Inverted hysteresis loops in magnetic multilayers showing macroscopic ferrimagnet behaviour

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ELSEVIER

Journalof magnetism and magnetic ~ l ~ materials

Journal of Magnetism and Magnetic Materials 196-197 (1999) 796- 798

Inverted hysteresis loops in magnetic multilayers showing macroscopic ferrimagnet behaviour L.M. Alvarez-Prado a'*, F.H. Salas b, J.M.

Alameda

a

aDepartamento de Fisica, Universidad de Ot.,iedo. c~ Cah,o Sotelo s.n. E-33007 Oviedo, Spaill bRobert Bosch GmbH. Quali~ Assurance H)'brid Derices. D-72762 Reutlingen, Germany

Abstract The study of the magnetization rotational processes in a macroscopic ferrimagnet (YCo2/GdCo2/YCo2 sandwich) under the simultaneous application of crossed alternating and steady DC fields, is reported. For the lower YCo2 layer, hysteresis loops with negative values of remanence and coercive field were found. A micromagnetic model is proposed to explain this behaviour. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Macroscopic ferrimagnet; Inverted hystresis loop; Amorphous alloy sandwich

In previous papers we reported the general magnetic properties of YCo2(100 nm)/GdCoz(100 nm)/YCo2(100 nm) sandwiches where YCo2 is an amorphous ferromagnet and GdCo2 is an amorphous ferrimagnet having the net magnetization Gd dominated. In zero field, the strong 3d-3d exchange interaction leads to a "'macroscopic ferrimagnet" arrangement. When a magnetic field is applied, the formation of Bloch walls within the Co sublattices at interfaces takes place at H,. These sandwiches allow us to study rotational magnetization processes being controlled by the compensation of gain in Zeeman energy and loss in wall energy [1]. In our experiment, two orthogonal magnetic fields HAC and Hoc are applied simultaneously in the film plane. HAC (ll easy axis) is a sinusoidal (50 Hz) field of fixed amplitude which is applied along the easy axis of the as-growth in-plane uniaxial anisotropy of the sandwich, while Hoc (2. easy axis) is a steady field. Fig. ! shows the hysteresis loops, as measured by transverse magneto-optical Kerr effect (T-MOKE) for some characteristic HDC values. Note that the penetration depth of

*Corresponding author. Fax: + 34-985103324; e-mail: [email protected].

visible light in metallic amorphous alloys is close 1o 40-50 nm, and for this reason T-MOKE arises only for the YCo2 layer. A full description of the experimental set-up and sample preparation is given elsewhere [2]. The aim of this paper is to discuss a theoretical model which explains the dependence of the hysteresis loops on HDC reported in Ref. [2], whose main characteristics are given in Fig. 1. From this figure several facts must be noted: If Hoc = 0 (not seen in the figure) the hysteresis loop looks as a typical easy axis one. As HDc increases the remanence intially decreases (as expected) and two transition fields (H,1 and H,2) become evident. At Hoc = Ho ~ 80Oe the remanence vanishes. For Hoc higher than this value both remanence and coercive force have negative values (i.e.: "inverted" loops). The processes can be described using a simple unidimensional micromagnetic model which takes into account the Zeeman, exchange and uniaxial anisotropy energies. Let gb(z) be the angle between the Co moments and the HDc direction, where z is the coordinate axis along the thickness (t) of the sandwhich. Fig. 2 shows the exact wall profile obtained from numerical calculations, for Hoc (2_e.a.) high enough to saturate the sample. Taking into account that the energy terms involved are only functions of the angle q~(z) and d~/dz we can approximate the exact (k(z) profile by a simple polygonal

0304-8853/99/$ - see front matter ,~) 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 9 35-4

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L.M. Alvarez-Prado et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 796- 798

~ 'H12

H _J_ e.a.= 64 Oe

yC(h~yC>z i

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i

i

H~

dc

I

t

-64

--

t

i

0 64 Hacll e.a. (Oe)

H~

H~

128

=

Fig. 1. Observed hysteresis loops, by T-MOKE, as the DC field changes from 0 to 226 Oe.

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Fig. 3. Main magnetization vectors for the (a) and (b) states. Single arrow (YCo2 layers). Double arrow (GdCo2 layer): Co subnetwork (thin arrow), and Gd (thick arrow). The DC field is always 70 Oe. The AC field is: (a) 200 Oe, (b) 130 Oe, (c) 00e, (d) - 1 Oe, (e) - 220 Oe. The three experimental transitions at HAc = Htl,HAc = Hc and J~"~AC Ht2 are marked.

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-128

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-200

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600

Fig. 4. Calculated hysteresis loops for the Hoc < H0 and Hoc > Ho cases. t

Fig. 2. (Upper diagram) Co magnetization angle through the film thickness. Points: exact profile when a saturation field is applied perpendicular to the e.a. Solid curve: approximated profile. (Lower diagram) Schematic representation of the trilayer.

curve, as shown in Fig. 2. The n u m b e r of free parameters is reduced to four: q51, ~b2 (i.e., ~b at z = 0 and z = t/2, respectively) and LI, L2 (i.e., wall widths for the YCo2, GdCo2 layers). Using this approximation to simplify the calculations, energy minimization results in two possible configurations (for given HAC and HDc) whose relative energy is dependent on particular HAC and HDc values. The experimental loops shown in Fig. 1 are explained by means of transitions between these magnetic states. In Fig. 3 a schematic representation of these magnetic configurations (a) and (b) is shown for fixed HDc and variable HAc, from positive to negative values. For HDc > Ho, configuration (b) is energetically favourable

except for high enough reverse fields where a transition occurs to state (a) at - Htz, giving rise to a slight increase in the component of magnetization of YCo2 along HAC. The calculated hysteresis loop for this case is shown in Fig. 4b and is in qualitative agreement with the experimental one when Hoc > Ho = 80 Oe. Note that in both cases the loops are "inverted". O n the other hand configuration (b) is energetically favourable for H ~ < Ho so long as HAc is higher than Htl where a transition to state (a) occurs, giving rise to a sudden increase in YCo2 magnetization. As HAc decreases to zero, configuration (a) remains energetically favourable (note the positive remanence). When the Hnc field is reversed, a transition to configuration (b) takes place, and the magnetization is also reversed. This critical field corresponds to the coercive force Hc. Finally, a third transition occurs from (a) to (b) at high enough values of reverse field ( - Hta). The calculated hysteresis loop related to the magnetic process which occurs when HDC < H0 is shown in Fig. 4a. There is qualitative agreement with observations (see Fig. 1 for Hoc = 64 Oe < Ho = 80 Oe).

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L.M. A h;arez-Prado et al. /Journal Of Magnetism and Magnetic MateriaLs 196-197 (1999) 796-798

It must be noted that both experimental and calculated hysteresis loops reported here are related to T - M O K E experiments, i.e., the magnetic observations relate only to the 40-50 nm thick YCo2 layer. In particular, "inverted" hysteresis loops should not be detected from bulk magnetometry, due to the contribution of the whole magnetic configuration of the trilayer.

References [1] B. Dieny, D. Givord, J.M.B. Ndjaka, J.M. Alameda, J. Appl. Phys. 67 {1990) 5677. [2] F.H. Salas, J.M. Alameda, R. Morales, L.M. Alvarez-Prado, G.T. P6rez, J. Phys. IV 8 {1998) Pr2-277.