The electrical resistivity in an ordinary metal can also be a function of the angle between the direction of the current and that of the magnetization. The special feature of ferromagnetic metals is that the effect can be relatively large at room temperatures and also occurs in polycrystalline material. The angular dependence can be represented by
where is the resistivity, the angle between current I and magnetization M and and are constants of the material. The extreme values for the resistivity are found for and ; the resistivity is lowest at . Obviously, the alloy chosen for the ferromagnetic strip should have the highest possible value for . In addition, it should be easy to rotate the magnetization in a magnetic field of the order of 8000 A/m (about 100 Oe) as produced by the magnetic tape. Alloys with a high permeability, a small coercive force and a relatively large that are suitable for this application include Ni89Fe11 or Ni70Co3O. At low temperatures can lie between 0.1 and 0.2; at room temperature is much smaller. For most of the strips we have used this effect amounts to only a few per cent. We shall now analyse the relationship between the resistivity and Hy, the field to be measured. It will be apparent that the dimensions of the MRH, i.e. the length l, thickness t and width w, play an important role in this relationship; see fig. 3. Starting with a strip mounted vertically we assume that the strip is in a homogeneous magnetic field. (In practice Hy decreases with distance from the tape.)
Fig. 3. The definition of the coordinate system. x,y,z and the length 1, width w and thickness t, as used in the description of the magnetoresistance effect. Hy is the field to be measured. M is the magnetization of the strip, I the measuring current; is the angle between these two vectors.
If Hy is equal to zero, the magnetization will lie preferentially in the longitudinal direction, that is to say along the z-axis. This is related to the demagnetization energy , (N is the demagnetization factor, the saturation magnetization), which is a measure of the energy of the magnetic field produced externally by a magnetized body. The larger the cross-section of the body in the direction of magnetization, the smaller the energy. When the direction of magnetization is rotated from z to y, the demagnetization energy changes in accordance with the relation
In the case t << w << 1, Nz can be neglected and Ny approaches t/w. Also, in the presence of Hy the energy contains a term
The resultant can be found by minimizing the sum of (2a) and (2b), and differentiating with respect to we find:
If we now set (an r.m.s. field), then we see that as long as HyH0 the solution is given by , while for larger values of Hy we have and hence . Using the result from relation (1) that there is a quadratic relationship between the change in resistivity and , we find:
This response function is shown in fig. 4 (curve I).
Fig. 4. Calculated response curves for a magnetoresistive head; the relative change in resistance is plotted against Hy, normalized to the demagnetization field H0 (see eq. 4). Curve 1 refers to the case of an ellipsoidal reading head, in which the demagnetizing field is homogeneous. Curve 2 is based on assumptions that correspond more closely with reality. The relationship between the variables is approximately linear in the region around the point of inflexion in the curve; at the associated field-strength (), is about 45°.
A reading head with a response function such as curve 1 of fig. 4 could not of course be used in practice as a linear transducer; for low fields (Hy << H0) the change in resistivity is almost zero and for high fields the response is independent of Hy. In practice the response function is somewhat flatter. This is related to the assumption, in the above derivation of the direction of orientation of M, that M has the same direction over the complete strip; this is not the case. In fact, it is only possible, to speak of a demagnetization factor N and a corresponding demagnetization field for magnetized bodies in the form of an ellipsoid of revolution. In practice, if the shape deviates from an ellipsoid then N has a kind of mean value, but the demagnetization field will no longer have the same direction and magnitude everywhere. Moreover, local inhomogeneities and anisotropic fields can be introduced during the fabrication of the strip. The results of numerical calculations for the case of an inhomogeneous demagnetization field have been shown as curve 2 in fig. 4. Even though the situation is thus better than curve 1 would suggest, a good practical reading head can only be obtained when special precautions are taken. These will be discussed in the following section.
A direct conclusion about the preferred dimensions of the strip can be drawn from the above calculations. The reading head is sensitive to field-strengths approximately equal to H0 and hence to (t/w)Ms. Since has a magnitude of about 1 W/m2 and w cannot be chosen greater than about 10m - otherwise the field from the tape would not extend beyond the strip - t follows directly from H0. For a field H0 of 104 A/m we obtain t = 0.1m.
Limits can also be defined for the thickness of the strip. The thickness should not be made less than about 20 nm, since it is difficult to deposit films that are both homogeneous and mechanically reliable at thicknesses less than this value; in the second place there is an increase in the resistivity of metals when the thickness is less than the mean free path for electron scattering. This extra resistance will not be anisotropic, so that the maximum effect will diminish. In nickel this free path length is about 30 nm at room temperature. On the other hand, the strip must not be made so thick that its resistance is no longer large with respect to the contact resistance; this occurs when t > 1 m.
In a reading head it is important that the output signal, and hence the change in electrical resistance, are proportional to the input signal, i.e. the variation in Hy. The response function obtained when the unperturbed magnetization is oriented along the z-axis is an even function of the field Hy, and consequently for small values of Hy the sensitivity is small and the distortion is large.
This can be improved by making use of the fact that the response curve has a point of inflexion and is approximately linear in a small region around this point. Closer study has shown that for the associated value of Hy the magnetization M is inclined at an angle of about 45° to the direction of the current (the z-axis). We can therefore obtain a linear response for small variations in Hy if we ensure that the current and magnetization are inclined at an angle of about 45°, There are two methods of achieving this result.
In the first method use is made of an auxiliary field Hb in the y-direction, whose magnitude is made comparable with the anisotropic demagnetization field H0; the field from the tape can now be considered as a relatively small variation hy. If Hy in equation (4) is replaced by Hb + hy, then provided we obtain:
When the last term is small (hy << H0), this relation is almost linear, with a slope of 2Hb/H02. The condition H0 >> hy determines the demagnetization field (and hence the thickness) and Hb/H0 determines the sensitivity. Linearization of the response by using an auxiliary field - either external or in the form of an anisotropic field - is certainly possible in practice, but it does present some problems. There is also the danger that such a field could affect the information written on the tape.
The difficulties associated with the use of an auxiliary field are avoided in the solution that has been found at our laboratories3. As explained above, it is desirable to start from the situation in which the current and the preferred direction of magnetization are at an angle of 45° to each other. An alternative method of obtaining this angle of 45°, instead of using an auxiliary field, is to make the current in a ferromagnetic material flow obliquely in the way illustrated in fig. 5. If the magnetic strip is partially covered by oblique stripes of a material of a much higher electrical conductivity, then the equipotential planes will also lie obliquely and the current through the intervening areas of NiFe will be at an angle of about 45° to the (unchanged) easy direction of the magnetization. The design shown in fig. 5 is called a 'barber pole' because of its resemblance to the red and white striped pole still sometimes seen outside barber's shops.
Fig. 5. The 'barber pole'. The current I in the ferromagnetic strip flows at an angle of 45° to the longitudinal direction, and hence to the preferred direction of magnetization, because stripes of a relatively good electrical conductor (shaded grey) are applied to the surface of the strip. In this way a linear response can be obtained without the use of an auxiliary field. At the edges of the strip - in a region roughly corresponding to the triangles ABC, the direction of the current does of course differ somewhat from the ideal.
The response function of the barber pole can be calculated from equation (4):
Here is the angle imposed by the construction between the current and the direction of the magnetization in the unperturbed state. On rearranging and substituting we obtain:
When the response function is of course that of an 'ordinary' MRH, as already shown in fig. 4, curve 1.
We have now obtained a linear response function for small values of Hy (Hy << H0), with the gradient - i.e. the sensitivity of the head - determined by H0. The complete response function for an ellipsoid, also for large Hy is compared with that of an ordinary MRH in fig. 6. It can be seen that a linear relation between Hy and exists over a large range of fields (-0.7 < Hy/H0< 0.7); this range is greater than in the case of an auxiliary field Hb. Both for large values of Hy and for Hy = 0, the magnetization is at an angle of 45° to the current and the value of the resistance is given by .
Fig. 6. The response curve for a 'barber pole', calculated for homogeneous magnetization. The curve has an approximately linear section around Hy = 0. Curve 1 from fig. 4 is also shown for comparison; this curve is an even function of Hy, whereas the curve for the barber pole is not.
The calculated curve in fig. 6 again refers to the ideal case. As before, it is assumed that M is uniform, but in addition it is assumed that the current has the same direction everywhere. This is not true along the edges of the strip, of course, and the effect of the different current distribution in the triangles ABC in fig. 5 must really be studied in detail. An example of the calculated position of the equipotential planes at the edge of the strip is given in fig. 7. It is also possible to calculate the response function for this complicated case. The results are compared with the experimental values, in fig. 8. The agreement is good. An important difference from the ideal curve given in fig. 6 is the asymmetry between positive and negative values of Hy.
A minor complication is caused by the fact that although the magnetization M aligns itself preferentially along the z-axis it does not differentiate between the positive or negative z-direction. In an ordinary MRH this gives no cause for concern ( and give the same value of resistance), but in the barber pole this difference is certainly of importance, see fig. 9. This duality can be avoided by using a weak longitudinal auxiliary field, sufficiently strong to overcome the coercivity.
Fig. 7. The effect of the edges of the strip on the current distribution in the barber pole (see fig. 5). The thin lines represent the equipotential surfaces.
Fig. 8. Calculated response curve for the barber pole when the effect of the edge of the strip on the current distribution (see fig. 7) is taken into consideration. The crosses are measured values.
Fig. 9. In a conventional MRH it makes no difference if the magnetization M at Hy = 0 aligns itself in the positive or the negative z-direction; in both cases a particular value of Hy gives the same value of and hence the same change in resistance (see eq. 1). In the barber pole, however, where the direction of the current is not along the z-axis, it does make a difference.
From what has been said above it is easy to deduce the type of output signal to be expected from a reading head - with or without a barber pole. It can be assumed that this will differ depending on the application. The extent of the linearity region will always have to be matched to the maximum field-strength, which leads to different values of H0. For tapes, for which the maximum undistorted field emergent from the tape has a field-strength of about 12 x 103 A/m (150 Oe), the value of H0 should not be made less than about 24 x 103 A/m (300 Oe). A value of then gives a thickness t of , the maximum permissible value. If the track width is now assumed to be fixed, say at , then the total resistance of the strip is known () and the total change in resistance that can be obtained in the linear region is about .
For tapes containing CrO2 and metal powder the field emergent from the tape should be taken to be rather stronger. In situations where the head is not in contact with the tape, the field should be taken as weaker.
By making H0 very small, a very large sensitivity can be obtained and very weak fields (such as the Earth's magnetic field) can be measured provided that they are not superimposed on another stronger field. At very small values of H0 the anisotropy field HK of the strip is not negligible (it is about 102 A/m) and the sensitivity is no longer proportional to H02 (eq. 4).
Finally, there is the measuring current to be considered. This is limited by warming-up effects and possibly by diffusion due to electromigration (atoms being 'pulled along' by the current-carrying electrons). With a strip of dimensions , a current of up to about 100 mA is possible in practice (current density ; in strips that have been protected against corrosion a value of about can be obtained). The maximum output voltage is then about 3 mV, which is much more than can be obtained from a conventional inductive head at this track width and at low tape speeds (0.03 mV).
The dynamic behaviour is no less important than the static behaviour that we have been discussing so far. By dynamic behaviour we mean the way in which the response function depends on the frequency of the signals from the tape.
The rate at which the magnetization in the strip (and hence its resistance) can follow changes in Hy is very great and has very little effect on the frequency characteristic: this is determined by spatial factors. It is therefore better in the first instance to look at the wavelength characteristic.
For sinusoidally magnetized tapes, there is an exponential decrease in Hy in the y-direction, which depends on . Sine-wave signals recorded on the tape at equal amplitudes but different frequencies give spatial distributions of Hy that differ not only in the x-direction but also in the y-direction. This can be expressed by the equation
where is the amplitude of the field at the surface of the tape (y = 0). If we assume that the change in resistance is proportional to the mean value Hy of the external field over the strip, we can derive the wavelength characteristic as follows:
Here a is the distance from the lower side of the strip to the tape. The exponential decrease in Hy with y imposes a clear upper limit to the value of a.
Theoretical wavelength characteristics for strips with different values of width w are shown in fig. 10. It can be seen that the wavelength at which the curve begins to fail depends on w. This follows obviously from equation (9), since the mean field-strength over the strip increases as w becomes smaller.
Fig. 10. The calculated wavelength characteristic (log-log scale) for conventional magnetoresistive heads (fig. 1) for different widths w. It has been assumed that the amplitude of the field-strength at the surface of the tape is always the same. The sensitivities at the long wavelengths have been adjusted to be equal. The corresponding frequencies are plotted along the upper scale for a tape speed of 4.75 cm/s. The frequency at which the curve begins to fail off increases as w becomes smaller. The dashed line indicates the characteristic for an ideal inductive reading head.
Measured characteristics are shown in fig. 11. In principle, the decrease in sensitivity as a function of decreasing wavelength might be expected to be a disadvantage in read-out with an inductive head. In practice, however, the sensitivity of an MRH is so much larger, even at measuring currents much less than 100 mA, that the effect is not all that important in comparison. Moreover, the characteristic of an MRH of the type shown in fig. 1 has no zero points like those that occur with an inductive head.
Fig. 1l. The measured characteristic for a conventional MRH () and a barber pole of the same width () compared with that of an inductive reading head with a gap of (the curve). The sensitivities have been equalized at the longer wavelengths. (in practice, the sensitivity at a tape speed of 4.75 cm/s of an MRH with an auxiliary field is about 30 dB higher and that of a barber pole is about 27 dB higher.)
When a magnetic tape is read in a reading head there are four different sources of noise: the amplifier, the head itself, the tape and the mechanical contact between the head and the tape. In designing a reading head every attempt is made to make the noise contributions from the amplifier, head and the tape-head contact so small that the total noise is determined principally by the tape. The MRH can almost always meet these requirements because of its superior sensitivity. This is not the case with the inductive head, however, if it is used with a low-noise tape, a very narrow track, a low tape speed or if the head has a small number of turns. In addition it should be borne in mind that some contributions to the noise (such as the amplifier noise) are constant, whereas others depend on factors such as the gain or the measuring current, so that they cannot be compared directly.
The amplifier noise is not very important -good modern amplifiers have an equivalent noise resistance of less than 100 ohms. This contribution is much less important for an MRH than for an inductive head, because the output signal of the MRH is much larger.
The tape noise is a consequence of the fact that the tape is not a continuous magnetic medium, but consists of a 'suspension' of magnetic particles in a polymeric carrier. The tape noise should therefore be considered as a given quantity, the same way as the signal to be read.
The head noise is mainly resistance noise arising from the ohmic resistance of the MRH. Barkhausen noise is also present sometimes, especially when the strip contains more than one magnetic domain; this form of noise can easily be avoided by using a longitudinal auxiliary field of several hundred A/m. In the barberpole head this field is already present for other reasons.
It might be thought that an MRH with a higher resistance would produce more head noise. This is indeed true in an absolute sense, but not relatively. Resistance noise is proportional to the square root of the resistance. The measured signal, however, is derived from the relative change in the resistance, and is therefore proportional to R, so that the signal-to-noise ratio increases as R increases.
An important additional contribution is the 'temperature noise'. The resistance of the MRH does not only change because of the effect of a magnetic field, it also changes because of variations in temperature. These variations can be relatively large: 0.25 per °C. Because of irregularities in the surface roughness of the tape there are variations in the heat generated at the contact surface between the MRH and the moving tape, and there are also variations in the dissipation of the heat produced by the measuring current in the MRH. These effects can lead to temperature variations that affect the resistance significantly. It is therefore necessary to ensure that there is good heat dissipation. We use a wafer of silicon as the substrate. This material gives a good compromise between the different requirements demanded of the substrate: it is wear-resistant, a good conductor of heat, non-magnetic and a poor conductor of electricity. Temperature noise mainly contains components at low frequencies.
Finally, we should say something about the measuring current. Since the amplifier noise and the resistance noise are independent of the measuring current and since the shot noise is negligible, it seems desirable to make the measuring current as high as possible. However, this increases the temperature difference between the head and its surroundings, and hence the temperature noise. An MRH is so sensitive, however, that even with relatively insensitive heads () and a track width of , it is possible to use a measuring current of much less than 100 mA without the other noise contributions exceeding the tape noise. The noise performance of an MRH is better than that of an inductive reading head, particularly at narrow track widths and at low tape speeds.
The manufacture of a magnetoresistive head places no very high demands on technology. For thin NiFe films we use compositions such as Ni89Fe11 and for films thicker than we use Ni80Fe2O because of its low magnetostriction. The alloy is applied to the substrate by evaporation, with the use of a thin film of Ti as an adhesion layer, or by sputtering, when an adhesion layer is unnecessary. During the subsequent treatment the temperature should remain below about 400°C, principally because the magnetoresistance effect would otherwise become weaker ( becomes smaller). The barber-pole design has in fact few complications. The oblique stripes are obtained by sputtering a 'sandwich' of molybdenum, (adhesive layer, ), gold (conductor, ) and a second adhesion layer, typically of molybdenum. The exact shape can be obtained by the use of well known photoresist-and-etching methods. In the light of present-day semi-conductor technology, no great difficulties are encountered in mounting the contact leads or in applying a coating of silica to prevent corrosion.
Reading heads for special applications can also be made by the same process. A good example is the "track-sensing" head, which can be used to find out whether the position of a track is asymmetrical with respect to the MRH. The two halves of the barber pole are connected together in opposing sense, and no signal will be produced if the track is symmetrical. Another example is the interference-suppressor head, which consists of two detectors connected in opposition and mounted close together. The field from the tape affects only one of the two detectors, so that normally only one signal is obtained, but interfering magnetic signals from the surroundings will produce signals that will very nearly cancel. A three-track head in which this principle is applied is shown in fig. 12.
Fig. 12. Ferromagnetic strips and connecting leads forming part of a three-track MRH with barber poles mounted on a substrate. The light-coloured stripes are the conductors. When plates of wear-resistant material have been applied to both sides, the lower part of the unit is ground away. The resistance of the horizontal conductor is continuously measured during the grinding to give an indication of the rate of progress. A fourth strip located rather higher up does not respond to the field from the tape but compensates for the interference signals detected by the central reading strip.
Finally, we ought to mention that it is possible to make reading heads that are sensitive at very short wavelengths, without this causing saturation at the longer wavelengths. This is done by placing a plate of soft magnetic material such as Permalloy on either side of the strip and a short distance away from it. The plates shield the strip from contributions from parts of the tape that are further away, and they also conduct the magnetic flux; see fig. 13a. These heads are of course developed for weak fields.
When a MRH is used it is possible to work with narrow tracks (high track density), and with an MRH of the type just described it appears that information recorded at a density of over 1.5 107 bits/cm2 can be read6. An MRH strip can readily be combined with an inductive writing head of the thin-film type). In such a writing head the tape runs along two soft magnetic plates, which function as shields for the MRH strip (fig. 13b).
Fig. 13. a) An MRH that is sensitive to very short wavelengths yet does not saturate at the longer wavelengths can be made by shielding the strip (black) with a plate P of soft magnetic material. The sections of the tape beyond the chain-dotted lines do not contribute to the flux in the strip. b) If a coil C is included in a similar configuration then a combination of an MRH of the type shown in (a) and a thin-film type of inductive head is obtained.
To summarize and conclude, we believe we have made it clear that the use of the magnetoresistance effect in a ferromagnetic metal as a method of measuring magnetic fields with a high spatial resolution could become extremely important for applications related to magnetic recording. In this article we have only described read-out from magnetic tape, and we have compared the MRH with a conventional alternative, the inductive head. If we consider read-out from magnetic-bubble memories, however, the only acceptable possibility at the moment is read-out by means of the magnetoresistive anisotropy.