Appl. Phys. A 74 [Suppl.], S751–S753 (2002) / Digital Object Identifier (DOI) 10.1007/s003390201358

Applied Physics AMaterials
Science & Processing

Magnetic excitations in the antiferromagnetic phase of NdCu2
M. Rotter1,∗ , S. Kramp1 , M. Loewenhaupt1 , E. Gratz2 , W. Schmidt3 , N.M. Pyka4 , B. Hennion5 , R. v. d. Kamp6
1 Institut für Angewandte Physik, Technische Universität Dresden, 01062 Dresden, Germany
2 Institut für Experimentalphysik, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
3 Institut Laue Langevin, 38042 Grenoble, France
4 Technische Universität München, Forschungs-Neutronenquelle FRM-II, 85747 Garching, Germany
5 CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
6 Hahn Meitner Institut, 14109 Berlin, Germany

Received: 11 December 2001/Accepted: 8 January 2002 –  Springer-Verlag 2002

Abstract. Detailed investigations of the magnetic interactions
can be performed by comparing measurements with calculations of dynamical magnetic properties. In this study neutron
spectroscopy on single crystals was used to measure the magnetic excitations in the antiferromagnetic phase of NdCu2 .
This phase is characterized by a stacking of ten ferromagnetically ordered bc-planes with a propagation vector of (0.6 0 0).
The magnetic excitations have been calculated in the different magnetic phases, which can be stabilized by a magnetic
field along the crystallographic b direction (= easy axis). The
model is based on a mean field (MF) theory and fluctuations
are treated in the random phase approximation (RPA). The
dispersion of the magnetic excitations has been calculatedusing exchange parameters, which have been determined byneutron spectroscopy in the ferromagnetically aligned phasein a magnetic field of 3 T parallel to b. For the calculation theprogram package McPhase was used. The results are compared to data of neutron spectroscopy on single crystals.

present paper we report on measurements of the magnetic excitations in the phases AF1 and F1 and compare the data to
the predictions of the MF–RPA model.
1 Experimental
The inelastic neutron scattering experiments have been performed on a NdCu2 crystal with dimensions 4 × 5 × 7 mm3 ;the details of the sample are given in [1]. For the measurements in zero magnetic field the 4F2 triple axis spectrometerof the Laboratoire Leon Brillouin (LLB, Saclay) was used.
The experiments in magnetic fields parallel to b were doneon the IN14 and IN12 triple axis spectrometers of the In-

PACS: 75.50.Ee; 75.10.-b; 75.25.+z

The magnetic phase diagram of NdCu2 has been studied forfields aligned parallel to the crystallographic b direction, theeasy axis of this orthorhombic system [1]. Up to a field of 1 T
the zero field antiferromagnetic phase AF1 is stable. Between
1 and 2.5 T a ferrimagnetic phase F1 is found, which is followed by a complicated phase F2 (2.5–2.8 T). For magnetic
fields above 2.8 T the moments are aligned ferromagnetically(F3). The phase diagram has been modeled by a numerical
MF calculation using the McPhase (http://www.mcphase.de)program package.
In order to find out more about the magnetic exchange inthis system, the magnetic excitations have been measured andanalyzed in the phase F3 of NdCu2 . This has lead to a modelfor the exchange anisotropy in all RCu2 compounds [2]. In the∗ Corresponding author.

(Fax: +49-351/463-3199, E-mail: rotter@physik.tu-dresden.de)Fig. 1. Dispersion of the magnetic excitations along (h 1 0) in the AF1 phaseof NdCu2 . The calculation (•) is compared to experimental data measured
at 4F2-LLB (◦) and IN12-ILL (×). The different sizes of the symbols represent the intensities, vertical lines mark the center (Γ) and the zone boundary(ZB) of the magnetic Brillouin zone. The arrow indicates the position of themagnetic propagation vector in AF1

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stitute Laue Langevin (ILL, Grenoble) with a 5 T verticalmagnet for fields perpendicular to the scattering plane. Inaddition, the V2 triple axis spectrometer of the Hahn Meitner Institut (HMI, Berlin) was employed together with a 5 T
horizontal field magnet to access scattering vectors within theab-plane. At 4F2 and IN14 a graphite filter was used in order
to avoid λ/2 contamination of the primary neutron beam (atk f = 1.64 Å−1 ).
For the measurement of the dispersion of the magnetic excitations a temperature of 1.5 K was stabilized. Energy scansat constant scattering vector Q and scans of Q along theprincipal crystallographic directions of the Brillouin zone atconstant energy have been performed. The data were fitted bya set of Gaussian functions and evaluated by plotting the energy of the excitations versus Q in a plot with different point
size corresponding to the intensity maximum of the fitted
Gaussian peak. Figure 1 shows such a plot for the dispersionof the excitations in AF1 for q = (h 1 0). The calculated magnetic excitations were plotted in the same way and thus can becompared to the measured data.
Fig. 2. Dispersion of the magnetic excitations along (h 1 0) in the F1 phaseof NdCu2 in a magnetic field of 1 T applied along the b direction. The calculation (•) is compared to experimental data measured at V2-HMI (×),
and IN14-ILL (◦) [6]. The different sizes of the symbols represent the intensities, vertical lines mark the center (Γ) and the zone boundary (ZB) of themagnetic Brillouin zone. The arrow indicates the position of the magnetic
propagation vector in F12 Results and discussion
The calculation is based on the following Hamiltonian:H = Hcf + Hex + HZe ,Hcf =Blm Olm (Ji ) ,1  α αββJ J (ij)Jj ,2 ijαβ iHZe = −g J µ B HJi .

100 ni,lm

Hex = −Q = (0.65 1 0)
T = 1.5 Kµ0Hb=(1)

0Ti

0.6 T
Intensity (neutrons / 3 min)

1.0 T

2.4 T

2.62 T
Q = (0.35 0 2)
3.0 T
50 n

Here the first term, Hcf, describes the crystal field Hamiltonian of the 4 f electrons on each Nd3+ ion. The secondterm, which is an order of magnitude smaller, describes theanisotropic bilinear exchange interaction between different
Nd ions. The exchange tensor J αβ (ij) is assumed to be diagonal and the orthorhombic distortion of the nearly hexagonal
crystal is neglected. The third term in (1) is the Zeeman energy due to an applied magnetic field H.
Using the Hamiltonian (1) in McPhase the magnetic
phases have been modeled by a numerical mean field procedure similar to that described in [1], however without
considering the effect of inter-doublet mixing. Because theexchange interaction in NdCu2 is long range, the exchange
has to be considered up to the 12th nearest neighbor in thea direction (corresponding to 26 Å) in order to reproduce thedifferent magnetic structures correctly [3]. A MF–RPA [4, 5]
calculation of the magnetic dynamics was based on the resultsof this simulation of the static properties. Note that this calculation is not a fit to the experimental data: the dispersion of
the magnetic excitations for the phases AF1, F1 and F2 wascalculated using the exchange parameters given in [2].
Figures 1 and 2 show the calculated dispersion in comparison with experimental data in the phases AF1 and F1,respectively. The different sizes of the symbols correspond tothe measured or calculated intensities. Part of the data (F1)have already been published [6], however without comparison to this model calculation. The complicated magnetic unit

05.5 T

0.51
Energy (meV)1.52Fig. 3. Constant Q scans measured at IN14 (ILL) at different applied fields.
All spectra correspond to the reduced wave vector q = (0.35 0 0). If l = 0
only half of the modes can be seen (see text)

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cell (20 Nd atoms in AF1, 6 in F1, 32 in F2, and 2 in F3)
produces a correspondingly large number of modes. However
due to the structure factor along the (h 1 0) direction only halfof 20, 6, 32, and 2 modes can be seen in AF1, F1, F2 andF3 . Similar to F3 [2] the data in AF1 and F1 exhibit a minimum in the excitation energy at about (2/3 1 0) associatedwith high scattering intensity. Note that this position is different from the magnetic propagation vector (in AF1: (0.6 0 0),
in F1: (2/3 0 0), indicated by the arrows in Figs. 1 and 2). We
take this as a proof of the strong anisotropy of the magnetic
exchange interactions in all magnetic phases.
Further information for the identification of magnetic
modes can be gained by measuring the detailed field dependence of the excitation spectra at a fixed q value. Figure 3
gives an example of such an analysis at the reduced wave
vector q = (0.35 0 0). If l = 0 only half of the modes can beseen. Therefore the spectra at Q = (0.65 1 0) are shown. At
equivalent points in reciprocal space other modes could additionally be identified, because the intensity varies strongly
with Q. In order to compare how the two modes in the phaseF3 are resolved in spectra with l = 0, scans at Q = (0.35 0 2)
are shown in Fig. 3.
After fitting the spectra by Gaussians, the data of the fielddependence at the reduced wave vector q = (0.35 0 0) can
be compared to the McPhase calculation in Fig. 4. The mainfeatures of the experimental data are well predicted by the numerical analysis. Some quantitative discrepancies such as theexact energy value of the lowest mode in AF1 are due to restrictions of the MF–RPA approach and additional terms inthe Hamiltonian, which have not been considered.
In conclusion we emphasize that the identification of all
magnetic modes in complex systems is not possible frominelastic neutron scattering data alone, because the intensity of the magnetic excitations varies rapidly and the resolution is limited. Therefore it is necessary to rely on a numerical model for the identification of the modes. The program package McPhase has been developed to address thisproblem. It provides an easy-to-use tool for the simulation of static and dynamic properties of complex magneticsystems.

Fig. 4. Field dependence of the magnetic excitations at the reduced wave
vector q = (0.35 0 0) as measured at IN14 and IN12 (ILL). The data were
derived from spectra at several equivalent Q values. The lines indicate theresults of the McPhase calculation

Acknowledgements. Part of this work was performed within the program of
the Sonderforschungsbereich 463 (funded by the Deutsche Forschungsgemeinschaft).

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