Magnetic anisotropy in ferromagnetic thin films

Physica 34 349360

Bransky, J . Hirsch, A. A. 1967

MAGNETIC ANISOTROPY IN FERROMAGNETIC THIN FILMS *) by J. BRANSKY

and A. A. HIRSCH

t)

Department of Physics, Technion - Israel Institute of Technology, Haifa, Israel

Synopsis Measurements of the induced magnetic anisotropy in thin iron and nickel films were performed by means of the magnetoresistance effect (MRE) in three perpendicular directions, at 120’K and 300°K. Two kinds of induced anisotropies were detected. The first one is independent of the magnetic field Ha, which was applied during the deposition of the film. It is related in both materials to an angle of incidence effect, arising from the geometry of the deposition. This anisotropy in thin iron films has a radial symmetry in the plane of the film, and decreases to zero with the growing thickness of the film. In nickel films the same kind of anisotropy was found to exist in a wide range of thicknesses, increasing with the growth of the film, but having a circular symmetry. The second anisotropy, detectable in relatively thick iron films (5000 A), is aligned with its easy magnetic axis parallel to the field Hd. Its magnitude was found to be about 0.1 Ki at 120’K (Ki is the first cubic magnetocrystalline anisotropy constant for iron) and decreased at room temperature. The MRE in the transverseperpendicular direction points to the presence of a preferred orientation described by plane (111) as contact plane with the substrate, and by the [ 1121 direction in this plane parallel to Ha. This preferred orientation also accounts for the magnitude, direction and temperature dependence of the field induced anisotropy. This interpretation is based on a magneto-elastic interaction due to magnetostriction and isotropic tensile stresses in the plane of the film.

1. Introdzcction. A great deal of work has been done in recent years on the subject of induced uniaxial magnetic anisotropy in thin films of ferromagnetic metals, but as the process responsible for this anisotropy seems to be quite complicated, no final conclusions have been achieved. Thin films deposited on an amorphous substrate, in a conventional high vacuum of about 10-e mm of Hg, are in general granular. All the metallic grains of the films are usually single crystals, and may have one-domain or multi-domain magnetic structures. In this work an attempt has been made to separate the different factors controlling the magnetization reversal in thin films of iron and nickel. The *) The research reported in this document has been sponsored in part by the U.S. Air Force Office of Scientific Research, OAR, through the European Office, Office of Aerospace Research, U.S. Air Force, under Grant AF EOAR 63-71. t) Also at The Negev Institute of Higher Education, Beersheba, Israel.

-

349 -

1.

350 magnetic

anisotropies

BRANSKY

AND

A. A. HIRSCH

can be classified in three main groups:

stress aniso-

tropy, crystal anisotropy, and shape anisotropy. Each of these anisotropies cannot by itself account for the observed values of anisotropy energy, for the direction of easy magnetic axes, and for their temperature dependence. However, it will be shown that all these anisotropies co-exist and may have a mutual influence. The experimental investigations on the magnetic anisotropies in this work, contrary to those done previously, were carried out by measuring the magnetoresistance effect (MRE). The study of the magnetic properties of thin films by this method has some outstanding advantages. It is relatively simple, can be carried out directly after deposition, without any alteration of the conditions of the film, such as the atmosphere, temperature, etc. The measurements do not affect the structure of the samples and can be performed in a wide range of temperatures. Moreover, the supplied information is three-dimensional. Very thin films, containing very small quantities of ferromagnetic metals, can be investigated. The magneto-resistance loops describe the magnetization reversal in the films and provide information about their crystallographic and magnetic structures. If the grains of the films were one-domain, single crystals with a uniaxial magnetic anisotropy, a magnetization loop with large coercive force and high remanence would be expected in the magnetic easy direction. This almost square loop would give a vanishing MRE. The anhysteretic magnetization curve, in the magnetic hard direction i), would give a relative change in the resistance AR/R represented by a coerciveless curves)

AR/R

= A + Cj2,

(1)

where A and C are constants, and j is the reduced magnetization. (j = M/M,, where M is the magnetization in the direction of the magnetic field, and M, is the spontaneous magnetization). The actual films did not obey this idealized one-domain relation; they exhibited a pronounced multi-domain behaviour superimposed on the process of magnetization rotation, and were analyzed

accordingly.

2. Experimental results. The films were deposited on microscope slides by evaporation in a special device, designed as vacuum chamber and as cryostat. A detailed description of this device is given in an earlier paper3). The deposition was carried out in the presence of a direct current magnetic field, applied in the plane of the substrate. The direction of this inducing field Ha was parallel (longitudinal) or perpendicular (transverse) to the electric current used for the resistance measurements. In order to compare only films which are identical in all respects except in the direction of Hd, a cross shaped pair of films were produced. Four electrical contacts were baked into the substrate at the ends of the cross, and a cross-shaped mask

MAGNETIC

ANISOTROPY

IN FERROMAGNETIC

THIN

351

FILMS

fitted the films in between. During the magneto-resistance measurements of one film, its partner was open circuited. This arrangement was found not to affect the results appreciably. The resistance changes were measured by means of a low frequency alternating current bridge, amplified, filtered and recorded on the vertical axis of an oscilloscope screen. The horizontal axis of the oscilloscope was connected to the output of a Halltron, supplying a voltage proportional to the driving magnetic field. The frequency of this field was 0.02 Hz. The MRE loops were traced in three perpendicular directions: the longitudinal II/II,the transverse-parallel 1111 and the transverse-perpendicular 111. The first two directions were in the plane of the film. The measurements were performed at room temperature as well as at a temperature of about 120°K. All the measurements for each pair of films were performed as a function of their thickness; the deposition was recontinued directly after the measurements of the MRE. A typical set of MRE loops for a pair of iron films (la and 2~) is given in fig. 1. The first line in this figure shows the changes in the resistance as function of the driving magnetic field, in the three principal directions for the film la. This film was deposited in the presence of a magnetic field Hd of about 2000 oersteds, applied in the longitudinal direction. The second line (fig. 1) illustrates the MRE loops in the same three principal directions for the second film 2a, for which Hd was in the transverse-parallel direction.

1

2a 1 a009

tid IIH a009

a009

\I1

l/l

Fig. 1. Magnetoresistance loops of a pair of iron films deposited at 300°K presence of a field Ha of 2 kOe, which was applied in the longitudinal direction film

la and in the transverse

direction

of the film

2a. The thickness

in the of the

of each film

is

800 A. The loops are traced at 120’K with a frequency of 0.02 Hz. Vertical scales: in oh per large division are indicated on the top of each picture. Horizontal

scales: in kOe per large division 1.5 for the

l/l

are 0.66 for the ji//[and effect.

l/11 effects,

and

352

J. BRANSKY

AND A. A. HIRSCH

The films la and 2a have a thickness of about 800 angstroms. These MRE loops were traced at 120°K. Similar loops were recorded for the same pair of films at room temperature. The vertical scale is indicated on each figure. It is important to note that in both films the longitudinal l//iieffect is smaller than the transverse-parallel one I/II. Fig. 2 represents the same set of measurements for a pair of films (1 b and 2b), about 5000 angstroms thick. This pair was indeed grown on the previous one, by recontinuing the deposition. Here it can be seen clearly that the smaller effects are the longitudinal /l/j\ for lb, and the transverse parallel l/II for 2b, which represent the magnetization reversal in the direction of the inducing field Hd.

IRON FILMS

5000 A

2b ]

,-,dIIH

0.0 I I

0.01 I

Fig. 2. Magnetoresistance presence

Vertical Horizontal

of a pair

of a field of 2 kOe which

lb and in the transverse The loops

loops

are traced scales:

direction

at 120°K

0.022

of iron

was applied

films

deposited

in the longitudinal

of the film 2b. The thickness

with

a frequency

in 0A per large division

scales:

\/II

1.5 for the

of each film is 5000 A.

on each picture

are 0.33 for the ll/lj and l/I

in the

of the film

of 0.02 Hz.

are indicated

in kOe per large division

at 300°K direction

l/Ii

effects,

and

effect.

Fig. 3 represents a similar set of data for a pair of nickel films (1 c and 2c) of about 10000 angstroms thick. The films lc and 2c were deposited in similar conditions as la, 2a and 1b, 2b. Contemplating the results it is obvious that the iron films do not behave like oriented one-domain particles. They all exhibit a magnetization process of multi-domain particles. The coercive force is of the same order of magnitude for the longitudinaland transverse direction of each film. The outstanding difference between the two directions is the magnitude of the MRE. If these films have a multidomain structure, the magnetization process will start with irreversible However, these domain walls are not domain boundary displacements.

MAGNETIC ANISOTROPY IN FERROMAGNETIC THIN FILMS

randomly

oriented. They seem to have a preferred

direction,

353

thus forming

domains in which the spontaneous magnetization is parallel to a defined axis. The magnetization reversal in this direction will be the easy one, being performed mainly by large magnetization jumps which will not be observed in the MRE loops. Therefore the MRE in the easy magnetic direction is expected to be small. In the hard magnetic direction the process of magnetization rotation is dominant ; no sudden magnetization and the MRE follows the whole cycle.

NICKEL FILMS

lc

jumps are expected,

I OOOOA

HAIIH

I 2c I

HAIIH

J

Fig. 3. Magnetoresistance loops of a pair of nickel films deposited at 300°K in the presence of a field of 2 kOe which was applied in the longitudinal direction of the film lc and in the transverse direction of the film 2c. The thickness of each film is 10000 A. The loops are traced at 120°K with a frequency of 0.02 Hz. Vertical scales: in y’ per large division are indicated on each picture. Horizontal scales: in kOe per large division are 1.65 for the I//\/and l/11 effects, and 1.5 for the _l_/1 effect.

A quantitative investigation of the magnetic anisotropy of these films will be based on the general relations for the MRE in the longitudinal and transverse directions, which can be written in the following form: VW,,,,

= N2

-

i3

(2)

WV%,,,

= WZ

-

i2)J

(3)

and with jrl = M,~/M, and j,.t = M,tIM, where M,I and M,t are the remanences of the magnetization loops in the longitudinal and the transverse directions respectively. The factor B can be calculated from the MRE representing the magnetization reversal in the hard magnetic direction, taking i = 1 at saturation and j = 0 at the peaks of the loop. These peaks correspond to

354

J.

BRANSKY

AND

A. A.

HIRSCH

the coercivity points of the magnetization loop, i.e. the points where j changes its sign4). The uniaxial anisotropy energy density can be evaluated by the difference in the energy necessary to magnetize

the films in the two planar directions:

Ku = (MS j H dj).,,, - (MSi H di),,,;,. irt

(4)

i,l

The reduced magnetization at saturation is equal to 1. The branches of the magnetization loops between jr and 1 obtained from the corresponding branches of the MRE loops by using equations (2) and (3) are shown in fig. 4 for the films 1a, 2a, 1b and 2b. All the investigated films were analyzed by the same method. The results are summarized in table I. The uniaxial anisotropy energy is derived from the surface differences, according to equation (4). TABLE ’

A comparison

of observed

values

of uniaxial

I

anisotropy

energy

density

in vacuum

deposited

iron and nickel films The temperattire of measurements in “K

Film number

Resistance

Film thick-

and

in

ness in

material

ohms

A

Uniaxial sotropy

anienergy

density

in

ergs/ems

Direction of field Hd during deposition longitudinal

120

la,

Fe

215

800

146000

120

2a,

Fe

230

800

215000

120

lb,

Fe

35

5000

45000

longitudinal

120

2b,

Fe

36

5000

43000

transverse

-

transverse

longitudinal

300

la,

Fe

225

800

115000

300

2a,

Fe

240

800

120000

300

lb,

Fe

42

5000

25000

longitudinal

300

2b,

Fe

43

5000

28000

transverse

-

transverse

120

lc,

Ni

10

10000

- 660000

longitudinal

120

2c,

Ni

12

10000

-615000

transverse

It is a remarkable result that all the loops corresponding to the transverseperpendicular MRE, where the driving field is perpendicular to the plane of the substrate, differ in sign for each pair of iron films, while the only external difference between them is the direction of the electric current (figs. 1 and 2, third row). This unusual reversal of the sign of the transverse loops does not occur either in iron films lacking an induced anisotropy, or in any kind of nickel films. 3. Spontaneous anisotrofiy. It can be seen in fig. 1 that the relatively thin iron films 1a and 2a (800 A) have, both of them, a longitudinal magnetic easy axis, regardless of the direction of the field Hd. As these films are the two

MAGNETIC

ANISOTROPY

IN FERROMAGNETIC

THIN

FILMS

355

parts of a cross, the distribution of their axes seems to have a radial symmetry. The density of the magnetic anisotropy energy as given in table I is approximately + of K1, at 120°K (Kr is the first cubic magnetocrystalline anisotropy constant for iron). About Q of this spontaneous anisotropy disappears at room temperature. Before discussing the origin of this anisotropy, it is important to note that the nickel films investigated in this work possess a similar anisotropy, but their easy axis is transverse for both parts of the cross (fig. 3, table I, films Ic and 2~). Thus, in the case of nickel, the spontaneous anisotropy seems to have a circular symmetry and exists in a wide range of thicknesses. It should be remarked that this type of magnetic anisotropies with radial or circular symmetry in the plane of the specimen would not have been detected if common torquemeter techniques had been used. Because of the geometry of deposition it is most plausible that the origin of this anisotropy should be related to a slight angle of incidence effects) 6). It is well known that the angle of incidence causes a shape anisotropy with its long axis perpendicular to the plane of incidence7) ; in our case circular chains are expected, which should create a transverse shape anisotropy in the two materials. In order to explain the different direction of this spontaneous anisotropy in iron films, additional factors affecting the magnetic structure of these chains have to be taken into account, such as magnetocrystalline anisotropy energy, as well as magnetoelastic energy introduced by thermostresses. The relatively large value of Kr of iron, at room temperature, will cause the elongated parts of the chains to split into a multi-domain structure, tending to form a flux closure ; the domain walls will be perpendicular to the long axis of the particles, thus creating a longitudinal magnetic easy axis in the plane of the film. The domain structure is dominated not only by the surface wall energy uw, which increases with Ki, but also by the magneto-elastic anisotropy energy density fete The polar axis of felis perpendicular to the plane of the film because of the planar isotropic thermostresses existing in all deposited films. These stresses result from adhesion to the substrate, and from the different thermal dilation

coefficients. The domain wall width D can be expressed by D oc (cw/fel) 8). By lowering the temperature from 300 to 120”K, K1 of iron increases only by 20%; however, fel will increase appreciably. Thus the domain width will decrease and the radial anisotropy will increase. The spontaneous anisotropy for iron is therefore expected to be longitudinal and to increase at lower temperature, as observed. In nickel, on the other hand, Kr at room temperature is very small, and the magnetostriction (a) responsible for fez has a large negative value. A single domain structure is expected with two easy magnetic axes: a stress induced one, perpendicular to the plane of the film, and a transverse one, in this plane, resulting from the shape of the circularly arranged chains. By lowering the temperature of the nickel films, Kl and therefore ow increase appreciably. But this effect is compensated for

356

1. BRANSKY

AND A. A. HIRSCH

by the large increase in fez;thus no essential change in the magnetic is expected, and the circular anisotropy is maintained.

structure

4. Field induced anisotropy. In the thicker iron films lb and 2b (fig. 2), thespontaneous anisotropy seems to vanish, as seen from table I. Here the easy axis coincides with the direction of field Ha applied during the deposition. The negative sign of the uniaxial anisotropy energy density, given in table I, points to the fact that the transverse direction is the easy one, according to the definition of K, expressed by equation (4). The magnitude of this field induced anisotropy energy density is only 0.1 K1 at 120°K. However, it is remarkable that its temperature dependence is similar to that of the spontaneous anisotropy discussed in the previous section. The latter fact would lead us to relate the field induced anisotropy to some kind of stresses. For polycrystalline iron (where il < 0) these stresses must be compressive field oriented microstresses, which cannot be justified, as already proposed and rejecteds). The polycrystalline model also fails to explain the results presented in the third rows of figs. 1 and 2, i.e. the transverseperpendicular effect. As already mentioned, these loops should normally obey the transverse MRE given by eq. (3) and therefore possess positive peaks. The appearance of negative peaks in the loops of the MRE, for the cases in which the current flows perpendicular to Hd, suggests the existence of a defined film structure, i.e. a preferred crystal orientation. If during the recrystallization of the films the magnetization vector tends to direct itself in the direction of the magnetic field Hd, the magnetic easiest

0

05

023

075

1

m1

MAGNETIC FIELD

Fig. 4. The magnetization

curves between

of iron films (la, 2a and 1b, 2b) deduced loops

at 120°K

in the 11/11 and

rpmanence

and saturation

from the corresponding

_~/il directions. The values given in reduced units.

of the two pairs

branches of the MRE

of the magnetization

are

MAGNETIC

ANISOTROPY

IN FERROMAGNETIC

THIN

FILMS

357

crystal axis, parallel to the substrate, will align itself with this direction, in order to lower the magnetic energy. In iron films the plane (111) is preferrably parallel to the substrate la) ; the [ 1121 direction is then the magnetic easiest one, and will most probably align itself with the field Ha. A similar process was proposed for nickel filmss). The direction [ 1 IO] is the magnetic hardest one in the plane of contact (111) and is perpendicular to [ 1121. The calculated difference in the anisotropy energies corresponding to the direction [112] and [ 1 IO] is Ks/54 (Ks is the second magnetocrystalline anisotropy constant for iron). The value of this difference is only about 3000 ergs/cma, and therefore cannot by itself account for the measured values; moreover, Ks is nearly temperature independent in our region. But indirectly, by its interaction with the thermostresses, this preferred orientation can explain the presented data very well. As was stated above, the existence of the [ 1121 preferred orientation can account for the negative peaks in the transverse-perpendicular MRE loops. This will be shown by the following analysis. Akulov’s equation for the magnetoresistance of a cubic ferromagnetic crystal is : (5)

where ao, al and a2 are magnetoresistance constants, and ai and pi are the direction cosines with respect to the crystal axes of the magnetization vector and electric current respectively. If we assume that the magnetization vector rotates in the plane defined by the easy direction [ 1121 and the direction of the transverse-perpendicular magnetic field [ 1111, the magnetoresistance can be calculated for the two perpendicular directions of the electric currents [ 1 IO] and [ 1121. If, as we suggested, the [ 1121 direction is parallel to Hd, these two directions will correspond to the two longitudinal directions for the pair of films forming the cross. Introducing into (5) us N 4ar as known for iron and the corresponding values of the direction cosines ,!&,one obtains the following results : for [I101

(AR/R) L/1 = A - a1[i2/2 - 2&i(1 - i2)*]

(6)

(AR/R),/,

(7)

and for [I121

= A’ - a1[7j2/2 - 29(1 - i2)*],

where A and A’ are constants, and j is the reduced magnetization. Equation (7) represents the usual transverse effect with a small reduction of the form j(l - is)“. But in eq. (6), representing the case in which the current flows in the hard magnetic direction [l IO], the term j( 1 - is)* occurs with a relatively large weight. A schematical representation of the terms occurring in eq. (6) for a standard magnetization loop is given in fig. 5. The last term is responsible for the negative peaks in the observed MRE loops as seen in

358

1. BRANSKY

fig. 5. It is important

to note that

AND A. A. HIRSCH

no other

elementary

crystallographic

plane of rotation of the magnetization vector, with (111) as the contact plane, will possess negative peaks in the calculated MRE loops. Nor will the polycrystalline model, or the [ 1 lo] and [OOl] preferred possibly present in iron films, possess negative peaks.

orientations

vs. H

- jV3

1 VS.

(j w-j*/31

Fig. 5.

Calculated

single crystal

loop of the transverse-perpendicular

of iron, corresponding

field is taken in the [ 1111 direction, and the electric composed

current

flows

to an arbitrary

magnetoresistance magnetization

the easy magnetic

in the [ 110: direction.

of two terms proportional

H

effect

for a

loop. The magnetic

axis lies along the [ 1121 direction The magnetoresistance

to : j 4 1 - j2 and -j2/3, magnetization.

loop is

j is the reduced

By this interpretation for the transverse-perpendicular effect, we were led to the surprising conclusion that the [ 1121 orientation can also account for the magnitude sign, and for the temperature dependence of the observed field induced anisotropy. As has already been mentioned, the similar temperature dependence of the two anisotropies found in iron films suggests that both of them are governed by the same effect, i.e. the planar thermostresses. The magnetostriction constant for iron, in the [112] easy direction, is positive : AlIz = (2/3)(3.2) 10-6, and

in

the perpendicular

hard direction Allo = -(2/3)

[ 1 lo] it is negative : (3.9) 10-s.

MAGNETIC

Thus the existence

ANISOTROPY

IN FERROMAGNETIC

of this preferred

orientation

THIN

FILMS

359

in the plane of the film will

produce, even by isotropic stresses, an easy magnetic axis in its direction, i.e. in the direction of Hd. The order of magnitude of this field induced anisotropy corresponds to the measured one (table I); taking a maximum value of 1010 dyne/cm2 for the diffused stresses T, as measured for iron films by Finegan and Hoffmanrr), we get: K,

= - (3/2)(il 110 -

jlllB) T = (0.7) 105 ergs/cma.

(8)

If we note that our films are about three times thicker, then the stresses are expected to be lower, and this calculated value will be in fair correspondence with the measurements summarized in table I for films lb and 2b. By lowering the temperature the thermostresses increase, as stated in the previous section, and cause the observed increase of K,. The favourable growth of the crystallites, having the magnetic easy axis parallel to the inducing field H d, can be justified by elementary energy considerations, thus providing us with a simple but general explanation for all the observed values. It is necessary to mention that the preferred [112] orientation exists already in the thinner iron films la and 2a, as is seen by the transverseperpendicular effect in fig. 1 (negative and positive peaks in the MRE loops), but the field induced anisotropy in the plane is covered by the much greater spontaneous anisotropy. The former becomes evident only when the thickness grows, the chains fill up, and the structure of the film becomes more homogeneous. The great negative magnetostriction of nickel hides this process in the nickel films. 5. Concluding remarks. The origin of the magnetic anisotropy induced by the presence of a magnetic field during the deposition is satisfactorily explained. The existence of a [ 1121 preferred orientation in iron films is consistent with x-ray investigationslo). It accounts, by its interaction with the isotropic planar stresses, for the direction, magnitude, and temperature dependence of the observed anisotropy values. This field induced anisotropy is easily hidden by other anisotropies greater by one order of magnitude, such as shape anisotropy caused by an angle of incidence effect, or as a stress induced anisotropy, as in the nickel films. A further proof for the proposed model could be a very accurate torque measurement, which could reveal the crystal anisotropy of the (111) plane, superimposed on the stress induced one. Acknowledgements. The authors wish to thank Mr. A. Yarom, Physics Department, Technion, for his aid in the calculations. The research reported in this document has been sponsored in part by the U.S. Air Force Office of Scientific Research, OAR, through the European

360

MAGNETIC

ANISOTROPY

IN FERROMAGNETIC

THIN FILMS

Office, Office of Aerospace Research, U.S. Air Force, under Grant AF EOAR 63-7 1. This research represents part of a thesis being written by Mrs. Judith Bransky in partial fulfilment of the requirements at the Technion - Israel Institute of Technology.

for the degree of D. SC.

Received 22-8-66

REFERENCES 1) Stoner, E. C. and Wohlfarth, E. P., Phil. Trans. roy. Sac. London AZ40 (1948) 599. 2) Bozorth, R. M., Ferromagnetism, Van Nostrand Co., N.Y. (1951). 3) Bransky, J. and Hirsch, A. A., “Magnetoresistance effect in ferromagnetic films as function of condensation conditions”, Proceedings of the International Symposium on Basic Problems in Thin Films Physics, Clausthal (September 1965), Vandenhoeck and Ruprecht, GGttingen (1966) pp. 429-436. 4) Hirsch, A. A., Physica 33 (1959) 581. 5) Knorr, T. G. and Hoffman, R. W., Phys. Rev. 113 (1959) 1039. J. F., J. Research Develop. 4 (1960) 163. 6) Pugh, E. W., Boyd, E. L., and Freedman, 7) Smith, D. O., Cohen, M. S. and Weiss, G. P., J. appl. Phys. 31 (1960) 1755. 8) Kittel, C., Rev. mod. Phys. 21 (1949) 541. 9) Yelon, A., Asik, J. R. and Hoffman, R. W., J. appl. Phys. 33 (1962) 949. 10) Sachtler, W. M. H., Dorgelo, G. and Van den Knaap, W., J. Chim. phys. 51 (1954) 491. 11) Finegan, J. D. and Hoffman, R. W., J. appl. Phys. 30 (1959) 597.