Download Applied field Mössbauer study of shape anisotropy in Fe nanowire

APPLIED PHYSICS LETTERS
VOLUME 85, NUMBER 20
15 NOVEMBER 2004
Applied field Mössbauer study of shape anisotropy in Fe nanowire arrays
Qing-feng Zhan, Wei He, Xiao Ma, Ya-qiong Liang, Zhi-qi Kou,
Nai-li Di, and Zhao-hua Chenga)
State Key Laboratory of Magnetism and International Center for Quantum Structures, Institute of Physics,
Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
(Received 14 June 2004; accepted 27 September 2004)
In order to investigate the magnetic anisotropy of Fe nanowire arrays from microscopic point of
view, 57Fe Mössbauer spectra were measured at various magnetic fields along and perpendicular to
the nanowire axis, respectively. On the basis of the absorption intensities of the second and the fifth
lines of sextet, the orientation of Fe magnetic moments can be detected. It was found that the shape
anisotropy dominates the overall magnetic anisotropy in the Fe nanowires. Furthermore, the
longitudinal and transverse demagnetizing fields of Fe nanowire, respectively, were deduced from
the effective hyperfine field at 57Fe nuclei as a function of applied field. The chain-of-spheres model
in conjunction with symmetric fanning mechanism was adopted to interpret the domain structure
and the parallel coercivity of magnetic nanowire arrays. © 2004 American Institute of Physics.
[DOI: 10.1063/1.1827330]
Recently, the fabrication and magnetic properties of
highly ordered magnetic nanowire arrays have been extensively investigated owing to their potential application in ultrahigh density magnetic recording media.1–4 The unique and
tunable magnetic properties of nanowire arrays arise from
the inherent shape anisotropy and the low dimension. In order to improve the density of magnetic recording approaching the super-paramagnetism limit, it is required that the
magnetic nanowires possess large uniaxial magnetic anisotropy to overcome the thermal fluctuation. It was proved that
Mössbauer spectroscopy is a powerful technique to investigate the magnetic anisotropy.5–7 Previous zero-field Mössbauer spectra of both Fe and FeCo nanowire arrays have the
characteristics of disappearance of the second and fifth absorption peaks in the sextet, implying that the easy magnetization direction lies in the axes of nanowires.8,9 However, the
dependence of hyperfine fields and the intensities of the second and fifth lines on the applied field is not well known. In
this letter, the magnetization process, i.e., the magnitude and
direction of Fe magnetic moments were investigated by applied Mössbauer spectroscopy on a local scale via the values
of hyperfine fields and the ratios of the intensities of the
second line to the third line or the fifth line to the fourth line
of magnetically split spectra. (Hereafter, we define them as
relative intensities of the second line and the fifth line, I2,5.)
The demagnetizing field and the shape anisotropy constant of
Fe nanowires were also derived from the hyperfine field as a
function of applied field.
The arrays of Fe nanowires were prepared by electrodepositing Fe into anodic aluminum oxide (AAO) templates.
The detailed procedures for preparing AAO templates and
electrodepositing
Fe
nanowires
were
described
elsewhere.8–10 Figure 1(a) shows the x-ray diffraction pattern
of the Fe nanowire arrays after completely dissolving the
aluminum substrate in an HgCl2 saturated solution. Only the
(110) diffraction peak is evident and the d value of average
interplanar spacing matches perfectly with the value of bulk
bcc Fe, which indicates the Fe nanowire arrays are bcc struca)
Electronic mail: [email protected]
ture with a [110]-preferred orientation along the nanowire
axis. The inset of Fig. 1(a) shows a transmission electron
microscopy image of a 20-nm-diam Fe nanowire after removal from the template, illustrating the nanowires were uniform with very large length-to-diameter ratio 共⬃375兲. Magnetization measurements of the Fe nanowire arrays were
performed at 10 K using a superconducting quantum interference device magnetometer. Figure 1(b) shows the hysteresis loops of Fe nanowire arrays in AAO films with the applied field parallel and perpendicular to the wire axis at 10 K.
The hysteresis loop measured along the wire axis indicates a
relative square with M r / M s ratio of 0.98 and a coercivity of
2842 Oe, while the hysteresis loop measured perpendicular
to the wire axis is sheared with a squareness of 0.07 and a
coercivity of 444 Oe. It is clearly seen from those features
that the easy magnetization direction of Fe nanowire is along
the long axis of nanowire, i.e., the [110] direction, rather than
the [100] in bulk bcc Fe. Magnetization measurement results
suggest that the overall magnetic anisotropy is dominated by
the shape anisotropy in Fe nanowires owing to the very large
aspect ratio.
In order to investigate the shape anisotropy of Fe nanowire arrays from a microscopic point of view, 57Fe Mössbauer spectra at various magnetic fields were measured by a
constant-acceleration Mössbauer spectrometer with a
57
Co共Pd兲 source at 10 K, with the ␥ beam parallel to the
FIG. 1. (a) X-ray diffraction patterns of Fe nanowire arrays. The inset shows
a transmission electron microscopy image of 20-nm-diam Fe nanowire after
removing from the template. (b) Hysteresis loops of Fe nanowire arrays at
10 K. H共//兲 indicates the magnetic field applied parallel to the nanowire axis.
H共⬜兲 denotes perpendicular to the wire axis.
0003-6951/2004/85(20)/4690/3/$22.00
4690
© 2004 American Institute of Physics
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Zhan et al.
Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004
4691
FIG. 2. Mössbauer spectra of Fe nanowire arrays in AAO films at 10 K with
various magnetic fields applied perpendicular to the nanowire axis.
nanowire axis. The magnetic fields up to 50 kOe both parallel and perpendicular to the nanowire axis are provided by an
Oxford Spectromag SM4000-9 superconducting split pair,
horizontal field magnet system. The values of velocities were
calibrated using a ␣-Fe foil at room temperature. Figure 2
shows the Mössbauer spectra of Fe nanowire arrays with the
applied field perpendicular to the nanowire axis. For the
zero-field Mössbauer spectrum, the second and fifth absorption peaks in the sextet almost disappear. As the magnetic
field increases, the relative intensities of the 2–5 lines also
increase. In magnetically split spectra, the relative intensities
of the 2–5 lines (corresponding to the ⌬m = 0 nuclear transitions) are given by I2,5 = 4 sin2 ␪ / 共1 + cos2 ␪兲, where ␪ is the
angle between the magnetic moment and the ␥ beam
direction.11 In the case of all Fe spins are collinear to the ␥
beam direction I2,5 = 0, while all magnetic moments are perpendicular to ␥ beam I2,5 = 4. Therefore, the disappearance of
the 2–5 lines for Fe nanowire arrays at zero field indicates all
Fe spins orient parallel to the nanowire axis. The increase of
I2,5 denotes all magnetic moments rotate continuously approaching the direction of applied field with increasing applied field. Figure 3(a) illustrates the average 具sin ␪典 as a
function of applied field. It can be noticed that all magnetic
moments align completely to the direction of applied field,
that is to say the Fe nanowires reach saturation completely at
the applied fields above 10 kOe. Furthermore, it can be seen
in Fig. 3(a) that the values of 具sin ␪典 obtained from Mössbauer results are in good agreement with the values of normal magnetization M / M s, where M / M S = 具cos共␲ / 2 − ␪兲典
= 具sin ␪典.
The effective hyperfine field Heff at 57Fe nuclei can be
expressed as
Heff = Hhf + Happ + Hdm ,
共1兲
where Hhf , Happ, and Hdm are the hyperfine field, the applied
field, and the demagnetizing field, respectively. It should be
noted that the hyperfine field at 57Fe nuclei is antiparallel to
the magnetic moment. The demagnetizing field is given by
Hdm = −NM, where N is the demagnetization factor which
depends on the direction of magnetization, and M is the magnetization vector. Once the magnetization reaches the saturation value, the demagnetizing field is constant. In the case of
applied field parallel to the nanowire, magnetic fields at iron
sites are collinear to the axis of nanowire. Therefore, all
Mössbauer spectra of Fe nanowire arrays with the applied
FIG. 3. (a) A graph of average 具sin ␪典 vs applied field Happ, comparing with
the magnetization curve of Fe nanowire arrays. (b) The effective field Heff
for Fe nanowire arrays as a function of the applied field Happ. The dots and
dashed lines are experimental and fitting results, respectively. The magnetic
field is parallel and perpendicular to the nanowire axis, respectively.
field parallel to the nanowire axis have the characteristics of
the disappearance of the 2–5 lines, and the magnitude of Heff
can be expressed as
Heff = Hhf − Happ + Hdm .
共2兲
The effective hyperfine field with applied field parallel to the
nanowire axis can be fitted in the formula of Heff = Hhf共Happ
= 0兲 − Happ within the range of error. The fitting curve and the
experimental dots are plotted in Fig. 3(b). Therefore, Hdm//
= 0 can be deduced. This result is consistent with the theoretical value of an infinitely long cylinder. In the case of
applied field perpendicular to the nanowire axis, the effective
field is not antiparallel to the applied field until all Fe spins
are collinear to applied field. Therefore, only after the magnetization reaches saturation, the magnitude of Heff can be
expressed by formula (2). The effective field after the
nanowires completely saturated can be fitted as Heff
= Hhf共Happ = 0兲 − Happ + 7.21 kOe, where the 7.21 kOe is the
saturation demagnetizing field. According to the demagnetizing field, the magnetization M and the angle ␪ between the
magnetic moment and the ␥ beam [Fig. 3(a)], Eq. (1) can be
used to calculate the magnitude of Heff in whole range of
external field. The calculated curve matches the experimental
data very well [Fig. 3(b)].
Herein, the chain-of-spheres model12 is quoted to interpret the domain structure and the magnetization process. Figure 4 is the sketches of the domain structure of a single
nanowire in external field. Each nanowire can be considered
as a chain of single-domain spheres. Since both the diameter
of Fe nanowire and the critical diameter of single-domain
sphere are about 20 nm, the chain-of-spheres structure is
easy to be formed, and the multidomain is likely to appear in
the transverse section of a thicker magnetic nanowire, which
results in the reduction of parallel coercivity and squareness.
Similar magnetic domain structure has been directly observed in Fe nanowire grown on the W(110) by scanning
tunneling microscopy.13 It is well known that the coercivity
and shape of the hysteresis loop depend on the magnetization
reversal process. We adopt the chain-of-spheres model in
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4692
Zhan et al.
Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004
between nanowires in AAO films is about 40 nm, which is
far larger than the exchange length, the exchange coupling
interaction between nanowires is not taken into account.
Therefore, the magnetic energy W of the nanowire system in
an applied field Happ on the angle ␪ can be written as
p
W = K sin ␪ −
2
FIG. 4. Schematic diagram of the chain-of-spheres domain structure of a
single magnetic nanowire, and the spin-flip in external field.
conjunction with symmetric fanning mechanism to interpret
the longitudinal coercivity of magnetic nanowire. In this
model, the magnetic nanowire is assumed to be an ideal
chain of single-domain spheres with uniaxial magnetic anisotropy. Only the magnetostatic energy and the dipole interaction are taken into account, and the domain energy is neglected. Using the chain-of-spheres model with symmetric
fanning mechanism, the longitudinal coercivity of the magnetic nanowires is deduced12 as
HC// =
␲M S
共6Kn − 4Ln兲,
6
共3兲
where
n
Kn =
兺
i=1
n−i
,
ni3
共n−1兲/2⬍i艋共n+1兲/2
Ln =
兺
i=1
n − 共2i − 1兲
.
n共2i − 1兲3
Here M S is the saturation magnetization of the magnetic
nanowires, and n is the number of the spheres in a single
nanowire, which is equal to the aspect ratio 共n ⬇ 375兲. Due to
the difficulty in measuring the weight of nanowires in AAO
films, the saturation magnetization of Fe nanowires cannot
be directly obtained from the magnetization measurement.
Considering the hyperfine field of Fe nanowire arrays
matches perfectly with that of bulk Fe at 10 K, it is reasonable to assume that the saturation magnetization of Fe
nanowires is the same as that of bulk bcc Fe. According to
the above-mentioned parameters, the longitudinal coercivity
of the Fe nanowires at 10 K is calculated to be 2726 Oe,
which agrees well with the experimental result 2842 Oe. For
the nanowire is composed of single-domain spheres in our
model, the transverse coercivity arises mainly from the magnetocrystalline anisotropy. However, the magnetocrystalline
anisotropy field 共HK = 2K1 / M S = 598 Oe兲 of Fe at 10 K is
fairly larger than the experimental coercivity 444 Oe.14 The
large deviation likely results from the exchange coupling between the magnetic spheres, which reduces the coercivity.
By means of applied field Mössbauer spectra, the shape
anisotropy can be evaluated quantitatively. Since the distance
冉 冊
兺 ␮FeHapp cos
␲
−␪ ,
2
共4兲
where the first term represents the overall magnetic anisotropy energy, the second term is the magnetostatic energy,
the K is defined as the overall magnetic anisotropy constant,
the ␮Fe is the magnetic moment of Fe, and the p is the Fe
atomic number per unit volume. This dependence gives rise
to the expression K = M SHapp / 2具sin ␪典, where 0 ⬍ ␪ ⬍ ␲ / 2.
Using M S of bulk Fe and the average 具sin ␪典 at different
applied fields [Fig. 3(a)], one can estimate the average magnetic anisotropy constant K ⬇ 7.3⫻ 106 ergs/ cm3. The shape
anisotropy constant is one order of magnitude larger than
that of the magnetocrystalline anisotropy constant K1 of bulk
Fe at 10 K,14 so the magnetocrystalline anisotropy can be
neglected reasonably in Fe nanowires.
In summary, Mössbauer spectra clearly show the process
of Fe spins rotated from parallel to perpendicular to the wire
axis with increasing the magnetic field perpendicular to the
axis of nanowire. The longitudinal and transverse demagnetizing fields of Fe nanowire are deduced from the effective
field of Fe nanowire arrays as a function of applied field. The
chain-of-spheres model with symmetric fanning mechanism
is adopted to interpret the domain structure and the high
coercivity along the axis of magnetic nanowires. Compared
with the shape anisotropy obtained from Mössbauer spectra,
the magnetocrystalline anisotropy is too small to be taken
into account in Fe nanowires.
This work was supported by the State Key Project of
Fundamental Research, and the National Natural Sciences
Foundation of China. Z.H.C thanks the Alexander von Humboldt Foundation for financial support and generous donation
of some of the Mössbauer equipment used.
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