I345 IEEE TRANSACTIONS ON MAGNETICS, VOL. 30, NO. 4, JULY 1994

Effect of Magnetic Saturation on Reproducing Characteristics of Magnetoresis tive Heads

Hirotsugu Fukuoka, Member, IEEE, Hiroshi Fukui, Member, IEEE, Makoto Aihara, Member, IEEE, Hisashi Takano, and Mikio Suzuki

Abstract-The reproducing characteristics of a magnetore- sistive head were studied. Using a two-dimensional finite ele- ment method, recording density characteristics and peak shift characteristics of the MR head were estimated with a satura- tion effect. Recording density characteristics changed with the magnetic saturation of the MR element with a large remanent magnetization and thickness product of the recording medium, but peak shift was not affected by it. Compared with the gap length dependence of the inductive head, the MR head had a lower D5,, and smaller peak shift than did the inductive head. ,

I. INTRODUCTION HE magnetoresistive (MR) head which has a simple T structure has been studied extensively due to its large

reproducing output at high recording density. Potter [ 13 extended the inductive head model to the MR head by adopting an imaginary coil surrounding the MR element. O’Connor et al. [2] discussed the effect of its saturation by introducing a nonlinear effect into the transmission line model. Tsang [3] discussed the saturation effect on asym- metry and amplitude of the reproducing output of the MR head. However, these studies did not consider the repro- ducing waveform or recording density characteristics. Understanding recording density characteristics is essen- tial to estimate the MR head performance. Furthermore, magnetic saturation strongly affects the reproducing wave- form and recording characteristics.

In the study presented here, the magnetic saturation ef- fect on the reproducing waveform of the MR head is dis- cussed using a two-dimensional finite element method. Introduction of superposition of the magnetization tran- sition in the recording medium makes it possible to study recording density characteristics and peak shift.

11. CALCULATION The MR head-medium geometry used in the study is

shown in Fig. 1. The MR head consists of an MR ele- ment, an adjacent shunt conductor and a pair of magnetic shields. Resistivities of the MR element and shunt con- ductor are assumed to be the same; i.e. current density of the MR element is equal to that of the shunt conductor. Magnetization of the medium is assumed to have only a

Manuscript received April 22, 1992; revised June 1, 1993. The authors are with Hitatchi Research Laboratory, Hitatchi Ltd.,

IEEE Log Number 9215619 7-1-1 Omika, Hitatchi, Ibaraki 319-12, Japan.

I - t x - Recording medium

Fig. 1. Schematic view of MR head.

longitudinal component, and its transition distribution is assumed to be a function of arctangent.

In the reproducing process, magnetization of the MR head is calculated using a two-dimensional finite element method. The basic equation to calculate its magnetization is given in terms of the vector potential A as follows:

(1)

where J is the current density vector, M is the magneti- zation vector, and uo is the reciprocal of the permeability in a vacuum. In this model, the vector potential and the current density vector have only Z-components. The mag- netization vector and the magnetic field vector are in the X-Y plane. A demagnetization field can be taken into ac- count, however no exchange interaction is considered. Output of the MR head is obtained through M, the mag- netization of the MR element calculated by the above basic equation. The recording medium moves in the X direc- tion, and output waveforms are obtained through the pro- cedure described later.

Non-linearity of MR element characteristics is taken into account to consider the saturation effect by assuming the magnetization characteristics of the MR element shown in Fig. 2. M y is the Y-component of the magneti- zation induced by the applied magnetic field H, and M, is magnitude of the saturation magnetization. M,, the X-component of the magnetization is negligible due to the small thickness of the MR element, which has a large de- magnetization field.

Resistivity of the MR element is represented as fol- lows:

rot(uo * rotA) - rotM = J

p = po + A p . COS* 0 (2)

0018-9464/94$04.00 0 1994 IEEE

1346 IEEE TRANSACTIONS ON MAGNETICS, VOL. 30, NO. 4, JULY 1994

0.6

0.4

0.2

0.0 0 5 10 15 20 25

woe) Fig. 2. Magnetization characteristics of MR element.

where 8 is the angle of magnetization rotation in the MR element. Fig. 2 shows My and M, which define 8 as fol- lows:

e = sin-' ( M ~ / M $ ) . (3) Then, reproducing output of the MR head is

V = A p . (MY/M,)* * TW * J * /3 - Vo. (4)

where (MY/M,)' is the averaged mean square value of My/M, in the MR element, which is induced by the mag- netic field of the recording medium and the bias field of the shunt conductor. Tw is track width and J is current density in an MR element. /3 is an output factor of the MR element, which is reduced by the shunt conductor, and is 0.5 here. Vo is output voltage of the MR element at the driving point with the bias field and without the medium that has magnetization transitions.

Magnetization distribution of an isolated transition in the medium is assumed to be a function of arctangent as follows:

M,(Isolated) = 2 / ~ M, arctan (xla), (5 )

where M, is the magnitude of the magnetization of the recording medium; a is a parameter representing magne- tization transition width, and is assumed to be 0.16 pm here. a is estimated by Talke-Tseng formula [4]. The es- timated medium is that M, is 800 emukc, thickness is 40 nm, corecivity is 1200 Oe and squareness is 0.85.

For inductive heads, superposition of isolated wave- forms is often used to predict reproducing output at high recording density. However, this conventional method is not applicable to the MR head due to its large non-lin- earity. Then we adopt superposition of magnetization in the recording medium to obtain the reproducing output at high recording density. At high recording density, mag- netization is assumed to follow a superposition of the iso- lated magnetization transition as follows:

m

ML = 2 / ~ * M, * C (-1)" n = -oa

- arctan [ { x - (2n + 1)h/4}/a] m

(-1)'exp ( - 2 ~ ( 2 n - l)a/h) = 4/1r - M, *

n = 1 2n - 1

cos (21(2n - l ) x / h ) , (6)

- Experimental 0 Analytical

Superposition 0 0.8 of the isolated U waveform

(p 0.4

0.2

z 0.0

.-

0 20 40 60 80 D(kFRP1)

(a) Recording density chaacterlsitics

c 3 1.0 Q c

0.5 U .- 8

0.0

z -0.5 -10 -5 0 5 10

X ( W )

isolated waveform

(b) Fig. 3 . Comparison of experimental and calculated results. (a) Recording density characteristics. (b) Isolated waveform. MR element thickness is 35 nm, height is 7 pm, gap length is 0.9 pm, head-to-medium spacing is 0.2 pm, Br . 6 is 400 G . pm.

where h / 2 is the distance of the magnetization transitions. Reproducing characteristics of the MR head obtained

in experiments are shown in Fig. 3. The recording density characteristics and isolated waveform show good agree- ment with calculated results. The dotted line represents recording density characteristics obtained by superposi- tion of the isolated waveform. Disagreement with exper- imental results is caused by the large nonlinearity of the MR head waveform.

111. ANALYSIS A. Recording Density Characteristics of MR Head

In the calculation to obtain reproducing output of the MR head, the bias field should be determined. The bias field is applied by the bias current through the shunt con- ductor. Bias current density is determined to balance the output amplitude for both polarities. Current density of the shunt conductor at its optimum driving point is shown in Fig. 4. Decreased MR element height is accompanied by increased optimum bias current density, because the bias field is required to overcome the demagnetization fields of the MR element. the optimum bias current den- sity does not depend on the thickness of the MR element. This is because decreased thickness of the MR element is accompanied by a decrease in the demagnetization field, and consequently a decrease of the required bias field. Here, the thickness of the shunt conductor changes with the thickness of the MR element to keep resistance of the shunt conductor equal to that of the MR element, so the

FUKUOKA, et al.: MAGNETORESISTIVE HEADS

MRE thickness

/. .' .., .. ,/. 10 ,. : ..2

T-3Onm

1347

MRE thickness 0 Tun=lOnm A TuR-15nm 0 TuR-30nm

0.0 2.0 4.0 6.0

MR height (pm) Fig. 4. Current density of shunt conductor which gives the optimum bias

field for a 0.3 pm gap length.

bias field per the bias current density decreases. Conse- quently the required bias current density does not depend on the thickness of the MR element. The following is dis- cussed under this condition.

Amplitude of the reproduced isolated waveform as a function of Br - 6 product of the recording medium is shown in Fig. 5. The amplitude increases with the in- crease in Br * 6 product of the medium and saturates at Br * 6 > 100 G - pm, where Br is remanent magnetiza- tion of the medium and 6 is medium thickness. The Br - 6 product represents the magnetic flux ability of the re- cording medium. Output saturation is due to magnetic sat- uration in the MR element. With an increase in the mag- netic field from the recording medium, the magnetization rotation in the MR element is close to go", and output of the element becomes a maximum at 90", that is M,,/M, = 1 in (4). Then, output is close to the maximum with in- creased magnetization saturation. Saturation is more se- vere for thinner MR elements, because they have a smaller demagnetization field, and are easily saturated.

Magnetization distributions in the MR element with and without the magnetic field from the recording medium are show in Fig. 6. The values of y, plotted on the x-axis, is the distance from the air bearing surface, and y = 0 is at the air bearing surface of the head slider. At the edges of the MR element, My induced by the bias field is small due to the large demagnetization field. When the magnetiza- tion transition of the medium moves past the MR head, My of the element increases and magnetization saturation occurs in it. The saturation area spreads due to the in- crease in the magnetic field from the recording medium of a larger Br - 6 product. The magnetic field decays promptly with increasing distance from the recording me- dium, and magnetization rotation decreases in the MR element with distance from the medium. At the air bear- ing surface My is small due to the large demagnetization field.

In Fig. 7, recording density characteristics of a satu- rated MR head with medium of Br - 6 = 400 G - pm and an unsaturated MR head with Br 6 = 100 G * pm are compared. In this calculation, we assumed these media have same magnetization transition width, because of the estimation of effect of magnetic saturation of the MR head on recording density characteristics. At high recording density, reproducing output is proportional to Br - 6, but

h N s 20 I

Br-ti(G*p.m) Fig. 5. Amplitude of isolated waveform as a function of Br . 6 product of the recording medium. MR element height is 3 pm, gap length is 0.3 pm, and spacing is 0.1 pm.

Fig. 6 is 15

I e

' 0.4

1 .o cn 0.8 % 0.6 ' 0.4

0.2

0.0

z

0 I 2 3

Y(PW . Magnetization distribution for MR element. MR element nm, height is 3 pm, gap length is 0 .3 pm, and spacing is

0.2

0.0 0 I 2 3

Y(PW . Magnetization distribution for MR element. MR element nm, height is 3 pm, gap length is 0 .3 pm, and spacing is

thickness 0.1 pm.

0 20 40 60 80 100

D (kFRPI) Fig. 7 . Amplitude of reproducing output as a function of recording den- sity. MR element thickness is 15 nm, height is 2 p , gap length is 0 .3 pm, and spacing is 0.1 pm.

at low recording density reproducing output for Br 6 = 400 G pm is only about twice as large as that for Br *

6 = 100 G * pm due to the saturation effect. Thus, D50 increases for large Br - 6 product. D50 is defined as the linear density at which the output falls 50%. D50 for various MR element heights and thicknesses are

shown in Fig. 8. For Br * 6 = 400 G - pm, D50 increases with decreasing MR element height and thickness. A thin- ner MR element has higher saturation due to the smaller demagnetization field. And for a smaller height MR ele- ment, the saturation effect is remarkable, because the ra- tio of the saturation area to the total element height in- creases. On the other hand, D50 is independent of MR element thickness and height for Br * 6 = 100 G * pm, because the head is not saturated. Thus the true perfor- mance MR heads is represented by D50 for the unsaturated condition, and the increase of D50 represents the extent of saturation of the MR element.

IEEE TRANSACTIONS ON MAGNETICS, VOL. 30, NO. 4, JULY 1994 1348

A MRE thickness I

0.0 2.0 4.0 6.0

MR height (pm) Fig. 8. Saturation effect on &. Gap length is 0.3 pm and spacing is

0.1 pm.

B. Peak Shijt of MR Head Peak shift of the reproducing waveform of dibit pat-

terns is studied next. Magnetization of medium is as- sumed to follow the superposition of two arctangent dis- tributions as described previously. Reproducing waveforms for the dibit pattern are shown in Fig. 9. Waveforms differ in their shape for different Br - 6 prod- ucts. The waveform shape for Br - 6 = 400 G * pm is broader than that for Br - 6 = 100 G - pm, but peak intervals of the reproducing waveforms are identical. Peak shift is caused by interference of the magnetic field from recording bits in the medium, and output saturation is caused by the magnetization saturation in the MR ele- ment, which is exposed to this field. Consequently, peak shift is independent of MR element saturation.

C. Gap Length Dependency of MR Head The MR head is compared with an inductive head with

respect to D50 and peak shift for various gap lengths. For the MR head, D50 depends on the saturation degree of the MR element as mentioned in the previous section. In this section, reproduction of the MR head is calculated under an unsaturated condition. The calculated D50 for the un- saturated condition shown in Fig. 8 is independent of MR element height and thickness. The inductive head com- pared here has an infinite pole tip and large throat height. Then, reproducing characteristics of the inductive head depend only on gap length.

Gap length dependence of D5,, is shown in Fig. 10. The MR gap length is the spacing between the two shields. Gap length dependency of D50 of the MR head is smaller than that of the inductive head. Previously MR heads were shown to read like an inductive head with a gap length equal to 0.6 times the gap length of the MR head [5]. This result was for a 1 .O pm gap length, a relatively large gap length, and the same tendency appears for the present re- sult. In large gap length region, it is understood that the MR element and two shields form two gaps, and the gap length of the inductive head is 0.5 times that of the MR head.

Peak shift of the dibit pattern, which has a bit length of 0.45 pm is shown in Fig. 11. The abscissa is gap length, the same as in Fig. 10, and peak shift is defined in the usual manner as the normalized shift in the detected po- sition of reproduced bits with respect to the positions

n

"E 2 10

s 5 ? o

s 5 -5

s 2 -10

W

Q \

0 - -3 -2 -1 0 1 2 3 x(clm)

Fig. 9. Waveforms of dibit pattern. MR element thickness is 15 rim, height is 3 pm, gap length is 0.3 pm, and spacing is 0.1 pm.

40 MR head 30 .

0.0 0.2 0.4 0.6 0.8 1.0

G(PW 10. Dso of inductive and MR heads.

o.4 inductive head

0.2

0.1

0.0 ... 0.0 0.2 0.4 0.6 0.8 1.0

G(pm) Fig. 1 1 . Peak shift of inductive and MR heads. Bit length is 0.45 pm.

where they were written. However D50 of the inductive head is larger than that of the MR head. But peak shift of the MR head is smaller and the gap length dependency is also small. D50 and peak shift are both indices of the re- producing ability at high recording density, however, their relationships with gap length differ. This is caused by the difference in the reproducing principle and the reproduced waveforms of the two heads.

JV. CONCLUSION Reproducing characteristics of the MR head, which is

a promising device for high density magnetic recording, were studied. The relationship between the reproducing characteristics and head configuration was established.

The shape of the MR element strongly affected its de- magnetization field. With smaller demagnetization field, the element was easily saturated, and reproducing output was larger. With larger saturation, higher D50 was ob- tained.

Gap length dependency of D50 and peakshift of the MR

FUKUOKA, et al . : MAGNETORESISTIVE HEADS 1349

head differ that of the inductive head. In some condition, D50 of MR head is smaller than Ds0 of inductive head, but the peakshift of MR head is smaller than the peakshift of inductive head.

REFERENCES

R. I. Potter, “Digital magnetic recording of theory,” IEEE Trans. Magn., vol. MAG-10, pp. 502-508, 1974. D. J. O’Connor, F. B. Shelledy, and D. E. Heim, “Mathematical model of a magnetoresistive read head for a magnetic tape drive,” IEEE Trans. Magn., vol. MAG-21, pp. 1560-1562, 1985. C. Tsang, “A theoretical study of the signal response of a shielded MR sensor,” IEEE Trans. Magn., vol. MAG-26, pp. 3016-3021. 1990. F. E. Talke and R. C. Tseng, “Effect of submicrometer transducer spacing on the readback signal in saturation recording,” IBM J . Res. Dev., vol. 19, pp. 591-596, 1975. D. E. Heim, “The sensitivity function for shielded magnetoresistive heads by conformal mapping,” IEEE Trans. Magn., vol. MAG-19, pp. 1620-1622, 1983.

Hirotsugu Fukuoka (M’92) was born in Japan in 1959. He received the B.S. degree from Science University of Tokyo, Japan, in 1982, and M.S. degree in Material Physics from Osaka University, Japan in 1984.

In 1984 he joined Hitachi Research Laboratory, Hitachi Ltd., where he has been working on research and development on thin film magnetic heads.

He is a member of the Magnetics Society of Japan, and the Institute of Electronics, Information and Communication Engineers.

Hiroshi Fukui (M’89) was born in Japan in 1944. He received the B.E. and M.S. degrees in electronic engineering from Hokkaido University, Ja-

pan in 1966 and 1968, respectively, and he received Ph.D. in electrical engineering from Tokyo University, Japan in 1990.

In 1968 he joined Hitachi Research Laboratory, Hitachi Ltd. He has mainly been engaged in research on characteristic evaluation of power semiconductor devices and modeling. Presently, he is engaged in research on thin film magnetic heads.

Dr. Fukui is a member of IEEE Magnetics Society, the Magnetics So- ciety of Japan, the Institute of Electrical Engineers of Japan, and the In- stitute of Electronics, Information and Communication Engineers.

Makoto Aihara (M’79) was born in Japan in 1951. He received M.S. de- gree in information from Tohoku University, Japan in 1978. In 1978 he joined Hitachi Research Laboratory, Hitachi Ltd., to work on the design of sensing device.

From 1982 to 1983 he was a Visiting Research Associate at the Depart- ment of Electrical Engineering and Science, University of Pennsylvania. Since 1984 he has been engaged in research and development of thin film magnetic heads.

He is presently a member of IEEE Magnetics Society, the Magnetics Society of Japan, and the Japan Society of Applied Physics.

Hisashi Takano was born in Japan in 1960. He received the B.E. and M.E. degrees from Tohoku University, Japan in 1983 and 1985, respectively.

In 1985 he joined Central Research Laboratory, Hitachi Ltd., where he has been working on research and development of thin film magnetic heads. Now he is a visiting researcher in the Center for Micromagnetics and In- formation Technologies Development of Electrical Eng., University of Minnesota.

He is a member of the Magnetics Society of Japan.

Mikio Suzuki was born in Japan in 1961. He received the B.E. and M.E. degrees from Tohoku University, Japan in 1984 and 1986, respectively.

In 1986 he joined Central Research Laboratory, Hitachi Ltd., where he has been working on research of read/write data channels of magnetic re- cording system.

He is a member of the Magnetics Society of Japan.