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Micromagnetic simulation of FeCo write head in perpendicular recording hard disk drives
RARE METALS Vol . 2 5 , Spec. Issue , Oct 2006, p .SO2
Micromagnetic simulation of FeCo write head in perpendicular recording hard disk drives QUAN Liang and WEI Dan Lab of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China (Received 2006-06-27)
Abstract: The single-pole tip (SIT) heads made of the high saturation FeCo ferromagnetic metals are crucial for the actualization of ultrahigh density perpendicular recording. The effective head field distribution in the medium is of key importance for the design of the SIT head, which would be analyzed by micromagnetic simulations in this work. Two 3D micromagnetic models of the SIT head were established to select a more appropriate method of modeling, with a magnetostatic image effect or a real soft magnetic material to model the image of the SPT head in soft under layer (SUL) . The results from these two designs were tested and compared to the ideal head field calculated by the Jacobi finite element method (FEM) ; and the design with the real soft magnetic material as image was proved suitable for simulating the ultrahigh density perpendicular recording write head.
Key words : SIT head ; perpendicular recording; micromagnetic simulation ; image
1.
Introduction
The longitudinal recording areal density would be limited around 100 Gb/in* by the thermal stability of the magnetizations in magnetic grains [ 1 ] . To overcome the insurmountable limitations of longitudinal recording, including transition jitters and superparamagnetic effects, it is natural to develop the perpendicular recording method, especially when the areal density for hard disk drive is required to attain 200 Gb/in' or above [ 21 . At present, perpendicular magnetic recording (PMR) is anticipated to push the recording density toward terabit per square inch, as the central advantage of PMR is the writability of large head field, sharp head field gradient and extremely high recording density. On the other hand, it was observed that the geometric and magnetic properties of a write head can greatly affect the write performance[ 31 . In this paper, we have developed two Corresponding author : Es.EI Dan
nanoscale perpendicular write head models with a maximum size of Id nm in each dimension, and the highest B , ( saturated magnetic flux density) FeCo soft magnetic materials to achieve the desired writing performance. Two micromagnetic models were developed to analyze the domain pattern and head field distribution with an SUL beneath the recording magnetic layer included. A simple Jacobi FEM model wa6 also set up for comparison. The micromagnetic modeling of the write head was briefly introduced, and the domain patterns and head field distribution of the simulation results were presented by the two designs.
2.
Micromagnetic modeling
The design generally includes the following components: a main pole, a return pole, a write shield, as shown in Fig. 1 , the circuits of driving currents are not included. All the magnetic components of the write head consist of soft magnetic material of FeCo
E-mail : weidan 63tsinghua .edu .cn
Quan
L . et a1 , , Micromagnetic simulation of FeCo write head in perpendicular recording drives
503
Main pole
Return pctlc
Writing shield
Fig. 1.
Schematic figure of the simulated write head.
with high B , ( set as 2 . 4 T in this paper) , and the head material is assumed to be uniform and to have a very small anisotropy due to crystalline anisotropic stress. The exchange length
1 =
&:
- is set as 120 nm (assuming the ex-
erg-cm-’, change constant A * = 1 - 2 x the anisotropy energy constant K1 on the order of lo4 erg*cm-3). The entire write head is discretized into small cubic elements with the size of 10 nm x 10 nm x 10 nm each, and every element represents a single domain magnetic grain. The number of total elements can amount to as many as 16-106. To analyze and assess the writing performance, we utilized the 3D micromagnetic simulation model of soft magnetic materials and devices, where the Landau-Lifshitz-Gilbert (LLG) equation in Eq . ( 1) were utilized to predict the movements of magnetic mpents.
where the gyromagnetic constant Y equals 1 7 . 6 rad/Oe/ps, and a is the dimensionless Landau damping constant. The simulating process would be completed when the maximum deviating angle of an element’s magnetization from
the local effective magnetic field drops below the threshold value given beforehand, so the magnetization distribution is considered stable and the process ends. The total free energy of the ferromagnetic system can be calculated with Eq . (2) , including different energy items listed below.
E ( I fi
1)
Eext=
-MsSi(;)*Hexp(;)
= Eo + E,,, +,E,
E , = Z i ( R i ’ ( ; )x
+ E,, + Em
(2)
(3)
(4)
relevant to the magnetic properties, four different energy items were summed up: the Zeeman energy E,,, due to the external magnetic field; the anisotropy energy E , from crystalline anisotropy field; the exchange energy E,, from exchange field among all clusters; the magnetostatic interaction energy E m from demagnetizing field among all clusters. The effective magnetic field H,( ;> in the ith cluster was calculated by the partial differentiation of the sum of total
RARE METALS , Vol. 2 5 , Spec. Issue , Oct 2006
504
80
80
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. 5 : t t I I I I t f : 2,
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Quan L .et al . , Micromagnetic simulation of FeCo write head in perpendicular recording drives
.
505
nm, as well as its image in the SUL . The drive field flows downward through the main pole and upward through the return pole, as labeled by the + / - signs inFig.3. In the first model (Fig. 3 ( a ) ) , the image in SUL is modeled by additional terms in the demagnetizing matrices, and the periodic boundary condition is applied only on z-direction. In the second model in Fig. 3( b ) , the image in SUL is modeIed by introducing the mirror main pole and the return pole of real FeCo materials, and the periodic conditions are applied in both y- and z-directions. Also in the first model (Fig. 3 ( a ) ) , the domain pattern in the main pole is split into two halves, and this is due to the giant demagnetizing field contributed by the magnetic poles at the upper edge of the main pole, which drives the moments ( y < 150 nm) reverse to the drive field. Therefore, the anti-parallel driving fields and demagnetizing fields split the main pole' s domain into two halves. There are no periodic boundary conditions in the y -directions ; therefore the edge magnetic moments in the return pole all are parallel to the surface by the large demagnetizing fields.
the correctness of the simulation[7-81 The following two sections respectively analyze the different results of the two micromagnetic models of SPT heads. In the Table 1, the basic magnetic and geometric parameters are presented. Table 1. Magnetic and geometric parameters * B,I KI L,l L,l L,l Wl DI 61 G,I tkt-1 T (ergicm3) nm nm nm nm nm nm nm nm 2.4 5ooo 12010065050 7 6 80 7 * B,: saturation magnetic flux density; K1: anisotropy energy constant; 1 , : exchange length; L,: main pole length; La: return length; W : main pole width; d : head medium spacing; G,: gap length; 6 : medium thickness; t inler : intermediate layer thickness
3.1. Domain pattern analysis Two micromagnetic models were set up with or without periodic boundary conditions along y-axis, as shown in Fig. 3. The SUL beneath the medium is introduced to achieve higher write field. The image has to be set in the SUL to ensure the surface of the SUL has a constant magnetostatic potential. The drive field from the coil is modeled by introducing magnetic edge poles 0 = B , at the top surface y = 250
400 ttttttttttttt
__..........
-4001 200
s
. 5 0 -200
3
"
0
500
+c+++t++s
200
o
-200
1000
xlnm
xlnrn
Fig.3. Domain patterns in the y-x cross-section (upper) and the H,field distributions at the center plane y = 0 of the medium (lower) : (a) fwst model ; (b) second model.
506
RARE METALS, Vol. 2 5 , Spec. Issue, Oct 2006
Contrarily, in the second model (Fig. 3 ( b ) ) , the periodic conditions applied in y direction eliminate the edge poles and the comesponding demagnetizing fields ; therefore, all the magnetizations in the main pole are well controlled by the driving field into one unified direction. It could be seen that the magnetic moments at edges y = + 250 nm and y = - 250 nm edges are really continuously distributed. This design can erase the large stray field yielded by the domain splitting in Fig. 3 ( a ) ; thus the SIT head field is well distributed in the medium (lowest part in Fig.3).
3.2. Head field distribution analysis Before presenting the result of micromagnetic simulation, the magnetic field distribution found by the Jacobi FEM method is presented in Fig.4. In the Jacobi method, the main pole’ s magneuic potential is fixed as + 1 while the return pole’s magnetic potential is set to be zero. The magnetic field distribution is found by
Fig. 5 .
solving a laplace equation of the magnetic potential in the space out of the soft magnetic materials. The initial magnetic potential of each outside site is randomly given, and the potential at a site is iterated by the average of the neighboring sites ’ potential (Ref. [ 61 ) . After a total I
iteration number r = - p N 2 ,
2
an accuracy of
lo-’ could be reached, where N is the total number of clusters. The field distribution found by the Jacobi method is close to ideal outcome. In Fig. 4(a ) , the protuberant part of the field distribution corresponds to the main pole position, the white part in Fig.4(b). The 3D contour plots of the SPT head field distribution in the central plane ( y = 0 plane in Fig. 3 ) of the magnetic medium is shown in Fig. 5 , which are the results of the two micromagnetic models individually. For the convenience of comparison and analysis, all the field distribution contour plots in following figures are turned up-side-down into the opposite direction.
SPT head field Hy by micromagnetic models : ( a ) f i t model ; ( b) second model.
Quan L . er ul . , Micromagnetic simulation of FeCo write head in perpendicular recording drives
Fig. 5 ( b ) shows the simulation result in the second micromagnetic model. With a driving pole of B , = 2 . 4 T, the peak value of the perpendicular SIT field H, can reach as high as 1 . 7 x 104 Oe, higher than the past results [ 9111. And the unwanted undershoots in the result of the first micromagnetic model are eliminated in Fig. 5 ( b ) , due to the periodic conditions applied on y-direction . In Fig. 6, the down-track profiles of the SPT head field are plotted along the central line ( y = 0 and z = 0) , where the dashed, solid and dotted lines respectively correspond to the first micromagnetic model, the second micromagnetic model and the Jacobi method. It
507
could be seen that the first micromagnetic model could not simulate the SIT head field correctly, where there are extra peaks of the perpendicular head field appeared, which are unwanted in the recording process. The second micromagnetic model has the best result. In Fig. 7 , the cross-track profiles of the SPT head field are plotted along the z direction in the center plane of medium for the three simulation models respectively. In the results of the second micromagnetic model, the dimensions (215.45 nm x 91.32 nm) , with respect to half of the peak field H, = 8685.55 Oe, just coincide with the main pole size ( 180 nm x 60 nm) .
3
s
. 3
-m* w
3
.LL
-4
0
200
400
600
800 1000 12001400
- -2 1 0
x!nm
Fig.6. Down-track Hy field profiles of the fwst micromagnetic model (dashed line), the second micromagnetic model (solid lines) and the Jacobi method (dotted line)
.
4.
Conclusions
A proper micromagnetic model was built up for the analysis of the SPT write head in the perpendicular hard disk drives, where the FeCo soft magnetic metals with a saturation magnetization B , = 2 . 4 T was utilized as the head materials. It is found that, in an SPT head with a 180 nm x 60 nm main pole and a driving magnetic poles o = B , , the maximum perpendicular field 1. 7 T confined within the dimension of 215.45 nm x 91.32 nm could be achieved for the ultrahigh density perpendicular recording. Acknowledgemnets: The author would like to thank Shi Y . for helpful discussion.
100
200
300 zlnm
400
500
6
Fig.7. Cross-track Hy field profiles of the Tmt micromagnetic model (dashed line), the second micromagnetic model (solid lines) and the Jacobi method (dotted line).
References [ 11 Khizroev S. K . , et al . , Recording heads with track width suitable for 100 Gbit/in2 density. IEEE Trans . Magn . , 1999, 35: 2544. [2] Khizroev S. K . , et a l . , MFM quantification of magnetic fields generated by ultra-small single pole perpendicular heads. IEEE Trans . Magn . , 1998, 34: 2030. [ 31 Schare J. , et al . , Design considerations for single-pole-type write heads. IEEE Trans . Magn . , 2003, 39: 1842. [ 41 Hubert A . , and Schtifer R . , Magnetic Domains : The Analysis of Magnetic Microstructure, New York Spring Press, Berlin, Heidelberg, 1998: 154. [ 51 William T. , et al . , Numerical Recipes Example Book [FORTRAN], Second Edition, Cambridge
508 University Press, Britain, 1994: 156. [ 61 Dan Wei, Fundamental of Electromagnetism in Materials ( in Chinese ) , Beijing Science Press, Beijing, 2005: 84. [ 71 Kanai Y . , et a1 . , Numerical analysis of narrowtrack single-pole-type head with side shields for lTb/inZ. Journal of Applied Physics , 2003, 93: 10. [ 81 Kanai Y . , et a1 . , Recording field analysis of narrow-track SPT head with side shield, tapered main pole, and tapered return path for 1Tblin’.
RARE METALS, Vol. 2 5 , Spec. Issue, Oct 2006 IEEE Trans. M a g n . , 2003, 39: 10. [9] Patwari M . , et al . , Unshielded perpendicular recording head for 1 %/in2. IEEE Trans. Magn., 2004, 40: 1. [ 101 Bai D. , et a1 . , Stitched pole-tip design with enhanced head field for perpendicular recording. Journal of Applied Physics, 2003, 93: 10. [ 11] Abelmann L . , et al . , Micromagnetic simulation of an ultrasmall single-pole perpendicular write head. Journal of Applied Physics, 2000, 87: 9 .
Micromagnetic simulation of FeCo write head in perpendicular recording hard disk drives QUAN Liang and WEI Dan Lab of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China (Received 2006-06-27)
Abstract: The single-pole tip (SIT) heads made of the high saturation FeCo ferromagnetic metals are crucial for the actualization of ultrahigh density perpendicular recording. The effective head field distribution in the medium is of key importance for the design of the SIT head, which would be analyzed by micromagnetic simulations in this work. Two 3D micromagnetic models of the SIT head were established to select a more appropriate method of modeling, with a magnetostatic image effect or a real soft magnetic material to model the image of the SPT head in soft under layer (SUL) . The results from these two designs were tested and compared to the ideal head field calculated by the Jacobi finite element method (FEM) ; and the design with the real soft magnetic material as image was proved suitable for simulating the ultrahigh density perpendicular recording write head.
Key words : SIT head ; perpendicular recording; micromagnetic simulation ; image
1.
Introduction
The longitudinal recording areal density would be limited around 100 Gb/in* by the thermal stability of the magnetizations in magnetic grains [ 1 ] . To overcome the insurmountable limitations of longitudinal recording, including transition jitters and superparamagnetic effects, it is natural to develop the perpendicular recording method, especially when the areal density for hard disk drive is required to attain 200 Gb/in' or above [ 21 . At present, perpendicular magnetic recording (PMR) is anticipated to push the recording density toward terabit per square inch, as the central advantage of PMR is the writability of large head field, sharp head field gradient and extremely high recording density. On the other hand, it was observed that the geometric and magnetic properties of a write head can greatly affect the write performance[ 31 . In this paper, we have developed two Corresponding author : Es.EI Dan
nanoscale perpendicular write head models with a maximum size of Id nm in each dimension, and the highest B , ( saturated magnetic flux density) FeCo soft magnetic materials to achieve the desired writing performance. Two micromagnetic models were developed to analyze the domain pattern and head field distribution with an SUL beneath the recording magnetic layer included. A simple Jacobi FEM model wa6 also set up for comparison. The micromagnetic modeling of the write head was briefly introduced, and the domain patterns and head field distribution of the simulation results were presented by the two designs.
2.
Micromagnetic modeling
The design generally includes the following components: a main pole, a return pole, a write shield, as shown in Fig. 1 , the circuits of driving currents are not included. All the magnetic components of the write head consist of soft magnetic material of FeCo
E-mail : weidan 63tsinghua .edu .cn
Quan
L . et a1 , , Micromagnetic simulation of FeCo write head in perpendicular recording drives
503
Main pole
Return pctlc
Writing shield
Fig. 1.
Schematic figure of the simulated write head.
with high B , ( set as 2 . 4 T in this paper) , and the head material is assumed to be uniform and to have a very small anisotropy due to crystalline anisotropic stress. The exchange length
1 =
&:
- is set as 120 nm (assuming the ex-
erg-cm-’, change constant A * = 1 - 2 x the anisotropy energy constant K1 on the order of lo4 erg*cm-3). The entire write head is discretized into small cubic elements with the size of 10 nm x 10 nm x 10 nm each, and every element represents a single domain magnetic grain. The number of total elements can amount to as many as 16-106. To analyze and assess the writing performance, we utilized the 3D micromagnetic simulation model of soft magnetic materials and devices, where the Landau-Lifshitz-Gilbert (LLG) equation in Eq . ( 1) were utilized to predict the movements of magnetic mpents.
where the gyromagnetic constant Y equals 1 7 . 6 rad/Oe/ps, and a is the dimensionless Landau damping constant. The simulating process would be completed when the maximum deviating angle of an element’s magnetization from
the local effective magnetic field drops below the threshold value given beforehand, so the magnetization distribution is considered stable and the process ends. The total free energy of the ferromagnetic system can be calculated with Eq . (2) , including different energy items listed below.
E ( I fi
1)
Eext=
-MsSi(;)*Hexp(;)
= Eo + E,,, +,E,
E , = Z i ( R i ’ ( ; )x
+ E,, + Em
(2)
(3)
(4)
relevant to the magnetic properties, four different energy items were summed up: the Zeeman energy E,,, due to the external magnetic field; the anisotropy energy E , from crystalline anisotropy field; the exchange energy E,, from exchange field among all clusters; the magnetostatic interaction energy E m from demagnetizing field among all clusters. The effective magnetic field H,( ;> in the ith cluster was calculated by the partial differentiation of the sum of total
RARE METALS , Vol. 2 5 , Spec. Issue , Oct 2006
504
80
80
$ 1 2% \j f i \ / I \ \ : .(a) '>I<
. 5 : t t I I I I t f : 2,
t 1 1 1 1 f 1:
it
>
(
0
80
s
~
r
,
r
r
f-
s
l
~
.
s
~
E
s
~
-(el
-
80---t----c-c--t
5
-++-----
40
-
-
4---4---c
-.
>
20
---------
A+------
. E
ao -
'
"
1
.
2
3
1
"
t
'
s
"
t t t t t t~
t t t t t t 1
t t t t t t
1
'
1
f t 1 t t t
t t t t
"
t t t t I t t t '
I
'
t: t: ti
t: t: t: '
-&v7/ /'/ I
f-// / / / / f I 60 -// / / f / f /- / // / / / / /40 -////////20
------+-
0
1
it t eo:t t it t 40:t t :t t 20:t t O G '
-44-----
----.-c---
- tmf
0
///////I
- / /f / / / / / -f,f 1 .r',f I .r'*( 1 /I,(-
Quan L .et al . , Micromagnetic simulation of FeCo write head in perpendicular recording drives
.
505
nm, as well as its image in the SUL . The drive field flows downward through the main pole and upward through the return pole, as labeled by the + / - signs inFig.3. In the first model (Fig. 3 ( a ) ) , the image in SUL is modeled by additional terms in the demagnetizing matrices, and the periodic boundary condition is applied only on z-direction. In the second model in Fig. 3( b ) , the image in SUL is modeIed by introducing the mirror main pole and the return pole of real FeCo materials, and the periodic conditions are applied in both y- and z-directions. Also in the first model (Fig. 3 ( a ) ) , the domain pattern in the main pole is split into two halves, and this is due to the giant demagnetizing field contributed by the magnetic poles at the upper edge of the main pole, which drives the moments ( y < 150 nm) reverse to the drive field. Therefore, the anti-parallel driving fields and demagnetizing fields split the main pole' s domain into two halves. There are no periodic boundary conditions in the y -directions ; therefore the edge magnetic moments in the return pole all are parallel to the surface by the large demagnetizing fields.
the correctness of the simulation[7-81 The following two sections respectively analyze the different results of the two micromagnetic models of SPT heads. In the Table 1, the basic magnetic and geometric parameters are presented. Table 1. Magnetic and geometric parameters * B,I KI L,l L,l L,l Wl DI 61 G,I tkt-1 T (ergicm3) nm nm nm nm nm nm nm nm 2.4 5ooo 12010065050 7 6 80 7 * B,: saturation magnetic flux density; K1: anisotropy energy constant; 1 , : exchange length; L,: main pole length; La: return length; W : main pole width; d : head medium spacing; G,: gap length; 6 : medium thickness; t inler : intermediate layer thickness
3.1. Domain pattern analysis Two micromagnetic models were set up with or without periodic boundary conditions along y-axis, as shown in Fig. 3. The SUL beneath the medium is introduced to achieve higher write field. The image has to be set in the SUL to ensure the surface of the SUL has a constant magnetostatic potential. The drive field from the coil is modeled by introducing magnetic edge poles 0 = B , at the top surface y = 250
400 ttttttttttttt
__..........
-4001 200
s
. 5 0 -200
3
"
0
500
+c+++t++s
200
o
-200
1000
xlnm
xlnrn
Fig.3. Domain patterns in the y-x cross-section (upper) and the H,field distributions at the center plane y = 0 of the medium (lower) : (a) fwst model ; (b) second model.
506
RARE METALS, Vol. 2 5 , Spec. Issue, Oct 2006
Contrarily, in the second model (Fig. 3 ( b ) ) , the periodic conditions applied in y direction eliminate the edge poles and the comesponding demagnetizing fields ; therefore, all the magnetizations in the main pole are well controlled by the driving field into one unified direction. It could be seen that the magnetic moments at edges y = + 250 nm and y = - 250 nm edges are really continuously distributed. This design can erase the large stray field yielded by the domain splitting in Fig. 3 ( a ) ; thus the SIT head field is well distributed in the medium (lowest part in Fig.3).
3.2. Head field distribution analysis Before presenting the result of micromagnetic simulation, the magnetic field distribution found by the Jacobi FEM method is presented in Fig.4. In the Jacobi method, the main pole’ s magneuic potential is fixed as + 1 while the return pole’s magnetic potential is set to be zero. The magnetic field distribution is found by
Fig. 5 .
solving a laplace equation of the magnetic potential in the space out of the soft magnetic materials. The initial magnetic potential of each outside site is randomly given, and the potential at a site is iterated by the average of the neighboring sites ’ potential (Ref. [ 61 ) . After a total I
iteration number r = - p N 2 ,
2
an accuracy of
lo-’ could be reached, where N is the total number of clusters. The field distribution found by the Jacobi method is close to ideal outcome. In Fig. 4(a ) , the protuberant part of the field distribution corresponds to the main pole position, the white part in Fig.4(b). The 3D contour plots of the SPT head field distribution in the central plane ( y = 0 plane in Fig. 3 ) of the magnetic medium is shown in Fig. 5 , which are the results of the two micromagnetic models individually. For the convenience of comparison and analysis, all the field distribution contour plots in following figures are turned up-side-down into the opposite direction.
SPT head field Hy by micromagnetic models : ( a ) f i t model ; ( b) second model.
Quan L . er ul . , Micromagnetic simulation of FeCo write head in perpendicular recording drives
Fig. 5 ( b ) shows the simulation result in the second micromagnetic model. With a driving pole of B , = 2 . 4 T, the peak value of the perpendicular SIT field H, can reach as high as 1 . 7 x 104 Oe, higher than the past results [ 9111. And the unwanted undershoots in the result of the first micromagnetic model are eliminated in Fig. 5 ( b ) , due to the periodic conditions applied on y-direction . In Fig. 6, the down-track profiles of the SPT head field are plotted along the central line ( y = 0 and z = 0) , where the dashed, solid and dotted lines respectively correspond to the first micromagnetic model, the second micromagnetic model and the Jacobi method. It
507
could be seen that the first micromagnetic model could not simulate the SIT head field correctly, where there are extra peaks of the perpendicular head field appeared, which are unwanted in the recording process. The second micromagnetic model has the best result. In Fig. 7 , the cross-track profiles of the SPT head field are plotted along the z direction in the center plane of medium for the three simulation models respectively. In the results of the second micromagnetic model, the dimensions (215.45 nm x 91.32 nm) , with respect to half of the peak field H, = 8685.55 Oe, just coincide with the main pole size ( 180 nm x 60 nm) .
3
s
. 3
-m* w
3
.LL
-4
0
200
400
600
800 1000 12001400
- -2 1 0
x!nm
Fig.6. Down-track Hy field profiles of the fwst micromagnetic model (dashed line), the second micromagnetic model (solid lines) and the Jacobi method (dotted line)
.
4.
Conclusions
A proper micromagnetic model was built up for the analysis of the SPT write head in the perpendicular hard disk drives, where the FeCo soft magnetic metals with a saturation magnetization B , = 2 . 4 T was utilized as the head materials. It is found that, in an SPT head with a 180 nm x 60 nm main pole and a driving magnetic poles o = B , , the maximum perpendicular field 1. 7 T confined within the dimension of 215.45 nm x 91.32 nm could be achieved for the ultrahigh density perpendicular recording. Acknowledgemnets: The author would like to thank Shi Y . for helpful discussion.
100
200
300 zlnm
400
500
6
Fig.7. Cross-track Hy field profiles of the Tmt micromagnetic model (dashed line), the second micromagnetic model (solid lines) and the Jacobi method (dotted line).
References [ 11 Khizroev S. K . , et al . , Recording heads with track width suitable for 100 Gbit/in2 density. IEEE Trans . Magn . , 1999, 35: 2544. [2] Khizroev S. K . , et a l . , MFM quantification of magnetic fields generated by ultra-small single pole perpendicular heads. IEEE Trans . Magn . , 1998, 34: 2030. [ 31 Schare J. , et al . , Design considerations for single-pole-type write heads. IEEE Trans . Magn . , 2003, 39: 1842. [ 41 Hubert A . , and Schtifer R . , Magnetic Domains : The Analysis of Magnetic Microstructure, New York Spring Press, Berlin, Heidelberg, 1998: 154. [ 51 William T. , et al . , Numerical Recipes Example Book [FORTRAN], Second Edition, Cambridge
508 University Press, Britain, 1994: 156. [ 61 Dan Wei, Fundamental of Electromagnetism in Materials ( in Chinese ) , Beijing Science Press, Beijing, 2005: 84. [ 71 Kanai Y . , et a1 . , Numerical analysis of narrowtrack single-pole-type head with side shields for lTb/inZ. Journal of Applied Physics , 2003, 93: 10. [ 81 Kanai Y . , et a1 . , Recording field analysis of narrow-track SPT head with side shield, tapered main pole, and tapered return path for 1Tblin’.
RARE METALS, Vol. 2 5 , Spec. Issue, Oct 2006 IEEE Trans. M a g n . , 2003, 39: 10. [9] Patwari M . , et al . , Unshielded perpendicular recording head for 1 %/in2. IEEE Trans. Magn., 2004, 40: 1. [ 101 Bai D. , et a1 . , Stitched pole-tip design with enhanced head field for perpendicular recording. Journal of Applied Physics, 2003, 93: 10. [ 11] Abelmann L . , et al . , Micromagnetic simulation of an ultrasmall single-pole perpendicular write head. Journal of Applied Physics, 2000, 87: 9 .