0. GEBEARDT and W. RICHTER: Ferromagnetic Thin Film Magnetoresistors

phys. stat. sol. (a) 60, 467 (1980)

Subject classification: 14.1 and 18.2.1; 21.1; 21.1.1

467

Sektwn Physik der Friedrich-Schiller- Universitat Jenal)

Quasi-Static Characteristics and Magnetic Properties of Ferromagnetic Thin Film Magnetoresistors

BY 0. GEBHARDT and W. RICHTER

Properties and output characteristics (quasi-static behaviour) of NiFe thin film magnetoresistors are investigated. The output characteristics are plotted and compared with theoretical results for various kinds of magnetic field and current directions relative to the easy axis of the films. Some types of experimental plots are in good agreement with the theory. The characteristics are used to a determination of the basic magnetic film.properties H k , H, , M,, and a,.

Es werden Eigenschaften und Kennlinien (quasistatischer Verlauf) von NiFe-Diinnschicht- Magnetwiderstinden untersucht. Die Kennlinien werden fur verschiedene Feld- und Strom- richtungen beziiglich der leichten Achse der Schichten experimentell dargestellt und mit theoreti- schen Ergebnissen verglichen. Einige der experimentellen Kurven stimmen mit der Theorie gut uberein. Die Kennlinien werden zur Bestimmung der grundlegenden magnetischen Schichteigen- schaften H k , H, , M , und a, genutzt.

1. Introduction

The physical fundamentals of the magnetoresistors are the anisotropic magneto- resistance effect and the magnetization processes in ferromagnetic uniaxial thin films. These are well-known effects and have been investigated by many authors (see for instance the review articles [ l , 21).

In this paper we have investigated the output characteristics of some NiFe magneto- resistors. The experimental plots are compared with the theoretical solution from the coherent rotation model of the Stoner-Wohlfarth theory [3].

The basic magnetic material properties Hk, H, , M, , and a, have been received from magnetoresistive characteristics.

Our experiments are carried out with the aim to construct magnetoresistive field and current sensors.

2. Theoretical Considerations

The anisotropic magnetoresistance effect found in ferromagnetic 3d transition metals and alloys, depends on the orientation of the magnetization relative to the current direction. I t s magnitude in NiFe and NiCo alloys (bulk material) can be greater than 5% a t room temperature [l].

The microscopic theory of the orientation effect has been discussed first by Smit [4] in connection with anisotropic scattering of 4s conduction electrons into 3d states of the transition metals. The resistance anisotropy results from a greater s-d transition probability for electrons moving in the direction of magnetization than in the perpendic- ular direction.

1 ) Max-Wien-Platz 1, DDR-6900 Jena, DDR.

468 0. GBBHARDT and W. RICHTER

The magnetorcsistance effect in a uniformly magnetized polycrystalline sample is described by the relation [l]

(1) Ag = ~ ( 5 ) - is the resistivity change which occurs when the saturation magneti- zation vector M,, is oriented a t an angle 6 and normal to the electric current vector I , respectively and the maximum change Apa is a characteristic of the material.

With a constant current the change of voltage difference a t the ends of a ferro- magnetic strip is a measure of its resistance R and may be called the magnetoresis- tive signal. The signal voltage is proportional to the current I through the magneto- resistor and independent of the polarity of 5.

As shown by different authors (see [5, 61) for films with an easy axis of magneti- zation in the film plane there exists an unambiguous relation between the direction of magnetization and an external in-plane field H if the inhomogeneous distribution of magnetization can be neglected. The angle p between the magnetization and the easy axis is determined by the relation

AQ/AQ& = cos2 f .

h, sin v - h, cos v + sin p cos q~ = 0 . (2) Reduced variables h, = H,/Hk and h, = H v / H k are introduced in order to get

dimensionless equations and H k means the anisotropy field. With regard to our experiments the special cases are of interest where one of the hard-axis (y-axis) or easy-axis (x-axis) external field components is constant and the other variable. A simple analytic way to compute the functions v(h,) or v(h,) by using (2) is to consider p as independent variable and h, or h, as parameter and then to compute h, or h, (see 171).

3. Sample Preparation and Experimental Details The non-magnetostrictive 81 Ni 19 Fe films were produced by vacuum evaporation of 83Ni 17Fe alloy under vacuum of Pa onto heated substrates of glass or silicon a t temperatures between 200 and 400 "C. The magnetic films were deposited at rates between 2 and 8 nmls in a magnetic field of 2 x lo4 Am-l.

Magnetoresistance measurements and records were made on strips 15 mm in length. The film thickness was t = 25 nm and the width w = 1 mm, so that the de- magnetizing field in the direction of w is smaller than 20 Am-' and can be neglected (see Section 4). For a special investigation of demagnetizing effects we have used 100 nm thick samples with width varying from 0.1 to 3 mm.

The strips were produced with various bias angles fpb between the easy axis and the current direction. A signal field h, could be applied in any direction to the strip. I n order to maintain the film in a single domain state and/or to obtain linear output characteristics it is favourable to add a constant bias field h, in easy or hard direction. The small resistance variation as a function of the signal field h b was plotted on an X - Y recorder, the dc-component was separated by using a bridge arrangement. Stray magnetic fields were separated by a magnetic shield.

4. Experimental Results and Discussions Taking into consideration an additional bias angle qb one gets for the angle p be- tween the direction of magnetization and the direction of current in (1) the relation

Consider first that the bias angle pb is zero, so that with (1) the strip resistance va- riation is

[ = v b - v - (3 )

ARlAR, = C O S ~ v . (4)

Characteristics and Properties of Ferromagnetic Thin Film Magnetoresistors 469

I

' 3 -2 -7-hc 0 h, 1 2 3 h, --

Fig. 1. Magnetoresistive signal curves for Pb = 0, ___ experimental curves, - - theoretical curves, e.a. easy-axis. a) h, = hb, h, = h,: (1) h, = 0, (2) h, = 0.23, (3) h, = 1.18, (4) h, = 2.06. b) h, = h,, h, = h,: (1) h, = 0, (2) h, = 1.0, (3) h, = 1.76, h, = 1.76, (4) h, = 2.94

If h, = h, and h, = h,, we have experimentally obtained the signal plots as shown in Fig. 1 a, if the films were previously polarized along the easy axis and the field changes from h, = 0 to its maximum value. The dashed lines are calculated numerically by using ( 2 ) and (4). If h, = 0 (transverse magnetoresistance curve), one gets simply

AR/AR, = 1 - h: ; lhsl 5 1 * (5) One can see that the theoretical field dependence of the transverse loop 1 is parabolic until saturation. The experimental static curve shows a deviation from the theoretical model, caused by an inhomogeneous rotation of M a t fields near saturation as a re- sult of inhomogeneous demagnetizing effects a t the film edges and/or formation of domain walls. The quadratic extrapolation to saturation determines the value of the average anisotropy field H,. In alternating signal fields with amplitudes smaller than lh,l = 0.8 the tranverse loop has the expected reversible character, at higher fields it becomes a hysteresis loop, for reasons which will be discussed later. By using the transverse loop one can get the value of the anisotropic magnetoresistance ratio ARJR I, where we have found values between 1.5 and 29L.

A bias field in easy direction leads to closed loops in alternating saturation signal fields h, and a flattening of the curves 2 to 4.

In hard-axis bias and easy-axis signal fields one gets signal plots as shown in Fig. 1 b. The irreversible switching of magnetization (curve 1) a t h, = h,, where h, = H J H , means the easy-axis coercitive force, was observed a t lower signal fields than expected from the coherent rotation model and is caused by domain wall motions. A hard-axis bias field somewhat larger than Jhbl = 1 leads to closed loops (curves 3, 4) caused by coherent rotation of M,.

Consider second that cpb = n/4. Because of the cos2 6 dependence of magneto- resistance an optimum sensitivity S = 1/R, - dR/dH, a t H , = 0 will be expected at cpb = x/4. With (1) and (3) one gets the relation

AR/AR, = sin cp cos cp + 112. (6)

The experimentally obtained signal plots in hard-axis signal fields are shown in Pig.

470 0. GEBHARDT and W. RICHTER

-3 -2 - 7 0 7 2 3 4 -

Fig. 2. Magnetoresistive signal curves for q.y, = 3214, - experimental curves, - - - theoretical curves, e.a. easy-axis. a) h, = hb, h, = h,: (1) h, = 0, (2) h, = 1.47, (3) h, = 2.94. b) h, = h,. h, = hb: (1) h, = 1, (2) h, = 1.47, (3) h, = 2.94

2a. The transverse magnetoresistance loop (hb = 0) is determined by ARIAR, = h,(l - h;)llz + 112 ; l h s l 5 1 (7)

and the theoretical field dependence has a point of inflection at 16, = 0. The behaviour of the transverse magnetization curve in alternating signal fields is that mentioned above. With an easy-axis bias field and small hard-axis signal fields one gets nearly

(8) The relation in correspondence with our experimental result suggests a flattening and a higher linearity of the curves if hb increases. I n easy-axis signal fields (Fig. 2 b) one gets also closed loopes, if the hard-axis field is somewhat larger than lhbl = 1 and for small signal fields one has approximately

(9) If h b is close in magnitude to lkb l = 1, the sensivity of the magnetoresistorissignif- icantly multiplied, however, due to inhomogeneities of the film and formation of do- main walls, it remains finite.

The observed effect of the opening of the transverse magnetoresistance loop in alternating saturation signal fields has been discussed first by West [8] and is caused by the magnetic ripple or angular dispersion in real films. When for example the film is first saturated by a field in hard direction and the field i s reduced to zero, the single domain splits into long strips with antiparallel magnetization along the average easy axis. As can be shown, the energy minimum for this configuration occurs for wall transitions less than 180°, consequently it leaves a nonzero component of magneti: zation along the hard direction as a finite remanence. As shown in Pig. 3a and b a value of R results which is smaller than RI, and a strong decrease of sensitivity is observed if q b = n/4.

By saturation of the film apart from the hard axis a t an angle a , the magnetization homogeneously rotates back to the easy axis. The angle a , then is equal to the maxi-

AR/ARa = hs/(hb + '1 + 1/2 ; < Ihb + 11 *

AE/ARa = h,/(hb - 1) + 112 ; lhsl < Ihb - 11 -

Characteristics and Properties of Ferromagnetic Thin Film Magnetoresistors 47 1

m - e.a.

(gf e a. +-+7--l

-3 -2 - I I h! -

Fig. 3. Magnetoresistive signal curves in alternating magnetic saturation fields (experimental curves), e.a. easy-axis. a) h, = 0, h, = h,, = 0. b) h, = 0, h, = h,, qb = 4 4 . c) h, = h,/V2, h, = hJ2, Vb = n/4

mum angular dispersion of the film (see [6, 91). The sensitivity of the magnetoresistors will be preserved in any signal fields, if for example this is applied a t an angle a = = n/4 to the easy axis (Fig. 3c). Fields outside the astroid critical curve lead only to a change in polarity. Closed loops in hard-axis alternating signal fields caused by homogeneous rotation of M , also exist, if an easy-axis bias field h, is applied, SO that

sina, = h, . (10) Equation (10) allows a simple determination of a,.

By using magnetoresistance methods we have determined the basic magnetic film properties Hk, H,, and 01, of various samples in dependence on substrate temperature during film deposition (see Fig. 4).

If the lateral film dimensions are not very large as compared with the film thick- ness the magnetic behaviour can be influenced by demagnetizing fields. By assuming that the cross-section of the strip of width w and thickness t is elliptical, so that tho

t 3

Fig.4. Dependence of Hk, H,, and a, on sub- strate temperature T, during the deposition of the film; film thickness t = 25 nm

472 0. GEBHABDT and W. RICHTER

fl$ - Fig. 5. Influence of the sample geometry. a) Magnetoresistive signal curves (hz = 0, h, = h,,

= 0) in dependence of the strip width, ~ experimental curves, - - - theoretical curves. ( 1 ) w = 3 mm, .(2) w = 0.5 mm, (3) w = 0.25 mm, (4) w = 0.1 mm, film thickness t = 100 nm. b) Reduced effective anisotropy field hk,,ff as a function of the demagnetizing factor Nw

demagnetizing field in the film is uniform, one gets for its magnitude in direction of w (see U O l )

H, = - N , M , , (11)

where N , = t / ( t + w ) = t/w means the demagnetizing coefficient and M , = IMJ i,he magnitude of saturation magnetization.

Assuming a stripe-shaped film with its easy axis parallel to the length of the strip the effective anisotropy field (see [ll, 121) is

Hk,lrff = Hk + N w M ~ - (12)

The signal curves of four samples with various N , were plotted by using of hard- axis fields (Fig. 5a). The quadratic extrapolation is used for the determination of the reduced effective anisotropy field hk,leff = Hk,leff/Hk. From Fig. 5 b one can find the value of the anisotropy field Hk without demagnetizing effects.

A valuation of M , is possible by using (12) and Fig. 5b. One gets an average valueof M , = 8 x 105Am-l.

5. Conclusions

The quasi-static characteristics of NiFe thin-film magnetoresistors are in good agree- ment with the theory for a large number of external field configurations. Deviations may be caused by the formation of domain walls in alternating hard-axis saturation fields and by inhomogeneous demagnetizing effects a t the film edges (non-elliptical cross-section).

The determination of the magnetic film properties Hk, H,, M,, and 01, by using the magnetoresistive output characteristics is a useful method and requires no elab- orate equipment.

If a current bias angle of yb= n/4 is used, there exist field configurations which in connection with small values of angular dispersion am may generate a high sensitivi- t y and linear output characteristics of magnetoresistors in small magnetic fields. These are well suitable properties for applications of magnetoresistors such as field or current detectors.

Characteristics and Properties of Ferromagnetic Thin Film Magnetoresistors 473

Aelmowledgernents

We thank Dr. P. Weber and Dr. K. Bluthner for help in the preparation of the samples and Prof. K.-H. Berthel, Prof. W. Andra, and Dr. P. Weber for helpful discussions and a critical reading of the manuscript.

References [l] T. R. Mc GUIRE and R. I. POTTER, IEEE Trans. Magnetics 11,1018 (1975). [2] D. A. THOMPSON, L. T. R~MANKIW, and A. F. MAYADAS, IEEE Trans. Magnetics 11, 1039

131 E. C. STONER and E. P. WOHLFARTH, Phil. Trans. Roy. SOC. (London) A240,599 (1948). [4] J. S m , Physica (Utrecht) 16, 612 (1951). 151 W. ANDRA, phys. stat. sol. 2, 941 (1962). [6] E. W. PUGH, Phys. Thin Films 1, 300 (1963). [ 7 J H. J. OGUEY, Proc. IRE 48, 1165 (1960). [C] F. G. WEST, J. appl. Phys. 32, 290 (1961). [:j] H. HOFFMANN, Z. angew. Phys. 18, 499 (1965).

(1975).

[lo] J. A. OSBORN, PhyS. Rev. 67, 351 (1945). [ l l ] R. P. HUNT, IEEE Trans. Magnetics 7, 150 (1971). [12] J. H. J. FLUITMAN, Thin Solid Films 16, 269 (1973).

(Received May 5, 1980)