Magnetization response in bulk nanostructured magnets

https://doi.org/10.1016/j.msea.2006.02.322Get rights and content

Abstract

Small-angle neutron scattering (SANS) experiments on nanostructured Fe reveal grain-size-dependent magnetic correlations with a minimal correlation length for grain sizes on the order of the bulk domain-wall width. To investigate the evolution of these correlations during the magnetization process, we performed SANS experiments in external fields of various strengths. In intermediate fields, we find anisotropic scattering profiles with an unusual intensity enhancement for scattering vectors parallel to the field direction. These observations are compared with a modeled granular microstructure containing magnetic domains of arbitrary size and orientation, demonstrating that magnetic domains extend over several grains and have a magnetization that is tilted considerably away from the external field direction. Since the domain size does not change significantly with the magnitude of the external field, we conclude that the magnetization process does not proceed via domain-wall motion. Rather, our SANS data suggests that the magnetization process proceeds by simultaneous reversal of a few adjacent domains, presumably in the form of small avalanches. The latter supposition is supported by theoretical arguments showing the existence of marginally stable domains within the random-anisotropy model.

Introduction

Nanostructured materials, i.e. materials with grain sizes in the nanometer range, often reveal significant differences in their properties when compared with the coarse-grained bulk material [1]. This is particularly true of magnetic nanostructured materials, where the grain size is far smaller than the size of a usual domain and becomes comparable to the width of a domain wall. When nanoparticles are consolidated into a solid, not only the grain size but also the exchange interaction between the grains markedly influences the macroscopic magnetic properties. In solids, as opposed to isolated nanoparticles [2], the magnetic correlation is not necessarily confined to one grain, but can extend over many individual grains. This can generate new magnetic properties.

Indeed, with decreasing grain size the intergrain exchange progressively dominates the magnetization process. Below a characteristic grain size, the magnetic moments of neighboring grains are forced to align parallel to each other in accordance with the random-anisotropy model (RAM) originally developed for amorphous ferromagnets [3], [4], [5]. In Refs. [6], [7], [8], this model was used to describe the magnetic properties of nanostructured materials. Comparing the coercivities of various Fe-based nanocrystalline alloys with the predictions of the RAM, a sharp decrease in the coercive field with decreasing grain size was found. Other studies on nanostructured materials have also revealed magnetic correlations which extend over several grains [9], and thus support the above model.

We present here systematic study of the grain-size dependence of the magnetic properties of nanostructured metals. We start with the description of macroscopic magnetization measurements and show for nanostructured Fe that the coercive field depends strongly on grain size [10]. We then describe magnetic small-angle neutron scattering (SANS) measurements and show how macroscopic magnetic properties, such as the coercive field, result from the interplay of microscopic parameters, e.g. grain size, intergrain coupling and anisotropy. In particular, we show that the magnetic correlation length extends over several grains when the grain size is smaller than the corresponding bulk domain-wall width. Neutrons are sensitive to variations in both atomic density and magnetization and thus are a unique tool for studying the compositional and magnetic correlations simultaneously.

Finally, we investigate the dynamics of such intergranular magnetic correlations during the magnetization process. Since the magnetic scattering depends on the angle between the scattering vector and the magnetization vector, we are able to measure the magnetization direction of the correlated domains relative to the external field [11]. By analyzing the contours of equal intensity on a two-dimensional SANS detector, we can follow the evolution of the magnetic domains during the magnetization process and compare this measured SANS data with calculated lines of equal SANS intensity.

Section snippets

Experimental procedure

The nanostructured samples were produced by the inert-gas condensation process [12] and consolidated in situ in a high vacuum of 10−6 Pa. The consolidation was usually performed at a pressure of 2 GPa for 2–5 h at room temperature or at elevated temperatures (up to 473 K). To induce grain growth, some samples were additionally annealed at up to a temperature of 700 °C for 24 h in a tube furnace in a vacuum of 10−4 Pa. The grain size (and strain) of the samples was determined by X-ray diffraction

Experimental results

Fig. 1 shows the average magnetic correlation length L as a function of the average grain size D for nanostructured Fe, as obtained from SANS [7]. The correlation length shows a pronounced variation according to grain size, with a clear minimum for D = 20–35 nm. The room temperature coercive field, seen in the inset, likewise shows a pronounced variation with grain size and passes through a maximum at around 35 nm, i.e. for a grain size where the correlation length is minimal. Apparently, the

Zero-field magnetic correlations and random-anisotropy model

Both the results of the magnetization and the SANS measurements shown in Fig. 1 are consistent with the RAM [4], [5], [6], [7]. The observed increase in the correlation length with decreasing grain size provides evidence of a coupling between adjacent grains. This increase cannot be explained by dipolar interactions between uniformly magnetized grains, since the dipolar energy density would then scale with the grain size and thus lead to a decrease in the correlation length. For magnetic

Summary and conclusions

In conclusion, we performed small-angle neutron scattering on nanostructured Fe samples of various grain sizes. The magnetic correlations that form spontaneously in zero-field show a strong grain-size dependence with a minimum for grain sizes in the range of 20–35 nm, the same range where the coercivity shows a maximum. In the low grain-size regime, the magnetic correlations extend over many grains, which (together with the grain-size dependence of the magnetic properties) can be explained well

Acknowledgements

The authors are grateful to W. Wagner (PSI Villigen), G. Kostorz (ETH Zurich) and A. Wiedenmann (HMI Berlin) for stimulating discussions. This work was supported by start-up funds from the ETH Zurich (J.F.L.) and by SFI grant 05-RFP-PHY0023 (H.B.B.).

References (18)

  • H. Gleiter

    Acta Mater.

    (2000)
  • G. Herzer

    J. Magn. Magn. Mater.

    (1992)
  • H. Gleiter

    Prog. Mater. Sci.

    (1989)
  • J.F. Löffler et al.

    Mater. Sci. Eng. A

    (2001)
  • A. Hernando et al.

    Phys. Rev. B

    (2004)
  • R. Harris et al.

    Phys. Rev. Lett.

    (1973)
  • R. Alben et al.

    J. Appl. Phys.

    (1978)
  • E.M. Chudnovsky et al.

    Phys. Rev. B

    (1986)
  • J.F. Löffler et al.

    Phys. Rev. Lett.

    (2000)
There are more references available in the full text version of this article.
View full text
Copyright © 2006 Elsevier B.V. All rights reserved.