TbFeCo exchange-coupled bilayer films

Journal of Magnetism and Magnetic Materials ! 11 (1992) 63-70 North-Holland

Anomalous torque curves in PtCo/TbFeCo exchange-coupled bilayer films J. Nakamura, J.O. A r t m a n ~, R. Malmh~ilI

2,

M. Takahashi, M. Ojima

h~formation Storage Research Department, Central Research Laboratory, Hitachi, Ltd., Kokubunji, Tokyo 185, Japan

and

K. Shimazaki Tsukuba Research Labora'ory, Hitachi Maxell, Ltd., Mitsukaido, lbaraki 300-25, Japan Received 8 July 1901; in revised form 18 November 1991

The torque curves, T(oe), of P t C o / T b F e C o (RE-dominated) bilayers behave unexpectedly when the applied field H is directed close to the perpendicular (o~ --: 0). The P t / C o and TbFeCo films separately are characterized by positive effective magnetic uniaxial anisotropy. Consequently we expect T(o~)/a to be negative near a = 0. However, we find T(a)/o~ to be large, positive and approximately constant near a = 0. In this angular region the relaxation of the wall associated with the bilayer exchange coupling drives the P t / C o and TbFeCo layer magnetizations in opposite directions. On the thin wall modt/ basis, the wall energy, o-,~, h;f,~'red from the ensuing torque slope is about two and a half times the ~rw computed from Ke~ r loop shifts. Fhe bilayer free magnetic energy density, E(a,), must be even [ E ( a ) = E ( - a)] and in the form of an inverted parabola near a = 0. Physically more realistic distributed wall models must conform to the required symmetry as well as to fit experimental data.

1. Introduction The application of exchange-coupled P t C o / TbFeCo films to magneto-optical (MO) recording with short wavelength laser radiation had been proposed earlier by some of the present authors [1]. As part of our continuing investigation of the

Correspondence to: Dr. R. Maimh~ili, Mailstop 2S/21, Central Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo 185, Japan. 1 On leave from the Departments of Electrical & Computer Engineering and Physics, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. 2 On leave from Royal Institute of Technology, S-100 44 Stockholm, Sweden.

magnetization process in such films we report now on Kerr effect and magnetic torque measurements. Of particulzr interest is an unexpected "anomalous" behavior of the torque cun'e found in many of these films when the external magnetic field is applied in a direction close to that of the normal to the film.

2. Experiment In fig. 1 we show (a) the torque curve, (b) the Kerr MO hysteresis loop and the structural cross-sectic,n of a representative P t / C o multilayer spec~.men composed of alternating 12 A P t

0304-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights re,;erved

64

J. Nakamura et aL / Anomalous torque curves

dyn.cm

/

Area = 0.71 c m = H = 16 k O e

0.5

-0.5

(a) Torque curve

(b) Kerr hysteresis loop 150h=

sublattice magnetization. The torque and Kerr effect traces correspond closely to what would have been obtained by the simple addition of the individual traces such as those in figs. 1 and 2. Finally, in fig. 4 we display the torque and Kerr curves and the cross-section for a P t C o / TbFeCo bilayer in which the TbFeCo layer is RE-dominated; i.e., the RE sublattice magnetization is dominant at room temperature. The rotational hysteresis region has widened appreciably. We see that the torque curve when the applied field is directed close to the film normal is approximately linear with a large, positive but finite slope. Since a curve with a modest negative slope was expected here (see figs. 1-3) we refer to this phenomenon as the "anomalous" region of the torque curve. The interpretation of the Kerr loop for this specimen has been discussed briefly in a previous presentation [2].

(c'~!Structure cross-soction Fig. !. A 150 ,~ thick P t / C o multilayer specimen: (a) torque curve at H = 16 kOe, (b) Kerr effect hysteresis loop and (c) structure cross-section.

dyn ,cm

Area = 0.69 c m : H = 16 k O e

1.0 0.5 0

and 5 ,~ Co layers for a total thickness of 150 .,~. The torque curve is normal in appearance, i.e., the "effective" or net anisotropy is positiw: (magnetization normal to the film plane is favored energetically) and the magnetic symmetry is uniaxial. The Kerr loop is also is normal in appearance. In fig. 2 we show the torque and Kerr curves and the structure cross-section of a representation TbFeCo film. Once more the results are as expected. The TbFeCo film is magnetically uniaxial with positive anisotropy. Some rc,tatio"~al hysteresis is seen in the torque curve when the applied field is close to the horizontal plane. In fig. 3 we show the torque cur,,e, Kerr loop and structure cross-section for a P t C o / T b F e C o bilayer specimen. At room temperature, the transition-metal (TM) sublattice magnetization in this TbFeCo layer dominates over the rare-earth (RE)

-0.5 -1.0

(a) Torque curve

.

.

.

.

--

i 0.1=~L._. 1 kOe

(b) Kerr hysteresis loop

~

5oo, 15oA

(c) Structure cross-section Fig. 2. A 150,4, thick TbFeCo specimen: (a) torque curve at H = 16 kOe, (b) Kerr effect hysteresis loop and (c) structure cross-section.

65

J. N a k a m u r a et al. / Anomalous torque curces

3. Theory

dyn.cm

Area = 0.73 em 2 H = 16 kOe

3.1. Basic concepts

1.0 c, 0.5 d',,

",

The essential features of the Kerr effect loop and the torque curve can be obtained, at least qualitatively, from a theoretical formulation popularized by Kobayashi and co-workers [3]. It is tacitly assumed that a very thin magnetic interfacial transition region is located at the physical interface between the two magnetic layers, which are denoted by A and B. In somewhat more general form than given in ref. [3], the magnetic free energy per unit area, E, for such a coupled system can be written as

;:

!

1 \, l Art! \i 2'r~

-0.5

(a) Torque curve

j~

~~

+ tBMa{HK~ ~' sin 2 0 a - H

° %oo

(b) Kerr h y s t e r e s i s

loop

cos(ot -0B)}

K * M A M B cos(Oa - Oa).

(1) ~

..... 5 0

1

I dyn.cm

TbFeCo

PtCo

°'

1

E = tA MA{HKA 5 sin z 0A -- H cos( a - 0A) }

+

'

15oA A

Substrata ]

(c) Structure cross-section

Area

= 0.71 cm 2 H = 16 kOe

Fig. 4. A [150 ,~ thick Pt/Co]/[150 ,~ TbFeCo] bilayer specimen: (a) torque curve at H = 16 kOe, (b) Kerr effect hysteresis loop and (c) structure cross-section. Tbe TbFeCo is REdominated.

0.5 0 -0.5

(a) T o r q u e curve

l"b-

l~ -COmomentI

~PtCo i~,¢lTbFeC O

0.25oL~

2

kOe

(b) Kerr hysteresis loop 500A

13oA looA I

Sul:strate

(c) S t r u c t u r e c r o s s - s e c t i o n

Fig. 3. A [130 ,~ thick Pt/Co]/[100 ,~ TbFeCo] bilayer specimen: (a) torque curve at H = 16 kOe, (b) Kerr effect hysteresis loop and (c) structure cross-section. The TbFeCo is TMdominated.

Here t,x and t B are the layer thicknesses, M A and M B the corresponding magnetizations per unit volume, HKA and HKa the appropriate effective anisotropy field values. The applied magnetic field is directed at the angle a to the normal, the magnetizations M A and M B are directed at the angles 0A and 0 B, respectively, to the normal. The constant K * , which is positive, represents the antiferromagnetic coupling between the two layers on either side of the interface. As an alternative to the K * coupling term in eq. (1), an angularly dependent wall energy of the form, t

r, . . . . ,,~ _ -

~'~'rL,~V¢[ I T

%.ual UA

~1

UB/j

,

('~)

can be introduced [3]. Clearly, operationally both forms of coupling are equivalent. In the present case we assign the P t / C o multilayer system, which we assume to behave monolithically magnetically, to A. The TbFeCo, in which the rare-earth mo-

66

J. Nakamum et al. / Anomalous torque curces

ment is assumed to dominate, then corresponds to B. The cos(0 A - 0 a) dependence of the interfacial exchange energy (eq. (1)) or the wall energy (eq. (2)) presumably follows intuitively from the classic exchange interaction concept. However, a basic theoretical derivation for such an expression, in the manner used here, does not seem to exist. As demonstrated by Kobayashi and coworkers [3] for example, the Kerr MO hysteresis loop is shifted by an "exchange field", Hcx. It follows that for the loop in fig. 4b ( Hex)B=trw/2MBtB=K*MAMB/MatB.

(3)

The torque (per unit area), T, follows from - O E / a a . However, first the equilibrium conditions must be satisfied. We demand OE/O0 A = 0 and OE/aO a = 0. Consequently, tAMA{HKA sin 0A cos 0A -- H sin( a - 0A) } K * M A M B sin(0A -- 0B) ----0,

-

(4)

and

or using eqs. (4) and (5), 1

T = --tAMAHKA -5, sin 20 A 1

-

tBMBHKB 5 sin 20 B.

(8)

Upon addition of eqs. (3) and (4) a useful expression is obtained, i

tAMA{HKA ~ sin 2 0 A - - H sin(a -- 0A) } 1

+ t a M B { H K B 5 sin 2 0 B - - H sin(re-- 0B)} = 0 .

(9) 3.2. Simplified analysis in the angular region near a = O: the anomalous region

As shown in fig. 4, the torque curve in the anomalous region is fairly linear, that is T ( a ) / t e is approximately a constant. For the analysis of the torque curve in this region we feel it reasonable then to assume that in eqs. (4)-(9) the sine functions can be replaced by their arguments. It follows then that, tAMA( HKA + H ) O A - t A M A H ot

t B M B { H K B sin 0 a cos O B - H

s i n ( a - 0u) }

+ K * M A M B sin(0A-- 0B) ----0.

- K * M A M B ( O A - 0B) = 0,

(5)

tBMB(HKB + H ) O B - t B M B H a

For the equilibrium to be stable, 02E/aO~x > 0 and 02E/O0~ > 0, and [4],

a2E OZE

Ù0A 2

02E

+ K*MAMB(OA--OB) =0,

(11)

T(c~) = --tAMAHKAOA--tBMBHKBO B,

~:

(12)

and

aoAa0B t > o.

tAMA(HKA + H ) O A + tBMB(HKB + H ) O B

The critical angle orientations are defined by ~)2E/002

(10)

--- 0 o r ,

= ( t A M A + tBMB)H a.

(13)

From eqs. (10)-(12) one obtains,

H cos(a - 0A) = K*MAMBCOS(O A - OB)//tAMA - HKA cos 20A,

(6)

a

and from a2E/O0~ = O,

-- HKB COS 20 B.

(7)

Returning to the determination of the torque, T, we find, T = - - t A M A H sin(c~ -- 0A) -

tAM A

( HKB+H

+ T(o¢)1

a

H cos( e¢ - 0~) = g * M a M ~ c o s (0 A - O B ) / t B M B

- t B M B H sin(a

HKB--HKA

0B) ,

)1

(14)

t A M A" , HKu- -- H.~A, -H'

and

a

HKA -- HKB

tBM B

1

( H~x+H

T(a)

) 1

+ - a

(15) /13MB

HKA-HKB

-1t"

67

J. Nakamura et al. / Anomalous torque curt'es

Once OA/a and OB/a have been determined, K*MAM B follows from ci~.hcr eqs. (10) or (11) which we rewrite in the forms,

rad 2, the interface energy K *MAMt~ is expressed in units of erg/cm2 and is expected to be positive. Also, it follows from eqs. (1) and (2) that,

K * M A M a = tAMA( HgA + H)OA/(OA-- OB)

% = 2K*MAMB.

-- tAMAH a / ( OA -- Ou),

(16)

and

3.3. Simpl(fied torque expression near a = 0 in the absence o f coupling

K * M A M 8 = taMB( HK8 + H ) 0 8 / ( OA - 08) -

t B M B H

a / ( 0 A- 08).

(17)

The relationship between T ( a ) / a and the applied field H in the anomalous torque region is of interest. Eqs. (10) and (11) can be solved to yield:

Finally, we note the torque relation that exist in the region nc~-: a = 0 when the two layers are uncoupled. It follows from eqs. (10)-(12) when K *M AM B = 0 that,

T( a) =

OA/aH

taM a

--

a

H HKA H+HKA

= tAMA[ taMs(HKB + H ) - K * M A M B ] / A

- tBMBK*MAMB/A,

(22)

H HKB

(18)

-

-

tBMB H + HKB '

(23)

now, for positive HKA and /'tKB , T(a)/o~ is negative. See figs. 1-3.

and OB/aH

= tBMB[ tAMA( HKA + H ) - K *MAMB]/A

-- tAMAK*MAMB/A .

(19)

with

A = [tAMA(ItKA + H ) - K * M A M B ] X [tBMB( [-A'KB+ H ) - K*MAMB]

- ( K * M A M B ) 2. Upon substitution into eq.

(20)

(12),

T(o,) ~ a l l = -- t A MA HKAOA/a H -- t B M B H K B O B / a H .

(21)

W~ note that T ( a ) / a is found to be a complicated algebraic expression whose numerator contains a term linear in H and whose denominator contains terms in H and H2 The quantities tAMA, tBMB, Hr, A and HKB are determined from data taken on separate A and B specimens. The ratio T ( a ) / a is found from examination of the anomalous torque curve taken at an applied field H. For t~M~ in units of i0 -3 e m u / c m 2, H in units of kOe, and T ( a ) / a in units of e r g / ( c m rad) 2, equivalently d y n / c m

3.4. A non-mathematical intuitil'e explanation of the torque anomaly The exchange coupling between the Co spins in the P t / C o layer and the FeCo spins in ~he TbFeCo layer is ferromagnetic; i.e. the parallel alignment of the Co and FeCo spins cGnsequently is favored energetically. In a RE-dominated TbFeCo layer the Tb magnetic moment dominates over the FeCo moment and the Tb and FeCo spins are strongly antiferromagnetically coupled to each other. Hence, the coupling between the TbFeCo and P t / C o layer magnetizations appears to be antiferromagnetic. If both the (positive) anisotropy energy and the Zeeman energy contributions are sufficiently large, the net P t / C o and TbFeCo magnetizations will be in (..... ;¥al~nmont A¢. a c ' n n ~ e q u e n c e _ a type of domain wall [3], necessarily with stored e n e r ~ , will be generated. In the "anomalous" torque region near ~ = 0 the torque due to the anisotropy is very small. The energized domain wall "spring" relaxes, tending to drive the magnetizations in the two layers in opposite angular directions, see fig. 5.

Z Nakamura et al. /Anomalous torque curces

68

:~/ ]

MA

"=

.MA\\~

'":-

/

-

i

/ K~, YbFeCo .,7 (RE-dominated)

Fig. 5. Orientation of the P t C o / T b F e C o bilayer specimen magnetic momenls when the applied field H is direc:ted close to the vertical.

The anomalous torque segment thus is associated with repulsion of the magnetization in the angular region in which the anisotropy torque is small.

sity, K*MAM B, of 5.53 erg/cm 2, corresponding to a o"w value of 11.1 erg/cm 2 (eq. (22)). Thus the coupling energy deduced from the slope of the anomalous torque segment is about three times that inferred from the Kerr effect hysteresis loop displacement. In two other P t C o / T b F e C o films for which both Kerr effect and torque data were obtained [5], similar trends were noted [6]; in these bilayers the trw values deduced from torque data all were about two and a half times those inferred from the Kerr effect hysteresis loop shifts.

5. Discussion 4. Calculations

The pertinent magnetic data for the specimen, whose torque and Kerr effect responses were shown in fig. 4, are listed in table 1. The magnetic moment per unit area, t M, and the effective anisotropy fields, H K, were obtained from vibrating sample magnetometer and torque magnetometer measurements, respectivel3, made on separate individual films with characteristics similar to those composing the bilayer. The exchange field ( H e x ) B for the TbFeCo was determined from the Kerr effect loop displacement in the bilayer film [2], as depicted in fig. 4b. The value of T(a)/a, the angular slope of the torque per unit area in the anomalous region of the bilayer, was computed from fig. 4a. The Kerr shift of 8.0 kOe corresponds to (eq. (3)) a wall energy density, trw, of about 4.4 erg/cm 2. The torque slope of 33.3 erg/(cm tad) 2 yields (eqs. (14)-(17)) an exchange energy denTable 1 Magnetic data for the P t C o / T b F e C o bilayer specimen Layer tM [10 -3 e m u / c m 2 ] H K [kOe] (Hex) n [kOe] T(a)/a [erg/(cm rad) 2]

A Pt/Co 0.948 1.89 - 1.59

B TbFeCo 0.276 14.71 _ - 1.56

bilayer

8.0 33.3

Since the proposed application of exchangecoupled ferrimagnetic bilayer films is for magnetooptical me,nory storage, these films usually are investigated routinely only with magnetic fields applied perpendicular to the surface [2,3]. Under such circumstances the presumed angular dependence of the free energy, eqs. (1) and (2), in particular that of the exchange or wall energy, is not tested experimentally. A number of papers have appeared, however, in which additional torque components have been observed in rare earth-transition metal alloy systems [7-13]. Only one of these concerned a specimen fabricated specifically with interfaces [7]. In this paper, on compositionally modulated T b / F e C o films, Tanaka and co-workers report an observation of an additional torque component at a - 0, 180 and 360 °. The Tb and FeCo layers were deposited with the same thickness. The overall anisotropy changed from positive to negative as the modulation period was decreased; no further explanation for the additional torque component was given. Hartmann and co-workers [8] reported observation of an additional torque component near = 0 in an investigation of GdTbFe films with Al, Cr, CrNi and Cu coatings. Here also the positive anisotropy of the films was decreased "almost [to] negative effective anisotropy"; this occured following annealing in air. The torque anomaly depicted here is quite broad. The annealing was believed to promote the growth of a

J. filakamura et al. / Anomalous torque curces

surface oxide layer of progressively increasing thickness. No further discussion of the anomaly was given. Ito and co-workers [9] reported observation of "a small furbelow at --. 0, 180 and 360 °'' in a TbFeCo specimen, which was associated with surface oxidation; no further discussion was given. Takayama and co-workers [10] made a study of ( G d R E ) - F e C o films in which Tb, Dy and Ho were substituted for the Gd. An anomaly was seen in the torque curve for a GdTbFeCo specimen. No explanation of the ano.maly was presented. Earlier, Tsunashima and co-workers [11] had associated torque anomalies in an amorphous GdCo film with a depth profiling of the saturation magnetization and magnetic anisotropy constant. Perthel and co-workers [12] has associated torque anomalies found in sputtered GdCo films with a specific sin40 uniaxial anisotropy term. Shen and co-workers [13] in a oxidation study of GdTbFe attributed the effects seen to a superposition of an oxidized layer (with in-plane magnetic anisotropy) and the positive anisotropy bulk layer. Explicit plots of the simulation results are not given in the paper. In our examination of the P t C o / T b F e C o bilayer system, the anomaly did not appear in isolated P t / C o or TbFeCo films. It did not appear in bilayers in which the TbFeCo magnetization was transition-metal dominated. It did appear in bilayers in which the TbFeCo magnetization was rare-earth dominated. Thus our association of the anomalous torque behavior with the presence of bilayer interfacial exchange coupling (an euphemism for a domain wall)was apparently the first report of its kind [14]. One may speculate that some of the unusual phenomena discussed in refs. [7-13] may be explained by similar mechanisms. However, difficulties exist in accounting theoretically f[u~ the _L ....... "rh,~ . . . .v.X., . .. p.u L. t.v ff ;,, ~-I_PII~ILK.~PLLL~IIC1L. ll~,.~ A; ~.utio~.,l ixa the wall energy, o-w, values inferred separately from the Kerr loop shifts and torque slopes is based on observation at the moment of only a limited number of specimens; nevertheless, we anticipate that the discrepancy will be found to be of general occurrence. The P t / C o "layer" in •

60

our specimens actually was a mult!layer composed of alternating 12 ,~ Pt and 5 A Co layers for a total thickness of 150 A. For the purposes of testing the theoretical concepts, there would be less ambiguity if this layer were magnetically monolithic. The torque curve is antisymmetric with inversion through the origin, that is T ( - a ) = -T(cD. It then follows that the free energy E must be symmetric with inversion; E(-a, 0A, - 0 B ) = E(a, 0A, 0B). Moreover, in the "anomalous" region near a = 0 the free energy E geometrically must be in the form of an inverted parabola. These symmetry requirements are all satisfied by the free energy density expression as given in eq. (1). However, the simple form of the bilayer modelling as employed here has been criticized by Kaneko and co-workers [15] as being physically unrealistic. The application of distributed domain wall models to the bilayer problem is under consideration by us [16]. Possibly the difficulty in reconciling the torque and Kerr loop data could be resolved recourse to a suitable distributed domain wall model. In this connection it should be noted that the distributed domain wall model in the form presented in ref. [15] cannot satisfy the symmetry requirements.

6. Conclusions The torque curves, T(a), of exchange-coupled P t C o / T b F e C o bilayer films behave unexpectedly when the applied field H is in directions close to the perpendicular (a = 0). In these specimens both the P t / C o and TbFeCo films separately are characterized by positive effective magnetic uniaxial anisotropy. Consequently, in the absence of coupling we expect T(a)/a to be approximately constant and negative near a = 0. However, for bi!ayers prepared with a rare-earth dominated TbFeCo layer we find T(~)/o~ to be large, approximately constant and positix~ near o~ = 0. This phenomenon can be understood on the basis of the thin wall model, for which analyses can be made readily. The relaxation of the wall which exists for angles near a = 0 drives the

70

at. Nakamura et al. / Anomalous torque curces

P t / C o and TbFeCo layer magnetizations in opposite angular directions, producing an anomalous segment of the torque curve. However, the domain wall energy inferred, using the thin wall model, from the torque curve slope in this anomalous region and is about two and a half times the value computed from the Kerr effect hysteresis loop shifts for the same specimens. In such specimens, the torque measurements provide a test of the angular dependence of the wall energy. The free magnetic energy density, E(a), must be in the form of an inverted parabola near a = 0. A more physically realistic distributed wall model must conform to these symmetry requirements. Our investigations into an appropriate modelling of the wall are continuing.

References [1] M. Takahashi, J. Nakamura F. Kirino, Y. Miyamura, N. Ohta and R. Suzuki, 35th Ann. Conf. Magn. Magn. Mater. (San Diego, CA, USA, 29 Oct.-1 Nov. 1990) abstract BB-03. [2] M. Takahashi, J. Nakamura, T. Niihara and K. Tatsuno, Proc. Magn. Opt. Rec. Intern. Syrup. '91, Magn. Soc. Jpn. 15 SI (1991) 49.

[3] T. Kobayashi, H. Tsuji, S. Tsunashima and S. Uchiyama, Jpn. J. Appl. Phys. 20 (1981) 2089. [4] E. Goursat, A Course in Mathematical Analysis, voi. 1 (Dover, New York, 1959) p. 118. [5] J. Nakamura, unpublished data. [6] J.O. Artman, unpublished analyses. [7] M. Tanaka, H. Yuzurihara and T. Tokita, IEEE Trans. Magn. MAG-23 (1987) 2955. [8] M. Hartmann, K. Witter, J. Reck and H.J. Tolle, IEEE Trans. Magn. MAG-22 (1986) 943. [9] H. lto, M. Yamaguchi and M. Naoe, J. Appl. Phys. 67 (1990) 5307. [10] S. Takayama, F. Kirino, Y. Suzuki, S. Okamine and N. Ohta, IEEE Trans. Magn. MAG-23 (1987) 2611. [11] S. Tsunashima, K. lmamura, T. Fujii, S. Uchiyama and M. Masuda, Jpn. J. Appl. Phys. 16 (1977) 1051. [12] R. Perthel, W. Keilig, R. Kosicik, U. R6pke and C.-G. D'Ambly, Phys. Stat. Sol. (a) 40 (1977) K135. [13] D.F. Shen, X.Y. Yu and Z.S. Shan, J. Appl. Phys. 67 (1990) 5319. [14] Our findings were reported first in an unpublished postdeadline conference presentation: J. Nakamura, J.O. Artman, R. Maimh~ill, M. Takahashi and M. Ojima, Magneto-Optical Recording Intern. Symp. '91 (Tokyo, Japan, 16-18 April 1991)abstract 18-U-10. [15] M. Kaneko, K. Aratani, Y. Mutoh, A. Nakaoki, K. Watanabe and H. Makino, Jpn. J. Appl. Phys. 28 $3 (1989) 27. [16] J.O. Artman, R. Malmh~ill, J. Nakamura, Y. Suzuki, H. Miyamoto and M. Ojima, J. Magv,. Soc. Jpn. 15 $2 (1991) 599.