Resonant Soft X-ray Reflectivity in the Study of Magnetic Properties of Low-Dimensional Systems

Abstract

In this review, the technique of resonant soft X-ray reflectivity in the study of magnetic low-dimensional systems is discussed. This technique is particularly appealing in the study of magnetization at buried interfaces and to discriminate single elemental contributions to magnetism, even when this is ascribed to few atoms. The major fields of application are described, including magnetic proximity effects, thin films of transition metals and related oxides, and exchange-bias systems. The fundamental theoretical background leading to dichroism effects in reflectivity is also briefly outlined.

1. Introduction

X-ray reflectivity is typically applied in the hard X-ray regime to study the interface morphology of layered materials by exploiting the charge density contrast between adjacent layers [1]. Synchrotron X-ray sources have made it possible to scan the photon energy at resonance, in correspondence with specific elemental absorption edges, so as to add to the technique both additional layer-resolved selectivity and sensitivity to the chemical and electronic structure [2,3,4,5,6,7]. In particular, in the soft X-rays, the L_2,3 edges of 3d transition metals and the M_4,5 edges of rare earths become accessible, which carry fundamental information on the magnetic properties thanks to their pronounced magnetic circular dichroism effects [8].

Resonant soft X-ray magnetic scattering (or reflectivity) has advanced following the great success of X-ray magnetic circular dichroism (XMCD) in absorption, and permits one to disentangle the spin and orbital contributions to magnetism with elemental specificity [8]. XMCD in absorption is typically carried out on ultrathin films, since the information depth is limited to a few atomic layers. This limitation is due to the attainment of the magnetic-dependent absorption coefficient by measuring the electronic yield from the sample following its interaction with the X-ray beam. Therefore, the probed depth is limited by the inelastic mean free path of the outgoing electrons.

Basically, as the penetration depth of X-ray photons is much larger than that of the electrons, reflectivity contains all information at the origin of XMCD in absorption, but it also carries precious quantitative information on buried layers, buried interfaces, and morphology. In fact, in most typical cases, resonant soft X-ray magnetic reflectivity (RSXMR) is applied to derive magnetic depth profiles in layered materials. On the other hand, the intimate interplay between optical, magnetic, and structural properties may complicate considerably the experimental signal, especially across absorption edges where the optical constants present huge variations within photon ranges of a few eV. This may also be convenient in some cases, since by precise tuning of the photon energy one can emphasize (or mask) the information pertaining to selected layers or buried interfaces. In any case, in order to extract useful information from the experimental data, a simulation of the optical response is mandatory. This requires knowledge (or estimation) of the complex optical constants of the (anisotropic) materials, including magnetic effects and the layered structure of the system. These quantities are most often derived on the basis of best fits to the experimental data.

It should be noted that studies using RSXMR can be divided into two groups: (i) those that privilege angular scans at fixed, selected photon energies across and outside specific elemental absorption edges, and (ii) those that privilege energy scans across the edges at fixed, selected angles. These two visions typically reflect the ‘cultural’ origin of the experimental teams involved, with prominent expertise in either structural studies through diffraction techniques or in the investigation of electronic properties through spectroscopy. These two visions actually converge in exactly the same physics and phenomenology, and should simply be seen as two sides of the same coin.

The origin of the magneto-optical response can be ascribed to the different density of free states (holes) for spin-up and spin-down electrons in the valence-band due to Stoner splitting in a magnetized solid [9,10]. Absorption and resonant scattering of radiation depend on the polarization state and its relative orientation with respect to the direction of magnetic moments. Investigation of the ferromagnetic state of transition metals through XMCD and RSXMR measurements that use circularly polarized radiation with a photon energy tuned on $\mathrm{n}p\to {\mathrm{n}}^{\prime }d ({\mathrm{n}}^{\prime }>\mathrm{n})$ absorption edge is most common [9]. In the analysis of resonant X-ray reflectivity measurements, the response of the system is conveniently described by a macroscopic (relative) dielectric tensor $\overleftrightarrow{\epsilon }$ that connects the displacement vector $D$ and the electric field $E$ through the constitutive relation $D={\epsilon }_0\overleftrightarrow{\epsilon }E$, with ${\epsilon }_0$ being the vacuum permittivity. If we look for a solution in the form $E\left(r,t\right)=E_0{e}^{i\left(k\cdot r-\omega t\right)}$, where $k$ is the complex wavevector and $\omega$ is the angular frequency of the radiation, the wave equation in the medium is written in matrix form [11,12,13,14]:

$$\left(\overleftrightarrow{kk}-k^2\overleftrightarrow{1}+\frac{{\omega }^2}{c^2}\overleftrightarrow{\epsilon }\right)E=0$$

where $\overleftrightarrow{kk}$ is a 3×3 tensor of components ${\left(\overleftrightarrow{kk}\right)}_{ij}=k_i{k}_j, i,j=x,y,z$ and $\overleftrightarrow{1}$ is the unitary matrix.

The investigated sample is usually a multilayer composed of slabs with different chemical compositions and/or different magnetic moments, each having thickness $t_i$. Two adjacent slabs are separated by a horizontal plane interface with root-mean-square (rms) roughness $r_i$. The electromagnetic fields propagating into the multilayer can be calculated imposing the boundary conditions at the interfaces for the electric and magnetic field of the electromagnetic radiation.

In order to simulate the reflectivity signal, a reasonable structural model—to later be refined through fitting—is a prerequisite. The propagation of the light beams in the layered system should then be simulated. The ‘simplest’ approach may be based on isotropic homogeneous layers with homogeneous magnetization. In this case, the Parrat formalism [15] is often used to simulate the reflectivity. Anisotropic materials can be treated and more refined results can be obtained applying the 4×4 matrix method [16,17,18,19,20,21,22,23,24,25,26], where each layer is considered anisotropic and described by a suitable dielectric tensor. Since the chemical (compositional) depth profile can be different from the magnetic profile, two independent structural models could be necessary in order to simulate the chemical contrast and magnetic responses.

In this review, we do not aim to be exhaustive but to give the interested reader a concise picture of the capabilities of the technique and its fields of application.

2. Methods

2.1. Experimental Setup

RSXMR requires photon tunability and circular (or elliptical) polarization of the light beam. This requires synchrotron radiation. RSXMR is typically carried out either on bending magnet beamlines, where elliptical polarization is obtained by selecting angular portions of the photon beam above or below the synchrotron ring orbital plane, or on beamlines equipped with insertion devices capable of circular polarization.

An example of the first type of beamline is shown in Figure 1a. This refers to the BEAR beamline [27,28,29] at the Elettra synchrotron radiation facility in Italy. The beamline operates in the photon energy range between 3 and 1600 eV. A polarization selector consisting of movable slits is positioned at the beginning of the beamline, just before the first optical element (parabolic mirror P1). It permits one to select the light polarization status: linear, by selecting the central portion of the beam, or left/right circular (elliptical), by moving the slit’s aperture above/below the orbital plane.

A scheme of a typical (specular) reflectivity experiment is presented in Figure 1b: a magnetic field is applied parallel to the sample plane, inducing magnetization in the different layers/materials that compose the sample; the magnetizer is generally designed to permit experiments either in remanence magnetization or in applied field, depending on the specific type of investigation; the reflected intensity is measured with a photodiode; the sample and photodiode can be rotated independently around an axis perpendicular to the incoming beam and parallel to the sample surface to achieve θ–2θ scattering geometries; rotations of the sample and detector are typically realized through coaxial high-precision rotation stages (goniometers) equipped with differential pumping to guarantee UHV during measurements; and X-ray absorption experiments are often carried out at the same time by measuring the drain current or the emitted photoelectrons (total/partial electron yield mode) and/or by measuring the fluorescence photons (fluorescence yield mode) while the photon energy is scanned.

2.2. Origin of the Magnetic Dichorism Effect

The magnetization $M$ breaks the inversion symmetry of the system, introducing an antisymmetric term in the dielectric tensor $\overleftrightarrow{\epsilon }$. It is possible to demonstrate [11,30] that, for a system that should be optically isotropic in the absence of magnetization, if $M$ is directed along the $\widehat{z}$ axis, the dielectric tensor becomes:

$$\overleftrightarrow{\epsilon }=\left(\begin{array}{ccc}{\epsilon }_{xx}& {\epsilon }_{xy}& 0\\ -{\epsilon }_{xy}& {\epsilon }_{xx}& 0\\ 0& 0& {\epsilon }_{zz}\end{array}\right).$$

(1)

In general, the elements of $\overleftrightarrow{\epsilon }$ are complex numbers. If we consider a second-order expansion in $M_z$ for the elements of the tensor, the off-diagonal term is written as ${\epsilon }_{xy}=-iQ{M}_z$, while the diagonal terms are given as ${\epsilon }_{xx}={\epsilon }_{M=0}-\frac{1}{3}G{M}_z^2$ and ${\epsilon }_{zz}={\epsilon }_{M=0}+\frac{2}{3}G{M}_z^2$, where ${\epsilon }_{M=0}$ is the electric permittivity with null magnetization and $Q$ and $G$ are the first- and second-order magneto-optic coefficients, respectively. In X-ray spectroscopy, the antisymmetric and off-diagonal elements ${\epsilon }_{xy}=-iQM$ and ${\epsilon }_{yx}=-{\epsilon }_{xy}=+iQ{M}_z$ are responsible for the XMCD effect and the dichroic reflectivity observed in RSXMR measurements when circular or elliptical polarization are employed. The additional terms of the diagonal depend on $M^2$ and are responsible for the X-ray magnetic linear dichroism (XMLD) that furnishes complementary information to XMCD and are used, in particular, in the study of antiferromagnetic materials [9] with ${\epsilon }_{xy}=0$. The second-order expansion in $M_z$ is exact for systems with spherical symmetry, whereas, in cubic crystals, higher-order terms are present. The off-diagonal and diagonal elements of $\overleftrightarrow{\epsilon }$ are odd and even functions of $M_z$, respectively [30].

When the radiation propagation direction is parallel to the magnetization direction (the $\widehat{z}$ axis), it can be shown that the wave equation has as solutions, i.e., polarization eigenstates, the left ($+$) and right ($-$) circularly-polarized radiation [11] corresponding to the values of refractive index given by:

$$n_{+}=\sqrt{{\epsilon }_{xx}+i{\epsilon }_{xy}}, n_{-}=\sqrt{{\epsilon }_{xx}-i{\epsilon }_{xy}}.$$

This is intimately related to two different values of the absorption coefficient ${\mu }_{\pm }=2\frac{\omega }{c}\mathrm{Im}\left\{n_{\pm }\right\}$, which are responsible for dichroism in X-ray absorption, measured through XMCD. Dichroism is given, in this case, by:

$$\mathsf{\Delta }\mu ={\mu }_{+}-{\mu }_{-}=2\frac{\omega }{c}\mathrm{Im}\left\{n_{+}-n_{-}\right\}\approx 2\frac{\omega }{c}\mathrm{Re}\left\{Q\right\}M.$$

Absorption measurements with opposite photon helicity provide the two absorption coefficients (${\mu }_{+}$) and (${\mu }_{-}$) as a function of the photon energy $\hslash \omega$, or equivalently, the imaginary part of the two refractive indices $n_{\pm }=n_{\pm }^{\prime }+i{n}_{\pm }^{″}$. Defining the average $\overline{n}=\frac{1}{2}\left(n_{+}+n_{-}\right)$ and dichroic $\mathsf{\Delta }n=\left(n_{+}-n_{-}\right)$ refractive index, from the experimentally measured imaginary parts $\overline{n}″=\frac{1}{2}\left(n_{+}^{″}+n_{-}^{″}\right)$ and $\mathsf{\Delta }{n}^{″}=n_{+}^{″}-n_{-}^{″}$, the real parts ${\overline{n}}^{\prime }=\frac{1}{2}\left(n_{+}^{\prime }+n_{-}^{\prime }\right)$ and $\mathsf{\Delta }{n}^{″}=n_{+}^{″}-n_{-}^{″}$ are calculated through Kramers–Krönig relations [31,32].

The real and imaginary parts of the refractive index can then be used to compute the dielectric tensor and to derive the specular reflectivity (and related dichroism) according to the procedure described by us in [25].

3. Applications

In this section, a series of examples of the main applications of RSXMR are presented. As indicated above, we do not aim to be exhaustive, but to give the interested reader a concise picture of the capabilities of this technique and its major fields of application.

3.1. First Studies

The first applications of RSXMR focused on metallic single crystals, thin films, and multilayers. The magneto-optical response was tested using circularly as well as linearly polarized light, identifying in both cases a marked difference in the reflectivity signal upon the reversal of the external magnetic field applied to the sample or after changing the polarization of the incident beam. Different approaches based on scattering theory or the Maxwell equations have been used in the interpretation of the experimental data. A substantial equivalence was obtained. The sensitivity of the technique to different atomic elements, together with the structural and morphological information provided by the interference effects, demonstrated the significant potential of resonant X-ray reflectivity in the study of complex magnetic heterostructures.

The sensitivity of X-ray resonant reflectivity with linearly polarized light was investigated by C. Kao and co-workers [33] on an Fe single crystal immersed in an external magnetic field (Figure 2a). A large asymmetry was observed at the L absorption edge upon switching the field polarity. The asymmetry signal was much larger compared with other conventional techniques based on the Kerr effect or photo-absorption with circularly polarized light, thus confirming the high potential of reflectivity in studying the magnetic properties of materials. C.-CX. Kao et al. applied RSXMR at Co L_2,3 edges to a magnetic multilayer structure made of GaAs/ZnSe/Fe/Co/Al₂O₃ [34] (Figure 2b). The relevant changes in dichroic reflectivity observed by varying the angle of incidence were successfully interpreted in terms of interference effects due to the multilayer structure, using the classical electromagnetic theory. J.B. Kortright et al. [35] demonstrated the equivalence of the classical approach, based on the solution of the Maxwell equations, and the theory of resonant atomic scattering in the interpretation of the resonant X-ray magneto-optical transmission and absorption measurements; they applied their formalism to the study of Fe layers grown on SiN_x membranes and capped with a SiC thin film. An Fe/C multilayer was extensively investigated by H-Ch Mertins and co-workers [36] by means of X-ray resonant reflectivity at Fe L_2,3 edges using linearly and circularly polarized light, thereby obtaining the magnetic contribution to the Fe optical constants. M. Sacchi et al. [37] reported the complete determination of the Fe dielectric tensor, and in particular of its off-diagonal terms, by combining resonant X-ray absorption (Figure 2c). The same approach was also successfully adopted to study the magnetic properties of a Ni(110) single crystal using linear and circular polarized light [38]. The magnetic properties related to Fe and Mn atoms in Ir/Fe_0.9Mn_0.1/Ir and Ir/Fe_0.7Mn_0.3/Ir multilayers were investigated by J.M. Tonnere et al. [39] using RSXMR at the Fe and Mn L_2,3 absorption edges, exploiting a transverse geometry; this allowed them to measure the very low magnetic moment of Mn, which was found to be equal to 0.2 µB.

3.2. Magnetic Proximity Effects

Circular dichroism revealed through X-ray reflectivity has been used extensively to study multilayers formed by the repetition of ferromagnetic and nonmagnetic thin films. These systems present relevant technological properties, with their electrical resistance being strongly affected by the relative magnetization of the adjacent layers. In particular, these heterostructures can exhibit the so-called tunnel magnetoresistance (TMR) and giant magnetoresistance (GMR) effects, exploited in the fabrication of compact high-performance digital memories and magnetic sensors. Specifically, when two magnetic layers separated by a nonmagnetic stratum present the same magnetization direction, the probability that an electron travels across the structure is maximum, whereas in the opposite configuration the probability is negligible. These multilayer systems show important interface effects related both to the modification of the bulk crystal structure, due to the lattice mismatch between layers of different composition, and to the direct role of the interface electronic orbitals. Due to its chemical specificity, RSXMR can be successfully used to study separately the magnetic behavior of the different elements. In addition, at grazing incidence, the interface effects can be strongly emphasized. In this way, it is possible to obtain information on the detailed magnetic profile, which provides a diagnostic tool for layer thickness optimization during growth. Magnetization due to the direct orbital hybridization at the interface between ferromagnetic and nonmagnetic layers has been widely observed.

M. Abes et al. [40] studied the magnetization of Mn and Cu in a [Co/Cu(x)/CuMn/Cu(x)] multilayer by varying the thickness, x, of the copper layer. Magnetization was induced in the CuMn diluted alloy due to its proximity to the ferromagnetic Co layer. It was found that the Mn spin polarization increased by decreasing the copper interlayer thickness, demonstrating the interfacial nature of the Mn and Cu magnetization. In particular, Mn changed its coupling with the Co magnetic moment from antiferromagnetic to ferromagnetic as a function of the distance from the Co layer.

A [Fe₇₀Co₃₀/Pd]_n multilayer was characterized by N Awaji et al. [41], who found an enhancement of Fe and Co spin polarization in a region adjacent to the Pd layer with a thickness of about four atomic monolayers, in contrast to a reduction in the magnetization at the immediate interface, which was associated with atomic intermixing. RSXMR also evidenced magnetization proximity effects in Pt and Ir buffer layers that were used to study the interfacial Dzyaloshinskii–Moriya interaction (an antisymmetric exchange interaction between two neighboring magnetic spins, favoring spin canting [42,43]) in Co₂FeAl thin films, as reported by M. Belmeguenai et al. [44]. A magnetization of Pt at the interface with Co in a Pt/Co bilayer was detected using angle resolved X-ray resonant magnetic reflectivity by J. Geissler et al. [45]. The resultant magnetic moment was mainly localized to within 1 nm of the Pt layer at the Pt/Co interface (Figure 3a). The magnetization of Pt grown on ferromagnetic Fe and Co₃₃Fe₆₇ layers was also studied by D. Graulich et al. [46]. An induced magnetization was even detected in Au films in contact with ferromagnetic materials: the magnetization in Au in a Fe/Au bilayer and in an Fe/Au/Fe trilayer was investigated by N. Hosoito et al. [47] at the Au L₃ edge and a detailed magnetic depth profile was obtained. It was found that the induced magnetization in Au was pronounced close to Fe interfaces and reduced in the interior of the Au layer, with an attenuation length longer than 15 Å. Fe/Ce/La/Ce, Fe/La/Ce/La, and Fe/CeH_2-δ multilayers were studied by N. Jaouen et al. [48] to highlight the magnetization inside the Ce layers. An antiferromagnetic coupling of α-like Ce with Fe was observed (Figure 3b) in Fe/Ce/La/Ce and Fe/La/Ce/La structures. Magnetization extended unexpectedly inside the Ce layer. This behavior was ascribed to the strain induced in Ce in the α-like phase. On the other hand, an Fe/CeH_2-δ multilayer, where Ce was in the γ-like phase, revealed a strongly localized magnetization at the interface with Fe. In relation to spintronic devices, a Pd/Co/Pd trilayer was investigated by D.-O. Kim et al. [49] to measure the Pd magnetic polarization induced by Co. The main effects were localized at the two interfaces between Co and Pd, but the induced magnetization was strongly enhanced at the top Co/Pd interface with respect to the bottom Pd/Co interface. Interestingly, this anisotropic proximity effect was not found to be correlated to a different morphological or physical structure of the two interfaces. The behavior of spin polarization across a Pt layer coupled in a planar heterojunction with different ferromagnetic materials was studied using RSXMR by C. Klewe et al. [50]. Quantitative interpretation of the experimental data was given following an ab initio approach. Higher magnetization in Pt was found for Pt/Fe heterojunctions, while smaller values were obtained by coupling Pt with Ni. Using the ReMagX software [3,51], Krieft et al. [52] presented and discussed different strategies and iterative optimization approaches to fit X-ray reflectivity spectra of ferromagnet/Pt layered structures. If $I_{+}$ and $I_{-}$ represent the intensities of reflectivity collected with right and left circular polarization, respectively, the fitting of the average spectra $I=\frac{1}{2}\left(I_{+}+I_{-}\right)$ provides the density depth profile of the different elements; therefore, the thickness and roughness of the various layers can be derived. This structural model is then used to fit the asymmetry ratio $\mathsf{\Delta }I=\left(I_{+}-I_{-}\right)/\left(I_{+}+I_{-}\right)$, which gives the spin polarization depth profile of the magnetic species. This scheme of analysis can be applied as a very general approach to fitting the spectra obtained in magnetic reflectivity experiments [49]. Proximity effects have also been observed in Pt/Fe bilayers [53] and were compared with Pt/NiFe₂O₄ to verify the presence of anomalous Nernst interfacial effects. The results obtained by fitting the RSXMR measurements were compared with ab initio calculations, revealing the presence of an enhancement of the interfacial magnetization only in the Pt/Fe system, which excluded a role of the interface in the Seebeck effect observed in Pt/NiFe₂O₄.

A Pt/Co/Ta trilayer was extensively studied by A. Moskaltsova et al. [54]. The magnetization profile of the Pt layer was extracted for different sequences of Pt, Co, and Ta films in the trilayer heterojunction. A spin polarization due to proximity was found only for those configurations in which Pt was in contact with Co, excluding a significant role of Ta. Ta was also used as a buffer layer to study the profile and entity of the magnetic coupling between Pt and Co by A. Mukhopadhyay et al. [55] and the induced magnetization profile in the Pt layer was quantitatively determined (Figure 3c). The role of proximity effects in the interfacial Dzyaloshinskii–Moriya interaction stabilizing Nèel domain walls in magnetic materials was investigated with RSXMR at the Pt L₃ edge in a Pt/Co/Au,Ir/Pt structure, where Au and Ir played the role of spacers [56]. Results indicated a clear dependence of proximity-induced spin magnetization in Pt on the thickness of the spacer layers, together with a change in the organization of the magnetic domains, which was explained in terms of the interfacial Dzyaloshinskii–Moriya interaction. This last effect was also observed for greater thicknesses of the spacer layers, where the proximity effect was no longer present. R. M. Rowan-Robinson et al. [57] also used polar magneto-optical Kerr effect magnetometry to study the current-induced magnetization reversal in a Pt(5 nm)/Co(0.6 nm)/Pt(5 nm) trilayer designed to have weak perpendicular magnetic anisotropy. The magnetization reversal was observed for very low critical current density; this was related to the low anisotropy in perpendicular spin magnetization between the Co and Pt layers together with a low saturation value of magnetization. RSXMR was applied by L. Sève et al. [58] to investigate the magnetization of Ce and La in Ce/Fe and La/Fe multilayers as a function of the film thickness. The results obtained for La showed a clear proximity-induced magnetization localized mainly at the interface with the Fe film, while the amorphous structure of Ce grown on Fe induced a complex magnetic organization inside the Ce film: the magnetization extended across all of the Ce film with an oscillating behavior. Femtosecond laser pulses were applied by W. Szuszkiewicz et al. [59] to induce changes in the spin polarization at the interface in Pt/Co/Pt trilayers. X-ray reflectivity measurements indicated a rearrangement of interface magnetization from in-plane to out-of-plane after laser irradiation. This change was found to be irreversible and was related to the formation of a structural variation activated by the laser that produced a Pt-Co alloy at the Pt/Co interface.

3.3. Transition Metal Oxides

Due to the wide application possibilities in spintronic devices and the variety of compounds with specific magnetic properties, transition-metal oxides in the form of thin films or layered stacks likely represent the class of magnetic systems most studied with RSXMR. In particular, the interplay between electronic, magnetic, and structural properties—including interface effects—plays a fundamental role in different important, possibly interconnected, phenomena such as superconductivity, topological insulating phases, ferroelectricity, and ferromagnetism. Indeed, with its magnetic depth-, chemical depth-, and electronic state-profiling capabilities, RSXMR represents a unique instrument for the investigation of these systems.

Much work has been dedicated to manganites, whose magnetic properties are strictly related to their chemical composition and structural order, which in turn can be strongly influenced by lattice distortions, especially when the oxides are epitaxially grown on suitable crystalline templates. Coordination of oxygen sites can be varied thanks to epitaxial-growth strategies at the interfaces between materials in layered stacks, leading to a change of p-d hybridization, with strong influence on the magnetic behavior [60]. Rotation of the in-plane magnetic easy axis has been observed in manganite heterostructures by tailoring the interface oxygen network with a suitable choice of substrate [61] (Figure 4a). Complex magnetic structures have been detected (Figure 4b), such as the presence of a magnetic helix state in the LaNiO₃ layers in manganite-nickelate superlattices [62], with Ni-O ligand hole states from LaNiO₃ that are mostly filled due to electron transfer from interfacial Mn. Intermixing at the monolayer scale allows for control of charge transfer and induced magnetic moment in the nickelate layer [63], and antiferromagnetic order can be induced and stabilized in LaNiO₃ by interfacial coupling [64]. Metal or insulator phases, or their coexistence, and temperature-induced transitions have been observed in perovskite manganite superlattices [65]. In bilayer manganites, it was demonstrated that only the outermost Mn–O bilayer exhibits no long-range ferromagnetic order, whereas the next bilayer displays the full spin polarization of the bulk [66]. A temperature-dependent magnetic dead layer was observed at air-exposed LSMO surfaces [67], which may be related to the reduced magnetization present at the junction of manganite-based magnetic tunnel junctions, deteriorating the performance of these devices.

Thickness-driven electronic phase transitions have been studied in perovskite heterostructures such as La_2/3Sr_1/3MnO₃, with the observation of O 2p–Mn 3d hybridization coupled to layer-dependent octahedral tilts [68]. Magnetically diluted interface layers related to the chemical composition were detected in La_0.67Sr_0.33MnO₃/multiferroic BiFeO₃ bilayers [69]. RSXMR applied at LCMO/YBCO/STO trilayers revealed that the magnetization of the LCMO interface was controlled at low temperature by both the superconductor and the substrate [70]. Magnetic proximity effects in YBCO/LCMO multilayers have also been addressed by coupling RSXMR and neutron reflectometry [71]. Other interesting examples of applications of the technique include interface magnetization between the correlated metal CaRuO₃ and the antiferromagnetic insulator CaMnO₃ [72], the study of the interface between the half metallic Fe₃O₄ and the semiconductor ZnO [73], and the magnetization reversal of Cr at the CrO₂/RuO₂ interface [74].

Finally, it should be mentioned that RSXMR can be applied to obtain information on roughness, with the possibility of distinguishing between morphological roughness and magnetic roughness both at the surface and at buried interfaces. This has been applied and discussed [75] in reference to LSMO layers.

3.4. Exchange-Bias Systems

Exchange-bias [76] is the shift of the ferromagnetic hysteresis loop along the field axis that occurs in ferromagnet–antiferromagnet (FM–AF) systems as a consequence of the exchange coupling across an FM–AF interface. Due to the buried nature of the pinned and uncompensated moments at the interface between FM and AF materials, RSXMR appears to be particularly suitable for these type of studies.

In this context, S. Roy et al. [77] used specular reflectivity to measure the depth profile of the uncompensated spins at the FeF₂/Co interface (Figure 5a), finding uncompensated magnetization in the antiferromagnetic FeF₂ layer. Within 2–3.5 nm of the Co/FeF₂ interface, the magnetization of uncompensated FeF₂ was antiparallel to the spins of Co and rotated in conjunction with the Co spins. At distances greater than 3.5 nm from the interface, the uncompensated FeF₂ magnetization was pinned, providing a means of establishing bias. In a different study, the depth-dependent charge and magnetization density on an absolute scale across a permalloy/CoO interface was determined via resonant soft X-ray magnetic reflectometry [78,79].

The layer structure of uncompensated spins in a CoFe/IrMn/NiFe trilayer system was studied as a function of temperature by J-S. Lee et al. [80]. Two distinct uncompensated spin layers were found due to the distinct Mn coupling to each of the FM materials.

The coupling between Fe and the uncompensated Mn moments in exchange-biased Fe/MnPd bilayers was obtained through investigation of the magnetization depth profile derived from RSXMR at Fe and Mn L edges [81]. A complex interfacial configuration was observed [81,82] consisting of a two-monolayer-thick FM region and pinned uncompensated Mn moments extending far deeper, with both located in the antiferromagnet. Element-resolved magnetization profiles were also obtained on Fe/CoO layers [83] and element-resolved hysteresis loops were recorded at different temperatures [84]. A dual behavior of the interfacial uncompensated spins was studied in the prototypical exchange-bias NiFe/IrMn system [85], where frozen uncompensated spins were found to be present deep in the AF film, whereas rotating ones were identified closer to the interface (Figure 5b). A sign change of the exchange-bias from negative to positive was also observed by S. K. Mishra et al. [86] in NiFe/IrMn with soft X-ray resonant magnetic scattering.

An Fe/NiO/Co trilayer system was investigated at the L edges of Fe, Co, and Ni [87] below the Néel temperature, simultaneously providing information on the chemical composition and the elemental-resolved magnetization behavior. Similarly, through RSXMR it was possible to derive the element-resolved magnetization profile of all-manganite La_0.7Sr_0.3MnO₃/SrMnO₃/La_0.7Sr_0.3MnO₃ trilayers [88]. RSXMR also permitted the detection of a small but distinct magnetic moment, antiparallel to the Co moment, in the antiferromagnetic IrMn layer in a NiFe/Cu/Co/IrMn spin valve structure [89]. Frozen magnetic moments in NiFe/FeMn at the NiFe ferromagnet were observed by element- specific hysteresis loops [90]. A nearly pure orbital moment character was more recently inferred for the pinned moments in a Co/FeMn exchange-bias bilayer through the analysis of reflectivity [91]. Magnetization profiles were even derived from magnetic scattering in the hard X-rays, in particular at the Ir L edge in a MnIr/CoFe exchange-bias system [92].

3.5. Metallic Thin Films and Multilayers

The orientation of the magnetization in metallic thin films has been addressed with many techniques, including RSXMR. Metallic thin films, especially of transition metals, represent prototypical systems for the study of fundamental aspects of magnetism. Strain and epitaxy conditions may change the crystal structure of elemental metals, giving rise to artificially tailored magnetic properties that are not available in the corresponding bulk materials. RSXMR has been applied in prototypical studies: for example, to resolve the spin orientation structure of ultrathin fcc Fe films on Cu(001) [93,94]; to resolve the induced moment in uranium in U/Fe multilayers [95]; to probe the interlayer coupling in ferromagnetic/semiconductor multilayers [96]; and to measure the value of the magnetic moment, its orientation, and depth profiles in Fe/C [97], Gd/Fe [98,99,100], and Co/Mg [101] multilayers or in Cu/Fe/Cu trilayers on a semiconductor [102]. Carlomagno et al. [103] investigated, through resonant X-ray reflectivity, the structural and magnetic properties of a MgO/Co/MgO trilayer, evidencing difference in Co oxidation and roughness between the bottom (Co on MgO) and top (MgO on Co) interfaces, which was reflected in an asymmetric magnetization profile for the Co layer.

Vectorial analysis of magnetization has been performed through RSXMR to obtain information on the longitudinal and transverse components of the magnetization: transverse and longitudinal magnetic hysteresis loops have been determined in Co and FeCo films [104]. In- and out-of-plane magnetization and noncollinear profiles were determined with a subnanometer resolution in FePt multilayers [39] and in FeCo systems [105,106]. Perpendicular exchange coupling was measured at the interface between an antiferromagnet [NiO/CoO]₃ and a Pt-Co ferromagnet film on Pt(111): a rotation of the easy magnetization axis of the ferromagnet was detected along the antiferromagnet spins [107]. Perpendicular anisotropy was also investigated by RSXMR in Co/Pt multilayers [108]. Magnetization profiles were recorded for bcc Fe films grown on a vicinal Ag(001) surface, but capped below a Au layer, revealing an enhancement of the magnetic moment at the interface [109].

3.6. Other Cases

RSXMR has been fruitfully applied in other relevant situations.

It has been used to derive the magnetic profile and to relate it to the chemical depth profile in organic-inorganic layered materials, which is of consequence to organic spintronics: A. Verna et al. [110] probed the structural and magnetic properties of a ferromagnetic/organic interface, consisting of a polycrystalline Co layer deposited on a fullerene thin film, and found a sharp interface with limited intermixing and a null remnant magnetization.

With regard to spintronics, diluted magnetic semiconductors have also indicated a possible ability to control the spin behavior in devices. As an example, Fe/(Ga,Mn)As heterointerfaces have been epitaxially grown and presented a robust ferromagnetism of the interfacial Mn atoms induced by the proximity effect [111].

It is worth mentioning that recent time-resolved experiments have been successfully carried out by applying X-ray magnetic circular dichroism in reflectivity: an ultrafast optically induced ferromagnetic alignment of antiferromagnetic Mn in Co/Mn multilayers has been observed probing the L₃ edge of Mn in reflectivity after an ultrashort laser excitation [112]. Ultrafast, element-dependent demagnetization dynamics were studied in a Co/Pt multilayer with an X-ray-free electron laser by probing the Pt N_6,7 and Co M_2,3 edges [113]. Circularly polarized XUV light produced at the Fermi FEL at the Fe M_2,3 edge was used to measure resonant magnetic reflectivities in a permalloy/Ta/permalloy trilayer film, permitting detection of ultrafast changes of spin and charge density profiles [114]. Pump-and-probe time-resolved resonant X-ray reflectivity was also applied at the Fe 2p edge to measure the electronic and magnetic dynamics of ferromagnetic insulating BaFeO₃ thin films [115]: a transition into a metallic state induced by laser excitation was observed.

4. Conclusions

In this review, we have concisely described the basic concepts underlying resonant soft X-ray magnetic reflectivity. This technique is very powerful since it is able to discriminate and highlight the contribution to magnetism of single elemental species in a magnetic compound. It is also sensitive to the effect of few atomic magnetic moments, which may drive the macroscopic magnetic behavior in layered structures. We have described the general experimental requirements, the typical materials that are specifically investigated by this technique (thin films, buried interfaces, proximity effects, exchange-bias systems, and magnetic oxides) and the fundamental mechanisms that give rise to dichroism effects in reflectivity. This is always accompanied by references to the relevant literature so that the interested reader can readily expand her/his knowledge, if desired. The references also include a list of relevant studies where RSXMR has been successfully exploited with the aim of providing a wide but concise perspective of the different applicative fields.