Hirsch, A. A.Friedman, N.1963

Physica 29543-547

INDUCED MAGNETIC ANISOTROPY IN THIN FERRO­MAGNETIC FILMS INVESTIGATED AT LOW

TEMPERATURES

by A. A. HIRSCH and N. FRIEDMAN

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

Synopsis

A new method of investigation of induced magnetic anisotropy in thin films isgiven, which is based on the study of the magnetoresistance effect when two crossedmagnetic fields are applied. The experiments were carried out from liquid air down toliquid helium temperatures on thin evaporated films of pure nickel or pure iron placedin a rotated cryostat. It was shown that when the films are deposited in an externalmagnetic field in a vacuum of 10-6 mm of Hg, the easy axis of magnetization is inducedin the direction of the external field. Because of the dependence of the electric re­sistivity on the orientation of domain magnetization, the magnetoresistance effect canbe a useful tool in the investigation of the magnetization process and the anisotropiesof films. The experimental data were compared with a theoretical model suggestedfor the magnetization of films under the influence of two crossed magnetic fields.This model was elaborated by means of the approximation of coherent rotation ofelectron spins in a single domain particle, whose anisotropy was made up of a uni­directional, a uniaxial and a cubic magnetocrystalline component. It was found thatfilms deposited in an external magnetic field show a symmetry around the easymagnetization axis like a spheroidal particle around a polar axis. At very low temper­atures the induced magnetic anisotropy is more distinct because of vanishing thermalstresses. A process of formation of elongated grains or of chains of small particles seemsto be responsible for the induced easy magnetization axis.

Introduction. The origin of induced magnetic anisotropy in thin films offerromagnetic metals is not yet clear. It has been reported1) that in ironand nickel-iron films a very small part of this anisotropy might be causedby surface stresses. According to other authors 2) an isotropic strain inPermalloy films creates a magnetoelastic easy axis normal to the film.Magnetic investigations on thin films at very low temperatures seem to beimportant because of vanishing stresses due to differential thermal expansionbetween metal and substrate. It is assumed that films made by depositionin a vacuum of 10-6 mm of Hg, as studied in this work, have a granularstructure. Such films have normally a negative temperature coefficient ofelectric resistivity. Because of this granular structure a simple single domainmodel for the hysteresis phenomena in the films is suggested.

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544 A. A. HmSCH AND N. FRIEDMAN

Asymmetrical hysteresis in a uniaxial domain. The result of applyingtwo perpendicular crossed magnetic fields on a uniaxial single domain, onevariable H and another constant H', which are inclined at the angles eP and90° - eP to the easy axis, is the formation of asymmetrical hysteresismagnetization curves. One calculates these curves in the usual way assumingcoherent rotation of spins. The only important energy terms taken intoconsideration are conditioned by magnetic anisotropies (unidirectionalwhich stems fro:n the constant field H', magnetocrystalline and uniaxial)and by interaction between H and the spontaneous magnetization Ms. 'WhenHand H' arc in the [IOOJ and [OIOJ directions, ~ = 45°, and the cubicmagnetocrystalline anisotropy constant K is negative, one represents bemagnetization hysteresis curve in reduced unit by the relation

h = (2m2 - I)[m + tF(1 - rn2)- ! ] + h'm(l - m2)-a (1)

where m = MJNIs ; h = HMsJ2 IK[; h' = H'Ms/2 IKI and F = K u! IKI isthe ratio of unidirectional to magnetocrystalline anisotropy constants. Atlarge values of hi the asymmetrical loops (Eq. (1)) become asymmetricalreversible curves. The hysteresis of the magnetoresistance effect (MRE)

h·.a,~

·as 0 as ,--'-----'

Reduced magnetic field,. h

Fig. 1. Calculated transverse magnetoresistance curves in reduced units. The uniaxialdomain has a negative magnetocrystalline anisotropy constant. The field h is alongthe [100J axis. The constant field h' lies along the ~010J axis. The easy magnetizationaxis is parallel to ClIO]. The ratio of undirectionnl and magnetocrystalline anisotropy

constants F is 0.5.

shows also similar changes, as illustrated in fig. 1. One expresses the relativechange of resistivity by L1RJR = a(m; - m 2) where the factor a is negativeior a longitudinal MRE and positive for a transverse MRE; rn- is the reducedremanence. H becomes normal to the easy axis if the domain is rotated at90° around the [O:OJ axis from its previous position (Eq. (1)) and one gets asymmetrical loop described by

h = (1.S11~2 - 0.5) m + him V2(1 - m 2)- ! + Fm. (2)

whose slope dmjdh and coercive force decrease with increasing h', The MREis exhibited in this case by non-saturated symmetrical curves.

Experimental results and interpretanon, The transverse MRE studied inthin rilms varies with the angle ebetween II and the direction normal to the

INDUCED MAGNETIC ANISOTROPY IN THIN FERROMAGNETIC FILMS 545

substrate. One gets a transverse-perpendicular MRE (.U .1.) for (J = 0° anda transverse-parallel MRE (1./11) for e= 90°. Several values of eare obtainedby means of rotation of the cryostat containing the samples. The de and acresistance measurements were carried out on films of pure iron or nickeldeposited on to cover glass substrates (1 em X 0.3 em). The cathode ray

Fig. 2. Static transverse magnetoresistance curves of thin films. Maximum H = 2200Oe, (a) R = 70589 ohm, maximum tJRjR = 0.8%; (b) R = 3472 ohm, maximumLIRjR = 0.12%; (e) film deposited in a field of 75 Oe normal to the substrate. R == 19290 ohm, maximum iJRjR = 0.07%.

oscillograph traces are represented in fig. 2-4 with H' or (J as parameters.The formation of typical asymmetrical loops is demonstrated in fig.2(a)and fig. 2(b). Using the theoretical model, one concludes that the grains ofthese films have easy axes inclined to the substrate. The film whose MRE

16S0 oe.

Fig. 3. Static transverse magnetoresistance curves of thin films. Maximum H = 2200Oe, (a) R = 1828 ohm, tJRjR = 0.33%; (b) R = 1303 ohm, maximum LlRjR =

= 0.11 %; (e) H = 11959 ohm, maximum LIRjR = 1.25%. Frequency of current infilms is 2400 cps.

546 A. A. HIRSCH AND N. FRIEDMAN---------------------------------

is shown in tig. 2(c) was deposited in a field of 75 Oe normal to the substrate.The large coercive force and the slight asymmetry in the shape of the loopsat large values of H' indicate that an easy axis of magnetization has beeninduced in a direction nearly normal to the film. In the case of symmetricalloops with small coercive force (fig. 3(c)), these easy axes are probablyparallel to the plane of the substrate. Both transverse effects illustrated infig. 3(b) and fig. 3(c) can be explained by eq. (1) and eq. (2) respectively, ifthe plane (100) is parallel to the substrate and the proj ections of the magnet­ization vectors on (100) are parallel to the direction of the electric current.The films whose MRE traces are given in fig. 4 were deposited in a longitudi­nal field. The vanishing remanence in the MRE curves and their symmetry

IRON 80 'k NICKELIfO:i3(a) .il.! o.c. No..13JI.L « tt»•

16S0ot . \650 Of.

Fig. 4. Static transverse magnetoresistance curves in thin films. Maximum H = 2200Oe. (a) films deposited in a longitudinal field of 450 Oe. R = 20000 ohm, maximumARjR = 1.5%; (b) and (c) film deposited in a longtudinal field of 150 Oe. R= 18190

ohm, maximum LJRjR = 1.1%.

at large values of H' would be possible if an easy axis were induced in thedirection 01 the field applied during the deposition of the films. It can beseen from fig. 4(c) that the MRE shows a cylindrical symmetry with respectto the induced easy axis as in the case of a wire. The maximal values of LJRIRin films with a large uniaxial anisotropy, as found in this work, vary from1.1%to 1.5%. These values are similar to those reported in a previous work 3)on MRE measurements on thin nickel wires. The similarity between theMRE of these films and thin wires suggests that the induced anisotropymay be related to a process of formation of elongated grains or to an aggre~

gation of small particles m chains.

Concluding remarks. Vrambout and De Gr eve t) have shown by useof the magneto-optic Kerr effect, that in iron films a weak anisotropy axisexists which lies close to the long axis of the substrate. It has been shownby Van It t e r beek 5) that the temperature variation of the coercive force

INDUCED MAGNETIC ANISOTROPY IN THIN FERROMAGNETIC FILMS 547

in nickel films may be dissimilar for two different directions (transverse­perpendicular and transverse-parallel) when a single variable magneticfield has been applied. This behaviour was interpreted in an early work 6),assuming an easy magnetization axis which is parallel to the plane of thesubstrate.

The technique of using two crossed magnetic fields described here hasthe advantage of enabling one to determine more exactly how the easymagnetization axis inclines towards the substrate. The direction of this axismust be given in general by two angles (an azimuthal and a polar one).

Acknowledgemen ts. This work has been supported by the Air ForceResearch Division of the A.R.D.C., United States Air Force, through itsEuropean Office.

Received 5-11-62

REFERENCES

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581.