In the earlier lectures, we have discussed briefly about the writing to and reading the data from the disk medium. As the writing and reading processes are the core parts of the magnetic recording, we shall discuss for a quantitative understanding of the factors involved for the above processes so that the general design as well as the recent development can be understood.
Figure 29.1: Schematic drawing of the head field [1,2].
Field from the head:
As we know well that a sufficient writingfield(more than the coercivity of the medium) mustbe provided to the diskmediumto write magnetictransitions. Otherwise, the applied field close to or just below the coercivity reverse only half the magnetization due to the non-square nature of the hysteresis loops. Hence, in general, the applied field of 2 to 3 times the coercivity of the materials should be applied to reverse all the magnetization.
Note that a factor of 2.5 is commonly used in the recording process. Figure 29.1 displays the stray fields near the gap of the inductive head. While the direction of the arrow indicates the direction of the magnetic field, its length indicates the magnitude of the field strength. The arrow directions are horizontal at the center of the gap above the gap center.
However, the direction of the arrow changes at various angles with respect to the horizontal axis when we move in both directions away from the center. A careful observation of the picture suggests that the contour is circle. According to the Ampereβs
law, the magnetic field surrounding a straight conductor carrying current I is radially distributed, and the field is given as I/(2ο°r), where r is the radius of the circular path.
Following the above view and considering the head gap is small and the contour is circle, the field at a distance r can be determined as nI/ο°r A/m. Here, n is the number of coil turns and ο°r represents the integration of field over the semicircle.
For longitudinal magnetic recording, the interest is to calculate the field along the horizontal direction at a particular gap between the head and medium. The general equations for the x and y fields of a ring head of infinite poles derived by Karlqvist [1] are turn out to be,
π»π₯ π₯, π¦ =π»π
π tanβ1 π₯ + π/2
π¦ β tanβ1 π₯ β π/2 π¦
π»π¦ π₯, π¦ =βπ»π
2π ππ π₯ +π 2
2+ π¦2
π₯ βπ 2
2+ π¦2
(29.1)
where g is the head gap, Hg is the magnetic field strength inside the head gap due to the current in the coil. The complete derivation of the above equation by using various assumptions can be found in module 3 [1].The eqn.(29.1) has to be visualized more closely, as it plays a major role in the longitudinal magnetic recording.The difference of two arctangent functions is nothing more than the angle ο± subtended by the gap at a given location of (x, y), where the value of field is required, which is illustrated in Figure 29.2.
Figure 29.2: Karlqvist head field in terms of an angle.
(x,y)
ο±1
ο±2
ο± x y
g/2 g/2
Hence, the x-field equation in the eqn.(29.1) can be written as π»π₯ π₯, π¦ =π»π
π π (29.2)
where π1 = tanβ1 π₯+π/2π¦ and π2 = tanβ1 π₯βπ/2π¦ and π = π1β π2.
Figure 29.3: Normalized x and y components of the head field.
Using the above equation, the variations of Hx and Hy can be displayed, as shown in Figure 29.3 along the x and y axes. The value of Hx is the maximum when the angle ο± is the largest.The normalized values, the x-axis values are divided by the gap g and the field along x and y axes are divided by Hg, are displayed to make the universal plot, independent of g and Hg values. It is clearly seen from the figure that the field exhibits maximum value along the vertical axis and also shown growing larger with decreasing the values of y. Similar the field along y direction is zero near the gap center, but shows peaks at some distance from the center.
The important understanding from the above equation is how the horizontal component of the head field changes with increasing the distance away from the head tip. The relation for the variation of head field with increasing y can be calculated by setting x value as zero in eqn.(29.1). Hence, the eqn.(29.1) turns out to be,
π»π₯ 0, π¦ =2π»π
π tanβ1 π 2π¦ π»π¦ 0, π¦ = 0
(29.3)
It is clear from the figure 29.4 that the horizontal component of the x field at a given y value decreases sharply with decreasing the head gap. If the head gap tends to zero, then there is no x field available for writing the medium. Note that the assumption of head gap zero is the single pole head used for perpendicular magnetic recording.
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Relative Field Strength (H x/H g)
Spacing / head gap (y/g)
g = 1.00 g = 0.50 g = 0.25 g = 0.10
Figure 29.4: Variation of peak head field as a function of the ratio between the spacing and head gap (with different head gap values).
Problem on Head field Calculations:
1. Calculate the current required to produce a head gap field suitable to write a medium having the average coercivity of 1600 Oe. The head gap is 400 nm and the flying height is 100 nm. Assume that the medium thickness is small compared to the flying height.
Solution:
A field Hx is equal to 2.5 times of the coercivity of the medium is required for proper writing. Hence Hx = 1600 ο΄ 2.5 = 4000 Oe. Now, y/g = 100/400 = 0.25. For the value of y/g=0.25, the Hx/Hg is given as 0.7. Therefore, the gap field is Hg=Hx/0.7 ο¨ 4000 /0.7 ο¨ 5700 Oe (454 kA/m).
The magnetomotive force required to produce the head field is given as Hgο΄ g = 454 kA/m ο΄ 400e-9 ο¨182 mA for a single turn head. In case of 20 turn head, the current requires is around 9mA.
References:
[1]. R.M. White, Introduction to Magnetic Recording, IEEE Press, New York, 1985, Chapter. 3.3.
[2]. K.G. Ashar, Magnetic disk drive technology: Heads, Media, Channel, Interfaces, and Intergration, IEEE Press, New York, 1997.