J. A. Paixão (Univ. of Coimbra), P. J. Brown (ILL), B. Lebech (Risø Nat. Lab.), G. H. Lander (Inst. Transuranium Elements, Karlsruhe).
Interactions between elements with d and f magnetism are crucial
to many technologies. The richness of their behaviour, as well as the difficulty
in establishing detailed models, can be traced partly to the lack of a clear hierarchy
of interactions. In addition to the magnetic 3d and 4f states, there are the conduction
electrons, which are important in defining the nature of the long-range magnetic
order. The MFe4Al8 compounds, about which there are many conflicting
reports in the literature, including the suggestion that these materials are spin
glasses, provide an interesting test case. Using a combination of neutron and synchrotron
techniques, including the use in both cases of polarisation analysis, we have established
not only magnetic structure as a function of temperatures, but also how the different
sublattices interact with one other. This then provides a benchmark for theories
addressing these important problems; indeed, one theoretical paper has already appeared.
Since the early work on these systems some 20 years ago [1], it has been recognised that the strongest
magnetic interactions are between the Fe atoms and that, at the stoichiometry MFe4Al8,
it is principally antiferromagnetic in nature. (With further replacement of Fe for
Al, up to MFe10Al2 the materials are high-temperature ferromagnets
and have potential applications). The tetragonal unit cell is shown in Fig. 1. The
M atom is surrounded by 8 Fe atoms. If the latter have an perfect AF configuration,
then the molecular field at the M site is zero.
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Figure 1: One unit cell of the crystallographic structure of the MFe4Al8 series. Shown also is the unusual magnetic configuration of the UFe4Al8 compound. Weak ferromagnetism due to a moment of 0.47(3) µB on the U atom is complemented by an almost antiferromagnetic configuration of the Fe sublattice with moments of 1.08(2) µB. The Fe moments are canted by 16° in zero field by their interaction with the U sublattice. This canting angle increases with a magnetic field applied in the basal plane. Both sublattices order at ~ 150 K. |
Bulk measurements show the rare-earth materials to be purely antiferromagnetic, and
Fe Mössbauer studies [1] establish that the Fe ordering is between 150 and 180 K for all compounds.
The use of D10, together with single crystals, allowed us to identify the initial
ordering only of the Fe sublattice (at 170 K in the Dy material) as incommensurate
and probably cycloidal in nature. This was confirmed by using the neutron polarimeter
(IN20-cryopad), which showed that the envelope of the Fe modulation is circular.
The wavevector is qmag = [0.13, 0.13, 0] and has little temperature dependence.
As the temperature is lowered, there is a long-range ordering of the rare-earth component
[2]. This starts
in DyFe4Al8 at TDy ~ 50 K. At the lowest temperature
about 60% of the rare-earth moment is ordered; the configuration at ~ 15 K is shown
in Fig. 2. A careful examination of this cycloid with the neutron polarimeter (IN20-cryopad)
shows that the Fe and Dy cycloids are turning in opposite directions, but with the
same q wavevector. At lower temperatures the ellipticity of the Dy sublattice changes
sign and higher-order harmonics (up to 7th order) from the rare-earth
moments are seen; however, the envelope of the Fe cycloid remains circular at all
temperatures. The higher-order harmonics distort the envelope of the rare-earth cycloid
and may be viewed as establishing ferromagnetic interactions between the rare-earth
atoms. At the same time, the disordered component of the rare-earth moments develop
short-range ferromagnetic correlations. This inherent instability of the rare-earth
sublattice means that it can be easily modified in a field, an applied field of 0.5
T is sufficient to induce a large moment within the rare-earth sublattice. However,
the interaction with the Fe sublattice, which remains antiferromagnetic to very high
field, confines the directions of the rare-earth moments to the basal plane. It is
this unusual behaviour that led previous authors to claim the materials were spin
glasses.
The development with temperature of the ordered rare-earth moment in both the Dy
and Ho compounds is shown in Fig. 3. The 110+ satellite reflection arises
from both the Fe and rare-earth sublattices so that it is sensitive to the coherent
interference between the two. The different temperature dependencies may be explained
by a temperature-independent phase- factor between the modulations of the rare-earth
and Fe sublattices.
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Figure 2: The complex cycloidal magnetic configuration found in the rare-earth compounds – here shown for DyFe4Al8 at 15 K. Four unit cells are shown. The magnetic moments are always confined to the ab plane, with their propagation wavevector qmag = [0.13, 0.13, 0]. Notice that the Fe and Dy cycloids turn in opposite directions. At lower temperature additional higher-order harmonics in the diffraction pattern are observed and signify a further distortion of the envelope of the Dy cycloid. The Fe moment is = 1 µB, whereas the Dy moment is = 6 µB. The remaining Dy moment (to make up the free-ion moment of 9 µB) contributes to ferromagnetic diffuse scattering within the ab plane. |
The final piece to the puzzle is the behaviour of the conduction-electron states.
This has been examined by performing resonant x-ray magnetic scattering experiments
on the Dy L edges at the ESRF ID20 beamline using the same crystal as for the neutron
studies. These x-ray experiments focus on the Dy 5d electrons that belong to the
conduction band. We have found that they initially polarise at TN (170
K); i.e. their interaction with the Fe 3d states is sufficiently strong that they
are immediately polarised at TN rather than TDy ~ 50 K. Important
changes in their polarisation occur at TDy, which are related to changes
in the band splitting of the 5d states [3].
In comparison with the rare earth compounds, the interactions in UFe4Al8
are quite different. Previous reports on this material were also confusing, but again
single-crystal experiments at Risø and D3 led [4] to a clear-understanding of the magnetic
configuration, which is shown in Fig. 1. Here the antiferromagnetic modulation vector
is [000] so that no new peaks occur; the unit cell is thus easier to represent, but
the interactions are more complex than in the RFe4Al8 compounds.
Sandratskii and Kübler [5] have considered this configuration and shown that many of its features
can be explained by taking account of the larger (than in the rare earths) spin-orbit
coupling and hybridisation between the Fe 3d and U 5f electrons. The local symmetry
at the Fe site, which defines the directions for the Fe moments, gives rise to their
canting. UFe4Al8 is more anisotropic than the RFe4Al8
systems, showing interesting hysteresis behaviour when a field is applied within
the basal plane [6].
These effects, and the fact that both sublattices order at the same temperature,
are a consequence of hybridisation between them [5].
The present measurements illustrate the power of single-crystal neutron and x-ray
techniques (in both cases using polarisation analysis) to unravel complex sublattice
magnetic interactions in compounds containing d and f electrons. They also demonstrate
the profound differences in behaviour between the rare-earths and actinides in an
isostructural series.
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| Figure 3: The temperature dependencies of the 110+ and 121+ magnetic satellites. The former arise from both sublattices, whereas the latter arise from only the rare-earth sublattice. The changes at TDy ~ 50 K in panel a) and THo ~ 80 K in panel b) are due to the coherent interference between the two sublattices and indicates the appearance of long-range component at the rare-earth site. This is not observed readily at the 121+ position as the amplitude squared is too small. The dashed lines represent the extension of the intensity from the Fe sublattice only, and the solid lines are drawn taking into account a constant (with temperature) phase factor between the Fe and rare-earth magnetic sublattices. These phase factors are 42(6)° for the Dy compound and 150(8)° for the Ho compound. Thus, in panel a) we observe almost constructive interference, whereas in b) the interference is mostly destructive. The drop in intensity in panel a) for DyFe4Al8 below = 12 K is associated with the appearance of higher-harmonics, which are not included in our simple model. |
[1] K. H. J. Buschow and A. M. van der Kraan, J. Phys. F 8 (1978) 921. [2] J. A. Paixão et al., Phys. Rev. B, in press. [3] S. Langridge et al., Phys. Rev. Letters 82 (1999) 2187. [4] J. A. Paixão et al., Phys. Rev. B 55 (1997) 14370. [5] L. M. Sandratskii and J. Kübler, Phys. Rev. B 60 (1999) R6961. [6] G. Bonfait et al., Phys. Rev. B 53 (1996) R480.
