magnetic texture in films with perpendicular anistropy

Journal of Magnetism and Magnetic Materials 109 (1992) 375-382 North-Holland

. . . . . . . .

Magnetic texture in films with perpendicular anisotropy

P.V. Zhorin ~, Yu.A. Lisovsky b, I.G. Nikulov b and V.L. Stolyarov b a Institute of Microelectronics Technology and High Purity Materials, USSR Academy of Sciences, Chernogolocka, Moscow District, USSR t, Institute of Steel and Alloys, Moscow, USSR

Received 25 June 1990; in revised form 22 April 1991

The notion of magnetic texture in films for perpendicular magnetic recording is introduced. The characteristics of magnetic texture dispersion (A050) in Co-Cr films are also defined. The method of determination of material constants from the curves of film magnetization, including the first and second anisotropy constants K~ and K.,, as well as A050 is I~roposed. The effects of film structure have been studied on the basis of a magnetostatic model of a columnar structure. The shape anisotropy constant is estimated to have the value ,,- 5 x 105 erg/cm ~, when Ms in the volume of column is 400 G. The criteria for the applicability of films as perpendicular magnetic recording media are also formulated.

1. Introduction

Thin films of Co-Cr alloy are considered to be the most promising for perpendicular magnetic recording [1]. Various parameters were used as criteria for the applicability of films as recording media, namely, anisotropy constants K~ and K 2, coercive field, normal and in-plane, as well as combinations of these parameters [2-4].

ht the present article the notion of magnetic texture is introduced. The value of magnetic texture dispersion (A050) is a direct characteristic of magnetic moment orientation. The method of simultaneous determination of AOs0 and material constants on t,he basis of the Stoner-Wohlfarth approximation for the model of a continuous film is proposed [5]. The effects of the magnetostatic interaction in the discrete model of a film with columnar structure on the perpendicular aniso- trope, constant and magnetic texture dispersion are also considered~

2. Experimental

The Co-Cr films were deposited by rf diode and dc magnetron sputtering of Co-21 at% Cr alloy

targets (diameter 3 in.) onto a silicon (100) substrate using a magnetron of a special design [6]. The deposition rates were 0.4 and 6.5 nm/s, respectively, at 0.5 kW. The sputtering system was initially evacuated to 2 × 10 -7 mbar (ulti- mate vacuum pressure) before introduction of Ar sputtering gas. The Ar purity was 99.9995 vol%. The sputtering experiments were normally per- formed at an Ar partial prcssure 10-2-10 -3 mbar. The substrate temperature was varied from room temperature to 400 ° C. Before deposition of the films the substrates were cleaned by glow d~.s - charge (10 min, 600 V).

The film composition was analyzed using an electron microprobe. The measured Cr content ranged from 20 to 21.5 at%. The profilometer was used for the determination of the film thickness, which varied from 0.2 to 0.6 ixm. The impu- rity depth-composition profiles were analyzed by means of Auger electron spectroscopy. The dispersion of the c-axis orientation of the c~stallites 4050 in the films was evaluated using X-ray diffractometry by measuring the half-height width of the rocking curve for the hcp (002) peak. Transmission electron microscopy ~TEM) and scanning electron microscopy (SEM)were also used to study both the morpholo~ and the mi-

0304-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

376 P.V. Zhorin et al. / Magnetic texture in films with perpendicular anisotropy

crostructure of the films. Magnetic measurements were carried out using a vibrating sample magne- tometer (VSM) in magnetic fields of up to 17 kOe.

3. R e s u l t s a n d d i s c u s s i o n

3.1. Method of determination of film characteristics

It is known that perpendicular magnetic anisotropy can be caused by several factors. The most essential among them are magnetocrystalline anisotropy and the s,hape anisotropy of columnar structure [7,8]. Let us examine the influence of these factors on the orientation of the magnetization vectors in the film of Co-Cr alloy. The influence of magnetocrystalline anisotropy is studied in the continuous film model approximation.

Let us examine the case of external magnetic field orientation in the film plane. The orientation of the local magnetization vector is determined by the condition of equilibrium in an external magnetic field:

d dy (W~ + Wn + Wr~ ) =0, (1)

where y is the unit magnetization vector, W N the magnetostatic energy density, W~ the external field energy density, W~ the magnetocrystalline energy density:

y = M/M~ = cos 4~, (2)

0, M.~±n Wr~ = 2rrM, 2, M.~ IIn, (3)

W n = -HHM~ cos 6, (4)

W~ = K t sin2a + K2 s inaa . (5)

Here 6 is the angle between vectors of _magneti- zation M and external field strength H, c~ = av/2 - 0 - 4 , is the angle between vector M and the direction of the local vector of the easy axis 1 and ~ is the angle between I and the normal to the plane. From cq. (1), transforming the coordinates (H, y) into the coordinates (H/y, yZ), we obtain

I '~" I

12~. I I .I,

101

T ...1.._..~ ...... ,~,.L .,~.-.

i .~..o~-" I o,~..--°

!

I ÷ I

'~i÷ ' i

~ ~ . . . . . -+-----+- .. . . b ----+----I --m .0 .2 .4 .6 .~, 1.¢~ ~,¢~ ,d,

Fig. 1. Magnetization curve on ( H / y , y2) coordinates.

the equation containing the linear and nonlinear parts with respect to y 2:

~ 1 40) n =Y((nkt + ~Hk2 ) cos 2 0 - ~Hkz COS

+ y3Hk2 COS 40 + (sign 0)(1 --y2) -~/2

1 1 ×(--(Hk~ + ~Hk2 ) sin 20 + ~Hkz sin 40 1 +2yZ((Hk, + ~nk2 ) sin 2 0 - - H k 2 sin 40)

+ 2y4I-lHk2 sin 40). (6)

The linear part of eq. (6) corresponds to the coherent rotation of magnetization vectors. The nonlinear part of eq. (6) corresponds to turning of vector M from the easy axis to the external field direction. In this case when 0 = 0, eq. (6) becomes the known relation, obtained by Suck- smith and Thompson in ref. [9]. Therefore, the presence of a linear part on the magnetization curve in the coordinates (H/y, y2) in the interval 0 _<y _< 1 is indicative of the prevalence of the coherent rotation mechanism on the given part (fig. 1). The linear approximation of coherent rotation with the linear part of eq. (6) allows us to obtain two equations:

1 1 PI = ( H k l + 2 H k 2 ) COS 2 0 - 2Hk2 COS 40 , (7)

P2 = Hk2 COS 40, (8)

P. ~. Zhorin et al. / Magnetic texture in films with perpendicular anisotropy 377

i

0 • ,,." I

174 . " |

~.,~,

,~o .

~,] "~ • .~%

.0 . . . . . . . ,

0 --,11,""-'*"-" . 4 .~ .~ I[0 V 2 ÷

,i~

Fig. 2. Coordinates change for the angle definition 0.

where P~, P2 are the coefficients of linear regres- sion, Hkl and Hk2 are first and second anisotropy fields:

2K1 4K2 H k I -- ~ Hk2 = ~ (9,10)

To d.termine the parameter 0 we can use the nonlinear part of eq. (6). We isolate it by sub- tracting the linear part from the equation:

AH(1 --3'2) 1/2

= -½(Hk , + ½Hk2) sin 20 + ~"k2 sin 40

±H +YZ((Hk~+2 ~2) sin ZO -- Hkz sin 40)

+yaHk2 sin 40. (11)

By transforming the coordinates into the (AH(1 _y2)~/2, y2) on the given curve, we can also isolate the linear section (fig. 2). The approximation of its straight line with coefficients P3 and P4 allows us to obtain two more equations with respect to anisotropy fields and angle 0:

- , '-'H ±H sin 40, P3 - - ±(. Hkl + 2 kZ) sin 20 + s k2 (12)

' ( 1 3 ) P4 = (Hk~ + 2Hk2) sin 2 0 - - H k z sin 40.

A specific choice of three equatior~s cut of eqs. (7), (8) and (11), (12) to determine unknowr~ Hk~,

Hk2 and 0 is defined by the solution stability of the system.

To transfer from the local orientation of the magnetization vector to the characteristic of the magnetization distribution in the film, it is neces- sary to establish the !aw of distribution of vector component 1 with respect to the normal. The orientation distribution of the easy axis will be called magnetic texture.

Introduction of the notion of magnetic texture • in films with perpendicular magnetic anisotropy is of great importance for the determination of the quality of Co-Cr films, used as a material for perpendicular magnetic recording. The characteristic of magnetic texture dispersion is one of the basic parameters which determines the applica- bili~ of the film as a data carrier.

Assume the law of distribution of the component of vector ! as uniform in the film plane and its perpendicalar component as normal. After averaging the position of the easy axis vector in accordance with the given law of distribution we obtain the final system of equations for determination of film characteristics:

[ ! n + ~Hk2) exp[ P~ = (2 k~

k 1

+ w.Hkl + ~ H k 2 ,

[ !

P,=H~,.I ~_ exp \

1 ( + g exp

4 ln(2)

) 4 In(2)

In(2) + ~ ~

~ a O s o l I ( a r I I l n ( 2 ) ) - ' / z P3 = -- 2 .

X(H~, + 5Hk~)~F, 2, 7, 4 ln(2)

½Hk2H~F ~ 2, 5, ln(2) '

(14)

where ~Ft(p, q, z) is the Kummer function:

~ z" ( p + n - 1 ) ! q , z ) = .rt "

n=O • (q + n - l ) ! (15)


To produce equation system (14), we substitute /3:

cos(/3) =s in(0) cos(to) (16)

for 0 in eqs. (7), (8) and (12), and average them by all possible orientations of easy axis. The az- imuthal coordinate of easy axis (to) has a uniform distribution with the function p(to):

p( to) = 1 /2Fl r r . (17)

We assume that the angle between the easy axis and the normal to plane of the film has a Gauss- ian distribution:

1

#(0) = A050_ln_2_/rr__ t / 2 ( ( ) ) expi

0 2 In(2)

where AO50 is the parameter of distribution,

- -

(:8)

, t o ) ) p ( O ) p ( t o ) dO dto,

(19)

(sin/3)

= f = / 2 f 2 = s i n ( f l ( O , o ~ ) ) p ( O ) p ( t o ) dO dto.

~0 ~0

(20)

The magnetization cu~es were obtained from VSM measurements via the construction of a family of incremental hysteresis loops. Some re- suits of the determining of film parameters by this method are shown in table 1. The relative

~. 0.~. .i. . . . . ~ l ~ , . , - ~ . ~ " - - . ~ ' ~ ' ~ ' "

o.. .~,~..~.° .¢"" ~., . .,-".." . . . . .~ ' . . . ~ , . . " I

• . . . . . . . - I ...," ...~-'

.~ , - ~ " I I

I ¢ ' " ~ t . . ," .... II ~1,~ .~ ,.

""~' ,d ," I ~ ,'~," I¢ ,,/,~

.., I~ ~ .,~ ~,~ "'q~ ¢' ~ i

i ?1 ,' ,; /

,'~1~ ~ ~' flJ .~'

~ _ , L ~ L L ~ .... ~ .............. , q , , ~ i - - ~ . . . . . . . T . . . . . .

-2 0 ,.'~ 4 S ~. 10 1. 2 kl, K 0 E

Fig. 3. Hysteresis loops on the sample with the low magnetic texture dispersion.

error (%) was determined by standard statistical analysis of magnetization curve linear parts.

It appears from the given data that: 1) The K 2 / K ~ ratio for samples 1 and 2 is

substantially larger than it appears from the pub- lished data of measurements made by means of a rotary anisometer [6]. This is due to neglect of magnetic texture. Error in the determination of anisotropy constants increase with increasing Ads0. This effect is most pronounced when determining K e. The characteristic full hysteresis loops are ~h_own in fig. 3. It should be noted, that the value AdS0 (or its analogous value) can be determined from measurements made by a rotary anisometer. However, during Fourier analysis it is necessa~; to take into account both the amplitude and phase of a harmonics.. Here Q = ( K ~ +

Table 1 Magnetic properties of Co-Cr thin films

N M s A05 o A05o K1 [emu/cm 3] [deg] [deg] [105 erg/cm 3 ]

1 450 3.6 1.4 14.3 9 ~ 5% "~ 5% -- ' ~ / . .VO

2 450 8.5 3.q 6.6 6% 5% 3% 11%

3 370 50 16 0.4 3% 7% 4% 25%

4 420 83 10.2 0.8 3% 9% 5% 50%

Kz Q Hc .L Hclt [ 105 erg/cm 3] [kOe] [kOe]

4.9 1.9 1.8 0.32 i i% i4% 2% 2% 4.8 1.3 0.83 0.25

12% 18% 6% 6% 4.1 1.0 0.38 0.44 7% 10% 4% 4% 5.4 1.0 0.40 0.36

11% 14% 3% 3%

P.V. Zhorin et aL / Magnetic texture in films with perpendicular anisotropy 379

1..01 'T

I • ..2".,I

'1"

II II . . . . . . ~. " ' : : . . . . . . a~.,a~""

- oo ..~% • o ..-," "[.---" ~..,..

'if::"" ":':::':' .... ~ ...¢~ .- ' '~"' :- ,.. ,., .,-"I~U ~

, ~ b" t' '" / ~ .~ ¢.

~ .d ~ d ~ , ¢" .¢¢"

~,," ,,,,' ,," . /

I ..L. I,.'~ ,.,'°

_~_~~"_.~__.~__~__ ~ ~ . -'.'~ ~ " ~ (:; .-'~, ! g I v . . . . . . . . . . . . H . K ~E~ E

Fig. 4. Hysteresis loops on the sample with the high magnetic texture dispersion.

2Kz)/2arM~ 2, their relative errors (%) are shown below the measured values.

2) In samples 3 and 4, produced by technology variation, Kz/K ~ > 1. These samples are characterized by a large dispersion of the magnetic and crystalline texture. Such films have a significantly more developed columnar and granular structure as compared to samples 1 and 2. The characteristic full hysteresis loops of these samples are shown in fig. 4.

There is a pronounced difference between the values of K~ for the samples of the first and second groups. No such difference is observed for

the effective value of K 2 within the measurement error. This may be due to the fact that K 2 is determined mainly by the value of the second magnetocrystalline constant. Besides magnetocrystalline anisotropy, the effective value of K n can be determined by the components of diverse physical nature, namely, magnetostatic, magne- toelastic, exchangeable, surface, etc. In the case of C o - C r films, besides magnetocrystalline anisotropy, the local magnetostatic energy is likely to make the main contribution to the effective value of K~. These magnetostatic effects may be caused by the presence of inner nonmagnetic interfaces between ferromagnetic columns. Therefore, the effective value of anisotropy constant Kt determined by this method is primarily the sum of magnetocrystalline and magnetostatic contributions.

3.2. Magnetostatic energy of columnar structure

Attempts to study the magnetostatic interaction in relation to the geometric parameters of columnar structure were made in ref. [10]. Im- proper regard to the columnar structure field in interaction energy and the determination of the shape anisotropy constant are the disadvantages of this model.

Let us consider the discrete model of a ferromagnetic film with a columnar structure (fig. 5) with more stringent assumptions:

,,, ,

......./"'̧

,,o -x,.. ,,' L%

,," ,~, .,' ,,

I' I I !

.I.~.. ~ ' ~ .o,

• !1 I i ~, .;~

I " ;'1 "'i ,i' ', 2; i

_o,Z, ~, : I

::i

Zl

X ;,,o.,.__.m.-...~,~%...

f¢ i.; ¢~ ¢ ] ~'~

i , inn,_-: ~

I._ 1 1 "1~""1 '-. ' I L,%.. - ' - _ ~ •

I _ I~.~

i

../'" .. .,..

. /"

. ..... oo°--'-"~o. I

"%~1.0 [ ,~, ",, I I ~ I

I 'I M,-.-~ ~ ~ ,,1 I .

~1 I / I (~¢ ,, ,': ..

/-" i.

"---~ .... " I [.../ T ... ..j.

Fig. 5. Model of the ferromagnetic film with the columnar structure.


- the columns are identical ellipsoids of revolution, elongated in the direction of the normal to the plane;

- interfaces between them are nonmagnetic; - magnetization in the volume of column is uni-

form; - the set of columns is an infinite ordered 2D-

array in the film plane. In the present model we consider changes in

magnetostatic film energy in relation to the columnar structure parameters, such as film thickness (c), column diameter (a) and intercolumn distance (d). The shape anisotropy constant is determined as:

K=EII - E a. , (21)

where E~I corresponds to the density of the magnetostatic energy of a film with a columnar structure in which the magnetization vector orientation in columns parallel to the plane, E± is a normal to the plane. The columnar structure energy is derived from the following equation:

1 E = 2Hv f.(M"FIB) dV, (22)

4 2¢ where t; = 3-a'a is the volume of one column, M., is the magnetization in the column volume,

B = 4arM.,- NM., + Hcx. (23)

N is the ellipsoid demagnetization factor, He. , is external magnetic field created by the columnar structure in the volume of a selected column. When arranging columns in an array correspond- ing to the 4th order symmetry axis which is perpendicular to the plane, Hex takes the form:

o o

nc.~= ~ ( H ( n r + x , y , z ) + H ( n r - x , y , z)) n = !

+ ~, (H(x, k r + y , z) k = l

+ n ( x , k T - y , z ) ) ~ ~

+ E E n = ! k = l

+ H ( n T - x , kT-y~, z) -~ H(nT+x, k T - y , z) + H ( n T - x , kT + y, z)) . (24)

Here H(x, y, z) is the magnetic field created by an ellipsoid with magnetization M.~ outside its volume (x, y-coordinates in-plane, z normal to plane):

H ( x , y, z ) = - g r a d f ( x , y, z) , (25)

where f (x , y, z) is the scalar magnetic potential. At orientation of magnetization vectors perpendicular and parallel to the film plane, f takes the form:

f~_i" = 4arM~(o. 2 - . 1)(O. o arcth O.o- 1)eO.¢,

f_~x = 4rrMs(o.2 _ 1)( o.arcth O. - 1)eo.o~-,

• fli"

(26)

(27)

= 2"n'Ms(o. 2 - 1)(O'o(O . 2 - 1) - ~ - arcth O.o)

X eo.0((o. 2 1)(1 q'2)) 1/2 - - cos qt, (28)

fl~ x= 2axMs(O. 2 - 1)(O.(O. 2 - 1) - t - arcth O.)

X eo.o((o. 2 1)(1 T2) ) !/2 - - cos ~ , (29)

for the volume inside and outside the column, respectively. Here O., r, gr are the elliptic coordinates of elongated ellipsoids of revolution, e the linear coordinate parameter, O.0 the ellipsoid surface parameter.

The dependence of the shape anisotropy constant on the columnar structure parameters re- veals that the value of K can either be positive or negative. At K > 0, it corresponds to the direction of vector M~ perpendicular to the film plane and at K < 0 the magnetization vector in the columns is oriented in the film plane. The most important parameter is the form of the column characterized by the relation e = c/a. It is possible to consider two limiting cases: e >> 1 (a column shaped as a needle) and e -~ 1 (almost sphere-shaped column), At e >> 1 the presence of the perpendicular orientation of the magnetization vector is not dependent on the intercolumn spacing (fig. 6). At e ~ 1 inversion occurs of the sign of the anisotropy constant provided there is some spacing between the columns (d'). Fig. 7 shows d ' as a function of the parameter ~, with various film thicknesses,

This result can be explained as follows: for columns separated by nonmagnetic interlayers the

P. 1,5. Zhorin et al. / Magnetic texture in films with perpendicular anisotropy 381

3.0

~.;, 2.5 t

~ 2,0

~!

b~

, ~

. . . . - - ~ ,#,.. "~

~'

1. ~ . . _ _ - - ~ - ~-~ $ 2

1 o 0 ~ " ~ " .~e.. .~'#"

~ ~ . ~ ' ~ :~3 ~ ~ '

. . ~ - ~

. 0 . . . . ~ . . . . ; -~ ~,~ ~._~.~.. ~ ..~ :~ 4

~ 200 3~0 d , ~r'l - , ~

Fig. 6. D e p e n d e n c e of the anisotropy shape cons tan t on in t e rco lumnar distance: M s = 300 G; 1, 2, 3, 4 - a = 10, 100,

190, 210 nm, respectively.

distribution of the field lines of each column is identical to that of an isolated column. There- fore, at e 2> 1 the perpendicular to plane component H z is predominant in the columnar structure field distribution which does not change the position of vectors M S in the columns. In con- trast, at e-> 1 horizontal component H X is predominant inducing magnetization vector reorien- tation as a result of the change in the nature of the magnetic flux closure. In this case the exis- tence of perpendicular anisotropy is possible only at a weak magnetostatic interaction, i.e. at d > d'.

C4 I I

z o o tk

.,'r" r:n \ .~ . ~, \

-. 500 \ ~x ~ ~ ~

~ C~, X~, "~ ~ ', k~

'1, ~,: '~ ' k. "~

~ ~, "%. ~%~ 3 0 0 '~ "N ~"

C~ "~ x. ". .... ~ ~ "~. ~% ~,. ".~ "~. -.~ ' -~ ~ ~ ~, ~ " ~ ~ ~-.~ -~.. -~

~ ~ . . ~ . . " ~ . . . . 100+ ~ - ~ _ ~ - - - _ , ~ ~ _ ~ - ~ ~ - t

-~__~ , 0~ i l I ~ 1 . 0 0 i~ 0 1 . 2 0 i . ~ 0

Fig. 7. Dependence of d ' on e parameter .

The estimation of the shape anisotropy constant [11,12] at thc most typical parameter values for C o - C r films e.g. c = 2 5 0 nm, a - - 2 5 nm, d = 10 nm, M~=400 G, yields K = 5 × 10 ~ e rg / cm 3.

A pi'oper regard to the possible difference in the symmetry of column arrangement in the film plane gives an insignificant change in the value of K. For example, at a spacing between the columns limited by the radius of the exchange interaction ( < 10 nm), the change of the computed value of K is = 7%.

Hence, the proposed model of the magnetostatic interaction in a columnar structure allows estimating the shape anisotropy constant and re- vealing its behavior in relation to the geometric parameters as well as explaining the disappear- ance of perpendicular anisotropy when passing from a columnar structure to a fine crystal one.

3.3. The influence of the magnetostatic interaction on magnetic texture dispersion

In the analysis of the magnetic texture dispersion account should be taken of the magnetocrystalline anisotropy energy in the model of a ferromagnetic film with a columnar structure. A proper regard to the hexagonal axis misorientation is likely to lead to the change of the position of easy axis vectors in a columnar structure with respect to the normal of the film. In this case the total energy is difficult to minimize.

The assumption of the uniform distribution of easy axis horizontal projections enables us to simplify of the total energy minimization. Then the average strength of the horizontal component columnar structure field created by the horizontal components of the magnetization vectors in the columns will be equal to zero in the volume of the selected ellipsoids. Therefore, it may be as- sumed that the orientation of the column magnetization vectors remains parallel to the normal except for the selected ellipsoids.

The magnetization value in the columnar structure decreases proportionally with the mean misorientation of the easy axis:

(M~) = Ms(COS 0), (30)

where (cos O) is the mean cosine of the easy axis

382 P.V. Zhorin et al. / Magnet ic texture in f i lms with perpendicular anisotropy

misorientation angle in columns except for the selected one. The position of the magnetization vector in the selected ellipsoids is determined by the condition of equilibrium:

d .(WN + W~:) = 0, (31)

dy

where Wy i~ magnetostatic energy density determined by relation (22), W~ is magnetocrystalline anisotropy density:

W~=Kt s in2(~- 0) + K 2 s in4 (~- 0). (32)

Here ~ is an angle between the hexagonal axis and the normal to the plane in the selected ellipsoid, K~ and K 2 a r e the magnetocrystalline anisotropy constants in the volume of column. From eq. (31) we can obtain the dependence of the position of the easy axis on the position of the hexagonal axis. This curve shows the dependence of magnetic texture dispersion (A050) on crystalline texture dispersion (A0s0) by virtue of the arbitrary value of the ellipsoid in question.

The computed results are shown in fig. 8. The presence of the columnar structure changes the curve pattern more significantly as the parameter e decrease. For instance, at e = 1.1 and d = 10 nm the shape anisotropy constant K < 0. In this

I~'.~ ,_~,,

~ ~.l+

60

"::1 30

d,., d ....,"""

.... .:' ...,.,-- ..... .,.:;;%::--" ,./~" .......,.~"",.....7.;:::2 ,zS .....

o¢" 4.°°.°. .... ~,.'.~" ¢~ o~. , . . , . . ,~ . -'-*

~.-" ._,1:" - " 'q~ '~" 1 .~.~_: . . . . . . . . . ~ . . . . . . . . ,

~3 .~.t-.~ ~$0 . ,al~c. ~ , 1"~'.~.3

,. ,~, ,~ ~ ¢.1~ ~ "

.~ ,' I' ~; ,/,;'

,~ ¢ , "~ '¢ ' a' ~ ~

.~(" ,,~ o ~ , , . / / ~ .¢' ¢' .¢'

~1 ¢1 ,¢ ¢ ~¢: ,g.x ,*" (#. ¢¢

. / .,." ~,. .¢" ,~" ¢¢ , .. ,~,~¢ ~ ; .d. ~

. .~ ~¢ .,., ~ /." . . /" .... ...5;~... ~

Fig. 8. Dependence of the magnetic texture dispersion (AO50) on the crystalline texture dispersion (A0.s0): 1 - single column, 2, 3, 4 - a=25 , 100, 220 nm; M~=500 G, K t = 7 × 1 0 5

erg/cm 3, K., = 3 × 105 erg/cm 3, c = 250 nm, d = 10 nm.

case the columnar structure field tends to orient the magnetization vector in the plane. It is neces- sary to note that AO50 differs from zero when A050 = 0 at the given parameters of columnar structure.

Therefore, the results obtained enable us to compare dispersion of the magnetic and crystallo- graphic texture.

4. Conclusion

1) The characteristics of magnetic texture dispersion are determined by analysis of the magnetization curves for films with perpendicular magnetic anisotropy.

2) The K2/K ~ ratio increases with increasing magnetic texture dispersion.

3) The decrease of the ratio of film thickness to column diameter results in increasing between the horizontal components of magnetostatic field.

4) A relation between magnetic and crystalline texture dispersion was established. The character of the relationship is governed by column shape and the presence of nonmagnetic intercolumnar layers.

References

[1] S. Iwasaki, IEEE Trans. Magn. MAG-20 (1984) 657. [2] J. Worst, J.C. Lodder and T. Wielinga, Thin Solid Films

101 (1983) 75. [3] Y. Niimura, S. Nakagawa and M. Naoe, IEEE Trans.

Magn. MAG-23 (1987) 153. [4] J.E. Snyder and M.H. Kryder, J. Appl. Phys. 57 (1985)

4016. [5] E.C. Stoner and E.P. Wohlfarth, Phil. Trans. R. Soc. A

240 (1948) 74. [6] Ch.V. Kopezky, V.L. Stolyarov, L.S. Shabelnikov, P.V.

Zhorin and N.T. Simonishvili, Electronnaya Tekhnika 6 (1984) 3.

[7] R.D. Fisher, V.S. Au-Yeung and B.B. Sabo, IEEE Trans. Magn. MAG-20 (1984) 806.

[8] N. Honda, H. Awano, T. Samoto and J. Hokkyo, J. Magn. Magn. Mater. 35 (1983) 278.

[9] W. Sucksmith and JoE. Thompson, Proc. R. Soc. 225 (1954) 362.

[10] T. lwata, R.J. Prosen and B.E. Gran, J. Appl. Phys. 37 (1966) 1285.

[11] Yu.A. Lisovsky, I.G. Nikulov and V.L. Stolyarov, Izvestiya VUZov, Chyornaya Metallurgiya 7 (1987) 173.

[12] Yu.A. Lisovsky, I.G. Nikulov and V.L. Stolyarov, Poverkhnost, Fizika, Khimiya, Mekhanika 12 (1988) 137.

magnetic texture in films with perpendicular anistropy

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