International
Tables for
Crystallography
Volume I
X-ray absorption spectroscopy and related techniques
Edited by C. T. Chantler, F. Boscherini and B. Bunker

International Tables for Crystallography (2022). Vol. I. Early view chapter
https://doi.org/10.1107/S1574870720003547

Magnetism and magnetic materials

Andrei Rogaleva*

aESRF – The European Synchrotron, 38043 Grenoble CEDEX 9, France
Correspondence e-mail: rogalev@esrf.fr

The applications of X-ray magnetic circular dichroism in studies of magnetism are briefly reviewed. The major strengths of this technique, such as element and orbital selectivity and the capability to quantitatively detemine the spin and orbital magnetic moments, are illustrated with a variety of representative examples.

Keywords: X-ray magnetic circular dichroism; orbital magnetism; magnetic materials.

1. Introduction

In spite of the fact that the first accounts of magnetism date back to the ancient Greeks, the magnetic properties of materials continue to be among the most exciting scientific topics in contemporary physics. Magnetism is the basis of numerous modern and forthcoming technologies, having penetrated our everyday life. Magnetic materials form vital components in a large variety of devices ranging from the nanoscale magnetoresistance sensors (Chappert et al., 2007[link]) that have revolutionized information technology to large permanent magnets (Gutfleisch et al., 2011[link]), which are key ingredients for efficient energy conversion. However, there will be no further progress in the design of better performing materials without a deeper understanding of the mechanisms that control their magnetic properties.

The discovery of magnetic circular dichroism in X-ray absorption (XMCD; Schütz et al., 1987[link]) marked a major breakthrough in magnetism research, with objectives that previously would have been unattainable. XMCD is defined as the difference in X-ray absorption spectra recorded with left and right circularly polarized photons while the sample magnetization is kept either parallel or antiparallel to the direction of propagation of the incident X-ray beam. Because of the element and orbital specificity inherent to any X-ray absorption spectroscopy and the ability to probe extremely small sample volumes, XMCD offers remarkable possibilities for studying the magnetism of complex materials. Furthermore, the derivation of magneto-optical sum rules (Thole et al., 1992[link]; Carra et al., 1993[link]) has greatly strengthened XMCD, offering the unique capability for quantitative determination of the orbital and spin contributions to the total magnetic moment carried by an absorbing atom. It is important to underline that XMCD is a vectorial probe of magnetism, i.e. the signal depends on the relative alignment of the X-ray helicity, given by the X-ray wavevector k, and the quantization axis given by a sample magnetization M (k · M). In contrast to X-ray emission spectroscopy or Mössbauer spectroscopy, XMCD is averaged to zero when the local atomic moments are oriented randomly with respect to the incident X-ray wavevector as, for example, in paramagnetic materials in the absence of an applied magnetic field. XMCD is also silent for antiferromagnetic materials, where no net magnetization is present. However, another X-ray magnetic spectroscopy,X-ray magnetic linear dichroism (XMLD), can efficiently be used to study antiferromagnets (Scholl et al., 2004[link]) since it depends on the magnitude of the individual magnetic moments but not on their direction (van der Laan et al., 1986[link]). XMLD nicely complements XMCD, offering a means of measuring the anisotropy in the spin–orbit interaction, which can be related to the magnetocrystalline anisotropy energy (Dhesi et al., 2001[link]).

The development of X-ray magnetic spectroscopies has been boosted by the advent of third-generation synchrotron-radiation facilities, which offer the scientific community X-ray spectroscopy beamlines with greatly improved flux and full polarization control of the beam. Presently, there are more than 50 dedicated beamlines, which are in operation at practically all of the synchrotron-radiation facilities around the world (Wilhelm, 2013[link]). As a result, X-ray dichroism has become a routine experimental method in modern magnetism research. Today, the applications of XMCD are vast, and this method enables a broad range of novel and exciting studies of various magnetic materials ranging from bulk (Chaboy et al., 1998[link]) and thin films (Srivastava et al., 1998[link]) to nanoparticles (Antoniak et al., 2006[link]), clusters (Barthem et al., 2012[link]), single-molecule magnets (Mannini et al., 2009[link]) and even ad-atoms (Donati et al., 2016[link]). There are already several comprehensive review articles (Stöhr, 1999[link]; Nakamura & Suzuki, 2013[link]; van der Laan & Figueroa, 2014[link]; Rogalev & Wilhelm, 2015[link]) as well as book chapters (Stöhr & Siegmann, 2006[link]; Rogalev et al., 2006[link]) on XMCD. The present report deals with some recent achievements in this field which illustrate the great potential of XMCD to resolve actual problems in magnetism research. As a full account of these results is obviously beyond the scope of this review, we limit ourselves to a selection of the most prominent applications and effects.

2. Orbital magnetic moment

The disentanglement of spin and orbital magnetic moments has been of interest in magnetism research from the very beginning, and is still a formidable experimental and theoretical challenge. One of the most valuable features of XMCD is the possibility of quantitatively determining the orbital magnetic moment in amplitude and direction and in an element-selective manner. Although very small in bulk metallic 3d transition metals, the orbital magnetic moment plays a key role in magnetic properties important for technological applications. Bruno (1989[link]) was the first to discuss that magnetocrystalline anisotropy is due to the anisotropy of the orbital magnetic moment. It was confirmed by XMCD that the orbital moment is indeed larger for an energetically preferred direction of magnetization (Dürr et al., 1997[link]). Notwithstanding, a considerable enhancement of the orbital moment of 3d metals was observed in Co/Pd and Co/Pt multilayers (Weller et al., 1994[link]) compared with pure cobalt film. Another aspect of the orbital moment is its sensitivity to the dimensionality of the system. Increased orbital moments have been observed for decreasing thicknesses of ferro­magnetic cobalt overlayers on a Cu(100) surface (Tischer et al., 1995[link]) and in artificially ordered FeCu compounds (Kuch et al., 1998[link]). An even more drastic enhancement of the orbital moment is observed with a further reduction in dimensions from 2D to one or zero dimensions (Gambardella et al., 2002[link]).

Unlike the first-row transition-metal compounds, orbital angular momentum is less quenched for 4d and 5d transition-metal ions. The unquenched orbital moment is strongly coupled to the spin via spin–orbit interaction, which competes with electronic correlations and crystal field effects. Due to the strong spin–orbit coupling in transition-metal oxides, the electronic properties are altered from metallic to a Mott insulator with an exotic magnetic behaviour described by both spin and orbital components. The realization of this novel spin–orbit-induced Mott-insulating ground state was found in many oxide materials based on Ir4+ ions using resonant magnetic X-ray scattering (Kim et al., 2009[link]), and a dominant role of orbital moment in their magnetic properties was elucidated by XMCD at the Ir L2,3 absorption edges (Laguna-Marco et al., 2010[link]). Whereas the strong magnetic interactions between the iridium ions in oxides eclipse the information on the local electronic structure, the intrinsic magnetic properties of the constituent Ir4+ ions in the paramagnetic [IrF6]2− complex have been quantified using XMCD data obtained at 2.5 K and under a 17 T magnetic field (Pedersen et al., 2016[link]). These [IrF6]2−-based materials have been shown to constitute the most realistic molecular model systems for Mott insulators and could be used as a building blocks for new molecule-based materials with designed topologies and exotic physical properties.

The physics of 5d compounds appears to have a remarkable similarity to those of actinide systems, where experiments show (Moore & van der Laan, 2009[link]) that strong spin–orbit effects persist even in the presence of 5f electron delocalization. A particularly interesting feature of the light actinides is that the orbital and spin moments of the 5f states are of the opposite sign, with the orbital contribution being larger than the spin. This usually results in their partial or even complete cancellation, i.e. a magnetic ion with net zero moment. This was first inferred from a polarized neutron scattering experiment (Wulff et al., 1989[link]) on a UFe2 Laves phase ferromagnet and was perfectly confirmed by XMCD measurements at the M4,5 edges of uranium, deducing values for the spin and orbital moments of −0.2 μB and 0.21 μB, respectively (Finazzi et al., 1997[link]). This result is indeed an excellent illustration of a unique ability of the XMCD technique to separately determine the spin and orbital contributions of absorbing atoms.

3. Spintronics

The rise of spin-current physics, together with enormous technological advances in engineering layered structures with tailored spin–orbit interactions, have placed 4d and 5d transition metals at the heart of the emerging fields of spin-orbitronics, magnonics and caloritronics. In this context, magnetic properties at the interfaces between ferromagnetic materials and nonmagnetic metals with large spin–orbit coupling play a central role. Some of these heavy metals, such as platinum and palladium, have been demonstrated by XMCD to exhibit a so-called magnetic proximity effect, i.e. they acquire interfacial induced magnetic moments whenever they are in contact with 3d metallic ferromagnets. L2,3-edge XMCD measurements reveal ∼0.3 μB induced in Pt atoms at an atomically sharp interface with nickel (Wilhelm et al., 2000[link]) and as large as 0.4 μB per Pd atom at an interface with iron, decaying to half this value by the third monolayer (Vogel et al., 1997[link]). Moreover, indirect exchange interactions were shown to have an effect on the magnetism of palladium in the Ni81Fe19/Cu/Pd structure: a significant magnetic polarization induced even through 3 nm of copper has been detected by palladium L2,3 XMCD (Bailey et al., 2012[link]). However, it is still an open question whether induced magnetic moments are ubiquitous when layers of 4d or 5d atoms are grown on magnetic insulators. This is the key question for the correct interpretation of the spin Hall magnetoresistance and the newly discovered unidirectional magnetoresistance phenomena and, more generally, to understand the mechanisms of pure spin-current generation (Kajiwara et al., 2010[link]). To unravel a possible role of magnetic proximity effects at ferromagnetic/nonmagnetic interfaces, XMCD spectroscopy appears to be the method of choice due to its element selectivity and monolayer sensitivity. A very careful XMCD study at the L3 edge of ultrathin layers (thicknesses of less than 2 nm) of platinum on Y3Fe5O12 resulted only in an upper limit for the induced total magnetic moment of 0.003 ± 0.001 μB (Geprägs et al., 2012[link]). Note that the field-induced moment due to paramagnetism in platinum was found to be ∼0.0011 μB per Pt atom and per tesla (Bartolomé et al., 2009[link]). Thus, the observed magnetoresistance cannot be attributed to proximity-induced magnetic moments at platinum and could originate from a subtle manifestation of spin–orbit interaction at the symmetry-breaking metal interfaces (Grigoryan et al., 2014[link]).

In contrast to the widely used metallic spin devices, semiconductor-based spintronics may offer a greater wealth of possibilities, allowing the combination of storage, detection, logic and communication capabilities on a single chip and the production of a multifunctional device. Diluted magnetic semiconductors (Dietl et al., 2000[link]) were proposed as the most promising candidates. An intrinsic ferromagnetic response of various diluted magnetic semiconductors has been confirmed by XMCD (Edmonds et al., 2005[link]; Sarigiannidou et al., 2006[link]) but, unfortunately, ferromagnetic ordering was found in all of them well below room temperature. An alternative approach would be to investigate a layered system alternating a metallic ferromagnet with a ferromagnetic semiconductor such as a europium chalcogenide. Despite the fact that their ordering temperature is very low, a magnetic proximity effect could play the role of an effective field to maintan ferromagnetism. XMCD studies of Co (7 nm)/EuS (2 nm) multilayers (Pappas et al., 2013[link]) led to the conclusion that EuS is antiferro­magnetically coupled to Co and that divalent Eu ions carry a magnetic moment of about 0.5 μB at room temperature. This value is still 15 times smaller than the Eu2+ moment at magnetic saturation, but remains quite large since it is almost equal to that of bulk nickel metal. These findings pave the path for the fabrication of room-temperature spintronic devices using other 3d metal/EuS trilayers and multilayers (Poulopoulos et al., 2014[link]). Moreover, since EuS is a semiconductor with a direct band gap at about 1.65 eV, the combination of magnetic properties at room temperature with band-gap tuning due to quantum confinement may merge spintronics and optoelectronics as, for example, in spin-controlled light-emitting diodes.

4. Element-selective magnetometry

Understanding the magnetic switching in magnetic materials is of crucial importance for the design of permanent magnets, magnetic read heads in hard disk drives and many spintronic devices. Multilayers consisting of magnetically hard layers interleaved with magnetically soft layers have proved to be an excellent model system for such studies. In these systems, the magnetization reversal process is assumed to occur via the development of exchange springs in the soft material before the magnetization of the hard material is reversed. Magnetic exchange springs are artificially tailored magnetic domain walls: they develop in a material whose magnetization is pinned locally, for instance by exchange coupling, but may be rotated by applying an external magnetic field far from the pinning centre. However, the detailed mechanism of magnetic switching remains unclear and is usually rather complex, depending on the microstructure, the composition and other factors. Typical examples of exchange spring magnets are DyFe2/YFe2 superlattices composed of alternating layers of a hard (DyFe2) and a soft (YFe2) ferrimagnet. Antiferro­magnetic interactions at the interfaces in such heterostructures lead to a variety of novel phenomena: magnetic bias (Nogués & Schuller, 1999[link]) and exchange spring-driven giant magnetoresistance (Gordeev et al., 2001[link]) and negative coercivity. The latter is supposed to be caused by the net antiferromagnetic moment when the magnetic exchange spring unwinds under a reduced magnetic field. To unravel the mechanisms of magnetization reversal one needs to know the behaviour of both the hard and soft layers separately, which is not possible with conventional magnetization measurements since they probe the whole superlattice. XMCD, which is inherently an element-selective technique, allows one to measure the magnetization of the DyFe2 and YFe2 layers independently and therefore to directly determine the location of the magnetic springs. Layer-selective magnetization curves were recorded by monitoring XMCD signals either at the Dy L3 edge or the Y L3 edge as a function of the applied magnetic field (Dumesnil et al., 2002[link]). For a [DyFe2 (50 Å)/YFe2 (200 Å)] superlattice, the hysteresis loops show a drastic evolution from a low-temperature regime to a high-temperature regime (Dumesnil et al., 2004[link]). At temperatures below 100 K, the first step in magnetization observed in a positive field is due to the expansion of magnetic springs in the soft layers, whereas a second step occurring in a large negative field is assigned to the irreversible switch of the hard layers. However, at 200 K the superlattice magnetization exhibits a completely different behaviour that could be unravelled from the layer-selective magnetization curves. As is illustrated in Fig. 1[link], it is a superposition of an almost square loop with a negative coercive field in YFe2 and an atypical loop observed for DyFe2 layers. This strange magnetic behaviour could be described by three processes: (i) a smooth reversal in positive magnetic field, (ii) a sudden switch back, simultaneously with YFe2 magnetization reversal, in a small negative field or (iii) the compression of magnetic walls in larger negative fields. This result unambiguously demonstrates that the magnetic domain walls are located in the hard compound. The thermal evolution of the reversal process has been attributed to the thermal variation of the Zeeman and the magnetocrystalline anisotropy energies in the DyFe2 layers. At high temperatures, it then becomes more favourable that the YFe2 magnetization remains along the applied field and the magnetic walls expand, due to interface-exchange coupling, in the hard DyFe2 layers. This example demonstrates the undeniable capability of the XMCD technique to provide unique information on the mechanism of magnetization of a heterostructure combining a hard magnetic material with a soft magnetic material.

[Figure 1]

Figure 1

Magnetization curves for a [DyFe2 (50 Å)/YFe2 (200 Å)] superlattice at 200 K. (a) Layer-resolved curves recorded with XMCD signals at the L3 edge of yttrium (green line) and the L3 edge of dysprosium (blue line). (b) Macroscopic magnetization measured with a SQUID magnetometer (red line) and a linear combination of layer-resolved curves (purple line).

5. Magnetization dynamics probed with X-rays

Many fundamental magnetic processes take place on a timescale of about 100 ps, which is the characteristic time for magnetic materials given by the exchange interaction. This is why understanding how magnetization responds to a fast, external stimulus is at the forefront of magnetism research, with important implications for magnetic data storage and processing as well as for future spintronics devices. Typically, the magnetization dynamics can be initiated using an external stimulus such a pulsed magnetic field, a spin-polarized current or a light pulse (Kirilyuk et al., 2010[link]). Experiments are usually performed using a pump–probe technique taking advantage of the time structure of synchrotron radiation, i.e. the XMCD signal is measured at different time delays with respect to a magnetic pulse generated, for example, by a micro-coil. In the first time-resolved XMCD experiment it was demonstrated that the dynamics of magnetization reversal of individual layers in complex magnetic heterostructures can be resolved on a nanosecond timescale (Bonfim et al., 2001[link]). An alternative way to study magnetization dynamics with X-rays is X-ray-detected ferromagnetic resonance, in which XMCD could be used to probe the resonant precession of either spin or orbital magnetization components in a strong microwave pump field (Goulon et al., 2007[link]). On application to magnetic bilayers (Stenning et al., 2015[link]), multiple modes have been found describing the dynamics of the coupled layers, with a low-energy and a high-energy mode corresponding to in-phase and anti-phase oscillation, respectively, between the layer magnetizations. Moreover, for each mode one could resolve the amplitudes and relative phases of the precessing magnetization in the adjacent layers given by exchange coupling at the interface. This is an interesting aspect of this technique since it has the ability to distinguish between static and dynamic exchange coupling.

However, practical considerations limit the use of these approaches to around a 100 ps timescale, whereas ultrashort laser pulses easily reach the femtosecond timescale. By using ultrafast, femtosecond laser excitation and 100 fs soft X-ray pulses with circular-polarization XMCD measurements, the photoinduced magnetization switching in a ferrimagnetic Gd(FeCo) alloy was investigated (Radu et al., 2011[link]). Surprisingly, ultrafast magnetization switching in a material with antiferromagnetically coupled spins is shown to evolve over a transient ferromagnetic state. This transient state develops due to the different dynamics of the gadolinium and iron magnetic moments in the alloy: the iron moments switch within 300 fs, while those of gadolinium take five times longer. This experiment demonstrates that two magnetic sublattices which are not in equilibrium can show different magnetization dynamics. Thus, a spin system driven out of equilibrium by a single femtosecond laser pulse can evolve in an energetically unfavourable way and with a less than 1 ps switch from an antiferromagnetic to a ferromagnetic type of ordering. These results may contribute to the development of a novel concept of manipulating magnetic order in different classes of magnetic materials on timescales of the exchange interaction. Given the fact that the observed magnetization dynamics scale with the magnitude of elemental magnetic moments in the alloy, one can design new magnetic materials with tailor-made properties possessing optimized and even tunable switching characteristics.

6. Conclusions and outlook

In the short span of about 30 years since its discovery, X-ray magnetic circular dichroism has evolved from a scientific curiosity to become a workhorse technique in magnetism research. The XMCD technique, initially developed by the X-ray spectroscopy community, was very rapidly adopted by other communities, providing unique information on the electronic and magnetic structures of diverse materials ranging from bulk ferromagnets and paramagnets to nanoparticles, magnetic nanostructured systems and dilute magnetic semiconductors etc. Nowadays, the applications of XMCD are vast and provide almost endless possibilities for studying magnetic materials. Despite the fact that magnetic X-ray absorption spectroscopy covers a wide spectral energy range from soft to hard X-rays, not all experiments are technically feasible over this wide energy range. In particular, magnetic imaging on the nanoscale using X-ray transmission microscopy (Fischer et al., 2006[link]) and in X-ray holography, using the coherent properties of synchrotron radiation (Eisebitt et al., 2004[link]), as well as the investigation of ultrafast magnetic dynamics phenomena (Wietstruk et al., 2011[link]), are best performed in the soft X-ray range thanks to the large magnetic contrast, whereas XMCD experiments under extreme conditions, such as high pressure (Torchio et al., 2011[link]), pulsed high magnetic fields (Matsuda et al., 2009[link]), electric fields (Miwa et al., 2017[link]) and their combination with high or very low temperatures, are best performed in the hard X-ray range. The development of X-ray magnetic spectroscopy-based techniques goes in parallel with the spectacular increase in the brightness of next-generation synchrotron-radiation sources and with the appearance of XFELs. Indeed, coherent beams with full control of the polarization state as well as subpicosecond X-ray pulses are opening new perspectives to unravel the microscopic origin of magnetism on suitable timescales and length scales. More future applications will certainly emerge, offering unique research possibilities not only in physics but also in chemistry, biology and earth sciences.

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