Neutron-diffraction study of the magnetic ordering in superconducting NdRh4B4

The results of neutron-diffraction measurements are reported which confirm the development of long-range magnetic order in superconducting NdRh4B4. Two distinct antiferromagnetic transitions occur below the superconducting phase-transition temperature Tsc — — S. 4 K, one at TMH-1. 5 K and the other at TMq-1. 0 K. In both phases the body-centered tetragonal sublattice of Nd atoms orders antiferromagnetically with the Nd'+ moments aligned along the unique c axis. The magnetic moment is modulated sinusoidally along the [100j direction in the higher-temperature magnetic phase and along the [110j direction in the lower-temperature phase. The measured saturation moment is could be detected in the higher-temperature magnetic phase within an experimental sensitivity of 0. 3p~.


INTRODUCTION
The crystal structures of two classes of metallic rare-earth ternary compounds, the rare-earth (R) molybdenum chalcogenides RMo+s (X=S,Se) (Refs. 1 and 2) and the rare-earth rhodium borides RRh4B4 (Refs. 3 and 4), allow sufficient separation between the magnetic rare-earth ions that superconductivity and long-range magnetic order often occur simultaneously, as described in several recent review articles.
Of the compounds in these two classes which have been studied thus far, those in which superconductivity and long-range magnetic order have been found to coexist microscopically order antiferromagnetically.
For the two superconducting compounds ErRh4B4 (Refs. 10 and 11) and HoMo6Ss (Refs. 12 and 13), the development of long-range ferromagnetic order results in a re-entry to the normal state. Although neutron-diffraction determinations of the magnetic structures of several of the Chevrel-phase compounds have been reported, only ErRh4B4 of the rhodium borides has been studied in this way.
Measurements of the electrical resistance, heat capacity, upper critical magnetic field, and static magnetic susceptibility of NdRh4B4 by Hamaker et al. ' indicate that superconductivity and long-range magnetic order coexist in this compound.
We report here the results of neutron-diffraction measurements which confirm the occurrence of two distinct phases with long-range magnetic order below Tsc. In the higher-temperature magnetic phase, for which TMH-1. 5 K, the body-centered tetragonal (bct) sublattice of Nd moments orders antiferromagnetically with a sinusoidal modulation of the moment along the [100] direction. In the lower-temperature magnetic phase TML-1.0 K there is a change in the direction of the modulation wave vector to [110]. In both phases, the moments are aligned along the unique c axis.

EXPERIMENTAL DETAILS
The sample of NdRh4B4 was prepared by arcmelting NdB6 and Rh in the relative proportion 1:6. The isotope "8 was used since it has a substantially smaller absorption cross section for slow neutrons than does naturally occurring boron. In order to remove small traces of carbon which are found with the "B isotope, the NdB6 was synthesized by precipitation from molten Al.  FIG. 1. Neutron-diffraction data above and below the magnetic phase-transition temperatures for the angular range over which magnetic peaks were observed. 5 and y label magnetic satellites and are defined in the text.
RhB~~which is also formed stabilizes the primitive tetragonal NdRh4B4 phase. In addition to the RhB~~, which has a hexagonal NiAs-type structure, a second impurity phase is present: NdRh6B4, the structure of which is not as yet determined although its characteristic x-ray diffraction pattern is known. The resultant mixture has the chemical composition NdRh686 which requires the following weight fractions of the constituents: NdRh684, 0.09; RhB», 0.25; NdRh4B4, 0.66. This makeup is consistent with the relative intensities of x-ray powder-diffraction data. According to ac susceptibility measurements, the small amount of NdRh6B4 present in the sample orders magnetically at the relatively high temperature of about 4.9 K. The RhBi i, on the other hand, is neither superconducting nor magnetic between 0.06 and 20 K. This is discussed in more detail by Hamaker et al. ' The presence of these two impurities does not affect the determination of the magnetic structure of the NdRh4B4 phase whose magnetic diffraction peaks are quite distinct and display a unique temperature dependence as shown in the following section.
The sample, of volume O.S cm (=4.7 g), used in the neutron-diffraction study was ground into a fine powder and loaded into a flat rectangular aluminum container mounted inside a liquid He cryostat. In the present case, a flat sample geometry is preferable due to the relatively high absorption of the compound. The transmission of the sample was measured to be 0.44 for a thickness of 0.1 cm. Diffraction measurements were performed at the Brookhaven High Flux Beam Reactor with a triple-axis spectrometer in the elastic scattering mode. Two configurations were used.
One arrangement consisted of, in succession, a 20' in-pile beam collimator, pyrolytic graphite monochromator, 40' collimator, pyrolytic graphite filter (to suppress higher-order wavelengths), sample, 40' collimator, pyrolytic graphite analyzer, and 60' collimator preceding the detector. The incident neu-0 tron wave vector was 2.55 A ' and the mosaic block distributions of monochromator and analyzer were of the order of 30' full width at half maximum. The other arrangement was similar to that described above but without the analyzer and at an incident wave vector of 2.635 A

RESULTS AND DISCUSSION
Complete diffraction patterns for scattering angles from 5' to 90' were obtained at temperatures above, below, and between the magnetic phase transitions. Structure factors obtained from the nuclear peak intensities of the primary phase measured by neutron diffraction above TMH are consistent with those calculated on the basis of the tetragonal structure of NdRh4B4 reported by Vandenberg and Matthias, in which the magnetic Nd + ions occupy the corner and body-centered tetragonal positions with a =5.333 A and c=7.468 A. Figure 1 shows diffraction data at three temperatures over the angular range where magnetic peaks were observed. The poor signal-to-noise ratio of the magnetic scattering in particular can be attributed to three principal factors: the relatively high-absorption cross section of the compound, the dilute concentration of magnetic moments (one Nd + atom for every nine atoms), and the relatively low average moment of Nd in this compound (as deduced below). The intensity of the larger impurity peak shown in Fig. 1 (100) and (102)  Background and impurity contamination have been subtracted out. served in the lower-temperature magnetic phase.
As in the 0.62-K pattern, no satellite is observed about (001). It can be inferred from these data that the magnetic structure is once again that of a sinusoidally modulated body-centered antiferromagnet with the Nd + moments alternately parallel and antiparallel to the c axis but with a modulation wave vector I qMH I =0.135 A directed along [100] rather than [110]. In Fig. 1 (and also Fig. 3 and Table I) the quantities 5 and y are used to label satellites where 5= I qMH I in units of a =2m/a (5=0. . 115) and y-: in units of a' (y=0.083). Table I compares the observed peak positions and integrated intensities to those calculated on the basis of the model for the magnetic structures proposed above. For both the lowerand highertemperature magnetic phases, agreement between the theoretical and measured angular positions is good and within the experimental uncertainty in scattering angles of =0. 2'. In order to make a more reliable comparison of integrated intensities, additional data were obtained. Figure 4 shows some of these additional data corrected for background and underlying impurity peaks. The theoretical and measured integrated intensities in each of the two magnetic phases are, within the quoted experimental uncertainty, consistent.
It should be noted that within experimental error I qML I is -" the length of the (110) reciprocal- In both the lowerand higher-temperature magnetic phases, the widths of the satellites (as determined froin more accurate data) are those given by the resolution of the spectrometer, which shows that the magnetic correlations are long 0 range, with a minimum correlation range of 300 A. The temperature dependence of the intensity of a representative satellite from each of the two magnetic phases is shown in Fig. 3. By comparing the intensities of the (1y,y, O) satellite and the (101) nuclear reflection in the lower-temperature magnetic phase at 0.62 K, we calculate that the maximum amplitude of the Nd + magnetic moment at saturation is 3.4+0.5 Bohr magnetons, whereas the free-ion value is 3.27p~.
As mentioned in the Introduction, those superconducting compounds which eventually develop long-range ferromagnetic order do so at the expense of the superconducting state. More precisely, in ErRh4B4 and HoMo6S8 the competition between ferromagnetism and superconductivity produces a compromise long-wavelength oscillatory which orders antiferromagnetically in the superconducting state in zero-applied magnetic field, the application of a field less than the upper critical field for superconductivity results in the development of long-range ferromagnetic order coexistent with the superconducting state. Nevertheless, it cannot be concluded that the induced ferromagnetism is coexisting with the superconductivity in the same manner as the antiferromagnetism. ' It is of interest to note that the magnetization measurements of Hamaker et al. ' give evidence for the development of a ferromagnetic component of the Nd + magnetization in the higher-temperature magnetic phase. The onset of a ferromagnetic component to the Nd + magnetization at TMH might account for the depression of the upper critical field at TMH, while a decrease of the ferromagnetic component (possibly to zero) at TML could be responsible for the abrupt increase of the upper critical field at TML. With increasing H, the peak associated with the transition at TMi is shifted to lower temperatures, whereas applied magnetic fields cause the opposite effect at TMH. Since enhancement (depression) of the magnetic-ordering temperature by H is generally characteristic of ferromagnetism (antiferromagnetism), we have another indication of fer-geomagnetic behavior in the higher-temperature phase.
However, measurements of the intensities of nuclear Bragg diffraction peaks in zero-applied magnetic field above TMH, between TMH and TML, and below TMi revealed no significant differences. Calculation shows that the uncertainties in the measured intensities place an upper limit of the order of 0. 3@ii on the magnitude of a ferromagnetic component in the higher-temperature magnetic phase.