Journal of Magnetism and Magnetic Materials 156 (1996) 123-127
M -
Jeurnel of - - magnetism
ned ELSEVIER
I n v i t e d paper
magnetic materials
Novel magnetic structures and nanostructures B. Barbara * Laboratoire de Magndtisme Louis Nt~el, Grenoble, France Abstract
An overview of new fields of investigation of novel magnetic structures is presented. These structures going from nanometer to micron scales are generally made of ferromagnetic particles deposited on normal or superconducting films, or of multilayer structures. They are studied by conventional SQUID magnetometry (ensemble or array of particles) or near-field techniques (single particle measurements).
1. I n t r o d u c t i o n
Progress made during the last decade, in the observation, the analysis and the handling of matter, leads to the elaboration of well-controlled artificial structures from micron to sub-micron and nanometer sizes. This opens new fields of investigation in science and technology [1]. In this short and non-exhaustive overview, some of the results obtained (0r to be obtained) on novel magnetic structures will be stressed. Small magnetic particles (generally belonging to the 3d-transition metal series) are obtained by different methods calling for various skills: - Micron to sub-micron particles (or more elaborated artificial structures) can be patterned by X-ray or electron lithography of magnetic films, deposited beforehand on a non-magnetic (or semiconducting, or superconducting) substrate by sputtering, MBE, laser ablation, etc. - Nanometer magnetic clusters can be obtained with non-miscible elements or by ultra-fast quench (e.g., vapour quench in cold gas expansions, sputtering, etc.). Recent applications to magnetism of the techniques of Cluster Beam Deposition [2-5] or of techniques of Synthesis in Molecular Chemistry [6,7] allow a large variety of nanometer scale magnetic systems to be obtained: 3d or 4f transition metal free clusters going from a few atoms to about l(100 atoms, 3d or 4f clusters of about a few nanometers in diameter deposited on any substrate, 3d ion clusters embedded in molecular crystals with preservation of the cluster-to-cluster translational symmetry, etc. The use of natural constituents of the metabolic system of animals (e.g., ferritin particles) also show great promise for nanoscale magnets. Conventional SQUID magnetometry is highly appropri-
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ate for the investigation of the magnetic properties of an ensemble or arrays of particles and near field techniques allow a powerful approach of submicronic and nanoscopic magnetism. Magnetic Force Microscopy [8] or magnetoresistance [9] can be used to observe magnetisation decay on single particles or wires. Micro-Hall or Micro-SQUID sensors [10], Optical Near Field techniques (e.g., using magneto-optic Kerr effect) [11], can be extremely powerful for static and dynamical investigations of submicronic and nanometer particles (fundamental and applied purposes). Magnetic domain obervations become available at the micron scale (Lorentz microscopy [12] and maybe dichroism) and nanometric scale (electronic holography [13]). They constitute an important tool for detailed understanding of the magnetization reversal in small particles, in particular when comparisons with numerical calculations can be done. These calculations, based on Brown's equations of micromagnetism, can be performed for submicron particles of arbitrary characteristics (magnetisation, anisotropy and exchange energies, shape, etc.) [14,15]. All of these new developments in fundamental submicron and nanoscale studies will certainly constitute the basis for novel magnetic devices, as can be observed with the recent revolution of 'magnetelectronics', the electronics of spin-polarised transport [16]. Today magnetic particle tapes dominate the industry of recording. Smaller and smaller particles are required in order to realize magnetic tapes, made of submicron and nanometer scale particles, with a low enough level of noise, without thermal (or quantum) limitations, etc. Would this be possible? The answer to this question will probably be given in the next few years, in the light of fundamental studies. 2. M i c r o m a g n e t i c c a l c u l a t i o n s
Micromagnetic calculations proceed from first principles for continuum media [14,15]. The starting free energy
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B. Barbara/Journal of Magnetism and Magnetic Materials 156 (1996) 123-127
generally contains four energy terms: anisotropy, exchange, Zeeman and magnetostatic energy (due to dipolar interactions). This last non-local term, makes analytical calculation difficult. Due to the fast development of high speed computers, numerical simulations now have a tremendous impact on micromagnetic calculations. In order to describe particles as large as possible, these calculations must take advantage of the fact that, on the atomic scale, the exchange energy is several orders of magnitude larger than the anisotropy and dipolar energies. This ensures moment deviations to be negligible over a certain length scale d, of the order of a few nanometers. The volume of the particle is divided into small elements of volume = d 3 (cubic, hexagonal, etc.) fitting as well as possible with the particle contour. This allows us to compute magnetic configurations for particles of several thousand magnetic moments. Dynamics, usually described by the Landau-Lifshitz-Gilbert equation, offers a more realistic way to reach equilibrium. It also allows us to see that the different stages of the magnetization reversal in, e.g., the single magnetisation jump of a small enough particle (few nanometers) are highly non-collinear, with vortex, or flower-like configurations [17]. In larger disc-shaped particles, the calculated hysteresis loop is reversible in low fields and shows two irreversible jumps near saturation. Spin configuration views show that these jumps are due to single vortex nucleation on one side of the particle, followed by its annihilation on the opposite side. The reversible part of the hysteresis loop results from the vortex motion. Similar hysteresis loops have been measured (micro-SQUID technique) on sub-micronic particles of equivalent sizes and similar shapes. Single vortex dynamics in the nucleation and annihilation regimes have been studied [10]. In even larger particles or thin films, several vortices and anti-vortices can be nucleated and coexist due to local energy barriers (e.g., grain boundaries). Here magnetization jumps near saturation should also be related to vortex-antivortex annihilation, as this has been shown in a 2d-XY random anisotropy model [18], or the similar case of a ferromagnetic film with fine polycrystalline structure [19]. 3. Magnetic microscopy and near-field studies In recent years a number of magnetic microscopes have been developed that can provide data to test micromagnetic calculations, as well as to make easier the interpretation of single particle magnetisation measurements. Below, some of them are shortly described. The Magnetic Force Microscope (MFM) is an Atomic Force Microscope (AFM) with a magnetic tip. The spatial resolution, of the order of 10 nm, is approximately five times smaller than available lithography particles. Detailed knowledge of the response to MFM is not trivial in particular because the calculation of magnetic and geometric properties of the tip in the presence of the sample, is not easy to achieve. Nevertheless the use of AFM and
MFM to probe spatially the topography of the sample surface and the local magnetic fields generated by submicron magnetic structures, leads in some cases to high resolution and high-precision results (e.g., the case of a chain of magnetosomes in magnetostatic bacteria [8] or of patterned ferromagnetic particles within a GaAs semiconductor enabling spin-dependent electronics [20]). Research to understand inner domain wall structures in films and particles, using AFM and MFM, has been initiated in different groups [21,22]. A Scanning Tunneling Microscope can also be used as a chemical vapour deposition system, for nanolithography [23] or for reversing locally the magnetization of a film when the magnetic tip plus external field exceed the local coercive field in the film [24]. Magnetic Scanning Near-field Optical Microscopy (MSNOM), uses the magneto-optical Kerr effect, for magnetic imaging. It provides spatial resolution beyond the Rayleigh criteria, as fine as A/40 (where A is the wavelength of the light) and femtosecond temporal resolution. In this technique, a small collecting aperture is scanned very close to the sample surface. It has recently been used to image excitonic spin behaviour in locally disordered magnetic semiconductor heterostructures [11] (MnSe introduced within 12 nm wide ZnSe/ZnCdSe quantum wells during MBE growth). A marked contrast between luminescence intensity and polarisation profiles yields evidence for the carrier spin orientation within the (ion beam implanted) spin-dependent energy landscape. Also based on Kerr effect, the recording of Bragg-diffracted patterns from two-dimensional arrays of micrometer-scale ferromagnetic particles gives information on particle magnetization profiles averaged over the array [25,26]. The zero order reflection is proportional to the average particle magnetisation, and gives access to the array hysteresis loop. Higher order reflections give non-conventional loops to be connected with field evolutions of higher magnetization moments of the distribution. Recent experimental and theoretical approaches allow a better understanding of this simple method, which however has to average domain structures over all the particles of the array [27]. The use of different modes of Lorentz microscopy can lead to visualization of the domain configuration in individual micron (and maybe submicron)-sized ferromagnetic particles [12]. In particular Foucault imaging recorded during a magnetisation experiment allows us to connect the shape of the hysteresis loop with the evolution of the domain configuration. Interestingly, some of the loops observed at the micron scale, compare well with those, directly measured on the submicron scale (using microSQUIDs, [10]). The micromagnetic interpretation of the latter in terms of vortex nucleation, propagation and annihilation, can be linked to the magnetic domain evolution of the former, if vortices are considered as reminiscent of local domain and domain wall configurations with flux closure.
B. Barbara/ Journal of Magnetism and Magnetic Materials 156 (1996) 123-127 In Electron Holography (EH) the image of a nanometer object can be reconstructed by pointing a light beam on to the electron hologram (interference pattern) of this object. Standard electron holography employs transmission electron microscopes. EH provided the first evidence for the Aharonov-Bohm effect and therefore for the physical reality of vector potentials [l 3]. Nanometer objects such as vortices in superconductors or magnetization vector changes in ferromagnetic nanoparticles have been observed by this method, which could also be used for the observation of magnetic vortices and poles, etc. 4. Magnetization measurements at the submicron scale Magnetization measurements of single ferromagnetic particles have been performed using a Nb micro-bridgedc-SQUID as magnetic flux detector, between 0.1 and 6 K up to 5 kOe. This is a unique technique for static and dynamical hysteresis loop determination [10]. Three types of measurements are now possible: (i) Hysteresis loops for various directions of the applied field, (ii) Switching field distributions, and (iii) Switching time distributions. The hysteresis loops, characterized by the existence of more or less magnetization jumps depend on the shape and thickness of the particles in accordance with numerical calculations done tor particles with similar characteristics. The smallest particles (Ni, Co and CoZrMoNi with dimensions 50 x 100 x 30 nm 3) have square hysteresis loops, the magnetization reversal taking place at the switching field H~w through a single jump faster than 100 /.~s (our time resolution). This behaviour is, at first sight, in agreement with the Stoner-Wohlfarth (SW) model for a single domain particle. However the example of numerical simulation considered in section II [17], suggests some deviations from this model. Effectively, measured variations of H~w(0) (where 0 is the angle between H and the ellipse's longest axis A) show deviations form the SW model. These deviations, recovered by numerical simulations, effectively result from a vortex nucleation. Switching field histograms are obtained when the applied field is ramped at a given rate d H / d t . The most probable switching field and rms-deviation (H~_~ and o-) can be plotted vs. temperature T and d H / d t . H~w scales to Kurkij~irvi's model [10], based on Arrhenius switching of a single energy barrier (this model, initially constructed for a Josephson junction has been recently adapted to a ferromagnetic particle [2830]). The temperature and field dependence of the mean relaxation time r is derived from this scaling plot. In switching time experiments, the field is rapidly set to a given value H and the particle magnetization switches in a time t. The integrated switching time probability P(t) obtained, can be parametrized by the deformed exponential: P(t) = e -(~/~)~ where r is the mean relaxation time. /3 represents the width of the non-integrated (instantaneous) switching time probability. It has the same meaning as the width o- of the switching field distribution (in first
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approximation, /3= r/o'). In both switching field and switching time approaches, the mean relaxation time r follows accurately an Arrhenius law with a mean single energy barrier above 0.8 K and is independent of temperature below this temperature. This low temperature deviation from the Arrhenius law might be related to Quantum Tunneling of the Magnetization. The thermal variation of the distribution widths (o- and /3) disagrees with Kurkij~irvi's model (which accounts for thermal noise only) showing excess noise in real submicron sized particles. This noise probably results from the existence of different paths in the magnetization reversal process due to the conjugated surface effects of non-collinear magnetic configurations and particle roughness. Rather similar conclusions can be drawn from MFM experiments [31], although the non-controlled effect of the applied field on the magnetic tip, make the experiments indirect. Finally magnetoresistance experiments on narrow Ni wires have been performed to study the motion of domain walls along the wire [9]. Besides spin commutation in giant magnetoresistance nanostructures [1], this study on thin wires shows the relevance of MR experiments in the study of submicron systems. Here the wires are fabricated, using a step-edge technique (nanotubes can also be prepared [32,33]). Longitudinal Magnetoresistance ( M parallel to H ) depends strongly on the width of the wire (200-400 A). The explanation tbr this effect could be related to spin-orbit electrons dephasing in weak localisation [34], Interestingly similar observations of size-dependent longitudinal MR have been independently observed on FeNi wires, which might also be interpreted in terms of weak localization. Besides the origin of the MR mechanism, the MR curves show abrupt jumps of resistance, which are interpreted in terms of domain wall depinning. Besides micro-SQUIDs and MFM this technique offers new possibilities for submicron magnetic investigations. 5. Nanoscale magnets Owing to the cost in exchange energy ~ Jl 2 (where J is the exchange constant and l the particle size) non-collinear magnetic configurations associated with dipolar interactions (as discussed for submicron particles) tend to vanish at the nanometer scale. Although other sources of non-collinearities might be relevant, such as particle surface changes of the exchange or anisotropy energies (due to the bonding of surface atoms with those of the substrate, atmosphere, etc.), one can be tempted to consider nanometer scale magnetic particles as very small magnets. In Mnl2 acetate-complexes (12 isolated ferrimagnetic Mn-ion clusters), magnetic relaxation and ac-susceptibility experiments are well described by a single exponential time decay (/3 = 1). The relaxation time follows the Nrel law r = r 0 e x p ( - K V / k T ) [35] above T,. = 2 K and shows below this temperature, an impressive plateau, which can be due to MQT [36]. Furthermore the value of the energy
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B. Barbara/Journal of Magnetism and Magnetic Materials 156 (1996) 123-127
barrier E derived from these experiments, verifies the expression E = KV, where K is the anisotropy energy obtained from M ( H ) measurements and V is the cluster volume. This relation has also been checked in antiferromagnetic artificial ferritin [37]. Lower temperature experiments show (as in Mnl2) deviations from the Nrel law. Here below Tc = 200 inK, a resonance line is observed in the magnetic susceptibility spectra which has been attributed to a coherent quantum tunneling between the two anisotropy wells. The resonance frequency decreases exponentially with the mean particle volume, in a way similar to the law given above, accordin~_~_[_he MQT theory of antiferromagnets u = uoexp( - V~/X ± K / / z B) [38]. Very recently telegraphic noise has been observed in a self-organized structure of antiferromagnetic clusters ErAs. These clusters form few nanometer thin quantum wires with, in between, some isolated particles. The two relaxation times associated with back and forth motion between the two anisotropy wells, verify the N6el law above 0.5 K and are independent of temperature below this temperature. Here, too, the phenomenon of MQT has been invoked [39]. Recent developments in molecular beam technology offer the opportunity to study free clusters with nearly perfect mass selection (atomic size resolution) in the typical range 2 to 1000 atoms. The evolution of their atomic and magnetic properties can be followed precisely by stepwise addition of atoms, through measurements of optical absorption, Stern-Gerlach deflection. A variety of symmetries, lower than the Bravais lattice, are allowed and observed (in particular icosohedral). A few examples of interesting magnetic properties: in rare earths like Gd or Tb, the cluster moment can either be superparamagnetic or blocked depending on their size (e.g., Gd21 and Gd23 are locked and Gd22 is superparamagnetic) [2]. In 3d transition-metal clusters (Fe, Co, Ni), low temperature average magnetic moments increase in decreasing cluster size, consistently with the more localized character electronic wave functions [3].
6. Complex systems Single particle measurements, are extremely valuable for the understanding of submicronic arrays of particles. As an example the hysteresis loop of an array of billions of particle is very similar to that of a single particle taken among them. In particular the coercive field of the array is very close to the mean switching field of the particle. However the broadening of the transition, observed for the arrays, is much larger than the width of the switching field distribution observed for the single particle. This is due to the non identical character of lithographed particles. Slight distributions (in particle size, shape, roughness, etc.) induce a quenched switching field distribution, which adds to that of the single particle. Note that the important role of
switching field distributions in complex assemblies of particles (e.g., Ba-ferrite particles) leads to generic behaviour of the magnetic relaxation, hysteresis loop, etc. [40] The comparison between measurements in single particles and arrays of particles, should allow us to study to what extent ergodicity is stable in comparison with weak quenched disorder. When deposited on a superconducting substrate, ferromagnetic particles lead to a non-uniform superconducting state resulting from a modulation of the effective magnetic field along the film. In this case the resolution of the ld Ginzburg-Landau equation shows the existence of a cross-over between an extented solution in low field and a modulated one in large field (with bound states localized in the bottom of the well created by the modulated field) [41]. The alternations of positive and negative fields suggest the corresponding vortex state to be a lattice of vortices and antivortices. These results have been tested using a simpler system where a controlled spatially modulated magnetic field (created by a meander-like Nb submicron lithography) is applied perpendicularly to the film. Although much less controlled the submicron ferromagnetic particle network shows a quasi-periodicity in the MR with a period of the order of one flux quantum in one cell of the array [42]. The strong dependence of the MR on the magnetization state of each particle also shows the impact of micromagnetism.
7. Conclusion Nowadays, the possibility of elaborate magnetic objects, going from submicron to nanometer scales, together with the emergence of new techniques of investigation, open new and interdisciplinary trends in magnetism, superconductivity, semiconductivity and molecular chemistry. A link should also be made between biological systems molecular chemistry, and magnetism (photosynthesis in plant cells or ion-storage proteins in animals [7]). For the first time the limits of validity of the Stoner-Wohlfarth model are tested in single particle measurements, which give new and unexpected results, in both thermal and quantum regimes [43]. Detailed understanding of the magnetisation reversal of real particles should help to optimize high density magnetic recording.
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[26] M. Schlenker et al., New Trends in Magnetism, Eds. J.L. Moran-Lopez and J.M. Sanchez (Plenum Press, New York, 1994). [27] D. Vanlabeke et al., preprint (1995). [28] J. Kurkij~irvi, Phys. Rev. B (1971) 832. [29] L. Gunther et al., Phys. Rev. B 49 (1994) 3926. [30] A. Garg, Phys. Rev. B 51 (1995) 15 592. [31] M. Lederman et al., Phys. Rev. Lett. 73 (1994) 1986. [32] B. Doudin et al., Nanostructured Mater. 6 (1995) 521. [33] G. Guerret-Pi6court et al., Letter to Nature 373 (1995) 761. [34] H. Fukuyama, private communication. [35] L. NEel, Ann. Geophys. 5 (1949) 99. [36] C. Paulsen et al., J. Magn. Magn. Mater. 140-144 (1995) 379. [37] D. Awschalom et al., NATO Workshop, Grenoble and Chichilianne, 1994, Eds. L. Gunther and B. Barbara (Kluwer). [38] B. Barbara et al., Phys. Lett. A 145 (1990) 205. [39] F. Coppinger et al., preprint (1995). [40] B. Barbara et al., J. Magn. Magn. Mater. 136 (1994) 183. [41] B. Pannetier et al., MQPCSN, Ed. C. Giovanella (World Publ., Frascati, 1995). [42] Y. Otani et al., J. Magn. Magn. Mater. 126 (1993) 622. [43] B. Barbara, J. Magn. Magn. Mater. 140 144 (1995) 1825.
