themoment is strongly dependent on the width of the DW. ForN  0 and N  1 DWs, the effect of softening is thelargest owing to the fact that the degree of noncollinearityis the largest in these two cases. As the width of the DWincreases the softening decreases because of the reductionof the angle between the nearest neighbor magneticmoments.Figure 3(a) shows the 5 4wire which has five atoms inone layer and four in the next layer resulting in threenonequivalent sites, each indicated by a different color.Although the average magnetic moment of the uniformlymagnetized 5 4 wire,   0:7B, is lower than that ofthe monatomic wire,   1:1B, we find that in the pres-ence of ultrathin DWs the spatial variation of the magne-tization displays qualitatively similar behavior. Figure 3(b)shows the magnetic moments found for three DW widths inthe 5 4 wire. The largest reduction in magnetic momentis nearly 90% for the central site of the N  1 DW, and theeffect is still substantial for the N  5 DW where theFIG. 1 (color online). (a) A monatomic wire with an N  1DW. The arrows show the orientation and relative magnitude ofcalculated magnetic moments. (b) DOS per atom of the uni-formly magnetized monatomic wire (dashed curve) and the localDOS (LDOS) at the center of an N  1 DW (solid curve).PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-2magnetic moment of the central layer is softened by about10%. The effect is significantly larger in the 5 4 wirethan that in the monatomic chain due to the enhancedhybridization reflecting an increase in the number of neigh-boring atoms.The magnetic moment softening affects dramatically theconductance across DWs. We calculate the conductance ofthe 5 4 Ni wire with an N  1 DW using the standardtechnique described in detail in Ref. [15]. It should benoted, however, that in Ref. [15] the Hamiltonian for theDW region was built by simply rotating (in spin space) theself-consistent potentials obtained for the uniformly mag-netized wire. Here we derive the Hamiltonian from theself-consistent potentials found in the presence of theabrupt DW. For comparison we also calculate the conduc-tance in the same way as Ref. [15], which allows us todetermine the contribution of magnetic moment softeningto the DW resistance.Figure 4(a) shows the spin-resolved conductance, GFM,of a uniformly magnetized 5 4 Ni wire as a function ofenergy E. The conductance is quantized in steps of e2=h,corresponding to the number of bands crossing the energyE. The bands are seen in Fig. 4(b) as being bound by thesharp peaks corresponding to the band edges. The conduc-tance in the zero-bias limit is given by the value at theFermi energy, EF, located at the center of the narrowminority band. For the 5 4 Ni wire it is 14e2=h.Figure 4(c) displays the conductance through an N  1DW, GDW. For a ‘‘rigid’’ DW (no softening of the magneticmoments) the Hamiltonian is constructed from the self-consistent potentials of the uniformly magnetized wire,while for the ‘‘soft’’ DW we use the potentials that yieldreduced magnetic moments in the DW region, as seen inFig. 3. We find that the magnetic moment softening in theDW leads to a reduction in the conductance at the Fermienergy from 5:38e2=h to 3:21e2=h.The origin of this phenomenon can be understood usinga simple tight-binding model of a monatomic chain with anabrupt N  0 DW. We model the majority states by a wideband, characterized by the (large) nearest neighbor hop-FIG. 3 (color online). (a) The 5 4 nanowire showing thethree nonequivalent sites and an N  3 DW. Each arrow repre-sents the magnitude and orientation of the average magneticmoment of the plane with 5 atoms. (b) The self-consistentmagnetic moments for several DW widths. The color in theplot corresponds to the site of the same color in (a).FIG. 4. (a) Spin-resolved conductance GFM and (b) density ofstates near the Fermi energy EF as a function of energy for theuniformly magnetized 5 4 Ni wire. (c) Conductance of theN  1 DW, GDW, as a function of energy for the rigid DW(dashed curve) and for the soft DW (solid curve).FIG. 2. Magnetic moments in the monatomic Ni wire as afunction of distance from the DW center for several DW widths.The N  1 plot corresponds to Fig. 1(a).PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-3ping parameter tmaj, to emulate the wide band near theFermi energy [see Fig. 4(b)]. The minority states aremodeled by a narrow band with (small) hopping tmin, offsetfrom the center of the majority band by energy . Tomodel magnetic moment softening we assume that theon-site energies of the two interface sites are shifted rela-tive to the uniformly magnetized leads. Majority states areshifted up by energy , and minority states are shifteddown by the same amount . This corresponds effectivelyto a reduction of the local exchange splitting by 2 on thetwo interface sites, and hence softening of the magneticmoment. The parameters for our model are chosen asfollows: tmaj  1, tmin  0:05, and   1. The results ofthe model are shown in Fig. 5. As is seen from Figs. 5(b)and 5(c), the model predicts a drastic reduction in theconductance as a result of magnetic moment softening.The origin of this reduction is the local perturbation inthe electronic potential which leads to stronger scatteringof transport electrons by the DW. When the on-site ener-gies of the interface atoms are shifted with respect to thenarrow minority band, which determines the energy win-dow for conductance, these sites act as additional scatterersthat hinder conductance.Scanning tunneling spectroscopy (STS) has been shownto reveal differences in the electronic structure of domainsand DWs in Fe nanowires grown on W(110) surfaces [11].It may be possible to use techniques such as STS to studythe changes in the electronic structure due to magneticmoment softening in narrow DWs predicted here. Wehope, therefore, that our theoretical predictions will stimu-late experimental studies of the electronic and transportproperties of atomic scale domain walls.This work is supported by Seagate Research, the NSF(Grants No. DMR-0203359 and No. MRSEC DMR-0213808), and the Nebraska Research Initiative. The cal-culations were performed using the Research ComputingFacility of the University of Nebraska-Lincoln.*Electronic address: tsymbal@unl.edu[1] F. Bloch, Z. Phys. 74, 295 (1932).[2] L. Landau and E. Lifshitz, Phys. Z. Sowjetunion 8, 153(1935).[3] L. Ne´el, J. Phys. Radium 17, 250 (1956).[4] P. Bruno, Phys. Rev. Lett. 83, 2425 (1999).[5] M. Pratzer et al., Phys. Rev. Lett. 87, 127201 (2001).[6] J. Prokop, A. Kukunin, and H. J. Elmers, Phys. Rev. Lett.95, 187202 (2005).[7] G. G. Cabrera and L. M. Falicov, Phys. Status Solidi (b)61, 539 (1974).[8] N. Agraı¨t, A. Levy Yeyati, and J. M. van Ruitenbeek,Phys. Rep. 377, 81 (2003).[9] V. Rodrigues, J. Bettini, P. C. Silva, and D. Ugarte, Phys.Rev. Lett. 91, 096801 (2003).[10] C. S. Yang, C. Zhang, J. Redepenning, and B. Doudin,Appl. Phys. Lett. 84, 2865 (2004).[11] M. Bode et al., Phys. Rev. Lett. 89, 237205 (2002).[12] C. H. Marrows, Adv. Phys. 54, 585 (2005).[13] H. Imamura, N. Kobayashi, S. Takahashi, and S. Mae-kawa, Phys. Rev. Lett. 84, 1003 (2000); L. R. Tagirov, B. P.Vodopyanov, and K. B. Efetov, Phys. Rev. B 65, 214419(2002); V. K. Dugaev, J. Berakdar, and J. Barnas, Phys.Rev. B 68, 104434 (2003); J. D. Burton et al., Appl. Phys.Lett. 85, 251 (2004).[14] J. B. A. N. van Hoof et al., Phys. Rev. B 59, 138 (1999);J. Kudrnovsky et al., Phys. Rev. B 62, 15 084 (2000);B. Yu. Yavorsky et al., Phys. Rev. B 66, 174422 (2002);J. Velev and W. H. Butler, Phys. Rev. B 69, 094425 (2004).[15] R. F. Sabirianov et al., Phys. Rev. B 72, 054443 (2005).[16] J. Hubbard, Phys. Rev. B 23, 5974 (1981); S. A.Turzhevskii, A. I. Likhtenshtein, and M. I. Katsnelson,Sov. Phys. Solid State 32, 1138 (1990); O. N. Mryasov,V. A. 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B, Vol. 113 (Plenum,New York, 1984).[22] To justify this model for the DW structure we performedself-consistent noncollinear calculations of the magneticmoment directions for the N  7 DW in a 5 4 Ni wire.We found that the converged magnetic structure representsa DW which has magnetic moment orientations almostidentical to those assumed within our model with devia-tions not larger than 2.FIG. 5. Results of a simple tight-binding model. (a) DOS of theuniformly magnetized state versus energy for majority- (wideband) and minority- (narrow band) spin electrons. (b) Con-ductance versus energy for a rigid DW (  0, dashed line)and for a soft DW (  0:2, solid line). (c) Conductance vs  forE  EF.PRL 97, 077204 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending18 AUGUST 2006077204-4

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Magnetic Moment Softening and Domain Wall Resistance in Ni Nanowires

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