DIRECT STUDIES OF NEEL (OR BLOCH) LINE DYNAMICS

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DIRECT STUDIES OF NEEL (OR BLOCH) LINE

DYNAMICS

J. Miltat, V. Laska, A. Thiaville, F. Boileau

To cite this version:

J. Miltat,

V. Laska,

A. Thiaville,

F. Boileau.

DIRECT STUDIES OF NEEL (OR

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JOURNAL DE PHYSIQUE

Colloque C8, Suppl6ment au no 12, Tome 49, d6cembre 1988

DIRECT STUDIES

OF

NEEL

(OR

BLOCH) LINE DYNAMICS

J. Miltat (I), V. Laska (I), A. Thiaville (2), F. Boileau (2)

(I) Laboratoire de Physique des Solides, B6t. 510, Universite' Paris-Sud, 91405 Orsay, France (2) CEA-IRDI-LETI, BP 85X, 38041 Grenoble, ~ r a n c e

Abstract. - N&l (or Bloch) line dynamics has been investigated in garnet epilayers characterized by huge and moderate damping parameters. Direct pressure velocities are found to be in fair agreement with expected values. Velocity saturation is, however, observed in moderately damped material. The gyrotropic coupling to wall motion is shown to produce a variety of line displacement behaviours.

In the limit of stationary and rigid wall and line motions, Slonczewski's equations of wall motion [I,

21 reduce to expressions equivalent to Thiele's equations [3], which express the existence of a gyrotropic coupling between wall and line motions. Conditions of rigid (undeformed) wall and line motions are intu- itively associated with large dampings ( a

>

1)

.

Un- der such conditions, line mobilities, resulting from a pressure applied on either the line (effective field

H,

:

direct line motion) or the wall (effective field H, : gyrotropic line motion) are equal to:

where:

pw is the mobility of a unichiral wall,

Ao and A0 are the usual wall and line width pararne- ters,

a Is the damping parameter, y the gyromagnetic ratio,

Q is the quality factor Q = K

/

2 s ~ : (K : uniaxial anisotropy constant, Ms : saturation magnetiza- tion),

t o be replaced by fl = K

/

( 2 s ~ :

+

K,)

if an "in-plane" secondary anisotropy, magnitude K,, is present.

The correction term

R,

order &-I, in the expression of

&

disappears if linearized Slonczewski7s equations are utilized. It is now known that line widths in materials satisfying Q

>

1 prove always larger than their analytical value sAo [4 and loc. cit.]. Since the direct pressure line mobility deduced from non-linearized m e tion equations may be viewed as the linearized mobility of a line with an increased width parameter:

it may, at first glance, seem that non-linearized equations are preferable. However, it may be shown, in a

straightforward way, that the static line width deduced from the non-linearized model is slightly smaller than rAo. The increased direct pressure mobility associated to the non-linearized model is therefore the result of the energy differentiation process rather than a consequence of a better estimate of the line structure.

The behaviour vs. Q1l2 and a of the reduced line mobilities:

obtained by numerical integration of the non-linearized equations of motions are shown in figures l a and b, re- spectively. Deviations from the simple laws M? =

~ 1 1 2 = MG (Eqs. (1) with A0 = Q'/~Ao) are noticed

to occur at small a values. They remain moderate in the case of direct line motion. The decreased

ME

and M: reduced mobilities for a

<

1 are linked to wall and line contractions during motion, resulting in an increased effective damping. As anticipated, computed mobilities converge towards their respective rigid motion values (Eqs. (1)) as a grows beyond 1 for all Q values.

If linearized equations of motion are utilized, the

R

correction affecting the direct pressure line mobility vanishes, as already mentioned, but the general features of figure l a remain valid. On the other hand, results pertaining to the gyrotropic motion line mobility prove hardly modified. This result is due to the fact that the wall and line energies only enter the equations of motion through functional derivatives to be estimated in the vicinity of static equilibrium where they vanish. As a consequence, both treatments yield virtually identical results.

Finally, simulation of line motion under pulsed field conditions indicate that, for direct motion, a fairly large line overshoot is anticipated to occur at small a's. Overshoot is, however, essentially linked t o the wall motion coupled to line displacement. It is anticipated t o be largely reduced if the wall is tightly pinned. Further, overshoot vanishes as a grows. In

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C8

-

1872 JOURNAL DE PHYSIQUE

Fig. 1. - Reduced line mobility vs. Q ~and / ~CY. K =

lo4

erg/cm3; A = 2 erg/cm : a) direct pressure; H, =

4 Oe, restoring force coefficient for wall displacement Ic =

lo5

Oe/crn; b) gyrotropic motion: H, = 1 Oe, k = 0.

the case of gyrotropic line motion, the line displacement is observed to be nearly rigidly coupled to wall motion a t line location. It follows that the net line displacement is vanishingly small, even for a

-

0.1. This result holds true for a wide variety of field pulse rise and fall times. The net displacement converges towards zero when a grows.

Line dynamics: grossly overdamped materials A stroboscopic imaging technique with 10 ns time resolution has allowed for the study of wall and line dynamics in thick (- 30 pm) garnet epilayers grown on (110) substrates. The easy axis is canted (- 17' from surface) as a result of the competition between orthorhombic (K,, K,) and cubic

(KI)

anisotropies [5]. The domain pattern consists in stripes nicely aligned along the [001] direction (period 220-260 pm). Bloch walls are asymmetric [5]: the fast rotation sec-

tion of the wall corresponds t o an effective anisotropy

K

=

K,

+

3K1

/

4 21 -3700 erg/cm3 (Q

-

4.9). K,

amounts to

-

2500 erg/cm3, yielding t2E 1.135, i.e. a value close t o 1. Lines locations are materialized by a small kink of the wall plane (Fig. 2a) and are therefore easily observed.

Fig. 2. - a) N6el lines in [Tb2.1Yo.g] (Fe4.56A10.44) 0 1 2

epilayers with canted easy axis. [I101 orientation. b) N b l (splay type) lines in [Gdl.4Bil.4Tmo.4Pr0.2] (Fe4.~Ga0.4) 0 1 2 epilayers with perpendicular easy axis.

[ I l l ] orientation. Scale mark: 20 pm.

Direct pressure wall and line displacements us. time and field amplitude (field pulse duration 50 ps, rise and fall time T, = ~f 20 ns) are shown in figures 3 and

4, respec6vely. The wall mobility (curve labelled W in Fig. 5) amounts to

-

9 cm/sOe. Such a low mobility implies a gigantic damping a N 15 (Eq. (I)), i.e. a

value about three times larger than expected [6].

Fig. 3. - Wall displacement [pm] vs. time [ p ] : CY _1.In ascending order: H = 3.92, 4.9, 5.98, 6.86, 7.84 Oe.

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J. Miltat et al. C8 - 1873

Fig. 5. - Wall (W) and line (L) velocities vs. H: direct pressure, a

>>

1.

The T

-

120 ps wall displacement relaxation time is

the result of the large damping as well as a small restoring force coefficient k due to the wide stripe period.

Line displacement proves almost linear with time during pulse and no overshoot is observed, as anticipated for this huge damping parameter. Figure 5 yields a line mobility equal to

-

15.6 cm/sOe (L in Fig. 6) and a coercive field

-

6.8 Oe, i.e. a value noticeably larger than the wall coercive field w 0.8 Oe. Accord-

ing to equations (I), the ratio p:

/

pw should be in- dependent of cr and equal to T A ~

/

2A0, namely 2.37 for 0 = 1.135. The computed ratio amounts to 2.15 whereas the experimental ratio is 1.73, i.e. a value close to ~ 0

/

2 ~= 1.67 ' ~(linearized equations). The

clearly that the ratio vs. field of the apparent line velocity over the wall velocity is not constant. Besides, the wall and apparent line velocities are of the same order of magnitude, in disagreement vrith relations (1)

or the result of numerical calculation (Fig. l b ) by a factor which may be as large as 10.

Data above refer to the observed largest line velocities. A pair of such lines is usually unwinding [7] as

shown in figure 7: lines A1 and A2 lying in wall a move in opposite directions and are easily annihilated under the action of a suitable direct pressure. Often, however, one line in the pair exhibits a reduced velocity [7]. One line, B2, in the pair B1 B2 (wall b) is be- having similarly to line A2. The other line of the pair, Bl, changes direction of motion at t

-

25 ps. Such lines may contain one or more Bloch points. The net displacement of such lines changes sign according to the length of the field pulse (not shown). Behaviours intermediary between those of line pairs A1 A2 and B1 B2 were also observed. It may therefore be won- dered whether all observed lines contain Bloch points.

discrepancy proves moderate.

Fig. 7. - Gyrotropic line pairs (A1 A2, B1 B2) and wall displacements (a, b) [pm] vs. time [ps], cw >> 1.

Line dynamics: moderately damped materials

Fig. 6. - Line displacement [pm] vs. time [ p ] : gyrotropic motion, cw

>>

1, i'orresponding to wall movement in figure 3.

The gyrotropic displacement vs. time and applied field of lines belonging t o a moving wall is shown in figure 6. Experimental data for wall (Fig. 3) and line motions have been recorded simultaneously. Several features are worth noticing: first, line motion does not couple to the backwards wall motion. Further, line overshoot is observed as the field increases. Second, it proves difficult to extract a line mobility from the data. Defining the apparent line velocity during pulse duration as the ratio of the line displacement at the end of the pulse over the pulse duration, it appears

NBel splay lines in bubble garnets may be observed by means of polarized anisotropic dark field optical microscopy [8]. Experiments were performed with a Laser Scan Microscope. One example of line images is shown in figure 2b (material parameters: h = 7.2 pm,

1 = 0.776 pm, Q

-

7.7, 4nMs = 185 G ) . Unfor- tunately, time resolved studies are little compatible with the scanning image formation mode. Therefore most results apply t o the net displacement of lines long after pulse end. In direct pressure experiments, an apparent line velocity is defined as the ratio of the net line displacement over the half-height width of H, ( t )

-

H,. Simulations of line movement indi-

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C8

-

1874 JOURNAL DE PHYSIQUE perimental apparent velocities are shown in figure 8:

velocities labelled a1 and a2 correspond to motions

in opposite directions (dynamic parameters a

--

0.11,

y

--

1.86 x

lo7

0e-I s-l). They prove unequal, a likely consequence of the presence of the earth magnetic field. It is observed that the experimental apparent velocities converge towards the theoretical apparent velocities (thick solid line) at small effective fields. Line velocity does, however, quickly saturate, a feature already observed [9, 101 (curve b is extracted from Ref. [lo], material parameters: h = 2.03 pm, 1 = 0.66 pm,

Q

= 5.4,

47rMs = 111 G , a = 0.12, y = 1.77 10' 0e-I s-I). Noteworthy is the large coercive field for direct pressure line motion in the present experiments, 4 Oe vs.

--

2 Oe for walls.

Fig. 8. - Line velocities us. H: direct pressure, a

-

0.1. Curve b is extracted from reference [lo].

The gyrotropic motion of lines in the observed material proved complex. At low drives and field pulses with long rise and fall time

(2

500 ns), the net line displacement was found to be erratic. Figure 9a shows an observed net displacement: the pulse was applied in the middle of the image acquisition time and the line moved from position A to position B. A residual wall displacement is, however, observable and simulations do predict a line net displacement in such cases. Often, the net displacement was zero: increasing the pulse width to 10 or 20 ms, a time scale large with respect to the inverse of the sc,anning sweep frequency, showed that, although the wall did move, no lateral line displacement did occur in the ascending part of the field pulse. Therefore, che line proved immobile along the wall in such cases. At short rise

( 5

50 ns) and long fall

(-- 1 ps) times, iiucleation of new line pairs was seen to occur at fields in excess of 35 Oe. Only in a nar-

row field range around 25 Oe was a "good" gyrotropic line propagation observed. The propagation probabil- ity was, however, no larger than 0.5. The winding or unwinding character of the line pairs could then be determined, a result confirmed by the application of

Fig. 9. - a) gyrotropic line net displacements, a

-

0.1 with residual wall displacement; b, c, d) gyrotropic line net displacements: inverted pulse asymmetries. (b: H = 0;

C: H = 26 Oe, Tr = 700 ns, rf = 40 ns; d: H = 26 Oe,

rr = 40 ns, rf = 700ns).

suitable direct pressures. Lastly, the net displacement of a given line was observed t o change sign if the rise and fall times are inverted as shown in figures 9b, c, d.

Discussion

Line velocities under the action of direct pressures are observed to agree satisfactorily with expected values. A clear-cut preference for the linearized or non- linearized motion models will, however, have t o await the outcome of additional experimental data. A velocity saturation mechanism (a 0.1) has been proposed

[lo]

but has received no experimental confirmation. In both materials studied, the coercive field for direct line motion proves significantly larger than the wall coercive field.

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J. Miltat et al. C8 - 1875

successive pulses yield equal net displacements. Al- though the data in figure 7 may appear to indicate that a reversible Bloch point(s) movement is possible, it is doubtful whether such a mechanism should be general. It should also be mentioned that experiments in the a

>>

1 and a 0.1 materials differ in one important respect: the field rise and fall times were always much shorter than the wall relaxation time in the overdamped material (20 ns vs. 120 ps) whereas the shortest rise or fall time was at best comparable with the wall relaxation time in the underdamped ma- terial (40 ns vs. w 8 ns). In the former case, well

developped out of equilibrium conditions are met. In the latter, nearly equilibrium propagation is achieved; in other words the effective drive field remains close to zero. A last remark about gyrotropic line motions in a

>>

1 materials ought to be made: it has been found that the line motion was extremely sensitive to bias fields even in conditions in which wall movement is unperturbed [7]. A possible reason for this astonish- ing behaviour might be the asymmetrical deformation, during motion, of adjacent wall segments, themselves characterized by asymmetrical profiles, under the action of the bias field. Consequently, some kind of direct force acting on the line may be envisaged. It has not y e t b e attempted to simulate the motion of asyrn- metrical walls: such an hypothesis therefore remains conjectural.

The present studies have emphasized the role of coercivity and, probably, of material inhomogeneities

such as, perhaps, growth bands ( a N 0.1). Some mod-

eling of line coercivity and its difference with wall coercivity proves necessary, Lastly, ways of introducing a conditional gyrotropic coupling in the equations of motion, as well as its physical grounds, must be worked out.

[I] Slonczewski, J . C., J. Appl. Phys. 45 (1974) 2705.

[2] Malozemoff, A. P. and Slonczewski, J. C., Mag-

netic domain walls in bubble materials (Academic Press, New York) 1979.

[3] Thiele, A.A., J. Appl. Phys. 45 (1974) 377. [4] Miltat, J. and Trouilloud, P., this volume. [5] Trouilloud, P. and Miltat, J., J. Magn. Magn.

Muter. 66 (1987) 194.

[6] Vella-Coleiro, G. P., Smith, D. H. and Van Uitert,

L. G., Appl Phys. Lett. 2 1 (1972) 36.

[7] Laska, V. and Miltat, J., IEEE Trans. Magn. 24

(1988) 1784.

[8] Thiaville, A., Boileau, F., Miltat, J. and Arnaud,

L., J. Appl. Phys. 63 (1988) 3153.

[9] Ronan, G., Theile, J., Krause, H. and Engemann,

J . , IEEE Trans. Magn. M A G 23 (1987) 2332. [lo] Heyes, N., Ronan, G. and Clegg, W., IEEE Trans.

Magn. 24 (1988) 1741.