56
60
5o-
3
40
0
C.R FLYNN and M.B. SALAMON
C-a.xL~ basal
[ ~ I ] O • m r [~=~I~] ~ "
layers
SINGLE-CRYSTAL NANOSTRUCTURES 57 250.0
200.0
o
co
Fig. 31. Magnetization magnetization.
150.0
100.0
50.0
4 0 K
I
0.0 i I I i I I
0.0 10,0 20.0 30.0 40.0
Internal Field (kOe)
curves for [Erl3.slY2s]10o showing the appearance of a state of intermediate
lock-in states, separated by discrete transitions. As fig. 29 shows, the turn angle of several Er/Y superlattices remains, to the contrary, nearly constant at 51-52 ° per layer from 70 K to 6 K. While both films and superlattices are strained, and neither exhibits a spontaneous ferromagnetic phase, only the N6el temperature of the superlattices is significantly modified by strain. This is shown in fig. 30, where films and superlattices with the same c-axis lattice parameters (measured at room temperature) are seen to have significantly different transition temperatures (Borchers et al. 1991). It appears that the more two-dimensional nature of the supeflattice components contributes to a lowering of the N6el temperature.
The magnetization process of Er/Y superlattices is much more complicated than that of Dy/Y owing to the sequence of commensurate lock-in states that are accessible. On application o f a field, the tum angle measure by neutron scattering shifts abruptly from 50.3 ° to 51.4 ° per layer. The latter represents a phase in which an alternation of the c-axis modulated structure is completed in exactly 7 Er layers. This state, which has three down- spin and four up-spin planes, has a net magnetic moment, and is stabilized by the applied field (Borchers 1990). This same 2/7 state was found to be favored in thin epitaxial films even in the absence of a field (cf. fig. 11). Other intermediate states have been observed in superlattices with differing Er-block thicknesses (Beach et al. 1990). The full saturation moment appears at a critical field Hc that is approximately 17 kOe at low temperatures, increasing to 30kOe near 6 0 K for all superlattiees studied. Magnetization curves for [Er13.slY2s]100, shown in fig. 31, reveal one such intermediate state, which appears at 40 K
58 C.P. FLYNN and M.B. S A L A M O N
3000.0
2500.0
2000.0
I000.0 ~
500.0 ~ i
0.0 I I , I , I i I ,
-0.45--0.35 -0.25 -0.15 -0.05 0.05 0,15 0.25 0.35 0.45
K (I-')
Fig. 32. Neutron scattering data for the sample o f fig. 31 in the intermediate state.
O 2
0 i
- I
- 0 . 1 0
~, \ I I I I
\ \
\ \
\
}
\ \ \
\ \
I I
\ \
%,
\
\
I I I I I
- O . O 6 - 0 . 0 2 0 . 0 2 0 . 0 6 IO ezz
Fig. 33. Extrapolated T = 0 critical fields (expressed as an energy) for epitaxial Er thin films and multilayers. The dashed line is calculated from eq. (11),
with an internal magnetic field of-~ 23 kOe (Borchers et al. 1988a). The neutron scattering patterns in fig. 32 for the same sample at 40 K, and in various fields, reveal a transition to a complex spin state near an
applied
field of 27 kOe (Borchers 1990). A tentative assignment of this structure to the alignment sequence 7T3+8T31 gives a moment 9/15SINGLE-CRYSTAL NANOSTRUCTURES 59 of the saturation value and approximately the correct positions for the neutron scattering intensity.
Figure 10 demonstrates that the field He, required to drive epitaxial Er films into the cone phase, increases as the film thickness decreases. This trend continues in the superlattices. However, it is not layer thickness but rather the coherency strain e0 that appears in eq. (12). This is apparent in fig. 33 where the extrapolated T = 0 value of Hc varies with the measured c-axis strain. The dashed line in that figure is obtained by equating the magnetic energy gained in the cone state to the sum of the magnetoelastic energy from eq. (11) and the exchange energy barrier. Values of the exchange energy, elastic constants, and magnetoelastic constants are those of bulk Er (Rosen et al. 1973).
5.2.1.5. Lu-based superlattices. Section 4.1.2 describes in detail the dramatic increase in the ferromagnetic transition temperature of thin Dy films (Beach et al. 1993b) grown on Lu. Nearly identical effects are observed in superlattices where the process can be studied in detail. Figure 34 shows how the magnetic order develops in [DylnlLus]70 (Beach et al. 1993a). Helimagnetic order appears near the bulk N6el temperature; the magnetic peaks shown here at 160K persist down to about 120K. At lower temperatures, the helimagnetic peaks gradually disappear and are replaced by increased intensity in the
2 0
0 0 0 1,-
2:
0 0
15
10
[DY141Lus]70
~_ 195 K
' nun _ j I
15
10
i
5
0 I I , I
1 . 9 2 . 0 2.1 2 . 2
, , 5 0 K , ,
2.3 2.4 2.5
K (A "1)
Fig. 34. Neutron scattering data for a Dy/Lu superlattice showing the appear- ance of helimagnetic order below 170K, which gives way to ferromagnetic order at low temperatures, evidenced by increased intensity of the Bragg peak at 2.23 ~ / .
60 C.P. FLYNN and M.B. SALAMON
15
o o T-
O o
0 I
1 . 9
[DylsILuls]4o
1 0 K j
• I
2.0 2.1 2,2 2.3
K (A "1)
2,4 2.5
Fig. 35. Neutron scattering data for the Dy/Lu superlattice that develops antiferromagnetic stacking of ferro- magnetic Dy blocks, signalled by the peaks marked with arrows.
O~
qD
8
45
40
35
30
2 5
15 ~
0.8 1.0 1.2 1.4 1.6 1.8 2.0
T/T c
Fig. 36. Temperature dependence of the Dy turn angle as a function of T/Tc,
where T c is the ferromagnetic Curie temperature. Shown are bulk Dy (line); a 400A f i l m (triangles); [Dy14]Lus]
(inverted triangles); [DylslLu22 ] (open circles); and [DylslLu15] (squares) and [Dy141Lu30] (solid circles).
Bragg peak and the superlattiee harmonics, which indicates the formation o f long-range
ferromagnetic order. However, a sample with thicker Lu layers, [DylslLu15140, exhibits an antiferromagnetic stacking o f ferromagnetic blocks at low temperature (fig. 35), exactly as in the Gd/Y superlattice shown in fig. 21 (Majkrzak et al. 1986). Unlike the Gd/Y case,
SINGLE-CRYSTAL NANOSTRUCTURES 61
3O
# LU Planes
2O
10
ALIGNED / / HELIX I I
FM
85 180
Temperature (K) Fig. 37. Approximate ph~tse diagram for the Dy/Lu system.
however, samples with 9, 11, 15, 20, 22 and 30 Lu layers in the spacer block all exhibit antiparallel stacking at low temperatures (Beach 1992). Only the 8 Lu-layer and 5 Lu-layer samples exhibit ferromagnetic stacking. A greatly enhanced ferromagnetic transition temperature has also been reported recently for [DyTtZr11140, for which the tensile mismatch is 10%, based on magnetization data (Luche et al. 1993).
As in the case of Dy/Y shown in fig. 23, there is a definite dependence of the turn angle on relative layer thickness, and therefore on strain. Exploiting the thin-film result in fig. 7, we plot in fig. 36 the turn angle in the Dy component vs T/Tc and hence strain (Beach 1992). Interestingly, ~Ony for Dy/Lu superlattices and the 400/k film, scale with bulk Dy, within experimental uncertainty. From these data we are able to construct the approximate phase diagram for Dy/Lu superlattices shown in fig. 37 (Beach 1992). This is an extension of the single-layer phase diagram of fig. 7.
Although it is not possible to follow the helical phase to low temperatures, we can still make an estimate of the coherence lengths at 160K. These are shown in fig. 38, along with the coherence of the aligned and antialigned ferromagnetic phases as measured at low temperature. The magnetic coherence in these superlattices is dearly much smaller than in the Dy/Y system, which itself results from strains associated with the appearance of ferromagnetic order in a superlattice system.
As described in sect. 2.3, the driving energy for ferromagnetism in Dy and Er is magnetoelastic (Cooper 1972, Rhyne 1972). For Dy, the single-ion magnetoelastic energy is minimized in the ferromagnetic state, which results in an orthorhombic distortion of the hexagonal structure. How does this transition occur in a superlattice that remains clamped to its substrate? Figure 39 provides the answer through h!gh resolution X-ray scans of the (209-1) peak in the reciprocal lattice plane normal to the c*-axis. In bulk Dy,
62 C.P. FLYNN and M.B. SALAMON 300
250 200 150 100 50 0 0
I I l I ~ l
,.J.
-.- O 1'
i
y..tP.+
I I I I I
10 20 30
t , . (atomic planes)
Fig. 38. Coherence lengths of the magnetic order in Dy/Lu vs Lu = layer thickness. Open circles, ferromagnetic alignment; solid circles, antiferromag- netic alignment; triangles, helimag- netic order.
(a) ~
I I
4.03 4.07
(b)
0.02
- 0 . 0 5 -
I I
4.03 4.07
O (A-l)
Fig. 39. X-ray intensity contour maps of the plane (h0/~l) near the (1071) lattice point: (a) low temperature; (b) room temperature. The dotted lines are fits to a domain model as described in the text.
the unique a-axis increases in length by 0.2%, and this decreases the hexagonal angle by 0.2 °. In a multidomain sample, each
(hOt~l)
Bragg peak is split in three by the distortion.The contour maps in fig. 39 show the room-temperature and low-temperature intensity distribution (Beach et al. 1993a). The dashed curves in the left panel are calculated by placing three identical asymmetrical Gaussians at positions expected for an orthorhombic distortion. The splitting is approximately 60% of that for bulk Dy. The linewidths are quite large, corresponding to domains approximately 400 A in diameter. At this size, the maximum atomic displacement within a domain is less than one-half of the lattice constant, which serves as a reasonable limit if no plastic deformation is to occur. The formation of these magnetoelastic domains is reversible; however, samples warmed to room temperature show some residual broadening that is not evident in samples that are subsequently aged for long periods (months).
SINGLE-CRYSTAL NANOSTRUCTURES 63 20
18
16
14
12
o
8
6
4~
2
-ML
_ • n n - - I - -
. . o , o .
-- I I
" 2 iof \ - -
I I - -
2.0 2.1 2,2 2.3
K (A "1)
Fig. 40. Destruction of the antiferro- magnetic alignment of Dy layers in
[Dy21[Lull]70 by an applied field. Note the metastability of the aligned state.
Rem = rernanent state.
Ho/Lu superlattices have been grown and studied by neutron diffraction (MeMorrow et al. 1993). Ho layers composed of 10 or 20 atomic planes, separated by 17 atomic layers of Lu, order in a basal plane helix near 130K, which persists to approximately 30 K. Below 30 K, an unusual phase develops, with ferromagnetic alignment in the basal plane, which is canted 30 ° out of the plane; the magnetization of successive Ho blocks is antiparallel.
The helimagnetic phase of Dy/Lu superlattices exists only over a narrow temperature range near TN. On application of a relatively small magnetic field at 160 K, the coherence of the helix is lost; for [Dy211LUll]70, a field of 1 kOe suffices to smear the helimagnetic peaks and shift magnetic intensity into the ferromagnetic peaks. At low temperatures, the antiparallel alignment of ferromagnetic Dy blocks is destroyed by an applied field.
Figure 40 shows the shifting of magnetic intensity from antiferromagnetic peaks (e.g. at 2.2 k -1) to ferromagnetic positions (e.g. at 2.17 ]k-l). Note also that the antiparallel state
64 C.P. FLYNN and M.B. SALAMON 1.0
0.5
o.0
-1.0
I I
..40 -20 0 20 40