Structure and magnetic properties in single-crystal iron film electrodeposited on a (110) copper crystal

212

Journal of Magnetism and Magnetic Materials 71 (1988) 212-218 North-Holland, Amsterdam

S T R U C T U R E AND M A G N E T I C P R O P E R T I E S IN SINGLE-CRYSTAL IRON F I L M E L E C T R O D E P O S I T E D O N A (110) C O P P E R CRYSTAL Yuji U E D A Department of Electrical Engineering, Faculty of Second Engineering, Muroran Institute of Technology, Muroran 050, Japan

and Minoru T A K A H A S H I Department of Applied Physics, Tohoku University, Sendai 980, Japan Received 24 April 1986; in final form 24 June 1987

Single crystal iron films with thickness of 100-1000 .~ were electrodeposited on the surface of copper single crystal substrates in order to estimate bow the characteristics of films differ from bulk iron. The structure and the magnetism of the film in the thickness range 100-1000 .~ were examined by electron diffraction and torque magnetometer. Electron diffraction patterns of iron films prepared on the (110) plane of a copper single crystal show the (211) plane of the iron body centered cubic crystal. The (111) direction of the iron lattice is parallel to the (110) of the copper substrate. A large uniaxial anisotropy was observed in addition to the magnetoerystalline anisotropy in the iron single crystal film. The origin of the anisotropy can be explained in terms of the reverse effect of magnetostriction produced by an internal strain due to the lattice misfit between the iron film and the copper substrate.

I. Introduction The study of the physical properties is interesting for the reason that the thin film may have a crystal structure different from the bulk state. For example, in iron film, the iron crystal shows a body centered cubic structure at room temperature. However, the structure in the thin film shows a face centered cubic structure; that is, it is possible in the film to prepare the metastable structure which cannot be prepared for bulk materials. Wright and Takahashi [1] attempted to prepare a stable fcc structure of iron by means of electrodeposition on the (110) and (100) planes of the copper single crystal. Kummerle and Gradman [2] prepared a `/-Fe film by means of ultra-high vacuum evaporation on the (111) face of the copper crystal. The magnetism for these epitaxial -/-films showed ferromagnetism, while the iron film on the (100) surface of the copper crystal was reported to be antiferromagnetic by Gonser et al. [3].

In the case of thin films, the effect of the substrate in the process of film growth cannot be overlooked for the magnetic properties of the film. If the lattice constant of the deposited film is different from that of the substrate, a strain due to a lattice misfit between film and substrate may exist in the film; that is, the lattice of the deposits is strained toward that of the substrate [4]. Since the magnetism in the strained state corresponds to the magnetism under a sufficiently large pressure, it is interesting to discuss the physical properties for these non-equilibrium specimens. As the behavior of the magnetic torque curve is influenced quite sensitively by the strain in the thin film, the study of the magnetic anisotropy by measuring the torque curve is important in discussing the strain effect on the magnetism of the film. The purpose of the present paper is to discuss the strain effect on the magnetic anisotropy of the film. Single crystal films of iron were prepared

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213

Y. Ueda, M. Takahashi / Electrodeposited single-crystal iron film

epitiaxially by electrodeposition on the surface of a single copper substrate; the crystal structure of the deposits was determined by reflection electron diffraction. Subsequently, the magnetism was investigated by measuring the magnetic torque curves.

It is observed that the large magnetic induced uniaxial anisotropy has been superimposed on the magnetocrystalline anisotropy in the torque curve of the film, and the easy axis of the induced uniaxial anisotropy is along the (110) direction of the iron film. The origin of the anisotropy can be explained in terms of the reverse effect of magnetostriction produced by an internal strain due to the lattice misfit between the iron film and the copper substrate.

3. Experimental results and discussion 3.1. Crystal structure

Fig. 1 shows an electron diffraction pattern of the film with a thickness of 1000 ~, electrodeposited on the (110) surface of the copper single crystal. The incident electron beam is along the (110) direction of the (110) face of the copper single crystal. As shown in this figure, the orientation of the crystal structure for epitaxially deposited films is parallel to that of the substrate. The interpretation of the pattern is given in fig. l b as the diffraction spots along the (111) direction on the (211) plane of a-Fe (bcc). From the electron diffraction presented above, it becomes clear that a (111) lattice direction on

2. Experimental procedure Copper single crystal (99.998% purity) of the substrate was grown by a modified Bridgman method. The substrate was cut from the single crystal rods so that the surface is the (110) plane by X-ray diffraction techniques. The dimension of the substrate was 7 x 7 mm 2 in area and 1 mm in thickness. The surface of the substrate was polished first mechanically and then chemically in an acidic solution containing 420 cm 3 of H2SO4, 30 c m 3 of HC1 and 180 cm 3 of H N O 3 per liter, to remove mechanical stress in the surface layer sufficiently. Single crystal iron films of thickness 100 to 1000 ,~ were prepared epitaxially by electrodepositing onto the (110) surface of the substrate at about 20 ° C with current densities of 2 m A / c m 2. The chemical composition of the electroplating bath was 140 g of FeSO4, 6 g of HaBO 3 and 3 g of NaC1 per liter. The pH of the solution was maintained at a value of 3.4. The crystal structure of the film was determined by reflection electron diffraction using 50 kV electrons. Magnetic torque was measured by means of a torque magnetometer in a uniform magnetic field of 5000 Oe at room temperature. To measure magnetic torque curves, the films were formed into circular shapes 6 mm in diameter.

\ /--~

"

,o1 1 p, 231

b

"\//'./'

"" Ogg

(211) Fig. 1. Electron diffraction patterns of iron single crystal film onto the (110) plane of the copper single crystal. Thickness: 1000 ./~.(a) Diffractionpattern; 00) interpretation of (a).

E Ueda, M. Takahashi /Electrodepositedsingle-crystal iron film

214

the (211) plane of the body-centered cubic iron (a-Fe) is parallel to a (110) direction on the (110) plane of the copper substrate, i.e., (211) (111) a Fe II(ll0) (110) Cu. Since the epitaxial growth is produced so that the misfit between the iron film and the copper substrate may be minimal, it is reasonable to consider such a fitting state as shown in fig. 2. 3.2. M e a s u r e d torque curve

Fig. 3 shows an example of the measured magnetic torque curves for the iron films with a thickness of 1000 ,A which is electrodeposited onto the (110) surface of the copper substrate. The torque curves were measured by rotating from the F e ~ l l l ) direction (Cu(ll0)) on the (110) plane of the copper in a uniform magnetic field of 5000 Oe at room temperature (Fig. 4). The intensity of the field was determined by ascertaining that the measured torque does not change with an increase of the magnetic field; that is, amplitude of the torque curves was saturated with the field used herein. The torque curve described in fig. 3 represents the results with removal of the torque curve observed slightly in the copper substrate only. Fig. 5 shows how torque curves change with film thickness when the thickness of the film electrodeposited onto the (110) surface of the copper substrate is decreased from 1000 to 100 ,~,. The wave shape of the torque is observed to change with a certain tendency as the film thickness decreases.

4L

Sustrate

Fefl

3 ~

Im

ThicCu(110} kness I000A

~

%

° o

6~ ~

lJ20

180 240

~-~ N

:~

36

~

-2

Fe ~/111> Fe Cu<110> Cu<100> FiB.3. Torquecurvesof theironfilmwiththicknessof 1000 electrodeposited on the (110) plane of the single crystalcopper

substrate.

<001>

/<100>

i

Cu(110)// Fe(211)

II

b= 4-- 2.48A ",'--Z.55A

=l•(t

:;%

(112) Plane b

111)

(021)

ZOl)

-
11,

Fe< 111> Cu<110> Tenstoff Hard a x i s

Fig. 2. The fit of the (211) a-Fe plane on a Cu(110) surface.

0 (TIO)

-

ooo)

11o)

Fig. 4. A direction of the rotating angle of magnetization on the (112) plane. (a) Schematic representation of the (110) plane in the cubic crystal with associated crystallographic direction; (b) rotating angle of magnetization.

Y. Ueda, M. Takahashi / Electrodeposited single-crystal iron film

215

is expressed as L = -- OEk//~O

= ~Ka(2 sin 20 + 7 sin 40) + 5-~K2(13 sin 20 + 20 sin 40 + 25 sin 60)

(2) The form of this curve is shown by the slender line in fig. 6.

&

3. 3. Fourier analysis of torque curves ...a t.o

0

60

120

180

ANGLE (

240 O

300

360

)

Fig. 5. Torque curves as functions of iron fdms electrodeposited onto the (110) surface of the single crystal copper substrate.

The wave shape of the measured torque curve cannot be explained only in terms of the magnetocrystalline anisotropy. The torque wave with the 20 component (of which the easy axis is the (111) direction) is separated from the actually observed curves by excluding the torque curves resulting from the magnetocrystalline anisotropy. It is estimated that the uniaxial anisotropy is superimposed on the magnetocrystalline anisotropy in the observed torque curves, and the easy axis of the uniaxial anisotropy is along the (110) direction of the iron film. This anisotropy energy of the uniaxial component presented in the film may be represented by

Eu Since the crystal structure of the iron film deposited onto the copper (110) plane is the (211) plane of the body-centered cubic lattice, we now consider the torque curves observed in the rotation of the magnetization on the (211) plane of the cubic crystal. The magnetic anisotropy energy E k for the rotation of the magnetization in the (211) plane of the cubic crystal may be expressed in terms of the angle 0 between the magnetization and the (111) lattice direction,

-K. sin:O,

=

where K u is the uniaxial anisotropy constant, and 0 is the angle between the direction of magnetization and the (111) direction. Thus the uniaxial

o o

4

&

~,

%

,'>.. X.". ,,,,soT,o,,Y

"~ 0 F--

Fe film

~.

SUBSTRATE Cu (llO) THI CKNESS

lO00A

0

E k = K1(½cos40 + ¼sin40) + K2 (~sin'O - ~sinSO + ~7cos60- {cos'0),

(3)

-2

-

"°',,\"X

.;l

/I

ANISOTROPY',~

7/) ,"II

360

(1) where K 1 and K: are the usual first- and secondorder cubic magneto-crystalline anisotropy constants, respectively. The expected torque equation resulting from the magrietocrystalline anisotropy

Fe

Fe

Cu KilO>

Cu

Fig. 6. Torque curve in the (211) plane iron film and wave shape combined by magnetocrystalline and uniaxial anisotropy.

Y. Ueda, M. Takahashi / Electrodeposited single-crystal iron film

216

torque is given by L = - a E J ~ O = K~ sin 20.

(4)

If now we assume that K , > 0, the uniaxial anisotropy energy in the (211) plane takes a minimum value for the (110) direction of magnetization. In this case, the easy axis of magnetization is along the (110) direction. Thus the uniaxial torque represented in eq. (4) is added to eq. (2), and the total torque in the (211) plane is expressed by L = L¢ + L~ + (1K 1 + ~K2)

sin 2 ( 0 - 0o)

+(

sin 4(0- 00)

rl +

+ s-~gK2 sin 6(0 - 00) + K . sin 2(0 - 0~),

(5) where 0 shows the deviation to measure between the starting direction and the (111) direction of the specimens, and 0~ shows the deviation from the origin of the superposed uniaxial 20 component. Then observed torque curves were assumed to be expanded into a Fourier series having the form 3

By using eq. (7), the magnetocrystalline ardsotropy constants K1, K 2 and the uniaxial anisotropy K u may be calculated from the torque curve measured in the iron films. The result of substituting these constants into eqs. (2) and (5) gives the torque curve L shown in fig. 6. It is seen that the curves of eq. (5) superimposed by using the calculated K1, K 2 and K u agree exactly with the measured torque curve. Assuming that the structure of the films with decreasing thickness does not change from the (211) plane of a-Fe with a thickness of 1000 A, the magnetocrystalline anisotropy constant K 1 and the uniaxial anisotropy constant K u calculated by Fourier analysis of the measured torque curves are plotted in fig. 7 and fig. 8, respectively as a function of film thickness. It is seen from fig. 7 that the magnetocrystalline K 1 is in the range of 4-8.2 × 105 e r g / c m 3. The values calculated from the thick film (in this case 1000 .~) almost agree with that of the bulk crystal [5] ( K 1 = 4.2 × 105 erg/cm3). The calculated crystalline anisotropy constant K 1 has a tendency to increase slightly as the thickness of the film decreases. A large value of the magnetocrystalline K 1 has

3

L = 2~ A : . sin 2nO + 2~. B2. cos 2nO. n=l

(6)

n=l

Substrate

By comparing with eq. (5) and eq. (6),

Cu ( 1 1 0 )

12

K 2 = -~56A6/cos 600 , lO

K 1 = ~ A 4 / c o s 400 - ~ K 2 ,

h

(7)

KI

A

K~ = a 2 / c o s 200 -

1K

1 --

~6K2,

....

where the deviation angle 0 is calculated from tan 400 = - B 4 / A a. The angle 0 calculated from the torque curves of the iron film is approximately zero (0-20 °). The deviation angle 0~ of the easy direction of the uniaxial anisotropy is given by tan 20' -- B: + 3-~76(48K 1 + 13K2) sin 20 A 2 + 3-~76(48K a + 13K2) cos 20"

8

-o

o

o o

(u

6

4

0

0

-

8

(8)

This value is also zero. Thus the easy axis of superposed uniaxial anisotropy observed in the iron film agrees with the (100> direction of the copper substrate.

I 200

I

I

I

400 600 800 THICKNESS ( A )

I

I

lO00

1200

Fig. 7. M a g n e t o c r y s t a l l i n e a n i s o t r o p y c o n s t a n t K 1 as a function of the film thickness.

Y. Ueda, M. Takahashi /Electrodeposited single-crystal iron film

seems that a strain due to the lattice misfit between film and substrate may exist in the film. Therefore, the magnetic anisotropy is produced by the reverse effect of magnetostriction. This magnetic anisotropy is estimated as follows: The strain ¢ due to the misfit of the <110> direction of the iron is given by

Substrate

Cu

217

(110)

O 6

100)

s

O

O

v 3

0

110

-- - 0 . 1 ~ ,

~o 4

=

110

¢ = 71 A l l / 1 = ~i( d ~ u ( l l O ) - d r e ( 2 ~ l ) ) / / d r e ( 2 ~ l )

Ku

A

I

I

I

I

I

I

200

400

600

800

I000

1200

THICKNESS (~)

Fig. 8. Uniaxial anisotropy constant K u as a function of the film thickness.

been reported in nickel thin film by Chikazumi et al. [6]. They therefore considered that the anisotropy may be explained in terms of the contribution of planar stress in the film arising from the lattice misfit between the film and the substrate crystal. In fig. 8 the uniaxial anisotropy constant K u is shown as a function of film thickness. As seen in fig. 8, the anisotropy constant K u depends markedly on film thickness and has a tendency to decrease with increasing film thickness.

3.4. Origin of uniaxial anisotropy As seen in fig. 6, a large uniaxial anisotropy of order of 10 5 with easy direction <110> is observed in addition to the magnetocrystalline anisotropy in measured torque curves. We will discuss the origin of this anisotropy. Since the (211) surface of a-Fe is fitted parallel to the copper (110) surface as shown in fig. 2, it

(9)

where --Cu(llO) ,40°°> and --Ve(211) ,4(110) are the lattice constants of the Cu<100> and the Fe<110> direction, respectively. Since the strain ¢ due to the misfit between the iron thin film and the copper substrate is not constant in the direction of the thickness, it from sheer necessity an average value. The constant of proportionality is expressed in terms of the coefficient ,/. The minus sign shows compression stress along the (110) direction of the iron (211) plane. Tension stress (or compression stress) o is assumed to be uniaxial along the (110) direction of the iron plane and is given by o = E(,

(10)

where E is Young's modulus. By using E = 2 × 1012 d y n / c m 2 for iron [7] o = - 2 × 1011,! d y n / c m 2.

(11)

For the iron films of the (211) plane deposited parallel to the (110) plane of the copper substrate, the physical meaning of the fact that the easy axis of the uniaxial anisotropy is along the <110> direction is considered as follows: Since the magnetostriction constant along the (111) direction in the case of the iron single crystal is given by h l l 1 < 0, the easy axis of the magnetization is along <111> for the compression of the <111> direction. Since internal stress in the films is exerted as a compressible force along the direction of Fe and as tension along the direction of F e < l l l > , the (111> direction in the iron film is the hard axis for magnetization as shown in fig. 2. These estimates agree well with the experimental results. We now estimate to what extent strain is produced in the films. The magnetoelastic energy Eo under the ten-

218

Y. Ueda, M. Takahashi /Electrodeposited single.crystal iron film

sion a is given by E a ~--. -- 3~k1000(o~2.}t?+ a2~¢ 2 22 _{_O¢3V 2 ~2 -- 1)

--3~kHlo(ala2VlY2 + ot21x3~t2V3 + 0t30tlV3"Y2),

(12) where a i and 3', are direction cosines of the magnetization and the applied tension, and A10o and h~10 are magnetostriction constants along the (100) and 0 1 0 ) direction. If the stress is in the direction of ~_111), the direction cosines are given by ~1 = 1 / V 3 , "Y2= 1 / ¢~, "/3 = 1 / v ~ . F r o m eq. (12) the elastic energy Eo is represented by

E,, = - Xmo ( a , a 2 + aza 3 + a3a ,).

(13)

If we now take the angle between the (111) direction and the magnetization direction ( = a) to be 0, E ° = -- 3~k1110 cos20,

(14)

so that

3 E J 3 0 = 3Xmo sin 20.

(15)

The uniaxial anisotropy constant K u is given by Ku = ~Xmo.

Acknowledgements

(16)

By using eqs. (11), (16) and the magnetostriction constant of iron h m = - 2 1 . 2 × 10 -6 [8], the uniaxial anisotropy constant K u is estimated by Ku = 6 × 106n d y n / c m 3.

1) The crystal structure of the iron films (of thickness 1000 .~) electrodeposited onto the (110) plane of copper single crystal shows the (211) plane of a-Fe(bcc). The (111> direction of the iron lattice is parallel to the (110) of the copper substrate. 2) The magnetocrystalline anisotropy constant K 1 shows slightly larger values ( K 1 = 4 - 8 . 2 x 10 5 erg/cm3). However, these values almost agree with that of the bulk crystal ( K 1 = 4.2 X 10 5 e r g / c m ) as the thickness increases. 3) It is observed that the large induced uniaxial magnetic anisotropy is superimposed on the magnetocrystalline anisotropy in the torque for iron films, and that the easy axis of the uniaxial anisotropy is along the (110) direction of iron. The uniaxial anisotropy decreases with increasing film thickness ( K u = - 2 . 0 - - 6.7 × 105 erg/cm3). 4) The origin of the uniaxial anisotropy can be explained in terms of the reverse effect of the magnetostriction. This magnetostriction is produced by internal strain due to the lattice misfit between the single crystal surface of the iron film and that of the copper substrate.

The authors wish to thank Professor S. Taniguchi for valuable discussions and members of the Takahashi laboratory for helpful advice during this work.

(17)

According to the data presented in the previous paper dealing with the magnetic anisotropy in single crystal nickel films [9], the coefficient ~ is estimated by 0.01 < ~1< 0.1. If we set v = 0.05, we have K u = 3 × 105 d y n / cm 3. This calculated value gives good agreement with the uniaxial constant K u obtained from the experimental curves.

References

4. Summary

[1] J.G. Wright, Phyl. Mag. 24 (1971) 271. M. Takahashi and T. Miyazaki, Meeting of the Physical Society of Japan, 1972. [2] W. Kummcrle and U. Gradmann, Solid State Commun. 24 (1977) 33. [3] Keunne and U. Gonser, J. Appl. Phys. 48 (1977) 2976. [4] D.W. Pashlcy, Advan. Phys. 5 (1956) 87. [5] R.M. Boyd, IBM J. 4 (1960) 116. [6] S. Chikazumi, Physics of Magnetism (John Wiley, New York, 1964). [7] R. Bozorth, Ferromagnetism (Van Nostrand, New York,

The results of the above investigation may be summarized as follows:

1951). [8] E.W. Lee, Rep. on Prog. in Phys XVIII (1955) 184. [9] Y. Ueda and M. Sato, J. Appl. Phys. 47 (1976) 3380.