Supedattice ordering

S~ttedng Wavevector, ~

5.2. Supedattice ordering

T h e s y n t h e s i s o f a p e r f e c t l y c o h e r e n t m a g n e t i c / n o n m a g n e t i c s u p e r l a t t i c e s t r u c t u r e d o e s n o t , o f c o u r s e , g u a r a n t e e t h a t l o n g - r a n g e m a g n e t i c o r d e r i n g w i l l o c c u r . Yet, i n a s u r p r i s - i n g l y l a r g e n u m b e r o f c a s e s , l o n g - r a n g e o r d e r d o e s i n f a c t a r i s e . A s d e s c r i b e d a b o v e , t w o b a s i c t y p e s a r e o b s e r v e d : (i) p a r a l l e l o r a n t i p a r a l l e l s t a c k i n g o f f e r r o m a g n e t i c l a n t h a n i d e

SINGLE-CRYSTAL NANOSTRUCTURES 47

(and iron-group) blocks; and (ii) propagation of helimagnetic or sinusoidal magnetization through many bilayers. Table 1 summarizes the structures that have been realized.

5.2.1. c-axis samples

Most rare-earth superlattice samples studied to date have been grown along the (0001) direction, or c-axis (Flynn et al. 1989a, Falicov et al. 1990). While MBE growth is more straightforward in this orientation, it is also convenient to have the chemical and magnetic modulation in the same direction.

5.2.1.1.

Gd/Ysuperlattices.

The Gd/Y system was one of the first rare-earth superlattices to be grown and studied, and was the first system in which alternation of the sign of the coupling across a non-magnetic spacer layer was observed (Kwo et al. 1987). As in the epitaxial crystal regime, the Gd magnetization lies in the basal plane, where the

I.O g

0.5

z t~

0.1 0.0 -O.IO -0.20

X THICKNESS (.~)

) 20 40 ^{6 0}

i i / I

i~ NGd=4 , NGd = I O + l

+

_{, I ~ / (a)}

+

/ \ (b)

@

Ii/ \ / \

+ ~ '+ +

I i I I

80

(c) I

I 0 20

Ny (ATOMIC LAYERS) 3 0

Fig. 20. Oscillation of the remanent mag- netization and saturation magnetic field for Gd/Y superlattices (from Kwo et al.

1985a).

10 a

i03

f

10 2

i + ¼

1 , i i

(OO02) 40 I- HSLR(III)-8OI-S-201 i~

.ki: 2.67 ~,-' I I

T: 150K i ]

H= 150 Oe ] ,a

[ G d ' o / Y ' 0 ] 2z5 - 2 e.~I ~''~ ! /

8t~

a l l

_

I o _ ,~. 7 ~ . A ~

+ _ ~ - 7 G d / Y

HSLR HSLR

EL (111) (111)

1.6oo ~.9oo 2 2 0 0 ~. 500

o(~, -I)

Fig. 21. Neutron scattering data from an antiferromagnetically aligned Gd/Y superlattice. Odd-numbered peaks arise from magnetic scattering (from Majkrzak et al. 1986).

48 C.P. FLYNN and M.B. SALAMON

demagnetization field overwhelms the weak c-axis anisotropy. This is made evident by the oscillatory dependence of the coercive field on Y spacer-layer thickness, with a period of seven Y layers (fig. 20). Note that the remanent magnetization is large when the coercive field is small. The interplanar antiferromagnetic exchange energy may be estimated from Jaf -=HsMt/4 (Parkin 1991) where t is the Gd-layer thickness; the value Jaf ~ 0.6 erg/cm is similar to values obtained for the coupling or transition metal blocks across, e.g. Cu. The conventional explanation (Yafet 1987a) is that the coupling arises from the same RKKY- like mechanism, described in sect. 2.1, and predicts the 7-plane period (approximately 50 ° per Y layer) in agreement with the susceptibility peak in fig. 1. Neutron scattering studies confirm that the magnetic structure of the superlattices that possess the maximal coercive fields consists of ferromagnetic Gd blocks, with blocks in adjacent bilayers oppositely aligned (Majkrzak et al. 1986). Additional magnetic peaks in neutron scattering (indexed with odd integers in fig. 21) lie exactly between the superlattice harmonics (even indices) as expected from doubling the superlattice periodicity. This was the first definitive demonstration of oscillatory exchange coupling, which has subsequently been observed in a wide range of magnetic/nonmagnetic superlattices and multilayers. Results on Gd/Y have been extensively reviewed by Majkrzak et al. (1991).

5.2.1.2. Dy/Y superlattices. The first superlattice system to show non-trivial long-range order was a sample denoted [Dy171Y14164, consisting of 64 bilayers, each composed of a Dy block of 17 atomic planes (8.5 hexagonal unit cells thick) and an Y block of 14 (7 hexagonal cells thick) (Salamon et al. 1986). Helimagnetic satellites, which first appear at 160K, close to the ordering temperature of bulk Dy, persist down to the lowest temperatures studied (~10K). As discussed in sect. 4.1, the suppression of the ferromagnetic transition is a consequence of epitaxy, and does not originate uniquely from the superlattice structure.

A number of similar c-axis samples were subsequently prepared and studied (Salamon et al. 1991, 1992a, Erwin et al. 1987, Rhyne et al. 1989). Typical neutron scattering data are shown in fig. 22. Note the constancy of both the main nuclear Bragg peak (~2.2 ~-1) and the superlattice harmonic (_~ 2.25 ]~-1). Ferromagnetic order, were it to appear, would add magnetic scattering intensity to those peaks. At 6 K, the widths of the magnetic peaks are comparable to those of the nuclear peaks, demonstrating that the magnetic and structural coherence are comparable. The increasing intensity and changes in relative intensity of the central and superlattice harmonic magnetic peaks result from the interplay of the mismatch between CDy and Cy with the changing value of QDy. From data sets such as these, it is possible to extract the temperature dependence of the turn angle for Dy and (modulo 2Jr/Ny) the effective turn angle in the Y. The result of such an analysis is shown in fig. 23 (Rhyne et al. 1987). The general result is that the turn angles observed in superlattice structures are larger than in elemental Dy at all temperatures below TN, and that the Y layers exhibit an effective turn angle of ~50°/plane, which is close to that observed in dilute YDy alloys. It is not surprising that the Dy turn angles are larger in superlattices; atomic planes near the interfaces lack further-neighbor atomic planes whose antiferromagnetic coupling determines the pitch of the helix. This justifies our

SINGLE-CRYSTAL NANOSTRUCTURES 49

[Dy,, Iv.,],,

T - I ~ m n : l e n ~

ic = 1 6 7 K

250 2OO

"E

• .~ 1so

n , .

v

_>,

i

100.

50,

°1.8o/ J=.oo ,.=o

/t

2.40 2.60

165 K 160 K

Fig. 22. Neutron scattering data from a Dy/Y superlattice. The intensity of the main Bragg peak is constant to 6 K, ruling out the development of ferromagnetic order.

assertion that interlayer coupling slightly perturbs the magnetic properties of the epitaxial crystalline blocks of which the superlattice is composed.

The absence of further-neighbor planes also induces some residual ferromagnetic order within each Dy block, but this is not coherent from bilayer to bilayer. Thus, in fig. 24 (Rhyne et al. 1989), the moment calculated from the coherent helical Bragg peaks falls below the expected 10/£B per Dy atom. The fact that the missing intensity appears as a broad feature centered on the nuclear Bragg positions indicates the presence of short- range, incoherent ferromagnetic order in each bilayer.

50 C.P. FLYNN and M.B. SALAMON

4 0

o l l

35

s

5 5 , , ,' , ^,

f

^{oD /~} 8 ~-Yloyers

50 ~'

Turn Angles

45 a [DYl6lY,9 189 /

30

25

20

I I

15 I l i O° , I

0 40 80 120 160

T(K)

Fig. 23. Temperature dependence of the turn angle in Dy and Y layers as a function of temperature for several superlattices.

The propagation of helimagnetic order through non-magnetic yttrium layers is a more elaborate process than that which couples ferromagnetic Gd blocks in Gd/Y superlattices.

Not only must the yttrium transmit the relative orientation of spins at the interfaces, but also the handedness (chirality) of the helix in each block. Consequently, the helical coherence that develops within each Dy block must influence the handedness of its neighbors. Yafet et al. (1988) superposed the RKKY-like oscillations of pairs of Dy planes to model helical coupling, arguing that due to band-matching only interfacial layers need be considered. The situation is quite different from that in dilute alloys, where the ordering temperature decreases with decreasing Dy concentration. We have seen in sect. 4.1 that thin Dy layers order at the bulk N6el temperature. The issue for coherent order rests on whether the indirect exchange coupling via the Y is sufficiently strong to induce the same chirality in successive Dy blocks. Because some helical order is required, and because anisotropy barriers grow as the order increases, ttaere will be an increasing tendency to develop "chiral stacking faults" as the exchange coupling is reduced. This is reflected in a reduction in the number of bilayers that contribute coherently, and consequently to a broadening of the magnetic peaks observed in neutron scattering. We can define the

SINGLE-CRYSTAL NANOSTRUCTURES 51 12

8

4

i i i i

(a) [DY151Y14]S4

~ / B r i l l o u i n

moment ^{- x}

120 180

T(K) 12

10

C 8 ¸

q.I

>

=>.

t- 4

m

2 -

(b) [DylslY14)s4

10K

0

1.80 2.70

t , i

1.95 2.10 2.25 2.40 2.55

o=(~.-1)

Fig. 24. Magnetic moment per Dy atom for a Dy/Y superlattice (a) deduced from the helimagnetic peaks;

(b) shows that a residual, incoherent ferromagnetic intensity is present, accounting for the "missing" moment.

magnetic coherence x length in terms of a magnetic peak width through ~m = 2:r/A/crnag,

w h e r e A/cmag = (A/caobs ----r~nuc) A . . 2 -,1/2 , A/Cobs is the measured width of the magnetic peak, and A/Cnuc is the width of a nuclear Bragg peak. This definition is employed to deconvolute the structural and magnetic coherence. A plot of the magnetic coherence length vs the inverse of the thickness t of the yttrium block is shown in fig. 25 (Rhyne et al.

1989). At an extrapolated thickness of 140~k, helimagnetic order is confined to single

52

200 I00

I I

C.P. FLYNN and M.B. SALAMON r (~)

50 30 25

I I ,t

500

A

400

c ~p

_1 _Q~ 30O

rO C

¢.-

8 z o o

I00 = 14o

single Dy Ioyer

I I I

0.01 0.02 0.03

l/t= (Y Thickness)-I(~ -I)

0.04

Fig. 25. Magnetic coherence length vs the inverse of the Y layer spacing. Dy layers are decoupled when the Y-layer thickness exceeds 140A.

Dy blocks. We emphasize again that, unlike the case of alloys, the N6el temperature remains high as the Y fraction increases; only the coherence in the growth direction is lost.

The low-temperature ferromagnetic phase of Dy can be induced by relatively modest magnetic fields applied along the easy axis in the basal plane. Neutron scattering data (Rhyne et al. 1989, Salamon et al. 1992a) on [Dy16Y19189 in fig. 26 show at 10K that as the helimagnetic state collapses abruptly between 5 kOe and 10kOe, the magnetic scattering intensity reappears in the structural Bragg peak and its superlattice harmonics; these are indicators of long-range ferromagnetism. At 130K, the transition is more gradual, and it occurs through the loss of coherence of the spiral, and the coexistence of helimagnetic and ferromagnetic states. When the field is reduced to zero after saturation, the helical phase reappears at 130K in all samples, but not at 10K. Figure 27 shows the behavior of the c-axis lattice parameter of [DylsY14164 as a function of applied field (Erwin et al. 1987). As the sample is magnetized, the c-axis increases in length by 0.1%, approximately one-half of the change that accompanies ferromagnetic order in the bulk. The larger lattice parameter persists when the field is

SINGLE-CRYSTAL NANOSTRUCTURES 53

[DY161Y19189 540

480 600

420

360

>' 300

C - 2 4 0

180

120

60

I

40 kOe

25 kOe ~ ]

1.84 1.94 2.04 2 . 1 4 1 . 8 4 1.94 2.04 2.14

Oz (~'-') Oz (~,-')

Fig. 26. Evolution o f the helimagnetic peaks in a field for a Dy/Y superlattice at 10K and at 130K. Note loss of coherence at 130 K.

subsequently reduced to zero at 10 K. On wanning above 130 K, the fully coherent helical phase returns, and the lattice parameter returns to its original value. It is clear that a substantial fraction of the magnetoelastic distortion that accompanies ferromagnetism in

54 C.P. FLYNN and M.B. SALAMON

o5 V fJ

2.638 I

l [DYlsIY14164 ] ~

after 25

kOe

at 1OK 2.836 I"FC 4kOe

2 . 8 3 4

(a)

2.8321 ~ 100 I 200 T(K)

t

~f~ • 10K o 130K

(b)

0 ' 1'0 ' ;0 ' 30 H(kOe)

Fig. 27. (a) Temperature dependence of the field cooled (FC), zero field cooled (ZFC) and saturated values of the c-axis lattice parameter of a Dy/Y superlattice; (b) cycling the field at 10K leaves the lattice parameter in its expanded state; at 130K, the change is reversible.

Dy is realized in the superlattices, despite the constraints imposed by epitaxy (Erwin et al. 1989, 1990).

5.2.1.3. Ho/Y superlattices. Ho/Y superlattices have since been grown and studied by neutron (Bohr et al. 1989) and magnetic X-ray diffraction (Majkrzak et al. 1991).

A coherent basal plane spiral forms, as in Dy/Y, with coherence extended over many bilayers. Analysis of the turn angles of the separate blocks also yields 51°/5( layer, and a temperature-dependent turn angle in the Ho layer that is significantly larger and less temperature dependent than that of bulk Ho. Unlike the Dy/Y case, higher-order harmonics were observed in a [Hoa01Y15150 supedattice, which indicates the existence of spin-slip structures. Fifth and seventh order harmonics were observed with an average turn angle of 40°/Ho plane. Jehan et al. (1993) suggest that this is evidence for a (2121) spin-slip sequence, a sequence not observed in bulk Ho, while Majkrzak et al.

(1991) assume a purely antiferromagnetic coupling through the Y layers, and obtain stacking sequences similar to those observed in the bulk. To date, no field dependences have been reported for these supedattices.

5.2.1.4. Er/Y superlattices. As discussed in sect. 4.1.3 above, epitaxial Er films order in a sinusoidal, c-axis modulated (CAM) structure near 85 K, as in the bulk, but do not develop a conical phase. A helimagnetic component does appear, but only substantially below the temperature (20 K) at which it appears in the bulk. Therefore, Er/Y superlattices permit the study of longitudinal order propagating in the CAM phase, and with it the possibility that long-range magnetic coherence might be more readily achieved. There are two likely sources of long-range coupling: (i) the phase difference across an Y block

SINGLE-CRYSTAL NANOSTRUCTURES 55

70 I

6O

so'

4 0 ¸

i f ;

¢ -

"E 3O

2 0

~o1,: ~ ~ ~ - , 2 0 K

8 2.0 2.2 2 . 4 2.6

K (~-I)

35 K

6K

Fig. 28. Development of helimagnetic order in an Er/Y superlattice below 20 K as shown near (0002).

is always an even or odd multiple of Jr - basically the same as Gd/Y or, (ii) the phase is determined by the number of Y planes in the bilayer, and can take on any value. Neutron scattering data, similar to those shown in fig. 18, have been collected for a number of superlattices with Y spacer layers varying between 19 and 25 atomic planes (Borchers et al. 1991). The phase shift, modulo 2~, across the spacer layer ranges from 0.7:r to 1.5Jr, and is consistent in every case with a phase advance of 51 ° per yttrium layer. The temperature independent intensity of the (10i0) peak in fig. 18 demonstrates, as found for Dy/Y superlattices and thin Er films, that the low-temperature ferromagnetic transition of the bulk does not occur in the epitaxial system. Nonetheless, helimagnetic order does occur near 20 K, as is apparent in fig. 28. However, when it does appear, it is considerably less coherent than the CAM structure; the helimagnetic peaks are barely resolvable, even a t 6 K .

56

60

5o-

3

40

0

C.R FLYNN and M.B. SALAMON

C-a.xL~ basal

[ ~ I ] O • m r [~=~I~] ~ "

layers