64 C.P. FLYNN and M.B. SALAMON 1.0
0.5
o.0
-1.0
I I
..40 -20 0 20 40
SINGLE-CRYSTAL NANOSTRUCTURES 65 does not recover after saturation at 10K (Beach 1992). The ferromagnetic remanence evident in fig. 40 can be readily observed in hysteresis loops. Loops for both [Dyl4[Lus]7o (aligned blocks) and [Dy16[Lu2o]8o are shown in fig. 41. Similar data shown in fig. 42 for Dy/Zr, reveal analogous behavior but with much larger coercive fields (Luche et al.
1993).
5.2.1.6. Other superlattice structures. Recently, Dy/Sc and Nd/Y supedattices have been grown (Tsui et al. 1993a). Long-range structural coherence is achieved despite the 8%
lattice mismatch in the former system. However, no magnetic order is observed at 160 K, and only short-range ferromagnetism can be detected at low temperatures. In a 60 kOe magnetic field at 10 K, the magnetic intensity appears on the Bragg peak and superlattice harmonics, and the broad, short-range peak disappears. These results are visible in the series of scans shown in fig. 43. The Nd/Y superlattices are the first to involve a light rare-earth element, and the first to mix dhcp (Nd) and hcp (Y) lattice types. This work is still in its early stage, and we defer further discussion (Everitt et al. 199511.
In addition to the simple supeflattice structures described above, a number of more complex structures have been fabricated. They include Fibonacci sequences of Gd and Y (Majkrzak et al. 1991) and lanthanide/lanthanide superlattices with competing anisotropics, such as Ho/Er (Simpson et al. 1994), Gd/Dy, and Dy/YDy (Camley et al.
1990). We refer the reader to the original sources for details.
8000
o Sc (0002)
~
400C :0 2 ~ . 6
Qc* (~,-i)
Fig. 43. Neutron scattering near the (002) peak for [DyglSCl4]~: (a) 160K;
(b) 10K; (c) 60kOe field at 10K.
66 c.P. FLYNN and M.B. SALAMON 5.2.2. a- and b-axis samples
It is clear from the previous sections that insertion of non-magnetic ab-plane layers does not preclude the appearance of long-range helimagnetic and c-axis modulated order. We infer that this arises because nesting features in the Fermi surfaces of the non-magnetic elements studied (Y and Lu) result in a magnetization wave surrounding substituted lanthanide atoms that decays slowly along the c-axis. However, the predicted absence of such features in the basal plane should ~ause a much more rapid decay of magnetization in those directions. It is possible (Du et al. 1988) to explore such effects through the fabrication of superlattice structures with the growth axis along either the crystalline a- or b-axis, so that the helical axis lies in, rather than normal to, the growth plane.
5.2.2.1. a-axis and b-axis Dy/Y. As in the case of c-axis samples, magnetic neutron reflections should be centered at [0002+r], where r=QDyCny/2Jr. For a superlattice grown along b, the superlattice harmonics are located a distance 2x/A from the principal Bragg reflections in the a* direction (Flynn et al. 1989b, Tsui et al. 199l). However, no magnetic satellites of the superlattice harmonics are present, as seen in fig. 44.
In these scans ~ = 0 corresponds to the c*-axis. The sharp peaks are the superlattice harmonics, and the broad magnetic satellite shows no superlattice modulation. Hence, helical order appears with a well-defined turn-angle, but it is incoherent in successive bilayers. Figure 45 summarizes the temperature dependence of the turn angle for various a- and b-axis-grown samples, with c-axis-grown data plotted for comparison (Tsui
1992).
t I I I I
°180 b_[Dy28~fg]
~i20
,-
-0.06
'-0.'02 0.02
¢
I
:¢o?z
0.06
Fig. 44. Neutron scattering scans for a b-axis Dy/Y supeflattice. Solid circles, scan through nuclear superlattice peaks;
open circles, scan across the helimagnetic peak. The absence of sharp supedattice harmonics indicates that the order is confined to each Dy layer.
SINGLE-CRYSTAL NANOSTRUCTURES 67
4 5 i I I . I I
' . ~ " [ I¥~d
4(3L o o • / o O- DYl9
35 / . t i . S "" " o - [Oy4slY,6]
= 5 0 - ' . . . " ."" " - ' c - [DylslY,4 ]
( -"
0 ) ,- - - - Bulk Dy
3 50 I00 150 200 2 5 0
T ( K }
~
4 5 ,-,-o.-.~ , , J .I ' "
o/_'., v b-[DyTIyz5 ])
4oF
o o,7_,''"
o b-[Dyaly,, ] 35~°°~_~,_--~--_*-~,~ -v,,," .
b-[~z61Ye]~_ .. . . : ~."~" ,,'" • 550A b-axis Dy
3 0 ] - . , . . " " .---c-[DYlflYl4]
2 5 | ( b 1 ~ : I , ---,Bulk Dyj
0 50 I00 150 200 250
T ( K }
Fig. 45. Temperature dependence of the turn angle for a-, b- and c-axis samples.
J(~)
"c*
b*
c
(b)
Fig. 46. (a) Schematic representation of if(q) and (b) its real-space envelope function. The inset in the foreground is the actual Fourier transform along c.
The absence of coupling for a-axis and b-axis superlattices can be understood within the RKKY model. The rapid rise and relatively fiat-topped peak of the susceptibility Xv(qz), as shown in fig. 1, give rise to long tails in the real space response. Figure 46a shows the exchange energy if(q) in the a*-c* plane, assuming that the sharp peak in the
68 C.P. FLYNN and M.B. SALAMON
susceptibility is independent of qx. The attenuation in the a* direction arises from the form factorjsf(q). The corresponding real space exchange interaction between two planes separated by a distance R is shown in fig. 46b. The actual oscillating function is sketched along the c-axis, while the envelope function J(R) is sketched in the b-c plane, which corresponds to the a*-c* plane in reciprocal space. A slow decrease in coupling with c-axis separation contrasts sharply with the rapid decrease in coupling along the b-axis.
Further, as pointed out by Tsui (1992), Dy layers with the c-axis in the growth plane drive the Y layer at QDy, which is off the peak in the Y susceptibility, further reducing the interaction.
5.2.2.2. b-axis Gd/Y. Gadolinium/yttrium superlattices were grown along the a-axis (Tsui 1992, Tsui et al. 1992) and are found to order as ferromagnetic blocks at "~290K, somewhat below the Curie temperature of bulk Gd. Just below Tc, all superlattices order with Gd blocks antiparallel; in b-axis [Gd191Ys]ss, the Gd blocks switch to parallel alignment below 100 K. Figure 47 shows the dependence of the antiparallel (solid circles) and parallel (open circles) neutron peaks on applied field for the above sample. Note that
A
O v O
t J
:t 500
(a)
4.OO
300
200
500 q 4.00 l
T = 9 0 K
_+_
0 0 o ~ 0 ¢ ¢ o ¢
T = 150 K
3O0
200 ~ v v
4o0 \
2oo . . . . ~ - _ ; ~ " ~ ' - 4
I
1 oo H (0e)
200
Fig. 47. Neutron scattering intensities of the fer- romagnetic (open circles) and antiferromagnetic (solid circles) peaks for b-[Gd]91Ys]s5. The zero- field state is ferromagnetic.
SINGLE-CRYSTAL NANOSTRUCTURES 69 the coercive fields are on the order of 50 Oe in the antiparallel alignment (at 200 K), in sharp contrast with the 5 kOe coercive field for Ny = 8 for e-axis Gd/Y as seen in fig. 20.
5.3. Interlayer coupling and long-range coherence
Previous sections describe how magnetic layers first develop intralayer order at the Nrel temperature, and its insensitivity to film thickness and interfacial effects. Much interest, in the case of superlattices, attaches to the way these rare earth nanostructures develop and maintain long-range interlayer order. The process by which successive layers order is a good deal more delicate than the behavior of a single layer, as it is mediated by weak coupling through nonmagnetic spacers. Nonetheless, inter- and intraplane order develop together at the Nrel temperature, without obvious temperature dependence of the coherence length either near or below the transition. It is interesting to compare the magnetic properties of the superlattices with other layered magnets, such as the series (CnH2n+INH3)2CuCI4 (Steiger et al. 1983). In that system, ferromagnetic CuC14 sheets are separated by organic molecules of increasing size. Up to n = 10, the Curie temperature remains close to that of the n = 1 sample, while even for n = 1, order is confined largely to a single plane, as evidenced by neutron scattering data which show a "ridge" of magnetic scattering rather than intensity localized near a Bragg peak. Many other "quasi-2D"
magnetic materials show two-dimensional correlations over a wide temperature range before ordering three-dimensionally at the Nrel or Curie point. Thus, the nature of magnetic ordering in the supedattices is unique, and at present there is little understanding of the energetics and kinetic processes by which quasi-long-range order is developed in these structures.
As is the case in lanthanide metals themselves, interlayer coupling must involve the polarization of conduction electrons within the non-magnetic spacers. To explain that process, Yafet (1987a) extended the RKKY mechanism (see sect. 2.1 and Appendix) by considering a pair of Gd monolayers embedded within an Y crystal. This treatment correctly predicts the alternating ferromagnetic and antiferromagnetic exchange coupling, but the inverse-square dependence of the coupling strength on the layer thickness (Yafet 1987b) is stronger than that observed (~t-l). Such ideas have been extended to other systems, taking into account the detailed Fermi surface of the spacer element (Bruno and Chappert 1991, Herman et al. 1992). Helimagnetic coupling requires, at a minimum, the superposition of the RKKY oscillations of two monolayers in each of the coupled lanthanide epitaxial crystals (Yafet et al. 1988). However, exchange coupling between two metals is strongly affected by Fermi-surface matching conditions. If the interfaces are perfect, electron states in the two metals are coupled only if they have the same transverse crystal momenta; i.e, A -- B kF±--kv±, where A and B refer to the two metals. Because of the existence of interracial potentials, the components parallel to the growth axes need not be conserved; i.e. k A ¢ k~ Yafet et al. (1988) exploited this feature to justify considering
Ell I1"
only the outer one or two atomic planes of each magnetic layer. The band structure features of the lanthanides (and yttrium) that give rise to the peaks in fig. 1, are flat sheets normal to the c*-axis located near the M-point. The separation between these sheets
70 C.P. FLYNN and M.B. SALAMON
=.
d)
¢D
==
UJ
10
0
-5
-10
-15