Using spectroscopic information for x ray magnetometry and magnetic microscopy requires detailed theoretical understanding of spectral shape and magnitude of dichroism signals. We have shown unambiguously that--contrary to common belief--spectral shape and magnitude of x ray magnetic linear dichroism (XMLD) are not only determined by the relative orientation of magnetic moments and x ray polarization, but also their orientations relative to the crystallographic axes must be taken into account for accurate interpretation of XMLD data

Arenholz, Elke

van der Laan, G.

UNT Digital Library

EPJ manuscript No.(will be inserted by the editor)Anisotropic x ray magnetic linear dichroismIts importance for the analysis of soft x ray spectra of magnetic oxidesG. van der Laan1,a and E. Arenholz21 Diamond Light Source, Didcot, Oxfordshire OX11 0DE, UK2 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CAAbstract. Using spectroscopic information for x ray magnetometry and magneticmicroscopy requires detailed theoretical understanding of spectral shape and mag-nitude of dichroism signals. We have shown unambiguously that—contrary tocommon belief—spectral shape and magnitude of x ray magnetic linear dichroism(XMLD) are not only determined by the relative orientation of magnetic momentsand x ray polarization, but also their orientations relative to the crystallographicaxes must be taken into account for accurate interpretation of XMLD data.1 IntroductionTo be able to engineer magnetic nanostructures comprised of multiple layers with very differentmagnetic properties for device applications in information storage technology requires a pre-cise determination of the spin structure in heteromagnetic nanostructures. Soft x ray magneticdichroism spectroscopies play an ever increasing role in improving our understanding of com-plex magnetic nanostructures as these techniques provide elemental and chemical site-specificmagnetic information with high sensitivity and tunable probing depth. X ray spectromicroscopytechniques such as photoemission electron microscopy (PEEM) add spatial resolution down toa few nm. Using spectroscopic information for magnetometry and magnetic microscopy, i.e.,to determine the alignment of magnetic moments relative to the crystal axes and to imagedomains, requires detailed knowledge and theoretical understanding of the spectral shape andmagnitude of dichroism signals as well as their dependence on the relative orientation of polar-ization, external field, and crystallographic axes.X ray magnetic linear dichroism (XMLD) was first predicted in 1985 [1] and observed ex-perimentally the year after [2]. Sum rules relate the integrated intensities of the L2 and L3XMLD to expectation values of charge quadrupole moment and anisotropic spin-orbit inter-action [3]. Measurements and theoretical description of the anisotropic x ray magnetic lineardichroism (AXMLD) were recently obtained at the L2,3 edges of the 3d transition metal oxidesNiFe2O4, NiO [4], Fe3O4 [5], and CoFe2O4 [6] and rare earth M4,5 edges of the ferromagneticsemiconductor EuO [7]. These results showed that—contrary to common belief—spectral shapeand magnitude of the XMLD is not only determined by the relative orientation of magneticmoments and x ray polarization but that their orientations relative to the crystallographic axeshas to be taken into account. Consequently, conclusions based on the interpretation of XMLDspectra without accounting for its anisotropy have to be reconsidered. In particular, previousconclusions for NiO [8–10] require a reinterpretation of the experimental data using these recentfindings [4]. The XMLD angular dependence reflects the symmetry of the crystal field and iswell reproduced using atomic multiplet theory [11]. The observed anisotropy in the XMLD isa general phenomenon expected in any magnetic system.a e-mail: g.vanderlaan@dl.ac.uk2 Will be inserted by the editor0.00.51.0-0.020.000.02850 855 860 865 870 875(a) NiFe2O4 / SrTiO3 (011)XA (arb. units)(b)  =  = 0o =  = 10o =  = 20o =  = 30o =  = 40o =  = 45o =  = 50o =  = 60oXMLD. (arb. units) =  = 70o =  = 80o =  = 90ophoton energy (eV)[100]HFig. 1. (Color online) Angular dependence of the Ni L2,3 XMLD in NiFe2O4/SrTiO3(011). Inset:experimental geometry of field H (black arrows) and linear polarization E (yellow arrows) at angle ε tothe [100] axis (dashed line). Top: X ray absorption (XA) spectrum. Bottom: XMLD spectra. Symbolsindicate the experimental data and (red) lines give the results of the modeled angular dependence.2 Ni2+ XMLDIn NiFe2O4 films the Ni2+ moments are coupled ferromagnetically and can be aligned in anyin-plane direction by a external magnetic field of ∼0.5 T. X ray absorption (XA) measurementsin arbitrary geometry were performed using the eight-pole resistive electromagnet [12] on beamline 4.0.2 at the Advance Light Source (ALS) with 100% linearly polarized x rays. The Ni L2,3XA is shown in Fig. 1(a).The angular dependence of the XMLD signal across the Ni L2,3 edges was obtained byrotating the orientation of x ray polarization E and external magnetic field H relative to thecrystalline axes, c.f., inset to Fig. 1(a), where E makes an angle ε relative to the [100] crystalaxis. The XMLD is the difference between XA spectra with H at angles µ and µ+ 90◦ to the[100] direction, i.e., Ixmld(ε, µ) = Ixa(ε, µ)− Ixa(ε, µ+ 90◦), i.e., we measured the XMLD withH, and hence the Ni moments, parallel and perpendicular to E and varied the orientation ofE relative to the crystal lattice. The XMLD angular dependence of NiFe2O4/SrTiO3(011) isdisplayed in Fig. 1(b) for ε = µ between 0◦ and 90◦. A strong anisotropy of the XMLD signalis observed. The Ni L2 XMLD signal reverses its sign for ε = 0◦ and 45◦ and disappears almostcompletely for ε = 90◦. This demonstrates that the spectral shape of the XMLD signal dependsstrongly on the orientations of E and H relative to the crystalline axes. Expressions for theangular dependence of the XMLD are governed by symmetry conditions [5]. For the geometrywith µ = ε the XMLD signals for the (001) and (011) planes in cubic lattice areI(001)xmld (ε)=12[I0 + I45 + (I0 − I45) cos 4ε] ,I(011)xmld (ε)=I0 −18(5− 2 cos 2ε− 3 cos 4ε) (I0 − I45) ,where the “fundamental spectra”, I0 and I45, are defined as Ixmld(ε= µ= 0◦) and Ixmld(ε=µ= 45◦), respectively. The correct description of the angular dependence in cubic crystal fieldrequires both I0 and I45 [5].Figure 1(b) shows the excellent agreement between experimental data and modeled angulardependence. Further confirmation comes from atomic multiplet calculations for the electric-dipole transitions Ni2+ 3d8 → 2p53d9 in octahedral crystal field. Figure 2 shows the remarkableWill be inserted by the editor 3Fig. 2. Top: Measured Ni L2,3 XA spectrum for NiFe2O4/SrTiO3. Bottom: Comparison of the exper-imentally obtained fundamental XMLD spectra I0 and I45 for NiFe2O4 and NiO (dots) and atomicmultiplet calculations for Ni2+ in cubic symmetry (lines).agreement between the calculated and experimental spectra for I0 and I45. All measured featuresin the spectra are reproduced by the calculation, although the feature at 855.5 eV appearsoverestimated.Comparison between NiFe2O4 and NiO in Fig. 2 shows that the fundamental spectra exhibitsimilar spectral shapes for the ferromagnet and antiferromagnet. This is extremely useful sincethe fundamental spectra can be measured more easily in a ferro- or ferrimagnet and the resultscan then be transferred to an antiferromagnet where the moments are not so easily rearranged.It is essential to take into account the crystal axes orientation for a correct interpretation ofthe XMLD for magnetometry and microscopy applications. Applying our method to revisit theexchange coupled Co/NiO(001) interface we observe, contrary to previous experimental reports[13], perpendicular coupling between Ni and Co moments, as has been predicted by some ofthe theoretical models [14,15], and we observe the formation of an antiferromagnetic domainwall parallel to the (001) plane upon magnetization reversal in the Co layer [4].3 Magnetic and charge anisotropyThe XMLD shows a large angular dependence for the high-spin half-filled Fe d5 configurationin Fe3O4 with cubic symmetry [5], despite the fact that both charge quadrupole moment andanisotropic spin-orbit interaction vanish in this case. The same is observed for tetrahedral Mn d5in the ferromagnetic semiconductor (Ga,Mn)As [16]. This suggests that the angular dependencecan not be ascribed to the magnetocrystalline anisotropy [17]. Instead, the angular dependenceis a property of the cubic wave functions for the 3d valence states with respect to the spinquantization axis. The AXMLD can be used to estimate the size of the crystal field splittingand allows determining the spin quantization axis with respect to the crystalline axes. Themagnetocrystalline anisotropy manifests itself only in the integrated intensities of the L3 andL2 XMLD signals [3,18,19], which are small compared to the huge angular peak variations.The electric-dipole selection rules restrict the set of final states that can be reached fromthe ground state. This gives different transition probabilities from the exchange-split core levelsto the crystal-field-split empty 3d states. Multiplet calculations show that the angular depen-dence of the XMLD signal disappears when the crystal field splitting goes to zero. Therefore,anisotropic XMLD is a property of the cubic wavefunctions for the d states with respect to thespin quantization axis, and not the anisotropic spin-orbit interaction.4 Will be inserted by the editorIn cubic crystal field symmetry the XMLD is a linear combination of the two fundamentalspectra, I0 and I45, each exhibiting a distinctly different spectral shape, but with the sameshape when rotating either E or H [5]. In contrast, in tetragonal distorted crystal field theXMLD is a linear combination of four fundamental spectra, with different shapes for rotationof either E or H [6]. The difference in the fundamental spectra for linear dichroism (i.e., rotationof E) and magnetic dichroism (i.e., rotation of H) allows us to assess the influence of the chargeanisotropy due to non-cubic distortion, as has been shown for CoO [6].In cubic systems the orientation of the spin axis with respect to the crystallographic axes canbe studied with PEEM by rotating E [20]. With caution, also non-cubic systems can be studiedby rotating E, as this is the preferred method for PEEM. In the case of strongly distortedcubic symmetry the analysis of the linear dichroism is more complicated due to the chargeanisotropy. On the other hand, the magnetic dichroism remains largely unaffected for such asymmetry distortion [6].4 Europium oxideRare earths systems also show AXMLD, although much weaker. The AXMLD at the Eu2+ M4,5edges of EuO(001) is very well described by the same model used for the cubic transition metaloxides [7]. Multiplet calculations for Eu 4f7 show that the magnitude of the AXMLD varieslinearly with the strength of the effective crystalline electric field (CEF). The measured AXMLDevidences a considerable energy splitting of the 4f orbitals. The observed charge anisotropypresent in each of the non-degenerate 4f states demonstrates the feasibility of pinning the 4fstates by the local environment and tuning by external conditions, chemical doping, or strainfor purposes in device applications.The Advanced Light Source is supported by the Director, Office of Science, Office of BasicEnergy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.References1. B.T. Thole, G. van der Laan, and G.A. Sawatzky, Phys. Rev. Lett. 55, (1985) 20862. G. van der Laan, B.T. Thole, G.A. Sawatzky, J.B. Goedkoop, J.C. Fuggle, J.M. Esteva, R.C. Kar-natak, J.P. Remeika, and H.A. Dabkowska, Phys. Rev. B 34, (1986) 65293. G. van der Laan, Phys. Rev. Lett. 82, (1999) 6404. E. Arenholz, G. van der Laan, R.V. Chopdekar, and Y. Suzuki, Phys. Rev. Lett. 98, (2007) 1972015. E. Arenholz, G. van der Laan, R.V. Chopdekar, and Y. Suzuki, Phys. Rev. B 74, (2006) 0944076. G. van der Laan, E. Arenholz, R.V. Chopdekar, and Y. Suzuki, Phys. Rev. B 77, (2008) 0644077. G. van der Laan, E. Arenholz, A. Schmehl, and D.G. Schlom, Phys. Rev. Lett. 100, (2008) 0674038. D. Alders, L.H. Tjeng, F.C. Voogt, T. Hibma, G.A. Sawatzky, C.T. Chen, J. Vogel, M. Sacchi, andIacobucci, Phys. Rev. B 57 (1998) 116239. J. Stöhr, A. Scholl, T.J. Regan, S. Anders, J. Lüning, M.R. Scheinfein, H.A. Padmore, and R.L.White, Phys. Rev. Lett. 83 (1999)186210. H. Ohldag, A. Scholl, F. Nolting, S. Anders, F.U. Hillebrecht, and J. Stöhr, Phys. Rev. Lett. 86(2001) 287811. G. van der Laan and B.T. Thole, Phys. Rev. B 43, (1991) 1340112. E. Arenholz and S.O. Prestemon, Rev. Sci. Instrum. 76 (2005) 08390813. A. Scholl, M. Liberati, E. Arenholz, H. Ohldag, and J. Stöhr, Phys. Rev. Lett. 92 (2004) 24720114. N.C. Koon, Phys. Rev. Lett. 78, (1997) 486515. T.C. Schulthess and W.H. Butler, Phys. Rev. Lett. 81, (1998) 451616. A.A. Freeman, K.W. Edmonds, G. van der Laan, N.R.S. Farley, T.K. Johal, E. Arenholz, R.P.Campion, C.T. Foxon, and B.L. Gallagher, Phys. Rev. B 73, (2006) 23330317. J. Kunes and P.M. Oppener, Phys. Rev. B 67 (2003) 02443118. G. van der Laan, Phys. Rev. B 55, (1997) 808619. G. van der Laan, Phys. Rev. B 57, (1998) 11220. S. Czekaj, F. Nolting, L.J. Heyderman, P.W. Willmott, and G. van der Laan, Phys. Rev. B 73,(2006) 020401

Anisotropic x ray magnetic linear dichroism - Its importance for the analysis of soft x ray spectra of magnetic oxides

https://digital.library.unt.edu/ark:/67531/metadc925619/m2/1/high_res_d/951785.pdf

Anisotropic x ray magnetic linear dichroism - Its importance for the analysis of soft x ray spectra of magnetic oxides

Abstract

Similar works

Full text

Available Versions

UNT Digital Library