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Surface modes in magnetic thin amorphous films of GdCoMo alloys
Journal of Magnetism and Magnetic Materials 37 (1983) 177-188 North-Holland Publishing Company
177
SURFACE MODES IN MAGNETIC THIN AMORPHOUS L.J. M A K S Y M O W I C Z
FILMS OF GdCoMo ALLOYS *
a n d D. S E N D O R E K
Academy of Mining and Metallurgy, Department of Solid State Physics, 30-059 Krak6w, al. Mickiewicza 30, Poland
Received 10 January 1983
Surface modes in spin wave resonance in thin amorphous films of (Gdj _xCox)l _yMoyalloys were studied. The samples were obtained with rf sputtering technique and a bias voltage was applied. Technological conditions were carefully pre-determined for which surface modes were excited in the resonance experiment. One surface mode was present for samples just after deposition and two modes could be observed in some cases for the same samples kept at room temperature for two or three months. The surface anisotropy constant K s was determined from the surface inhomogeneity (SI) model with symmetrical or non-symmetrical boundary conditions for one or two surface modes, respectively. The fitted K s values agree with theoretically predicted ones and they are also compatible with numbers found by experimentalists for monocrystalline, polycrystalline or amorphous films. For all samples we also determined the critical angles 0o's between the external magnetic field and the normal to the film plane for which the position of the surface mode coincides with the position of the first volume mode. The corresponding critical angles 0o's for the magnetization differ from ~r/4 which suggests the presence of surface inhomogeneities of the magnetization distribution.
1. Introduction Thin a m o r p h o u s films of R E - T M alloys are of m u c h interest for basic research as well as for their a p p l i c a t i o n . The onset of m a g n e t i s m or structure o f a m o r p h o u s m a t e r i a l s are typical current topics. S o m e of the a m o r p h o u s m a g n e t i c s exhibit cylindrical d o m a i n s , an i m p o r t a n t feature for p r a c t i c a l applications. A m o n g m a n y e x p e r i m e n t a l techniques emp l o y e d for the s t u d y of a m o r p h o u s thin film of R E - T M alloys, the low energy excitations of spin waves a n d f e r r o m a g n e t i c r e s o n a n c e p l a y an imp o r t a n t role. T h e m i c r o w a v e technique can be used for d e t e r m i n a t i o n o f some basic p a r a m e t e r s [ 1-8]: s a t u r a t i o n m a g n e t i z a t i o n M s, effective uniaxial m a g n e t i c a n i s o t r o p y field H r , exchange constant A or the g i r o m a g n e t i c factor y. Also, to some extent, one can c o n f i r m the h o m o g e n e i t y o f the s a m p l e s [9]. It should be stressed that the spin w a v e r e s o n a n c e t e c h n i q u e is the o n l y w a y of study* Supported by the Physics Institute of Polish Academy of Science. 0304-8853/83/0000-0000/$03.00
ing the surface modes. This sort of excitation is d u e to the surface a n i s o t r o p y energy being different from the b u l k value. The c o n t r i b u t i o n of the surface energy is significant in case of thin films w h e n one of the d i m e n s i o n s is d r a s t i c a l l y reduced. Possible excitations of surface m o d e s are controlled b y the state of the surface a n d close-tosurface i n h o m o g e n e i t i e s of the m a g n e t i z a t i o n . T h e r e f o r e some i n f o r m a t i o n on surface m a g n e t i s m is available from the spin wave r e s o n a n c e experiment. Thin a m o r p h o u s films of ( G d l _ x C o x ) l _ y M O y were studied in this p a p e r . T h e y are interesting n o t o n l y as m e m o r y elements with cylindrical d o m a i n structure b u t also for their m a g n e t i c properties. T h e effective m a g n e t i c m o m e n t for these alloys is t e m p e r a t u r e i n d e p e n d e n t for a wide range o f temp e r a t u r e s [10,11]. It can be c o n c l u d e d f r o m the spin wave r e s o n a n c e that the films are also m o r e h o m o g e n e o u s t h a n a m o r p h o u s films o f R E - T M alloys. T h e high h o m o g e n e i t y o f m a g n e t i z a t i o n for Gd-Co-Mo films allows for excitation o f the surface m o d e s [12,13] in the r e s o n a n c e of spin waves, if suitable b o u n d a r y c o n d i t i o n s are met.
© 1983 N o r t h - H o l l a n d
178
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
After many tests we were able to confine a set of technological parameters to the ones that produce surface modes. It is known from the literature that this sort of excitation is observed in monocrystalline samples but it is rather difficult to excite the surface modes in polycrystalline or amorphous films. Spin wave resonance was detected with an Xband microwave spectrometer. External magnetic fields could be applied for directions from perpendicular to parallel resonance. The observed surface modes were best described within the SI model which accounts for surface anisotropy and changes in saturation magnetization very close to the surface of the film. The experimental data on the position of surface modes and the first volume mode against the orientation of the external magnetic field determine the surface anisotropy constant and also the critical angles.
2. Experiment The amorphous films were deposited by a rf sputtering process. A mosaic target with Co matrix was covered with Gd and Mo bits. To get a wide range of concentrations, a set of targets was prepared with different content of Mo. This allowed us to obtain samples with concentration of Mo ranging from 3.5 to 16 at%. We then added Gd pieces onto the Co substrate of the target thus weighting the concentration of Co and Gd with a fixed Mo content in a film. The samples were deposited onto glass substrate Corning 7059 at a constant bias voltage U B = 100 V in argon atmosphere. The pressure was 6 × 10 -3 Torr and target-to-substrate distance was 45 mm. The composition of the films was taken with an X-ray microprobe; the thickness was measured by a very sensitive device for testing the smoothness of a surface, T A L Y S U R F . The spin wave resonance spectra were taken with a microwave spectrometer at 59.66 GHz. Samples of about 2 × 2 mm 2 were placed on a rotating support situated in the middle of a rectangular resonance cavity, the accuracy of orientation of the films with respect to the external magnetic field was less than one degree. The resonance spectra were taken
for all angles, from the perpendicular case when the field was applied normal to the film plane to the parallel case with the magnetic field in the film plane. The saturation magnetization was determined by a magnetic balance technique at room temperature. The uniaxial magnetic anisotrop~ field H~ was taken from resonance positions in perpendicular and parallel cases. For further studies only samples with a high homogeneity of magnetic parameters and chemical composition were carefully selected, on the base of results from a local site-to-site chemical analysis, torque curves, domain structure observation and resonance spectra for the perpendicular case, The spectra for samples with volume inhomogeneities split into several lines corresponding to different volume modes, which positions do not satisfy the known quadratic law H - n 2 even for higher order modes. From among the selected samples we identified films with volume modes only. The spectra of these samples comprise several lines and follow the H - n 2 law. Actually, we are interested in the other selected samples which exhibit surface modes and then we observe either two or three lines. For two lines, the intensity of the high-side field mode is lower than the intensity of the other mode. The first one is a surface mode and the other is a volume mode [3,14-17]. So we have one surface mode excited in this case. Two surface modes were excited for samples with three lines. The low field line is a volume mode with intensity much higher than intensities of the other surface modes. The only volume mode for samples with one or two surface modes is situated at a ferromagnetic resonance position or first volume mode position of the spin wave spectra: the two positions are close to each other.
3. Results The spectra obtained for samples with one surface mode and for different angles 8, between the applied magnetic field and normal to the film plane are presented in figs. 1-4. The critical angles 0c are marked. At 0 , = 8c all modes except one vanish or become very small [18]. We observe it as a transition of the surface mode into a volume one
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
A
I-
dP
fi
10
9
11
n~ R
Id-2
t•
/
~
~/kG/
179
rIq
9
11 H/k@/
10
9 10
9
11
H/kG/
8
10
9
11H/kCY
Fig. 1. Spin wave resonance spectra for different orientations of the applied magnetic field for sample A.
at the critical angle Oc when the position H u of the volume mode coincides with position H s of the surface mode, Hu = H s . Figs. 5 to 8 show the
dependence of H~ and H . on the angle 8.. It is seen that H s decreases faster than H u in some range of the angles O.. We expect to find a differI
dP
i
dH
dP dH
l
_J
__9
3
"
'
'
~,
AI~G/
~
6
d_P
dP
dH
f J
k
~ g
H'Z
-b~
4
s
6
HTNG/
Fig. 2. Spin wave resonance spectra for different orientations of the applied magnetic field for sample B.
180
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
_2
I
1
f
7
H/~G/
5.
s
6
H/kGl
3Z °
JF
H/kG/
3
Fig. 3. Spin wave resonance spectra for different orientations of the applied magnetic field for sample C. the bulk of the sample results mainly from the easy-plane shape anisotropy and easy axis anisotropy induced during the deposition process. The competition of these two anisotropies makes H,
ent angular dependence of H , and H s in amorphous films with easy axis of uniaxial magnetic anisotropy normal to the film plane for the following arguments. The effective field acting on spins in dP
I
___J 3
4
5
6
I dP
~
7 H/k6/
J
5
2
%°
I a~ dP I
S
z
~
-
6
~ ~TkG/
1
6 ~k6/
2
3
l
~ 5 HAG/
Fig. 4. Spin wave resonance spectra for different orientations of the applied magnetic field for sample D.
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys Hs,H~
Hs,Hu
/kG/
/kG/ 10 9
181
8
• surfQce mode xvolume mode
x
7
• surfoce mode x volume mode
9 8 ?
k= •°
6 5 4 3 2 1
6 5 4 3 2 1
o
6
X X
X X
10 10
20
30
40
50
60
70
80
90
20
~(
30
40
X
50
X
60
70
X
X
80
g0
O./°/
O.p/
Fig. 5. Dependence of the resonance fields H . and H s on the angle 0n for sample A.
Fig. 7. Dependence of the resonance fields H u and H s on the angle 0H for sample C. Hs~-Iu
IkO l
relatively weakly dependent on the angle 0n in the magnetic resonance experiment. And this is what we see in our experiment. For surface modes, the surface anisotropy of easy-plane type or easy direction type plays an important role, giving an extra contribution to the effective field acting on surface spins and so the angular dependence of this field would be more pronounced. We find in our experiment that the surface anisotropy is of the easy-plane type which is consistent with the fact that the surface modes can be excited only for this type of surface anisotropy. The samples were measured again after two or three months to see if there are any changes in the state of their surfaces. In some cases, for sample number D1, we got two surface modes when originally there was one surface mode. Spectra obtained for the sample with two surface modes are shown in fig. 9 for different 0n from perpendicular resonance to the critical angles 0d and 0c2 of the two modes. Hs~Hu
,%
• surfoce x
8 7 6 5 4
mode
vol.ume m o d e
°°
3 2 1
10
20
30
40
50
60
70
80
90 (~/o/
Fig. 6. Dependence of the resonance fields H u and Hs on the angle 0n for sample B.
8 7 6 5 4 3 2 1
• surfoce mode , volume mode °
•
°°
x xxx
x
x
x
~
x x
10
20
30
40
x
x
50
x
60
x
70
80
90
Oh/V
Fig. 8. Dependence of the resonance fields H u and H s on the angle 0H for sample D.
4. Discussion The SI model was employed to fit the experimental data. Symmetrical boundary conditions were used for one surface mode and non-symmetrical ones for the case of two surface modes. The model is described in the many papers of Puszkarski; ref. [19] gives a comprehensive review. We adopt a classical approach with equation of motion for spins in ferromagnetically ordered substances. In the SI model the boundary conditions include surface anisotropy energy and magnetization inhomogeneities close to the surface [20,21]. A simple form of the surface anisotropy E s --- - K s cos20 is taken, where K s is the surface anisotropy constant and O is the angle between magnetization and the normal to the film plane. Let us consider spins in the bulk of a film situated in ( x , y ) plane, see fig. 10. The external magnetic field H is in the (y, z) plane and makes an angle On with the z-axis; the microwave field h
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
182
I
V
-
~- .........
4 ~-~ . . . . . . . ~ .... ~ k G /
2
3
4
5
6
H/kG/
5
6
H/kG/
3o 1
I
_J
f
Fig. 9. Spin wave resonance spectra against OH for sample D1 with two surface modes.
is along the x-axis. The magnetization direction is given by angles 0, % In spherical coordinates one has
M = M~i + moo + m~c~,
(1)
where M~ is the saturation magnetization, m0 and rn~ are microwave components of the magnetization with m o / M ~ << 1 and m~/M~ << 1. It can be shown that the propagation of spin waves takes place along the normal to the film plane for thin metallic samples. So we can assume the microwave components of the magnetization in the form
The second term in eq. (3) is the torque from the exchange energy and the last perturbative term comes from the microwave field energy. Taking only linear terms, one get the following equations for the microwave components
1 drn ( z , t ) 7 dt
+~
-M~ho,
mo( z, t) = mOoe i~'-F k-~)
(2)
The equation of motion for magnetization M, with no damping term, is ~'+M×M2
v'ZM+M×h
1 02Emo(z,t) -aO -7
1 O2E + M, sin~ 3cg 30 rn'e(z' t)
m c e ( z , t ) = m 0~ ei(~,t T- kz)
dt - 7
2A - - W2rno(z, t) M~
,
(3)
s
where ~"= -q5 OE/OO + 0(1/sin 0) aE/O~ is the torque given by the density energy E.
1 d m o ( z , t) 7 dt
(4)
2A ~72m~(z, t) Ms 1
02E
M~ s i n 2 0 0qp 2
1
mer(z' t)
~)2E
MssinO OcpOOmO(z, t ) + M , h ~ . Substituting (2) into (4) one gets the dispersion
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
183
imaginary k = ik s, which describes damping of the microwave component of M with increasing distance from the surface, so this case corresponds to the surface modes. The resonance field H s for the surface mode is larger than ferromagnetic field H u for a uniform k = 0. Since the shift H ~ - H u is small, we get from (8) in the first approximation
/
2A k~ Hs = Hu + ~ cos(0 - O , ) "
Fig. 10. The coordinates system. relation [22]
M~ sin20 3q~2
x
M-~ ----S 30
l -
02E )2.
(5)
Mss-inO ~--~-3-0
The energy density E(O, q~) is the sum of contributions
(6)
E = E . + Ed + Ex ,
where E H = -MsH(sin O sin OH sin q~+cos O cos OH) is the energy of the external magnetic field H, Ed = 2~rM} cos20 is the demagnetization energy and E r = - K cos20 is the energy of uniaxial anisotropy. The equilibrium conditions 3 E / 3 0 = 0 and 3E/3¢p = 0 yield 9~= ~r/2, HM~ sin(0 - On) = -K¢ff sin 20,
(7)
where Keff= K - 2~rM2. With energy given by (6) the relation dispersion (5) becomes =
H c o s ( 0 - OH) + - - c o s Ms
x
20
+Mss k ]
cos(O-o.)+--2Keff cos2O+ 2Ak
]
2]
(8) For k 2 > 0 we get real k and so the microwave components (2) are of a cos-like form, e.g. we have volume modes. The case k 2 < 0 provides purely
(9)
The wave vector k~ results from boundary conditions. We will see that the allowed values of k s depend on the angle O and that there is a critical value O = #c for which k~ = 0 when the position of the surface mode coincides with the uniform mode, H s = H,. At this angle the surface mode ceases to exist and becomes a volume mode. The boundary conditions come from eq. (3) applied to the surface spins for which an extra surface anisotropy term E ~ - - - K s cos20 is present. We also account for the expected changes of magnetization M s near the surface. This yields the following boundary conditions [21] Ohm o + p m o = O, 3r,m,~ + qm~ = 0,
(10)
where p = - (KJA)
cos 20 + ( 3 n M s ) / m s
and
(10a)
q = _ ( K s / A ) cos20 + ( 3 n M s ) / m s .
The conditions (10) are to be applied to both surfaces of a film and On denotes the directional derivative along normal to the surface. The term ( O n M s ) / M s accounts for possible variations of the magnetization close to the surface [20]. Within the circular precession approximation [20,21], the boundary conditions lead to the equation for the allowed wave vectors k~ tanh(ksL ) - (P' +P2)ks,
(ll)
k2 + P,P2
where p ~ and P2 are values of p at the two surfaces of a film and L is film thickness. In general the effective pinning parameters are non-symmetrical, P, *=P2- This might be due to a different surface
L.J. Maksymowicz,D. Sendorek/ Surfacemodesin films of GdCoMoalloys
184 o(7, I
30
F o r symmetrical b o u n d a r y conditions p t = P2 °n13 one surface m o d e is seen. With the approximate solutions (12), one car rewrite (9) in the form
20
[(H~-Hu)C°s(O-OH)]'/2=(
i
2 ) ]K~I
10
× [cos 20-~(SnM~)/M~I. i.8 b.exp~,t.....17od.9 ...............
COS 20"
Fig. 11. Dependence of a = [(H~ - H~) cos(0 - 0H)]I/2 against cos 20 for sample A. anisotropy constant K s on both surfaces a n d / o r different (8.M~)/M~. It can be seen from (11) that for the unpinned case pt = P 2 = 0, one gets k~ = 0 which is just the condition for the critical angle v%. N o t e that #c = ~r/4 only if the magnetization variations (O,Ms)/M s are ignored, see eq. (10a). Eq. (11) for the allowed k~ is to be solved numerically. However, for typical parameters one can evaluate that k~L>> 1, unless we are very close to the critical angle and the two approximate solutions are then simply
kl=pl, k2 =p2.
(12)
Therefore we expect two surface modes if p~ ~ P2.
0Q
with OH known, the magnetization direction angk 0 is given from the equilibrium condition (7). N o ~ we can plot the left hand side of (13) againsl cos 20. If the model is correct we expect a straighl line, with deviations perhaps in the very vicinity ol the critical angle, about 2 °. We get the surfac~ anisotropy IKsl from the slope of this line, th~ interception with the x-axis gives the magnetiza. tion variation (8,Ms)/M s. The saturation magnetization M~ was k n o w r from magnetic balance measurements. The effective anisotropy constant Kerf was calculated from the expression [5] 2 K c r r / M , = - ½H~ - H ~ + [H~(H~
,
.f
40 30 20 10 0.4
f
0.5
0.6
o.7
o18
o19
lb c o s 20"
Fig. 12. Dependence of a = [(Hs - H,) cos(0
-
+ 1.25H/1)] '/2
(14)
where H~ and H ~ are the resonance fields for the uniform m o d e at parallel and perpendicular reso-
/G'~/ 50
(131
OH)]I/2 against cos 20 for sample B.
L J, Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
185
5O 4O 30
20
0.4
0s
t
L~29"
06
0'7
08
0~
-
cos 21)
Fig. 13. Dependence o f a = [(H, - H u ) cos(8 - 8H)] 1/2 against cos 28 for sample C.
OC
IG"~ 50 40 30 20 I0
--o.~
K'~
.
o~o.3
o~,
, o.s
o16
o.7
o~
ty~,_e39,
o'.9
_
lZ cos 20
Fig. 14. Dependence of t~= [(H~ - Hu) cos(8 - 8H)]1/2 against cos 2a for sample D.
nance, respectively. The values of H,I,I and Hu~ are k n o w n within error of about 20 G. We would like to c o m m e n t on the choice of the constant A. In this paper we take the value calculated in ref. [231. We believe the numbers are correct since we obtained a very good agreement for our A parameter measured from a spin wave resonance for volume modes with up to 7 lines, with A given in ref. [23]. Unfortunately, volume modes are excited for a concentration range different from concentrations with surface modes pre-
sent, so no direct measurement of .4 was possible. The experimental data from figs. 1 - 4 are calculated in the new variables suitable for testing eq. (13) and presented in figs. 11-14. It is seen that we get the straight line within the experimental error which confirms the proposed model. The fitted values of K s sound reasonable, and these are collected in table 1. In sample n u m b e r D 1 we got two surface modes after the film was kept at r o o m temperature for two or three months, the two straight lines from the two modes are shown in
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
186
Table 1 Parameters used in the model: L thickness of the film, M s - magnetization, H~ - resonance field for uniform mode in perpendicular resonance, HI - the field in parallel resonance, K - uniaxial anisotropy constant and A - exchange energy constant Parameters fitted from the model: 0~ exp(#~ exp) - the critical angle for the magnetic field (magnetization) direction as observed in Sample
Composition
L (A)
M~ (G)
H~ (G)
Hi (G)
K (erg/cm 3)
A (erg/cm)
A B C D
( G d 0.06 C 0 0 . 9 4 ) 0 . 9 4 M o o . 0 6
8500 9300 9300 6400
700 150 150 220
9520 3800 3810 3770
1100 2610 2680 2950
7.7 × 10 5
(Gd 0.1COo.9 )0.94MOo.06 (Gd 0.I COO.9 )0.94MO0.06 (Gd o.n C°0.89)0.88Moo.12
2.4×10 5
6.2 x 10 7 6.4x 10 7 6.4× 10 7 3×10 "
Sample with two surface modes D1 (Gd o.11Coo.89)o.88Moo.12
6400
230
3840
2920
2.6×10 5
3×10 7
fig. 15. O n e c a n see that the lines are n e a r l y p a r a l lel, so Ks'S o n b o t h s u r f a c e s are a b o u t the s a m e (see t a b l e 1). T h e d i f f e r e n c e in t h e r e s u l t a n t pinn i n g for the t w o m o d e s a n d , t h e r e f o r e , r e s u l t i n g in d i f f e r e n t c r i t i c a l a n g l e s Oc, is d u e to d i f f e r e n t v a r i a t i o n s o f m a g n e t i z a t i o n s (3nM~)/M~ o n the t w o surfaces. W e suggest t h a t it is the s a t u r a t i o n m a g n e t i z a t i o n d i s t r i b u t i o n n e a r the s u r f a c e s (or r a t h e r o n the free surface, n o t the o n e in c o n t a c t w i t h the s u b s t r a t e ) t h a t p e r h a p s c h a n g e s w h e n the s a m p l e is aging, w h i l e the s u r f a c e a n i s o t r o p y rem a i n s the same. T h e m o d e l is also s u p p o r t e d b y the fact t h a t the c r i t i c a l a n g l e s d e t e r m i n e d f r o m the e x t r a p o l a t i o n
5. C o n c l u s i o n S p i n w a v e r e s o n a n c e s t u d y of thin a m o r p h o u , f i l m s of ( G d l _ x C 0 ~ ) l >.M0v alloys i n d i c a t e thai w e c a n e x c i t e s u r f a c e m o d e s in t h e s e films. Surfac~
f i r s t s u r f o c e mode \
40 s e c o n d surf 30 20 10 ~c4T ~"
_ C>C p., 0.2
1.e~p=.~o
Uc~ ,-,J
. 0.3
~¢./. -..., .
.
0.4
.
0.6
.
.
0.7
.
o.s
8.4;,< 10 4
o f the s t r a i g h t lines a g r e e well w i t h the sam( a n g l e s o b s e r v e d d i r e c t l y in the r e s o n a n c e experiment. N e v e r t h e l e s s , t o o little is k n o w n to f i n d an 5 d e f i n i t e r e l a t i o n s b e t w e e n the s u r f a c e parameter,, a n d thickness, c o n c e n t r a t i o n o r t e c h n o l o g y of preparing samples.
oC /G'y 50
8 . 0 X 10 4
0.9
/
exP ~;-2 =30o
Fig. 15. The same as in figs. 11-14 for sample DI with two surface modes.
COS '20"
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
187
d i r e c t r e s o n a n c e e x p e r i m e n t , 0¢ fit (v~c fit) - the s a m e v a l u e e x t r a p o l a t e d a c c o r d i n g to eq. (13) (figs. 1 1 - 1 5 ) a n d K~ - s u r f a c e anisotropy constant
0ceXp
l~ceXp
0cfit
~fit
Ks (erg/cm 2)
5° 24 ° 23 ° 34 °
17 ° 31 ° 29 ° 39 °
5° 23 ° 22 ° 34 °
17 ° 28 ° 28 ° 39 °
- 3.4 -0.7 -0.9 -0.35
0eelxp = 37 ° 0¢e2xp = 26 °
O~lxp = 43 ° v~e~p = 30 °
0f~ t = 36 ° 0~f~t = 27 °
o'¢f~t = 42 ° 0 ~ t = 32 °
Ks, = - 0 . 3 Ks2 = - 0 . 4
modes were observed mainly in monocrystalline films. The surface inhomogeneity model and also the volume inhomogeneity model predict surface modes, if we are able to produce required surface parameters of a film such as easy plane type of anisotropy or some variations of magnetization distributions near the surface. In each case it is connected with the technology of producing samples which controls the process of growing a film and also determines the state of the surface. With m a n y experimental efforts we were able to estabhsh a range of technological parameters to get films with the surface modes. Still, we could not fully control the deposition process and we had to select samples to pick out ones with highly homogeneous bulk parameters and proper surface properties. The SI model predicts surface modes for some range of the effective pinning parameters on the two surfaces of a film. The pinning parameter is the sum of two terms, p = - ( K s / A ) cos20+ O, M s ) / M s. The first term comes from the surface anisotropy energy Es = - K s cos20 and is angular dependent. The other term describes changes of saturation magnetization near the surface. Surface modes can be excited only for positive p as for easy plane type of anisotropy. The value p = 0 determines the critical angle 0 c. If only the first term was present then 0 c = ~r/4. We observe Oc less then ~r/4 which means that the magnetization is decreasing near the surface, as expected. The SI model predicts a straight line for the angular dependence of resonance field in suitable
variables chosen according to eq. (13). Experimental data follow this linear dependence, figs. 11-15, and also the extrapolated critical angles coincide with values taken directly from experiment. We believe therefore that the model is basically correct. In some cases we got two surface modes for a sample kept at room temperature for some time. The change in the properties was associated with different states of the same free surface of the sample. It follows from fig. 15 that the change is due to different magnetization distribution while the surface anisotropy is the same. N o systematic relation is stated between surface state and thickness, composition or technological parameters during the deposition.
Acknowledgements We are grateful to Dr. Z. Obuszko for magnetic balance measurements of the saturation magnetization and to Mr. J. Sokulski for samples preparation.
References [1] R . C . T a y l o r a n d A. G a n g u l e e , J. A p p l . Phys. 47 (1976) 4660. [2] H . Nos~, 7 t h I C M T F , R e g e n s b u r g (1975). [3] G . S u r a n , R. K r i s h n a n , S h i v a P r a s a d , H. J o u v e a n d R. M e y e r , I E E E T r a n s . o n M a g n . M A G - 1 6 (1980) 1342. [4] L.J. M a k s y m o w i c z , A. K o l o d z i e j c z y k , H . J a n k o w s k i a n d J. W e n d a , T h i n Solid F i l m s 4 4 (1977) L23.
188
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
[5] L.J. Maksymowicz and A. Koz/owski, J. Magn. Magn. Mat. 15-18 (1980) 1098. [6] D.C. Cronemeyer, AlP Conf. Proc. 18 (1973) 85. [7] Z. Frait, I. Nagy and T. Tarnoczi, Phys. Lett. 55A (1970) 429. [81 I. Nagy, T. Tarnoczi and Z. Frait, Physica 86-88B (1977) 764. [9]. S. Prasad, R. Krishnan, G. Suran, J. Sztern, H. Jouve and R. Meyer, J. Appl. Phys. 50 (1979) 1623. [10] L.J.Maksymowicz, Z. Obuszko and D. Sendorek, to be published. [11] A.H. Eschenfelder, in: Ferromagnetic Materials, vol. 2, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1980) p. 345. [12] L.J. Maksymowicz, Physica 86-88B (1977) 1412. [13] L.J. Maksymowicz, Thin Solid Films 51 (1978) 205. [14] J.T. Yu, R.A. Turk and P.E. Wigen, 18th Ann. Conf. Magnetism and Magn. Materials, Denver (1972).
[15] J.T. Yu, R.A. Turk and P.E. Wigen, Phys. Rev. B 11 (1975) 420. [16] P. Wolf, Z. Angew. Phys. 14 (1962) 212. [17] P. Wolf, Basic Problems in Thin Film Physics (Vandenhoeck, G6ttingen, 1965) p. 392. [18] O.G. Ramer and C.H. Wilts, Phys. Stat. Sol. (b) 79 (1977) 313. [19] H. Puszkarski, Progr. Surface 9 (1979) 191. [20] M. Sparks, Phys. Rev. BI (1970) 3869. [21] J. Spalek and A.Z. Maksymowicz, Solid State Commun. 15 (1974) 559. [22] A.Z. Maksymowicz and K.D. Leaver, J. Phys. F3 (1973) 1031. [23] R. Hasegawa, J. Appl. Phys. 46 (1975) 5263.
177
SURFACE MODES IN MAGNETIC THIN AMORPHOUS L.J. M A K S Y M O W I C Z
FILMS OF GdCoMo ALLOYS *
a n d D. S E N D O R E K
Academy of Mining and Metallurgy, Department of Solid State Physics, 30-059 Krak6w, al. Mickiewicza 30, Poland
Received 10 January 1983
Surface modes in spin wave resonance in thin amorphous films of (Gdj _xCox)l _yMoyalloys were studied. The samples were obtained with rf sputtering technique and a bias voltage was applied. Technological conditions were carefully pre-determined for which surface modes were excited in the resonance experiment. One surface mode was present for samples just after deposition and two modes could be observed in some cases for the same samples kept at room temperature for two or three months. The surface anisotropy constant K s was determined from the surface inhomogeneity (SI) model with symmetrical or non-symmetrical boundary conditions for one or two surface modes, respectively. The fitted K s values agree with theoretically predicted ones and they are also compatible with numbers found by experimentalists for monocrystalline, polycrystalline or amorphous films. For all samples we also determined the critical angles 0o's between the external magnetic field and the normal to the film plane for which the position of the surface mode coincides with the position of the first volume mode. The corresponding critical angles 0o's for the magnetization differ from ~r/4 which suggests the presence of surface inhomogeneities of the magnetization distribution.
1. Introduction Thin a m o r p h o u s films of R E - T M alloys are of m u c h interest for basic research as well as for their a p p l i c a t i o n . The onset of m a g n e t i s m or structure o f a m o r p h o u s m a t e r i a l s are typical current topics. S o m e of the a m o r p h o u s m a g n e t i c s exhibit cylindrical d o m a i n s , an i m p o r t a n t feature for p r a c t i c a l applications. A m o n g m a n y e x p e r i m e n t a l techniques emp l o y e d for the s t u d y of a m o r p h o u s thin film of R E - T M alloys, the low energy excitations of spin waves a n d f e r r o m a g n e t i c r e s o n a n c e p l a y an imp o r t a n t role. T h e m i c r o w a v e technique can be used for d e t e r m i n a t i o n o f some basic p a r a m e t e r s [ 1-8]: s a t u r a t i o n m a g n e t i z a t i o n M s, effective uniaxial m a g n e t i c a n i s o t r o p y field H r , exchange constant A or the g i r o m a g n e t i c factor y. Also, to some extent, one can c o n f i r m the h o m o g e n e i t y o f the s a m p l e s [9]. It should be stressed that the spin w a v e r e s o n a n c e t e c h n i q u e is the o n l y w a y of study* Supported by the Physics Institute of Polish Academy of Science. 0304-8853/83/0000-0000/$03.00
ing the surface modes. This sort of excitation is d u e to the surface a n i s o t r o p y energy being different from the b u l k value. The c o n t r i b u t i o n of the surface energy is significant in case of thin films w h e n one of the d i m e n s i o n s is d r a s t i c a l l y reduced. Possible excitations of surface m o d e s are controlled b y the state of the surface a n d close-tosurface i n h o m o g e n e i t i e s of the m a g n e t i z a t i o n . T h e r e f o r e some i n f o r m a t i o n on surface m a g n e t i s m is available from the spin wave r e s o n a n c e experiment. Thin a m o r p h o u s films of ( G d l _ x C o x ) l _ y M O y were studied in this p a p e r . T h e y are interesting n o t o n l y as m e m o r y elements with cylindrical d o m a i n structure b u t also for their m a g n e t i c properties. T h e effective m a g n e t i c m o m e n t for these alloys is t e m p e r a t u r e i n d e p e n d e n t for a wide range o f temp e r a t u r e s [10,11]. It can be c o n c l u d e d f r o m the spin wave r e s o n a n c e that the films are also m o r e h o m o g e n e o u s t h a n a m o r p h o u s films o f R E - T M alloys. T h e high h o m o g e n e i t y o f m a g n e t i z a t i o n for Gd-Co-Mo films allows for excitation o f the surface m o d e s [12,13] in the r e s o n a n c e of spin waves, if suitable b o u n d a r y c o n d i t i o n s are met.
© 1983 N o r t h - H o l l a n d
178
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
After many tests we were able to confine a set of technological parameters to the ones that produce surface modes. It is known from the literature that this sort of excitation is observed in monocrystalline samples but it is rather difficult to excite the surface modes in polycrystalline or amorphous films. Spin wave resonance was detected with an Xband microwave spectrometer. External magnetic fields could be applied for directions from perpendicular to parallel resonance. The observed surface modes were best described within the SI model which accounts for surface anisotropy and changes in saturation magnetization very close to the surface of the film. The experimental data on the position of surface modes and the first volume mode against the orientation of the external magnetic field determine the surface anisotropy constant and also the critical angles.
2. Experiment The amorphous films were deposited by a rf sputtering process. A mosaic target with Co matrix was covered with Gd and Mo bits. To get a wide range of concentrations, a set of targets was prepared with different content of Mo. This allowed us to obtain samples with concentration of Mo ranging from 3.5 to 16 at%. We then added Gd pieces onto the Co substrate of the target thus weighting the concentration of Co and Gd with a fixed Mo content in a film. The samples were deposited onto glass substrate Corning 7059 at a constant bias voltage U B = 100 V in argon atmosphere. The pressure was 6 × 10 -3 Torr and target-to-substrate distance was 45 mm. The composition of the films was taken with an X-ray microprobe; the thickness was measured by a very sensitive device for testing the smoothness of a surface, T A L Y S U R F . The spin wave resonance spectra were taken with a microwave spectrometer at 59.66 GHz. Samples of about 2 × 2 mm 2 were placed on a rotating support situated in the middle of a rectangular resonance cavity, the accuracy of orientation of the films with respect to the external magnetic field was less than one degree. The resonance spectra were taken
for all angles, from the perpendicular case when the field was applied normal to the film plane to the parallel case with the magnetic field in the film plane. The saturation magnetization was determined by a magnetic balance technique at room temperature. The uniaxial magnetic anisotrop~ field H~ was taken from resonance positions in perpendicular and parallel cases. For further studies only samples with a high homogeneity of magnetic parameters and chemical composition were carefully selected, on the base of results from a local site-to-site chemical analysis, torque curves, domain structure observation and resonance spectra for the perpendicular case, The spectra for samples with volume inhomogeneities split into several lines corresponding to different volume modes, which positions do not satisfy the known quadratic law H - n 2 even for higher order modes. From among the selected samples we identified films with volume modes only. The spectra of these samples comprise several lines and follow the H - n 2 law. Actually, we are interested in the other selected samples which exhibit surface modes and then we observe either two or three lines. For two lines, the intensity of the high-side field mode is lower than the intensity of the other mode. The first one is a surface mode and the other is a volume mode [3,14-17]. So we have one surface mode excited in this case. Two surface modes were excited for samples with three lines. The low field line is a volume mode with intensity much higher than intensities of the other surface modes. The only volume mode for samples with one or two surface modes is situated at a ferromagnetic resonance position or first volume mode position of the spin wave spectra: the two positions are close to each other.
3. Results The spectra obtained for samples with one surface mode and for different angles 8, between the applied magnetic field and normal to the film plane are presented in figs. 1-4. The critical angles 0c are marked. At 0 , = 8c all modes except one vanish or become very small [18]. We observe it as a transition of the surface mode into a volume one
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
A
I-
dP
fi
10
9
11
n~ R
Id-2
t•
/
~
~/kG/
179
rIq
9
11 H/k@/
10
9 10
9
11
H/kG/
8
10
9
11H/kCY
Fig. 1. Spin wave resonance spectra for different orientations of the applied magnetic field for sample A.
at the critical angle Oc when the position H u of the volume mode coincides with position H s of the surface mode, Hu = H s . Figs. 5 to 8 show the
dependence of H~ and H . on the angle 8.. It is seen that H s decreases faster than H u in some range of the angles O.. We expect to find a differI
dP
i
dH
dP dH
l
_J
__9
3
"
'
'
~,
AI~G/
~
6
d_P
dP
dH
f J
k
~ g
H'Z
-b~
4
s
6
HTNG/
Fig. 2. Spin wave resonance spectra for different orientations of the applied magnetic field for sample B.
180
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
_2
I
1
f
7
H/~G/
5.
s
6
H/kGl
3Z °
JF
H/kG/
3
Fig. 3. Spin wave resonance spectra for different orientations of the applied magnetic field for sample C. the bulk of the sample results mainly from the easy-plane shape anisotropy and easy axis anisotropy induced during the deposition process. The competition of these two anisotropies makes H,
ent angular dependence of H , and H s in amorphous films with easy axis of uniaxial magnetic anisotropy normal to the film plane for the following arguments. The effective field acting on spins in dP
I
___J 3
4
5
6
I dP
~
7 H/k6/
J
5
2
%°
I a~ dP I
S
z
~
-
6
~ ~TkG/
1
6 ~k6/
2
3
l
~ 5 HAG/
Fig. 4. Spin wave resonance spectra for different orientations of the applied magnetic field for sample D.
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys Hs,H~
Hs,Hu
/kG/
/kG/ 10 9
181
8
• surfQce mode xvolume mode
x
7
• surfoce mode x volume mode
9 8 ?
k= •°
6 5 4 3 2 1
6 5 4 3 2 1
o
6
X X
X X
10 10
20
30
40
50
60
70
80
90
20
~(
30
40
X
50
X
60
70
X
X
80
g0
O./°/
O.p/
Fig. 5. Dependence of the resonance fields H . and H s on the angle 0n for sample A.
Fig. 7. Dependence of the resonance fields H u and H s on the angle 0H for sample C. Hs~-Iu
IkO l
relatively weakly dependent on the angle 0n in the magnetic resonance experiment. And this is what we see in our experiment. For surface modes, the surface anisotropy of easy-plane type or easy direction type plays an important role, giving an extra contribution to the effective field acting on surface spins and so the angular dependence of this field would be more pronounced. We find in our experiment that the surface anisotropy is of the easy-plane type which is consistent with the fact that the surface modes can be excited only for this type of surface anisotropy. The samples were measured again after two or three months to see if there are any changes in the state of their surfaces. In some cases, for sample number D1, we got two surface modes when originally there was one surface mode. Spectra obtained for the sample with two surface modes are shown in fig. 9 for different 0n from perpendicular resonance to the critical angles 0d and 0c2 of the two modes. Hs~Hu
,%
• surfoce x
8 7 6 5 4
mode
vol.ume m o d e
°°
3 2 1
10
20
30
40
50
60
70
80
90 (~/o/
Fig. 6. Dependence of the resonance fields H u and Hs on the angle 0n for sample B.
8 7 6 5 4 3 2 1
• surfoce mode , volume mode °
•
°°
x xxx
x
x
x
~
x x
10
20
30
40
x
x
50
x
60
x
70
80
90
Oh/V
Fig. 8. Dependence of the resonance fields H u and H s on the angle 0H for sample D.
4. Discussion The SI model was employed to fit the experimental data. Symmetrical boundary conditions were used for one surface mode and non-symmetrical ones for the case of two surface modes. The model is described in the many papers of Puszkarski; ref. [19] gives a comprehensive review. We adopt a classical approach with equation of motion for spins in ferromagnetically ordered substances. In the SI model the boundary conditions include surface anisotropy energy and magnetization inhomogeneities close to the surface [20,21]. A simple form of the surface anisotropy E s --- - K s cos20 is taken, where K s is the surface anisotropy constant and O is the angle between magnetization and the normal to the film plane. Let us consider spins in the bulk of a film situated in ( x , y ) plane, see fig. 10. The external magnetic field H is in the (y, z) plane and makes an angle On with the z-axis; the microwave field h
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
182
I
V
-
~- .........
4 ~-~ . . . . . . . ~ .... ~ k G /
2
3
4
5
6
H/kG/
5
6
H/kG/
3o 1
I
_J
f
Fig. 9. Spin wave resonance spectra against OH for sample D1 with two surface modes.
is along the x-axis. The magnetization direction is given by angles 0, % In spherical coordinates one has
M = M~i + moo + m~c~,
(1)
where M~ is the saturation magnetization, m0 and rn~ are microwave components of the magnetization with m o / M ~ << 1 and m~/M~ << 1. It can be shown that the propagation of spin waves takes place along the normal to the film plane for thin metallic samples. So we can assume the microwave components of the magnetization in the form
The second term in eq. (3) is the torque from the exchange energy and the last perturbative term comes from the microwave field energy. Taking only linear terms, one get the following equations for the microwave components
1 drn ( z , t ) 7 dt
+~
-M~ho,
mo( z, t) = mOoe i~'-F k-~)
(2)
The equation of motion for magnetization M, with no damping term, is ~'+M×M2
v'ZM+M×h
1 02Emo(z,t) -aO -7
1 O2E + M, sin~ 3cg 30 rn'e(z' t)
m c e ( z , t ) = m 0~ ei(~,t T- kz)
dt - 7
2A - - W2rno(z, t) M~
,
(3)
s
where ~"= -q5 OE/OO + 0(1/sin 0) aE/O~ is the torque given by the density energy E.
1 d m o ( z , t) 7 dt
(4)
2A ~72m~(z, t) Ms 1
02E
M~ s i n 2 0 0qp 2
1
mer(z' t)
~)2E
MssinO OcpOOmO(z, t ) + M , h ~ . Substituting (2) into (4) one gets the dispersion
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
183
imaginary k = ik s, which describes damping of the microwave component of M with increasing distance from the surface, so this case corresponds to the surface modes. The resonance field H s for the surface mode is larger than ferromagnetic field H u for a uniform k = 0. Since the shift H ~ - H u is small, we get from (8) in the first approximation
/
2A k~ Hs = Hu + ~ cos(0 - O , ) "
Fig. 10. The coordinates system. relation [22]
M~ sin20 3q~2
x
M-~ ----S 30
l -
02E )2.
(5)
Mss-inO ~--~-3-0
The energy density E(O, q~) is the sum of contributions
(6)
E = E . + Ed + Ex ,
where E H = -MsH(sin O sin OH sin q~+cos O cos OH) is the energy of the external magnetic field H, Ed = 2~rM} cos20 is the demagnetization energy and E r = - K cos20 is the energy of uniaxial anisotropy. The equilibrium conditions 3 E / 3 0 = 0 and 3E/3¢p = 0 yield 9~= ~r/2, HM~ sin(0 - On) = -K¢ff sin 20,
(7)
where Keff= K - 2~rM2. With energy given by (6) the relation dispersion (5) becomes =
H c o s ( 0 - OH) + - - c o s Ms
x
20
+Mss k ]
cos(O-o.)+--2Keff cos2O+ 2Ak
]
2]
(8) For k 2 > 0 we get real k and so the microwave components (2) are of a cos-like form, e.g. we have volume modes. The case k 2 < 0 provides purely
(9)
The wave vector k~ results from boundary conditions. We will see that the allowed values of k s depend on the angle O and that there is a critical value O = #c for which k~ = 0 when the position of the surface mode coincides with the uniform mode, H s = H,. At this angle the surface mode ceases to exist and becomes a volume mode. The boundary conditions come from eq. (3) applied to the surface spins for which an extra surface anisotropy term E ~ - - - K s cos20 is present. We also account for the expected changes of magnetization M s near the surface. This yields the following boundary conditions [21] Ohm o + p m o = O, 3r,m,~ + qm~ = 0,
(10)
where p = - (KJA)
cos 20 + ( 3 n M s ) / m s
and
(10a)
q = _ ( K s / A ) cos20 + ( 3 n M s ) / m s .
The conditions (10) are to be applied to both surfaces of a film and On denotes the directional derivative along normal to the surface. The term ( O n M s ) / M s accounts for possible variations of the magnetization close to the surface [20]. Within the circular precession approximation [20,21], the boundary conditions lead to the equation for the allowed wave vectors k~ tanh(ksL ) - (P' +P2)ks,
(ll)
k2 + P,P2
where p ~ and P2 are values of p at the two surfaces of a film and L is film thickness. In general the effective pinning parameters are non-symmetrical, P, *=P2- This might be due to a different surface
L.J. Maksymowicz,D. Sendorek/ Surfacemodesin films of GdCoMoalloys
184 o(7, I
30
F o r symmetrical b o u n d a r y conditions p t = P2 °n13 one surface m o d e is seen. With the approximate solutions (12), one car rewrite (9) in the form
20
[(H~-Hu)C°s(O-OH)]'/2=(
i
2 ) ]K~I
10
× [cos 20-~(SnM~)/M~I. i.8 b.exp~,t.....17od.9 ...............
COS 20"
Fig. 11. Dependence of a = [(H~ - H~) cos(0 - 0H)]I/2 against cos 20 for sample A. anisotropy constant K s on both surfaces a n d / o r different (8.M~)/M~. It can be seen from (11) that for the unpinned case pt = P 2 = 0, one gets k~ = 0 which is just the condition for the critical angle v%. N o t e that #c = ~r/4 only if the magnetization variations (O,Ms)/M s are ignored, see eq. (10a). Eq. (11) for the allowed k~ is to be solved numerically. However, for typical parameters one can evaluate that k~L>> 1, unless we are very close to the critical angle and the two approximate solutions are then simply
kl=pl, k2 =p2.
(12)
Therefore we expect two surface modes if p~ ~ P2.
0Q
with OH known, the magnetization direction angk 0 is given from the equilibrium condition (7). N o ~ we can plot the left hand side of (13) againsl cos 20. If the model is correct we expect a straighl line, with deviations perhaps in the very vicinity ol the critical angle, about 2 °. We get the surfac~ anisotropy IKsl from the slope of this line, th~ interception with the x-axis gives the magnetiza. tion variation (8,Ms)/M s. The saturation magnetization M~ was k n o w r from magnetic balance measurements. The effective anisotropy constant Kerf was calculated from the expression [5] 2 K c r r / M , = - ½H~ - H ~ + [H~(H~
,
.f
40 30 20 10 0.4
f
0.5
0.6
o.7
o18
o19
lb c o s 20"
Fig. 12. Dependence of a = [(Hs - H,) cos(0
-
+ 1.25H/1)] '/2
(14)
where H~ and H ~ are the resonance fields for the uniform m o d e at parallel and perpendicular reso-
/G'~/ 50
(131
OH)]I/2 against cos 20 for sample B.
L J, Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
185
5O 4O 30
20
0.4
0s
t
L~29"
06
0'7
08
0~
-
cos 21)
Fig. 13. Dependence o f a = [(H, - H u ) cos(8 - 8H)] 1/2 against cos 28 for sample C.
OC
IG"~ 50 40 30 20 I0
--o.~
K'~
.
o~o.3
o~,
, o.s
o16
o.7
o~
ty~,_e39,
o'.9
_
lZ cos 20
Fig. 14. Dependence of t~= [(H~ - Hu) cos(8 - 8H)]1/2 against cos 2a for sample D.
nance, respectively. The values of H,I,I and Hu~ are k n o w n within error of about 20 G. We would like to c o m m e n t on the choice of the constant A. In this paper we take the value calculated in ref. [231. We believe the numbers are correct since we obtained a very good agreement for our A parameter measured from a spin wave resonance for volume modes with up to 7 lines, with A given in ref. [23]. Unfortunately, volume modes are excited for a concentration range different from concentrations with surface modes pre-
sent, so no direct measurement of .4 was possible. The experimental data from figs. 1 - 4 are calculated in the new variables suitable for testing eq. (13) and presented in figs. 11-14. It is seen that we get the straight line within the experimental error which confirms the proposed model. The fitted values of K s sound reasonable, and these are collected in table 1. In sample n u m b e r D 1 we got two surface modes after the film was kept at r o o m temperature for two or three months, the two straight lines from the two modes are shown in
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
186
Table 1 Parameters used in the model: L thickness of the film, M s - magnetization, H~ - resonance field for uniform mode in perpendicular resonance, HI - the field in parallel resonance, K - uniaxial anisotropy constant and A - exchange energy constant Parameters fitted from the model: 0~ exp(#~ exp) - the critical angle for the magnetic field (magnetization) direction as observed in Sample
Composition
L (A)
M~ (G)
H~ (G)
Hi (G)
K (erg/cm 3)
A (erg/cm)
A B C D
( G d 0.06 C 0 0 . 9 4 ) 0 . 9 4 M o o . 0 6
8500 9300 9300 6400
700 150 150 220
9520 3800 3810 3770
1100 2610 2680 2950
7.7 × 10 5
(Gd 0.1COo.9 )0.94MOo.06 (Gd 0.I COO.9 )0.94MO0.06 (Gd o.n C°0.89)0.88Moo.12
2.4×10 5
6.2 x 10 7 6.4x 10 7 6.4× 10 7 3×10 "
Sample with two surface modes D1 (Gd o.11Coo.89)o.88Moo.12
6400
230
3840
2920
2.6×10 5
3×10 7
fig. 15. O n e c a n see that the lines are n e a r l y p a r a l lel, so Ks'S o n b o t h s u r f a c e s are a b o u t the s a m e (see t a b l e 1). T h e d i f f e r e n c e in t h e r e s u l t a n t pinn i n g for the t w o m o d e s a n d , t h e r e f o r e , r e s u l t i n g in d i f f e r e n t c r i t i c a l a n g l e s Oc, is d u e to d i f f e r e n t v a r i a t i o n s o f m a g n e t i z a t i o n s (3nM~)/M~ o n the t w o surfaces. W e suggest t h a t it is the s a t u r a t i o n m a g n e t i z a t i o n d i s t r i b u t i o n n e a r the s u r f a c e s (or r a t h e r o n the free surface, n o t the o n e in c o n t a c t w i t h the s u b s t r a t e ) t h a t p e r h a p s c h a n g e s w h e n the s a m p l e is aging, w h i l e the s u r f a c e a n i s o t r o p y rem a i n s the same. T h e m o d e l is also s u p p o r t e d b y the fact t h a t the c r i t i c a l a n g l e s d e t e r m i n e d f r o m the e x t r a p o l a t i o n
5. C o n c l u s i o n S p i n w a v e r e s o n a n c e s t u d y of thin a m o r p h o u , f i l m s of ( G d l _ x C 0 ~ ) l >.M0v alloys i n d i c a t e thai w e c a n e x c i t e s u r f a c e m o d e s in t h e s e films. Surfac~
f i r s t s u r f o c e mode \
40 s e c o n d surf 30 20 10 ~c4T ~"
_ C>C p., 0.2
1.e~p=.~o
Uc~ ,-,J
. 0.3
~¢./. -..., .
.
0.4
.
0.6
.
.
0.7
.
o.s
8.4;,< 10 4
o f the s t r a i g h t lines a g r e e well w i t h the sam( a n g l e s o b s e r v e d d i r e c t l y in the r e s o n a n c e experiment. N e v e r t h e l e s s , t o o little is k n o w n to f i n d an 5 d e f i n i t e r e l a t i o n s b e t w e e n the s u r f a c e parameter,, a n d thickness, c o n c e n t r a t i o n o r t e c h n o l o g y of preparing samples.
oC /G'y 50
8 . 0 X 10 4
0.9
/
exP ~;-2 =30o
Fig. 15. The same as in figs. 11-14 for sample DI with two surface modes.
COS '20"
L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
187
d i r e c t r e s o n a n c e e x p e r i m e n t , 0¢ fit (v~c fit) - the s a m e v a l u e e x t r a p o l a t e d a c c o r d i n g to eq. (13) (figs. 1 1 - 1 5 ) a n d K~ - s u r f a c e anisotropy constant
0ceXp
l~ceXp
0cfit
~fit
Ks (erg/cm 2)
5° 24 ° 23 ° 34 °
17 ° 31 ° 29 ° 39 °
5° 23 ° 22 ° 34 °
17 ° 28 ° 28 ° 39 °
- 3.4 -0.7 -0.9 -0.35
0eelxp = 37 ° 0¢e2xp = 26 °
O~lxp = 43 ° v~e~p = 30 °
0f~ t = 36 ° 0~f~t = 27 °
o'¢f~t = 42 ° 0 ~ t = 32 °
Ks, = - 0 . 3 Ks2 = - 0 . 4
modes were observed mainly in monocrystalline films. The surface inhomogeneity model and also the volume inhomogeneity model predict surface modes, if we are able to produce required surface parameters of a film such as easy plane type of anisotropy or some variations of magnetization distributions near the surface. In each case it is connected with the technology of producing samples which controls the process of growing a film and also determines the state of the surface. With m a n y experimental efforts we were able to estabhsh a range of technological parameters to get films with the surface modes. Still, we could not fully control the deposition process and we had to select samples to pick out ones with highly homogeneous bulk parameters and proper surface properties. The SI model predicts surface modes for some range of the effective pinning parameters on the two surfaces of a film. The pinning parameter is the sum of two terms, p = - ( K s / A ) cos20+ O, M s ) / M s. The first term comes from the surface anisotropy energy Es = - K s cos20 and is angular dependent. The other term describes changes of saturation magnetization near the surface. Surface modes can be excited only for positive p as for easy plane type of anisotropy. The value p = 0 determines the critical angle 0 c. If only the first term was present then 0 c = ~r/4. We observe Oc less then ~r/4 which means that the magnetization is decreasing near the surface, as expected. The SI model predicts a straight line for the angular dependence of resonance field in suitable
variables chosen according to eq. (13). Experimental data follow this linear dependence, figs. 11-15, and also the extrapolated critical angles coincide with values taken directly from experiment. We believe therefore that the model is basically correct. In some cases we got two surface modes for a sample kept at room temperature for some time. The change in the properties was associated with different states of the same free surface of the sample. It follows from fig. 15 that the change is due to different magnetization distribution while the surface anisotropy is the same. N o systematic relation is stated between surface state and thickness, composition or technological parameters during the deposition.
Acknowledgements We are grateful to Dr. Z. Obuszko for magnetic balance measurements of the saturation magnetization and to Mr. J. Sokulski for samples preparation.
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L.J. Maksymowicz, D. Sendorek / Surface modes in films of GdCoMo alloys
[5] L.J. Maksymowicz and A. Koz/owski, J. Magn. Magn. Mat. 15-18 (1980) 1098. [6] D.C. Cronemeyer, AlP Conf. Proc. 18 (1973) 85. [7] Z. Frait, I. Nagy and T. Tarnoczi, Phys. Lett. 55A (1970) 429. [81 I. Nagy, T. Tarnoczi and Z. Frait, Physica 86-88B (1977) 764. [9]. S. Prasad, R. Krishnan, G. Suran, J. Sztern, H. Jouve and R. Meyer, J. Appl. Phys. 50 (1979) 1623. [10] L.J.Maksymowicz, Z. Obuszko and D. Sendorek, to be published. [11] A.H. Eschenfelder, in: Ferromagnetic Materials, vol. 2, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1980) p. 345. [12] L.J. Maksymowicz, Physica 86-88B (1977) 1412. [13] L.J. Maksymowicz, Thin Solid Films 51 (1978) 205. [14] J.T. Yu, R.A. Turk and P.E. Wigen, 18th Ann. Conf. Magnetism and Magn. Materials, Denver (1972).
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