Effect of Si/Fe Composition, Substrate Temperature, and Substrate Orientationon the Structure and Magnetic Properties of Fe-Si Alloy Film
Takuya Aida1, Tetsuroh Kawai1, Mitsuru Ohtake1,2, Masaaki Futamoto1,
Fumiyoshi Kirino3, and Nobuyuki Inaba4
Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
2Faculty of Engineering, Kogakuin University, 2655-1 Nakano, Hachioji, Tokyo 192-0015, Japan1

3Graduate School of Fine Arts, Tokyo University of the Arts, 12-8 Ueno-Koen, Taito-ku, Tokyo 110-8714, Japan
4Faculty of Engineering, Yamagata University, 4-3-16 Jyonan, Yonezawa, Yamagata 992-8510, Japan

Fe100–xSix (x = 0, 2, 6, 10 at. %) alloy films are prepared on MgO single-crystal substrates of (001), (110), and(111) orientations at temperatures ranging between room temperature and 600 °C by using a radio-frequency
magnetron sputtering system. The film growth behavior, the crystallographic properties, and the magnetic
properties are systematically investigated. Fe-Si(001) single-crystal films with bcc structure are formed on MgO(001)substrates. The Fe-Si films deposited on MgO(110) substrates consist of epitaxial bcc(211) bi-crystals whoseorientations are rotated around the film normal by 180° each other. Fe-Si films grow epitaxially on MgO(111)substrates with two types of bcc(110) variant whose crystallographic orientations are similar to the
Nishiyama-Wasserman and the Kurdjumov-Sachs relationships. The orientation dispersion of Fe-Si film decreases
with decreasing the Si composition, with increasing the substrate temperature, and with decreasing the index of thesubstrate crystallographic plane. The Fe-Si films deposited on MgO(001) and (110) show in-plane magnetic
anisotropies reflecting the magnetocrystalline anisotropies of bulk Fe-Si alloy crystals. The Fe-Si films deposited on
MgO(111) show nearly isotropic in-plane magnetic anisotropies that possibly come from the multiple variant
structure. The coercivity decreases with increasing the Si composition and with decreasing the substratetemperature.
Keywords: Fe100–xSix (x = 0 – 10 at. %) alloy, epitaxial thin film, MgO single-crystal substrate, soft magnetic property
1.

Introduction

Fe-Si alloy is a typical soft magnetic material andhas been used in transformers, motors, etc. It is known
that the crystallographic structure and the magnetic
properties change depending on the Si composition andthe processing temperature1,2). In particular, Fe – 3
wt. % Si (≈ Fe – 6 at. % Si) alloys are widely used in therelated industries because of excellent soft magnetic
properties with high permeability, high saturation
magnetization (Ms), and low coercivity (Hc). In suchapplications, grain-oriented or non-grain-oriented
silicon steel sheets are generally employed, where theoverall magnetic properties are influenced by the
structure consisting of crystal grains. Therefore,
understanding the magnetic properties of Fe-Si crystals
with different orientations is very important to further
improve the overall soft magnetic properties.
There are some reports on the investigations
concerning the relationships of Si/Fe composition andcrystallographic orientation with respect to themagnetic properties by using bulk Fe-Si single-crystal
materials3,4). However, it is not easy to prepare bulk
crystal samples systematically varying the Sicomposition or the crystallographic orientation. In
contrast, it seems possible to prepare thin film crystal
samples,where
thecomposition
andthecrystallographic orientation can be respectively
controlled by the target composition and the orientationof single-crystal substrate. In the present study,

Fe100–xSix (at. %, x = 0 – 10) alloy thin films areprepared on MgO single-crystal substrates of (001),(110). and (111) orientations at temperatures ranging
from room temperature (RT) to 600 °C. The influences offilm composition, substrate temperature, and substrateorientation on the detailed structure and the magnetic
properties are systematically investigated.
2.

Experimental Procedure

Fe100–xSix (x = 0, 2, 6, 10 at. %) alloy films of 40 nm
thickness were deposited on polished MgO substrates of(001), (110), and (111) orientations by using aradio-frequency (RF) magnetron sputtering systemequipped with a reflection high-energy electron
diffraction (RHEED) facility. The base pressures werelower than 4 × 10–7 Pa. Before film formation,
substrates were heated at 600 °C for 1 hour to obtainclean surfaces. The distance between a target andsubstrates was fixed at 150 mm. The Ar gas pressure
was kept constant at 0.67 Pa. The RF powers for Fe,
Fe98Si2, Fe94Si6, and Fe90Si10 targets were respectively
fixed at 52, 59, 54, and 54 W, where the deposition rates
were 0.02 nm/s. The substrate temperature was varied
in a range from RT to 600 °C.
The surface structure was studied by RHEED. The
resulting film structure was investigated by 2θ/ω-scanout-of-plane and 2θχ/φ-scan in-plane X-ray diffractions(XRDs) with Cu-Kα radiation (λ = 0.15418 nm). The
surface morphology was observed by atomic force

A2
D 03

004

_

_ 006_
115_
_ 115
224
004
224

Fig. 1 RHEED patterns observed for (a) Fe, (b) Fe98Si2,(c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at 200 °C. [(e), (f)] Schematic diagrams of
RHEED patterns of (e) A2(001) and (f) D03(001)single-crystal surfaces simulated by using the lattice
constants of bulk (e) Fe (a = 0.2866 nm6)) and (f) Fe3Si (a= 0.5653 nm7)), respectively. The incident electron beam
is parallel to (a)–(d) MgO[100], (e) A2[110], or (f)D03[110]. The filled and open circles in (f) respectively
correspond to the fundamental and the superlatticereflections.

microscopy (AFM). The magnetization curves were
measured by vibrating sample magnetometry.
3.

Results and Discussion(b-1)
Fe98Si2

(b-2)

(c-1)
Fe94Si6Δθ50 = 0.98 °(c-2)

Δθ50 = 1.23 °(d-1)
Fe90Si10

20

(a-2)

Δθ50 = 0.84°

30

(d-2)
40

50
60
2θ (deg.)

70

80 –4

0

ω (deg.)4

Fig. 2 (a-1)–(d-1) Out-of-plane XRD patterns measuredfor (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(001) substrates at 200 °C. (a-2)–(d-2)
Rocking curves measured by fixing the diffraction angleof 2θ at the peak angles of A2(002) reflections in thepatterns of (a-1)–(d-1), respectively. The intensity isshown in (a-1)–(d-1) logarithmic or (a-2)–(d-2) linear
scale.

3.1

A2(001)[110] || MgO(001)[100].
Fe-Si(001) single-crystal films with A2 structure are
obtained on the substrates, where the Fe-Si(001) lattice
is rotated around the film normal by 45° with respect tothe MgO(001) lattice. In this configuration, the latticemismatch slightly increases from –4.0% to –4.4% withincreasing the x value from 0 to 10 at. %, where thelattice constants of bulk MgO (a = 0.4217 nm8)), Fe (a =0.2866 nm6)), and Fe89.5Si10.5 (a = 0.2853 nm9)) crystals
are used.
Figures 2(a-1)–(d-1) and 3(a-1)–(d-1) show theout-of-plane and in-plane XRD patterns measured for
Fe-Si films. Here, the scatteringvector of in-plane XRD_
is parallel to MgO[11 0]. Out-of-plane A 2(002) andin-plane A2(200) fundamental reflections are recognized,
whereas out-of-plane D03(002) and in-plane D03(200)

A2
D03

200

Δθχ50 = 0.81°

Δθχ50 = 0.95°(c-1)
Fe94Si6(c-2)

Δθχ50 = 1.19°(d-1)
Fe90Si10
30

(a-2)

(b-2)

(b-1)
Fe98Si220

Δθχ50 = 0.72°

KβIntensity (arb. unit)

(a-1)
Fe

A2(200)400

MgO(220)200_

Effect of Si/Fe composition
Figures 1(a)–(d) show the RHEED patterns
observed for Fe100–xSix alloy films with x = 0 – 10 at. %deposited on MgO(001) substrates at 200 °C. Clear
diffraction patterns are observed for all the investigatedcompositions. The Fe-Si films grow epitaxially on thesubstrates. bcc-based disordered A2 phase and ordered
D03 phase exist in Fe-rich region of the bulk Fe-Si
binary alloy phase diagram5). Diffraction patterns for
A2(001) and D03(001) surfaces were thus calculated byusing the lattice constants of bulk Fe (a = 0.2866 nm6))
and Fe3Si (a = 0.5653 nm7)), respectively. Figures 1(e)and (f) are the schematic diagrams of the simulated
patterns of A2(001) and D03(001) surfaces, respectively.
The observed RHEED patterns are corresponding to thepattern simulated for A2(001) surface. The epitaxial
orientation relationship is determined as

(a-1)
Fe

WL

(f) D03

Kβ(d) Fe90Si10

Δθ50 = 0.73°

WL(b) Fe98Si2

Intensity (arb. unit)

112 002 112

A2(002)

_

002
002

Kβ

(e) A2 004

MgO(002)(c) Fe94Si6(a) Fe

(d-2)
40

50
60
2θχ (deg.)

70

80 –4

0

ϕ (deg.)4

Fig. 3 (a-1)–(d-1) In-plane XRD patterns measured for(a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(001) substrates at 200 °C. The
scattering vector is parallel to MgO[110]. (a-2)–(d-2)
Rocking curves measured by fixing the diffraction angleof 2θχ at the peak angles of A2(200) reflections in thepatterns of (a-1)–(d-1), respectively. The intensity isshown in (a-1)–(d-1) logarithmic or (a-2)–(d-2) linear
scale.

superlattice reflections are absent. The XRD confirms
the crystal structure and the epitaxial orientation
relationship determined by RHEED.
Figure 4(a) shows the Si composition dependencesof lattice constants, a and c, of Fe-Si film. The lattice
constants are calculated by using the relation of (a, c) =(2 d A 2(200) , 2 d A 2(002) ). The Fe-Si lattices are slightly

1

Si composition (wt. %)
2
3
4

5

2000

a

1000

(a)

0.288

–1000

Bulk

–2000
2000

0.285

0
(b)

2

1

4
6
Si composition (at. %)

8

10

5

0

1.0

Δθ50

0.8

Δθχ50
0

2

4
6
Si composition (at. %)(b) Fe98Si2

1000

Si composition (wt. %)2
3
4

Magnetization (emu/cm3)00.6

θH = 45º (A2[110])

0

0.286

1.2

θH = 0º (A2[100])(a) Fec

0.287

Orientation dispersion
Δθ50, Δθχ50 (deg.)

Lattice constant c, a (nm)

0

8

–1000
–2000
2000

(c) Fe94Si6

1000
0

10

–1000

Fig. 4Compositional dependences of (a) lattice
constants of a and c and (b) orientation dispersion
values of Δθ50 and Δθχ50 of Fe-Si film prepared on
MgO(001) substrate at 200 °C. The lattice constants ofbulk Fe-Si crystals are cited from Ref. 9.

–2000
2000

(d) Fe90Si10

1000
0
–1000
–2000
–1000

–500

0
500
Applied field (Oe)1000

Si composition (wt. %)0 1 2 3 4 5
(a)

30
20
10

0

0 2 4 6 8 10
Si composition (at. %)Saturation magnetization
MS (kemu/cm3)

Fig. 5 Magnetization curves measured for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(001) substrates at 200 °C.

Coercivity HC (Oe)deformed along the c-axis due to accommodation oflattice misfits of about –4%. With increasing the Sicomposition, a and c values are decreasing. The
out-of-plane and in-plane orientation dispersions (Δθ50,
Δθχ50) are respectively estimated as the full widths at
half maximum of rocking curves measured by fixing thediffraction angles of 2θ and 2θχ at the peak angles ofout-of-plane A2(002) and in-plane A2(200) reflections, as
shown in Figs. 2(a-2)–(d-2) and 3(a-2)–(d-2). Figure 4(b)shows the Si composition dependences of Δθ50 and Δθχ50.
With increasing the Si composition, Δθ50 and Δθχ50
values are increasing. These results indicate that Si
composition in Fe-Si film affects delicately the crystal
unit cell size and the crystallographic quality.
Figure 5 shows the magnetization curves, where
the rotation angle of θH shows the applied field direction
with respect to A2[100] in A2(001). These films areeasily magnetized when the magnetic field is appliedalong A2[100], while the magnetization curves
measured along A2[110] saturate at higher fields.
Therefore, the magnetic properties of these films arereflecting the magnetocrystalline anisotropy of bulk
Fe-Si crystal with A2 structure.
It is recognized that the magnetization curvemeasured along A2[110] saturates at a lower magnetic
field and the coercivity decreases with increasing the Sicomposition from 0 to 10 at. %. The magnetic property
will be explained by considering magnetocrystalline

Si composition (wt. %)0 1 2 3 4 5
(b)

1.8
1.7
1.6
1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 6 Compositional dependences of (a) Hc and (b) Ms
values of Fe-Si films prepared on MgO(001) substrate at
200 °C.

anisotropy energy. When the magnetization rotates in
A2(001), the magnetic free energy is expressed as

400 °C(a-3)

600 °CFe98Si2
Fe94Si6
Fe90Si10

(b-1)

(c-1)

(d-1)

(b-2)

(c-2)

(d-2)

(b-3)

(c-3)

(d-3)

Fig. 7 RHEED patterns observed for (a) Fe, (b) Fe98Si2,(c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 400 °C, and(a-3)–(d-3) 600 °C. The incident electron beam isparallel to MgO[100].

1⋅K1⋅ (1 – cos4θM ) ,(1)8
where K1 is the magnetic anisotropy energy and θM is
the direction of magnetization. For Fe and Fe-Si alloy,
K1 is positive. Then, Ea becomes minimum at θM = 0°,
90° and becomes maximum at θM = 45°. Therefore,
A2[100] is the easy magnetization axis and A2[110] is
the hard magnetization axis. This calculation is well
explaining the measured magnetization curves. Figure 6
shows the Si composition dependences of coercivity (Hc)and saturation magnetization (Ms). Here, Ms value isregarded as the magnetization of Fe-Si film measured at
5 kOe. With increasing the Si composition from 0 to 10
at. %, the Ms value decreases linearly by about 11 %,and the Hc value decreases from 24 to 16 Oe reflecting
the soft magnetic property of Fe-Si alloy.

Fe
Lattice constant c (nm)(a-2)

Lattice constant a (nm)

RT

Fe

(a-1)

Fe98Si2

Fe94Si6

Fe90Si10
(a)

0.288
0.286
0.284
0.282

(b)

0.289
0.287
0.285
0.283

0

200
400
Substrate temperature (°C)

600

Fig. 8 Substrate temperature dependences of (a) c and(b) a values of Fe, Fe98Si2, Fe94Si6, and Fe90Si10 films
prepared on MgO(001) substrates.

Ea =Effect of substrate temperature
Figure 7 shows the RHEED patterns observed for
Fe-Si films with different Si compositions grown on
MgO(001) substrates at RT, 400, and 600 °C. Clear
diffraction patterns corresponding to A2(001) surface
are recognized for all the compositions, whereas any
patterns corresponding to D03(001) surface are notrecognized.
Figure 8 shows the substrate temperaturedependences on lattice constants, a, and c, of Fe-Si films
with different Si compositions. With increasing thesubstrate temperature, c value increases, while a value
decreases for all the Si compositions.
Figure 9 shows the substrate temperaturedependences on out-of-plane and in-plane orientation
dispersions, Δθ 50 and Δθχ 50 . With increasing thesubstrate temperature, the Δθ 50 and Δθχ 50 values
decreases for all the Si compositions. The

Orientation dispersion
Δθ50 (deg.)

Fe98Si2

Fe94Si6

Fe90Si10
(a)

1.4
1.1
0.8
0.5
0.2

(b)

Orientation dispersionΔθχ50 (deg.)

3.2

Fe

1.4
1.1
0.8
0.5
0.2

0

200
400
Substrate temperature (°C)

600

Fig. 9 Substrate temperature dependences of (a) Δθ50
and (b) Δθχ50 of Fe, Fe98Si2, Fe94Si6, and Fe90Si10 films
prepared on MgO(001) substrates.

crystallographic quality of Fe-Si film is improving
possibly through relaxation of film stress caused bylattice mismatch with the substrate.
Figure 10 shows the AFM images observed for Fe-Si
films with different Si compositions deposited at
different temperatures. The films deposited at RT, 200,
and 400 °C have flat surfaces with the arithmeticalmean roughness (Ra) values less than 2 nm. On the

400 ºC(a-3)

600 ºC(a-4)

RT

200 ºC
(c-2)

(c-1)

400 ºC(c-3)

600 ºC(c-4)

Fe

Fe94Si6RT
200 ºC(a-1) 50 nm (a-2)

0.2 nm2Ra:(nm) 0.5 nm
0

(b-1)

(b-2)

4
0

18

Ra:

1.6 nm

0

(b-3)

85

Ra:

9.8 nm00.1 nm3Ra:(nm) 0.1 nm
0

(d-1)

(d-2)

Ra:

(b-4)

2

2

Ra:

0.1 nm

0

0

56

Ra:

7.3 nm

0

(d-4)

(d-3)

Fe98Si2

Fe90Si10Ra:Ra:

0.2 nm3Ra:(nm) 0.2 nm
0

2
0

Ra:

3

0.2 nm072

Ra:

8.3 nm0Ra:

0.2 nm4Ra:(nm) 0.2 nm
0

2

3

Ra:

0.3 nm

0

0

72

Ra:

8.7 nm0

Fig. 10 AFM images observed for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 200 °C, (a-3)–(d-3) 400 °C, and (a-4)–(d-4) 600 °C.

A2[100]2000

200 ºCRT

400 ºCA2[110]600 ºC

(a-1)

(a-2)

(a-3)

(a-4)

(b-1)

(b-2)

(b-3)

(b-4)

(c-1)

(c-2)

(c-3)

(c-4)

(d-1)

(d-2)

(d-3)

(d-4)

1000
Fe

0

–2000
2000

0
–1000
–2000
2000
1000

Fe94Si6

Magnetization (emu/cm3)

1000

Fe98Si2

–1000

0
–1000
–2000
2000

Fe90Si10

1000
0
–1000
–2000
–2.5

0

2.5 –2.50

2.5 –2.5
Applied field (kOe)0

2.5 –2.5

0

2.5

Fig. 11 Magnetization curves measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(001) substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 200 °C, (a-3)–(d-3) 400 °C, and (a-4)–(d-4) 600 °C.

contrary, the Ra values of films deposited at 600 °C are
greater than 7 nm, where large islands with faceted
faces are formed as shown in Figs. 10(a-4)–(d-4). It isconsidered that migrations of deposited atoms areenhanced at a higher substrate temperature. The
variation of surface roughness as a function of substratetemperature is similar in these Fe-Si films.
Figure 11 shows the magnetization curves of Fe-Si
films at different substrate temperatures. The films

deposited at RT, 200, and 400 °C show the magnetic
properties reflecting the magnetocrystalline anisotropyof bulk Fe-Si crystal with A2 structure. With increasing
the substrate temperature up to 600 °C, the differencein the curves measured along A2[110] and A2[100]becomes small. The films are almost magneticallyisotropic in in-plane measurements. The reason ispossibly due to the shape anisotropy caused by thesurface undulation as shown in Figs. 10(a-4)–(d-4).

A2
D03

422AB
311A 311B

Fig. 12 RHEED patterns observed for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(110) substrates at 200 °C. [(e), (f)] Schematic
diagrams of RHEED patterns of (e) A2(211) and (f)D03(211) single-crystal surfaces simulated by using thelattice constants of bulk (e) Fe and (f) Fe3Si, respectively.
The incident electron beam is parallel to (a)–(d)MgO[001]. The filled and open circles in (f) respectively
correspond to the fundamental and the superlatticereflections. The reflections indicated by the gray circlesin (e) show that the A2(211) plane has a reconstructedsurface of p(3×1).

(a-2)

80

90 –4

0
ω (deg.)4

Fig. 13(a-1)–(d-1) Out-of-plane XRD patterns
measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d)Fe90Si10 films prepared on MgO(110) substrates at
200 °C. (a-2)–(d-2) Rocking curves measured by fixing
the diffraction angle of 2θ at the peak angles of A2(211)reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.

3.3

20

Δθχ50 = 1.60

30

(d-2)
40

50
60
2θ (deg.)

Effect of substrate orientation
Figures 12(a)–(d) show the RHEED patterns
observed for Fe-Si films with different Si compositions
deposited on MgO(110) substrates at 200 °C. Clear
diffraction patterns corresponding to A2(211) surface
are recognized, whereas diffractions corresponding toD03(211) surface are not observed, where the schematic
diagrams of RHEED patterns from A2(211) and D03(211) are respectively shown in Figs. 12(e) and (f). The
A2(211) RHEED pattern consists of two reflections, as
shown by the spots A and B in the diagram of Fig. 12(e).

70

0

80 –4

ϕ (deg.)Fig. 14 (a-1)–(d-1) In-plane XRD patterns measuredfor (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(110) substrates at 200 °C. The
scattering vector is parallel to MgO[001]. (a-2)–(d-2)
Rocking curves measured by fixing the _diffraction angle_of 2θχ at the peak angles of A2(0 1 1) + A2(01 1 )reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.

Lattice spacing (nm)

(d-2)
60
70
2θ (deg.)

(c-2)

(d-1)
Fe90Si1001

Si composition (wt. %)
2
3
4

5

(a)

dA2(211)

0.117
0.116
0.204

(b)

dA2(011)+A2(011)

0.203
0.202

Orientation dispersion
Δθ50, Δθχ50 (deg.)Δθ50 = 1.13°50

Δθχ50 =1.57(c-1)
Fe94Si6

0.118

(c-2)

(d-1)
Fe90Si10(b-2)

Δθ50 = 1.02°

Δθ50 = 1.09°(c-1)
Fe94Si640

Δθ50 = 0.94°

Δθχ50 =1.52(b-1)
Fe98Si2

(b-2)

(b-1)
Fe98Si230

A2(211)

WL

(a-1)
Fe

Kβ

422

MgO(220)

Intensity (arb. unit)

211

(a-2)

_

A2
D03

(a-1)
Fe

A2(011)+A2(011)

533A

Intensity (arb. unit)(f) D03Δθχ50 = 1.40_(d) Fe90Si10

200B

_

(b) Fe98Si2

022

MgO(002)

211AB
200A

011

0

2

0

1

_

222A

_

(e) A2_(c) Fe94Si6(a) Fe4
6
Si composition (at. %)8

Si composition (wt. %)
2
3
4

10

5

(c)

1.5
1.3
1.1
0.9

Δθ50
Δθχ50
0

2

4
6
Si composition (at. %)810Compositional
dependences of (a) dA2(211), (b)_dA2(0 1 1)+A2(01 1 ), and (c) Δθ50 and Δθχ50 of Fe-Si film
Fig. _15

prepared on MgO(110) substrate at 200 °C.

The epitaxial orientation relationship is determinedfrom the RHEED observation as follows,4

(type A)_
A2(211)[011] || MgO(110)[001].

(type B)The Fe-Si(211) films consist of two types of variant
whose orientations are rotated around the film normal
by 180° each other. In this configuration, the lattice
misfit value differs depending on the in-plane direction
at the Fe-Si/MgO interface. The lattice misfit value

Fe

Fe98Si2

Fe94Si6

Fe90Si10

(b-1)

(c-1)

(d-1)

(a-2)

(b-2)

(c-2)

(b-2)

(a-3)

(b-3)

(c-3)

(d-3)

(a-4)

(b-4)

(c-4)

(d-4)

(a-5)

(b-5)

(c-5)

(d-5)

(a-6)

(b-6)

(c-6)

(d-6)

(a-7)

(b-7)

(c-7)

(d-7)

_

(a-1)

1000
0

1000

_

–2000
2000

θH = 31° (A2[113])

–1000

0
–1000
–2000
2000

θH = 41°

1000
0

–2000
2000

θH = 45°

1000
0
–1000

_

–2000
2000

θH = 51° (A2[102])

Magnetization (emu/cm3)

–1000

1000
0
–1000

__

–2000
2000
1000
0
–1000
–2000
2000

__

1000
0
–1000
–2000
–1

0

1 –1

0

1 –1
Applied field (kOe)

0

1 –1

θH = 90° (A2[111]) θH = 68° (A2[213])

2000

along MgO[001] is about –4%. Although there exists a
fairly large mismatch of around –17% along MgO[110],
epitaxial growth of Fe-Si crystal is taking place. This
type of epitaxial growth where misfit dislocations are
introduced at the interface is reported for the Cr/MgO
system10,11). The mismatch is considered to be reduced
through introduction of misfit dislocations in the filmaround the Fe-Si/MgO interface.

θH = 0° (A2[011])_

A2(211)[011] || MgO(110)[001],

0

1

Fig. 16 Magnetization curves measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(110) substrates at 200 °C.

(231)
(120)
_ _

_

_

_

(131) (010)(011)(001) (113)
__

_

_ _

(102)
(213)

(102)
(213)

_

_

_

_

(c)

__

_

(111)

(100)

(113)
_

(120)
(231)

(011)

(211)

__

_

(011)

(113)

(131)

(111)

(120)
(231)
__

_

_

(211)

(001)

_

__

(011)

(010)

_

__

_

(131)

(131)
(100)

(213)
(102)

_

__

_

(113)

(111)

__

(b) Type B
(231)
(120)

_

(111)

_

(213)
(102)

_

(111)
__

_

(111)

(010)
(011)
_

41°

(011)
_

(010)

(100)

(001)

(211)
(100)

(001)

__

[111]

[011]

30
60
90
120
150
Angle from A2[011], θM (deg.)

180

[011]
20
_

Anisotropic energy (kJ/m3)

Fig. 17 Pole-figure maps showing the configurationsof A2{100} planes of (a) type A, (b) type B, and (c) type
A + B, where A2(211) is centered.

_

15
10
5
0

_

Si composition (wt. %)0 1 2 3 4 5
(a)

30
20

Saturation magnetization
Ms (kemu/cm3)

Fig. 18 Anisotropy energy in A2(211) as a function ofmagnetization direction. K1 is set to 47 kJ/m3.

Coercivity Hc (Oe)1⋅K ⋅ (4 – 8cos2θM + 7cos4θM ) .
(2)
12 1
Figure 18 shows the anisotropy energy, Ea, as afunction of θM calculated by using the equation (2). It isshown that the easy magnetization axis lies along θM =41̊ or 139̊ _and_ the first hard magnetization axis lies
along A2[111] and_ the second hard magnetization axis
lies along A2[011]. When the measured magnetization
curves shown in Figs. 16 are compared with thecalculation, it is noted that the angle-direction of easymagnetization axis is in agreement with the calculation
for all the compositions. However, the experimental
data shown in Fig. 16 show that the _first hardmagnetization axis lies parallel_ _ to A2[01 1 ] and thesecond one lies parallel to A2[111]. There is a differencein the order of magnetization hardness, suggesting that
there exists an additional influence from the film
detailed structure. The XRD data shown in Fig. 15(c)indicate that the dispersion in Fe-Si film sample varies
depending on the crystallographic orientation whichsuggests the presence of anisotropic film distortion.
Such kind of distortion may have affected themagnetocrystalline anisotropy.
Figure 19 shows the Si composition dependences of
Hc and Ms values of Fe-Si film deposited on MgO(110)substrate. With increasing the Si composition from 0 to
10 at. %, the Ms value decreases linearly by about 13 %,and the Hc value decreases from 28 to 19 Oe reflecting
the soft magnetic property of Fe-Si alloy.
Figures 20(a)–(d) show the RHEED patterns

Ea =(a) Type A_

Figures 13(a-1)–(d-1) show the out-of-plane XRD
patterns of Fe-Si films deposited on MgO(110)substrates. A2(211) reflections are recognized, whereas
D 0 3 (211) reflections are not recognized. Figures
14(a-1)–(d-1) show the in-plane XRD patterns. Only thereflections from A2 crystals and the MgO substrates
are recognized for these films. Figure 15 shows the Sicomposition dependences of lattice spacing, dA2(211) and__dA2(0 1 1)+A2(01 1 ), and orientation dispersion of Δθ50 andΔθχ50 of these films. With increasing the Si composition,__
the dA2(211) and dA2(0 1 1)+A2(01 1 ) values are slightly
decreasing, whereas the Δθ50 and Δθχ50 values are
increasing similar to the case of Fe-Si/MgO(001)system.
Figures 16(a)–(d) show the magnetization curves of
Fe-Si films deposited on MgO(110) substrates. Here, θH
is the direction of magnetic field applied _to the sample
expressed in angle measured from A2[011] direction in
the A2(211) film plane. These films are easily
magnetized when the magnetic field is applied alongaround θH = 45°, while the magnetization curves
measured along θH = 0° and 90° saturate at higher
fields. Figure 17 shows the pole-figure maps indicating
the distribution of low-index_ planes including A2{100}planes. The angle of A2[011] and in-plane component of
A2(010) is 41°. The magnetic free energy is written in
the following equation when the magnetization rotatesin (211) plane,

Si composition (wt. %)0 1 2 3 4 5
(b)

1.8
1.7
1.6

10
0

0 2 4 6 8 10
Si composition (at. %)

1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 19 Compositional dependences on (a) Hc and (b)Ms values of Fe-Si films prepared on MgO(110)substrates at 200 °C.

observed for Fe-Si films deposited on MgO(111)su bstrates at 200 ° C. Clear RHEED patterns
corresponding to A 2(110) texture [Fig. 20(e)] areobserved. These RHEED patterns consist of two_(f) D03 660
620NW 440
442KS

260NW
442KS
_

(d) Fe90Si10

Fig. 20 RHEED patterns observed for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(111) substrates at 200 °C. [(e), (f)] Schematic
diagrams of RHEED patterns of (e) A2(110) and (f)D03(110) single-crystal surfaces simulated by using thelattice constants of bulk (e) Fe and (f) Fe3Si,
respectively. The_ incident electron beam is_ parallel to(a)–(d) MgO[1 1 0],_ (e) A2[001] and A2[ 1 10], or (f)D03[001] and D03[110]. The filled and open circles in (f)respectively correspond to the fundamental and thesuperlattice reflections.

Type D

–22%

–17%

30

40

__

MgO

of

_

reflections, as shown by the spots C and D in the spot
map of Fig 20(e). The epitaxial orientation relationshipis determined by RHEED as follows,_A2(110)[001] || MgO(111)[110],(type C)__A2(110)[111] || MgO(111)[110].
(type D)
When the atomic arrangement of MgO(111) surface
which shows six-fold symmetry with respect to theperpendicular direction is considered, the A2(110)crystals of types C and D are interpreted to beconsisting of three and six variants whose orientations
are rotated around the film normal by 120° and 60°
eachother,
respectively.
The
crystallographic
orientation relationships of types C and D are similar to
the Nishiyama-Wasserman (NW)12,13) and the
Kurdjumov-Sachs (KS)14) relationships, respectively. In
these configurations, as shown_ in Fig. 21, large lattice_mismatches along MgO[11 2 ], –22%, and MgO[1 1 0],–17%, are involved at the A2(110)type C/MgO(111) andtheA2(110)type
interfaces.
The
D/MgO(111)crystallographic orientation relationships observed in
the present study is similar to those reported for the
Fe-based alloy films with bcc(110) orientation formedon MgO(111) substrates15,16).

(d-2)

50

Δθ50 = 2.40°

6070
2θ (deg.)

80

90 –4

0

ω (deg.)

4

002

220

(a-1)
Fe
Intensity (arb. unit)

relationships(d-1)
Fe90Si10004_

orientation

(c-2)

_

Fig. 21
Epitaxial
Fe-Si(110) || MgO(111).

[110]

Δθ50 = 2.31°(c-1)
Fe94Si6

110

Fe-Si
[111]

(b-2)

Fig. 22(a-1)–(d-1) Out-of-plane XRD patterns
measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d)Fe90Si10 films prepared on MgO(111) substrates at
200 °C. (a-2)–(d-2) Rocking curves measured by fixing
the diffraction angle of 2θ at the peak angles of A2(110)reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.

A2
D03

MgO[112]Δθ50 = 2.10°(b-1)
Fe98Si2_–4%Δθ50 = 1.73°

(a-2)

_

Type C

(a-1)
Fe

(a-2)
Fe

(b-1)
Fe98Si2(b-2)
Fe98Si2(c-1)
Fe94Si6(c-2)
Fe94Si6(d-1)
Fe90Si10(d-2)
Fe90Si10

20

30
40
50
2θχ (deg.)

A2(002)_(b) Fe98Si2

130NW

MgO(022)

121KS

110
220

MgO(222)211KS

310NW 220

A2
D03

A2(110)231KS

A2(110)

240NW

321KS

MgO(111)(e) A2 330

Intensity (arb. unit)(c) Fe94Si6(a) Fe

60

40

50
60
70
2θχ (deg.)

80

Fig. 23 (a)–(d) In-plane XRD patterns measured for(a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(111) substrates at 200 °C. _The
scattering vector is _parallel to (a-1)–(d-1) MgO[112] or(a-2)–(d-2) MgO[1 1 0]. The intensity is shown inlogarithmic scale.

Figures 22(a-1)–(d-1) and 23(a-1)–(d-2) show theout-of-plane and in-plane XRD patterns of Fe-Si films
deposited on MgO(111) substrates, respectively.
Reflections from A2 crystals are recognized, whereas
Reflections from D03 are not recognized.
Figure 24 shows the Si composition dependences oflattice constants, Δθ50, and Δθχ50. The lattice constants
are calculated by using the relation of

Lattice constant c, a (nm)1

Si composition (wt. %)
2
3
4

2000

5

θH = 90º (A2[110])(a) Fe

1000

0.287
Bulk

0.286
0.285

0
–1000

a

0.284
0.283

θH = 0º (A2[001])

_

0
0.288
(a)

c
0

2

4
6
Si composition (at. %)

8

–2000
2000

10

(b) Fe98Si2

50Magnetization (emu/cm3)

1

4.0
3.0

Δθ50

2.0
1.0

Δθχ50
0

2

4
6
Si composition (at. %)810

Fig. 24 Compositional dependences of (a) a and c and(b) Δθ50 and Δθχ50 of Fe-Si films prepared on MgO(111)substrate at 200 °C.

_

a = (dA2(110)2 + dA2(110)2)1/2,(3)

c = 2dA2(002).

(4)

The Fe-Si lattices are slightly deformed along the c-axis
in accommodation of lattice misfits of about –4%. With
increasing the Si composition, the a value is decreasing,while the c value does not change much. The Δθ50 andΔθχ50 values are increasing with increasing the Sicomposition.
Figure 25 shows the magnetization curves. Here,θH is the direction of magnetic field applied to thesample expressed in angle measured from A2[001]direction in the A2(110) film plane. The magnetic freeenergy is written in the following equation when themagnetization rotates in (110) plane,
Ea =1⋅K ⋅ (7 – 4cos2θM – 3cos4θM ) .
32 1

(4)

Figure 26 shows the anisotropy energy, E a , as afunction of θM calculated by using the equation (4). It isshown that the easy magnetization axis lies along
A 2[001]. Indeed, it was reported that Fe(110)single-crystal films were easily magnetized when themagnetic field was applied along the Fe[001]direction17). However, the films prepared in the present
study show nearly isotropic in-plane magnetic
anisotropies. This is possibly because that the films
prepared in the present study are not single-crystals
but epitaxial thin films consisting of three and six
variants whose orientations are rotated around the film
normal by 120° and 60° each other (Fig. 21). In this

–1000
–2000
2000

(c) Fe94Si6

1000
0
–1000
–2000
2000

(d) Fe90Si10

1000
0
–1000
–2000
–1000

–500

0
500
Applied field (Oe)1000

Fig. 25 Magnetization curves measured for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films grown on
MgO(111) substrates at 200 °C.

Anisotropic energy (kJ/m3)

0
(b)

[001]
20

_

5.0

[110]

[001]

30
60
90
120
150
Angle from A2[001], θM (deg.)

180_

Orientation dispersion
Δθ50, Δθχ50 (deg.)

1000

Si composition (wt. %)
2
3
4

15
10
5
0

Fig. 26 Anisotropy energy in A2(110) as a function ofmagnetization direction. K1 is set to 47 kJ/m3.

case, the in-plane magnetic property of epitaxial thinfilm will be influenced by the distribution of variant

30
20
10
0

0 2 4 6 8 10
Si composition (at. %)Si composition (wt. %)0 1 2 3 4 5
1.8(b)Saturation magnetization
Ms (kemu/cm3)

Coercivity Hc (Oe)Si composition (wt. %)0 1 2 3 4 5
40
(a)

1.7
1.6
1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 27 Compositional dependences on (a) Hc and (b)Ms values of Fe-Si films prepared on MgO(111)substrates at 200 °C.

crystals. The almost isotropic in-plane magnetic
anisotropies observed for the epitaxial thin films are
due to the complex variant structure.
Figure 27 shows the compositional dependences of
Hc and Ms values. With increasing the Si composition
from 0 to 10 at. %, the Ms value decreases linearly by
about 12 %, and the Hc value decreases from 34 to 19
Oe reflecting the soft magnetic property of Fe-Si alloy.
In the present study, Fe100–xSix (x = 0 – 10 at. %)epitaxial films are prepared on MgO single-crystal
substrates under similar experimental conditions. It isshown that single-crystal films of (001) orientation
grow on MgO(001), bi-crystalline epitaxial films with
(211) orientation grow on MgO(110), and epitaxial films
consisting of two types of (110) variant grow on
MgO(111) substrates. Although they are epitaxial thinfilm crystals, differences in quality and magnetic
properties are noted between these samples. For
example when the Δθ50 value, out-of-plane dispersion
which is a measure of crystallographic quality, iscompared between the samples prepared at 200 °C,
lower values are observed in the order of samples
prepared on MgO(001) < MgO(110) < MgO(111) for theinvestigated compositional range. The Δθ50 value isincreasing with increasing the Si composition for allcases. Similar tendency is also noted in the variation ofΔθχ50, in-plane dispersion, between these samples (Figs.
4(b), 15(c), 24(b)). The results indicate that the
crystallographic quality slightly degrades when
deposited on an MgO single crystal with higher index
plane.
Differences in coercivity are also noted between theepitaxial thin films. In-plane coercivity decreases withincreasing the Si content for the epitaxial Fe-Si films
grown on three kinds of crystallographic planes of MgO
single-crystal substrates (Figs. 6(a), 19(a), 27(a)). Whenthe coercivity is compared, lower values are observed in
the order of samples prepared on MgO(001) < MgO(110)< MgO(111) for the compositional range of x = 0 – 10
at. %. The low coercivities of Fe-Si(001) epitaxial films
are considered to be due to the high crystallographic
quality of single-crystal with low dispersion.
In the present study, Fe-Si single crystal films ofA2(100) orientation are obtained on MgO(100)substrate. The Fe-Si films prepared on MgO(110)substrate are epitaxial films of A2(211) orientation with
bi-crystalline structure, whereas the films formed on
MgO(111) are epitaxial films of A2(110) consisting ofvariants. By using these epitaxial thin films, it ispossible to investigate the magnetic properties such as
magnetostriction18), damping constant, etc. in relation
to the crystallographic orientation of Fe-Si magnetic
material. The thin film growth technique can beapplicable to the preparation of Fe-Si single-crystal
films, for example, with A2(110) by changing thesubstrate to GaAs(110) crystal19).

4.

Conclusion

Fe-Si alloy thin films are deposited on MgO
single-crystal substrates of (001), (110), and (111)orientations at temperatures ranging between RT and
600 °C by varying the Si composition, x, from 0 to 10
at. %. The effects of composition and substrateorientation on the structure and the magnetic
properties are investigated. Fe-Si(001) single-crystal
films are formed on MgO(001) substrates. Fe-Si films
epitaxially grown on MgO(110) substrates consist of
two (211) variants whose orientations are rotatedaround the film normal by 180° each other. Fe-Si(110)films grow epitaxially on MgO(111) substrates with
two-type
variants,
Nishiyama-Wasserman
andKurdjumov-Sachs relationships. The orientation
dispersion of Fe-Si film decreases with decreasing the
Si composition, with increasing the substratetemperature, and with decreasing the index of
substrate crystallographic plane. The magnetic
properties of films prepared on MgO(001) and (110) arereflecting the magnetocrystalline anisotropy of bulk
Fe-Si crystal with A2 structure. The Fe-Si epitaxial
films prepared on MgO(111) show almost isotropic
in-plane magnetic anisotropies which are related withthe multiple variant structure.
Acknowledgments A part of this work was supported
by JSPS KAKENHI Grant Numbers 25420294 and26820117 and Chuo University Grant for Special
Research.
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Received Nov. 30, 2015;

Accepted Mar. 30, 2016