Magnetic anisotropy in Fe/U and Ni/U bilayers
MMagnetic anisotropy in Fe/U and Ni/U bilayers
E.R. Gilroy, ∗ M.-H. Wu, M. Gradhand,
1, 2
R. Springell, and C. Bell H. H. Wills Physics Laboratory, University of Bristol,Tyndall Avenue, Bristol BS8 1TL, United Kingdom Institut für Physik, Johannes-Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
Magnetometry measurements of Fe/U and Ni/U bilayer systems reveal a non-monotonic depen-dence of the magnetic anisotropy for U thicknesses in the range 0 nm - 8 nm, with the Fe/U bilayersshowing a more prominent effect as compared to Ni/U. The stronger response for Fe/U is ascribedto the stronger 3 d -5 f hybridization of Fe and U. This non-monotonic behaviour is thought to arisefrom quantum well states in the uranium overlayers. Estimating an oscillation period from the non-monotonic data, and comparing it to Density Functional Theory calculations, we find that wavevector matches to the experimental data can be made to regions of high spectral density in (010)and (100) cuts of the electronic structure of α -U, consistent with the measured texture in the films.Unexpectedly, there are also indications of perpendicular magnetic anisotropy in a subset of Fe/Usamples at relatively large U thickness. I. INTRODUCTION
Spin-orbit coupling (SOC) profoundly affects the bandstructure of a material, leading to many exotic phenom-ena such as topological insulating states , and Rashbaspin splitting . In magnetic materials and spintronic sys-tems, large SOC is at the heart of magnetic anisotropy,the spin Hall effect (SHE) , and the Dzyaloshinskii-Moriya interaction observed in magnetic-heavy metalstructures . In the simplest picture the SOC of a ma-terial increases ∝ Z , where Z is the atomic number .Therefore there has recently been intense focus on spin-tronic systems containing relatively heavy non-magneticmetals such as Pt, Au and Ir, in which variety of ef-fects can be observed. For example, by growing thinfilms of these heavy metals next to magnetic materials,the spin currents produced by the SHE when a chargecurrent is passed in the heavy metal (HM) layer can beused for spin transfer torque switching of ferromagneticlayers at relatively low current densities . At the sametime, however, heavy metals cause enhanced spin damp-ing in the ferromagnetic layer , and are susceptible toproximity-induced magnetism. Induced moments havebeen detected in systems such as Fe/Pt and Co/Pt and are thought to inhibit the efficiency of spin currentdetection through the inverse SHE . Understanding theinfluence of the interfacial induced moment and the largeSOC is an important challenge.The presence of an overlayer on a ferromagnetic (FM)film can have significant influence on the magneticanisotropy of the system. It is well documented thatin thin FM/HM structures there can be an emergence ofperpendicular magnetic anisotropy, as the magnetizationof the ferromagnet is pulled out-of-plane by an interfa-cial anisotropy contribution . Additionally, when thethickness of the overlayer is altered, oscillations in themagnetic anisotropy can be detected . These oscilla-tions in anisotropy are thought to originate from quan-tum well states,which arise due to confinement of elec-trons at the interface . In the context of these fascinating effects, the study ofuranium - with the largest Z for a naturally occurring ele-ment - is of considerable interest as a HM in FM/HM het-erostructures. Previous X-ray magnetic circular dichro-ism (XMCD) measurements at the U M , edges haveobserved negligible induced moment in U when grown onNi and Co, but a relatively large moment when grownon Fe . Hence by varying the FM layer in FM/U het-erostructures it may be possible to disentangle the role ofthe induced moment and that of the large SOC in the U.This paper studies Fe/U and Ni/U in bilayer systems, i . e . with and without an induced moment in the U, respec-tively, focusing on the effect of the U overlayer thicknesson the magnetic anisotropy of the FM film. II. METHODS AND STRUCTURALCHARACTERIZATION
The samples were grown by d . c . magnetron sputteringat room temperature in an ultra-high vacuum chamberwith a base pressure of < × − mbar. The argonsputtering pressure was held constant at ( . ± . × − mbar for all layers. The substrates were 10 mm ×
10 mm × ∼ ∼
11 nm. To avoid oxidation a capof Nb with thickness fixed at ∼ ∼
10 nm thick for the Ni series. The uraniumthickness, d U , was varied in the range − nm. The de-position rates were 0.017, 0.03, 0.085 and 0.064 nm/s forthe Fe, Ni, U, and Nb respectively. Deposition rates werecalibrated and samples were characterised using X-ray re-flectivity (XRR). The GenX reflectivity software wasused to determine the thicknesses and roughness of eachsample. The errors on thickness produced by GenX aregiven as the value required to change the best fit figureof merit (FOM) by ± . The FOM used here gave equalweighting to both high and low intensity points. ExampleXRR data are shown in Fig .
1, showing excellent agree- a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b ment between the model and the fit. Over the range ofU thicknesses both the Fe and Ni the roughness did notsignificantly, other than at d U = 0 nm where the interfaceis FM/Nb (see inset of Fig . σ Fe = 1 . nm and σ Ni = 1 . nm are typical forroom temperature sputtered metal thin films. FIG. 1. [Color online] Example normalised low angle x-rayreflectivity data (symbols) for the Fe/U samples. Solid lineis a best fit using the GenX software, in this case giving d F e = 8 . ± . nm and d U = 6 . ± . nm. Root-mean-squareroughness of Fe and U, ( σ Fe and σ U respectively), determinedfrom the fit against d U are shown in the inset. Similar datawere obtained for the Ni series, and are discussed in AppendixA.FIG. 2. [Color online] High angle x-ray diffraction data forthe Fe series with d U = 3 . nm. The solid red line is the totalfit of three Gaussians fixed at the uranium triplet positions.Magneta and cyan lines are fits to (021) and (002) reflectionsrespectively. The black line is a second order polynomial fitto the background. X-ray diffraction data were also taken, both in θ − θ and grazing incidence geometries, to examine the possi-bility of texture in the polycrystalline samples. For Fe/U there was evidence of the U layer being oriented with pre-dominantly the [001] direction normal to the plane, witha smaller fraction of the layer also oriented in the [011](see Fig . × M vs appliedfield H , hysteresis loop measurements were carried outwith H applied both in the plane and perpendicular tothe plane of the samples. The in-plane angle θ rangedfrom − ◦ to 190 ◦ in 10 ◦ steps, relative to an arbitraryin-plane axis defined parallel to the main axis of the sput-tering chamber.Density Functional Theory calculations were carriedout using a fully relativistic Korringa-Kohn-RostokerGreens function method extended to include calcula-tions for the Bloch spectral function Further details ofthe calculations for the uranium crystal can be found inRef . III. RESULTS AND DISCUSSIONA. In-plane magnetometry
Typical in-plane M ( H, θ ) data are shown in Fig . d U = 6 . nm. There are clearchanges in anisotropy with in-plane angle θ . Figure 4shows the full evolution of the anisotropy through boththe coercive field, H c , and normalised remnant moment, M ∗ r with angle. The data show clear uniaxial anisotropy,with the easy and hard axes situated at 140 ◦ and 60 ◦ respectively. Small peaks in H c and M ∗ r seen around50 ◦ are likely due to stray fields within the sputteringchamber arising from the magnets within the sputteringguns. It is most likely that the uniaxial anisotropy arisesfrom the off-normal angle of incidence of the sputteredatoms relative to the substrate .The range of the coercive field, H c , as a function ofangle, as well as the average H c of each sample is used asa way of quantifying the anisotropy of the system. Therange is defined as H Range c = H c (max) − H c (min) , where H c (max) and H c (min) are the maximum and minimum val-ues of H c ( θ ) , respectively. The average H c is given by H Ave c = n n (cid:88) i =1 H ic , where n is the total number of angularscans.Figure 5 (left axis) illustrates the development of H range c with d U for the Fe series. As d U increases, therange displays clear non-monotonic behaviour. At d U ∼ H Range c is enhanced by a factor of two in compar-ison to d U = 0 nm. The right hand axis in Fig . H ave c for each sample. This closely follows the same non-monotonic form as H range c ( d U ) .Next we examine the FM = Ni samples as a comparisonwith the Fe samples. The samples showed very similar FIG. 3. [Color online] Room temperature in-plane M ( H ) loops for sample with FM = Fe and d U = 6 . nm. Moment M is normalised to the saturation value. Relatively hard (easy)axis behavior is observed for θ = 60 ◦ (150 ◦ ) . A subset of the M ( H, θ ) data are shown for clarity. Lines are guides to theeye.FIG. 4. [Color online] In-plane angular dependence of thecoercive field µ H , and normalised remnant moment M ∗ r forFM = Fe and d U = 6 . nm. Lines are a guide to the eye. uniaxial anisotropy to the Fe samples, strongly suggest-ing that the uniaxial anisotropy is induced through thesputtering process. Both the H range c and H ave c were abouta factor of four and two smaller than the Fe counterpartrespectively, as shown in Figs . H ave c ( d U ) showed a clear non-monotonic dependence notdissimilar to the Fe series, although for Ni the H range c ( d U ) does not clearly mirror the H ave c ( d U ) data in the wayfound for the Fe series data in Fig .
5. The reason for thisdisparity is likely related to the low switching field of Niand the small variation of H c with angle.From the hysteresis loops, the effective uniaxialanisotropy coefficient K eff was calculated using the FIG. 5. Range of coercive field µ H c (left axis) and average H c (right axis) vs d U for Fe series. Clear non-monotonic be-havior observed for both parameters. Lines are a guide to theeye.FIG. 6. [Color online] In-plane angular dependence of thecoercive field µ H , and normalised remnant moment M ∗ r fora Ni bilayer with d U = 0 . nm. Lines are a guide to the eye. method set out in Refs .
12 & 31: the total energy densityof the system, E is given by E = − µ (cid:126)H · (cid:126)M + K eff sin γ (1)where γ is the angle between the magnetization and theeasy axis direction. Minimising this with respect to γ results in H s = 2 K eff µ M s , (2)when the hard axis is perpendicular to the easy axis, asassumed is the case for all samples here. In Eqn . H s is the hard axis saturation field and M s is the saturationmagnetization. K eff was calculated assuming the activevolume of magnetic material was the volume of Ni and FIG. 7. Range of coercive field µ H c (left axis) and average H c (right axis) vs d U for Ni series. Non-monotonic behaviorobserved for average coercive field (right axis). Lines are aguide to the eye. Fe only, using the thicknesses measured from the XRRdata. We also used the combined volume of the Fe and Ulayers for the Fe series, as illustrated in Fig .
8. This takesinto account the possible role of an induced moment inthe Fe/U samples. We note that qualitatively the twoplots of K eff vs d U are similar. While K eff has a similarprofile to those of the quantities seen in Fig . FIG. 8. [Color online] Calculated uniaxial anisotropy coeffi-cient with increasing d U for Fe and Ni samples. Lines are aguide to the eye. In order to understand the non-monotonic changes inthe anisotropy of these two FM layers, we must exam-ine potential variations in the microstructure of the filmsdue to growth. It is assumed that the magnetic domaintype within the FM layers does not change, therefore it is expected that the coercive field will change monotoni-cally with roughness . In these sample sets, the rough-ness is approximately constant with d U for both FM se-ries, as can be seen in Fig . at the Fe/U interface or UNi for Ni/U. However, the Curie temperatures of UFe andUNi are 160 K and 21 K respectively. Therefore, if thesecompounds are present at the interface their magneticproperties would not contribute to the room tempera-ture magnetic anisotropy, and their influence on the mag-netic anisotropy would be monotonic with U thickness asabove. As there appears to be no complete explanationfor the non-monotonic anisotropy which is rooted in thematerial properties, we turn to electronic arguments.Oscillations in saturation or coercive fields as a func-tion of non-magnetic layer thickness have often been ob-served in heterostructures. These oscillations usually in-dicate a change in coupling between ferromagnetic layers.The period of this oscillatory exchange coupling of transi-tion metals seen previously is shorter than that observedhere, with Cr having the largest period of 1.8 nm . Sub-sequent work on heavy metal systems have shown simi-lar oscillations periods, with Co/Pt ∼ . However,the behavior observed here clearly do not fit the criteriafor interlayer exchange coupling as there is no secondaryFM layer to couple to. Instead we can look to quan-tum well states (QWSs), which while known for thereimportance in interlayer exchange coupling , can alsobe observed in bilayer systems. These QWSs arise fromconfinement of electron wavefunctions at the interface,which results in the formation of standing waves. Thecontribution to the magnetic anisotropy from these statescan come from either the ferromagnetic or non-magneticlayer . As either layer thickness is altered, there arechanges in the electronic states close to the Fermi energyof the FM, altering the magnetic anisotropy. In orderfor the QWSs in the non-magnetic layer to influence themagnetic anisotropy, there must be hybridization of or-bitals between the layers. From XMCD measurements it is already expected that there is strong hybridizationbetween the Fe 3 d and U 5 f orbitals. As there is no in-duced moment in Ni, it may be expected that there is nohybridization and therefore we would not expect to seeany non-monotonic behavior beyond the low d U interfa-cial effects. However, it has previously been suggestedthat there is weak hybridization between Ni and U ,which would allow the U overlayer to influence the mag-netic anisotropy of the nickel . Calculations of anisotropyenergy due to QWS in Pd/Co/Pd systems find oscilla-tions over a length scale of 20 monolayers ( ∼ ∼
2. nm) 20.As noted previously, XMCD studies on U/FM multi-layers observed an induced moment in U [Ref .
23] when inclose proximity to Fe. Wilhelm et al. suggested that thismoment is oscillatory within the U layer and its presenceis a result of hybridization of Fe d and U f orbitals.Within a single U layer, the induced magnetic momentwas predicted to oscillate with a period of ∼ T , for a quantum well statein real space can be related to a wavevector of /T in re-ciprocal space, adapting the discussion from Ref .
16. Inorder to quantitatively address the origin of oscillations,we have calculated the band structure of orthorhombic α -U using density functional theory. Given the dom-inant (001) texture found in the samples, we look forspecific features in the Bloch spectral function in the(100) and (010) planes, which include the [001] direction.The resulting Bloch spectral functions for these planesare shown in Fig . ( k x , k y , k z ) = (-0.24, 0, 0.2), (-0.312, 0, 0.222),(-0.153, 0, 0.057) and (0, -0.241, 0.057), (0, 0, 0.087) inthe (010) and (100) cuts, respectively. Here the units arein terms of π/a with a = 2 . Å the lattice constant of α -U. For points close to the BZ boundary the period ofoscillation is given by π/ ( k [001] BZ − k [001] ) , with k [001] BZ = π/c with c = 1 . a , resulting in . nm and . nm. For thepoints away from the BZ boundary the oscillation is de-termined by π/k [001] giving periods of oscillations of . nm and . nm, respectively. This is in very good quanti-tative agreement with the roughly nm period observedin the experiment.This simplified analysis relies solely on the 3D bandstructure of the U film and as such cannot account for in-terfaces effects or the distinct situation in different U/FMbilayers. In order, to go one step further we can analyzethe band structure of the FM materials in the dominantgrowth direction, Fe (011) and Ni (111). As it turns out,while for Fe both the majority and minority bands havesame symmetry bands at the Fermi energy, for Ni onlythe minority bands cross the Fermi energy in (111) direc-tion. This would indicate a formation of QW states inU/Ni to be more likely than in the corresponding U/Fesystem. Furthermore, as indicated in the Appendix, the U films in U/Fe show different growth directions leadingto a stronger averaging of any QW state periodicity. FIG. 9. [Color online] Theoretical Bloch spectral functions, S ( k ) , for α -uranium. Two-dimensional cuts are shown for lat-tice planes a) (010) and b) (100), respectively. The Brillouinzone boundary is shown as a grey-bordered rectangle in bothimages. The white arrows are indicating wave vectors con-nection two high density regions of the BZ and as such givingrise to possible oscillations in the region from . to . nm. B. Out-of-plane magnetometry
Out-of-plane magnetization measurements show onlyhard axis behaviour for a majority of the Fe samples,and all of the Ni series. However, three Fe/U samplesexhibit a clear open hysteresis loop, indicative of an easyaxis response with an applied field out-of-plane: exampledata are shown in Fig .
10. The out-of-plane behavior overthe whole range of d U is illustrated in Fig .
11. It appearsthat the out-of-plane easy axis samples may correspondto those with lower in-plane H ave c , however, the samplessize is to small to use this as a reliable indicator.As for the in-plane measurements, the material sci-ence arguments cannot easily explain the non-monotonicbehavior of the out-of-plane anisotropy. Perpendicularmagnetization is often attributed to an interfacial mag-netic anisotropy, K s , Ref .
15. Generally, samples in which
FIG. 10. [Color online] Room temperature out-of-plane M ( H ) loops for samples with d U ∼ d U . perpendicular magnetic anisotropy (PMA) is observedhave very thin ferromagnetic layers, on the order of <3 nm, [Refs . ]. To observe PMA in structures witha comparatively large FM thickness is unexpected. Itmay be that the presence of quantum well states also in-fluences the out-of-plane anisotropy, though it might beexpected that a continuous changes in PMA would beobserved across the series rather than sudden switching.Theoretical calculations on a number of Fe(001)/non-magnetic metal structures determined that certain met-als will promote PMA when in close proximity to Fe, Ref .
14. It was seen that metals with filled d bands, such asAu,Ag, exhibited PMA in the Fe layer, while those withpartly filled bands produced in-plane magnetization, withthe exceptions on Zr and Hf. Miura et al. suggest thatPMA is observed at the Hf interface due to unoccupied majority spin d states, and is enhanced by the large SOCof Hf. It is possible that this argument could be appliedto uranium. However, there are two main issues in thecontext of the work presented in this paper. In Ref . d band filling, it wouldbe expected that PMA is observed for every sample in theseries.An alternative origin of the PMA may be the inter-facial Dzyaloshinskii-Moriya interaction (DMI). PMA isa generally observed in samples which exhibit interfacialDMI. Interfacial DMI is a result of large SOC of the HMlayer interacting with FM spins at the interface betweenthe two. This causes a canting of spins, pulling them outof plane. The link between interfacial DMI an inducedmagnetic moments has been discussed both experimen-tally and theoretically , with differing opinions. Ifthe out-of-plane magnetization is indicative of interfacialDMI, then assuming the inverse relation of induced mo-ment and DMI from the calculations of Yang et al. , it isnot unreasonable to suggest that PMA is only seen at spe-cific thicknesses with small induced moment. However,even the largest induced moment observed in U would notbe expected to overcome DMI based on the calculationsby Yang et al. . Based on the presence of PMA alone, it isnot possible to draw solid conclusions on the existence ofDMI within these samples. Hence, from these data alone,it is not clear whether the observed PMA is a result of athickness dependant interfacial anisotropy in the systemor interfacial DMI due to large SOC of the uranium, andfurther investigation is required. IV. CONCLUSIONS
In conclusion, both the in-plane and out-of-plane mag-netic behaviour of FM/U bilayers as a function of d U havebeen investigated. For both ferromagnet types the in-plane properties change in a non-monotonic manner withincreasing d U . This behavior is likely linked to quantumwell states formed in the uranium overlayers. Compu-tational calculations of the Bloch spectral functions for α -U indicate possible regions in the electronic structurewhich might drive oscillations which are approximatelyconsistent with the non-monotonic data. Out-of-planemeasurements revealed perpendicular magnetization forsamples with thicknesses d U =1.7, 4.4 and 5.0 nm. Theunexpected presence of PMA in these relatively thickfilms can not be easily explained and significant furtherstudy would be required to pinpoint its origin. V. ACKNOWLEDGEMENTS
We thank N.-J. Steinke and G. Stenning at the ISISNeutron and Muon Source for access to and support withthe rotating anode x-ray diffractometer system. E.G. issupported by the Bath/Bristol Centre for Doctoral Train-ing in Condensed Matter Physics, under the EPSRC(UK) Grant No. EP/L015544. M.G. thanks the visitingprofessorship program of the Centre for Dynamics and Topology at Johannes Gutenberg-University Mainz. Thecomputational work was carried out using the compu-tational facilities of the Advanced Computing ResearchCentre, University of Bristol. ∗ Current address: Department of Materials Science and En-gineering, Sir Robert Hadfield Building, Mappin Street,Sheffield, S1 3JD, United Kingdom X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. , 1057(2011). A. Manchon, H. C. Koo, J. Nitta, S. Frolov, and R. Duine,Nature Materials , 871 (2015). J. E. Hirsch, Phys. Rev. Lett. , 1834 (1999). S. O. Valenzuela and M. Tinkham, Nature , 176 (2006). E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, AppliedPhysics Letters , 182509 (2006). L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, andR. A. Buhrman, Science , 555 (2012). A. Hoffmann, IEEE Transactions on Magnetics , 5172(2013). S. Heinze, K. Von Bergmann, M. Menzel, J. Brede, A. Ku-betzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel,Nature Physics , 713 (2011). Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I.Halperin, Rev. Mod. Phys. , 1375 (2005). S. Mizukami, Y. Ando, and T. Miyazaki, Phys. Rev. B ,104413 (2002). B. Zhang, A. Cao, J. Qiao, M. Tang, K. Cao, X. Zhao,S. Eimer, Z. Si, N. Lei, Z. Wang, et al., Applied PhysicsLetters , 012405 (2017). W. J. Antel Jr, M. M. Schwickert, T. Lin, W. L. O’Brien,and G. R. Harp, Phys. Rev. B , 12933 (1999). S. Y. Huang, X. Fan, D. Qu, Y. P. Chen, W. G. Wang,J. Wu, T. Y. Chen, J. Q. Xiao, and C. L. Chien, Phys.Rev. Lett. , 107204 (2012). Y. Miura, M. Tsujikawa, and M. Shirai, Journal of AppliedPhysics , 233908 (2013). S. Hashimoto, Y. Ochiai, and K. Aso, Journal of AppliedPhysics , 4909 (1989). J. E. Ortega and F. J. Himpsel, Phys. Rev. Lett. , 844(1992). S. Manna, P. L. Gastelois, M. Dąbrowski, P. Kuświk,M. Cinal, M. Przybylski, and J. Kirschner, Phys. Rev. B , 134401 (2013). P. Bruno, Phys. Rev. B , 411 (1995). F. J. Himpsel, T. A. Jung, and P. F. Seidler, IBM Journalof Research and Development , 33 (1998). M. Cinal, Journal of Physics: Condensed Matter , 901(2001). M. Przybylski, M. Dąbrowski, U. Bauer, M. Cinal, andJ. Kirschner, Journal of Applied Physics , 07C102(2012). R. Springell, F. Wilhelm, A. Rogalev, W. G. Stirling,R. C. C. Ward, M. R. Wells, S. Langridge, S. W. Zo-chowski, and G. H. Lander, Phys. Rev. B , 064423(2008). F. Wilhelm, N. Jaouen, A. Rogalev, W. G. Stirling,R. Springell, S. W. Zochowski, A. M. Beesley, S. D. Brown,M. F. Thomas, G. H. Lander, et al., Phys. Rev. B ,024425 (2007). M. Björck and G. Andersson, Journal of Applied Crystal-lography , 1174 (2007). M. Björck,
GenX V2.4.9 , http://genx.sourceforge.net/ (2008–2018). M. Gradhand, M. Czerner, D. V. Fedorov, P. Zahn, B. Y.Yavorsky, L. Szunyogh, and I. Mertig, Phys. Rev. B ,224413 (2009). T. G. Saunderson, J. F. Annett, B. Üjfalussy, G. Csire,and M. Gradhand, Phys. Rev. B , 064510 (2020). M.-H. Wu, H. Rossignol, and M. Gradhand, Phys. Rev.Lett. , 224411 (2020). H. Ono, M. Ishida, M. Fujinaga, H. Shishido, and H. Inaba,Journal of Applied Physics , 5124 (1993). N. Chowdhury and S. Bedanta, AIP advances , 027104(2014). F. Brailsford,
Physical Principles of Magnetism (D. VanNostrand Company Ltd., 1966). Y.-P. Zhao, R. M. Gamache, G.-C. Wang, T.-M. Lu,G. Palasantzas, and J. T. M. De Hosson, Journal of Ap-plied Physics , 1325 (2001). S. S. P. Parkin, Phys. Rev. Lett. , 3598 (1991). J. W. Knepper and F. Y. Yang, Phys. Rev. B , 224403(2005). C. Würsch, C. Stamm, S. Egger, D. Pescia, W. Bal-tensperger, and J. Helman, Nature , 937 (1997). L. Severin, L. Nordström, M. S. S. Brooks, and B. Johans-son, Phys. Rev. B , 9392 (1991). B. N. Engel, C. D. England, R. A. Van Leeuwen, M. H.Wiedmann, and C. M. Falco, Phys. Rev. Lett. , 1910(1991). M. T. Johnson, P. J. H. Bloemen, F. J. A. Den Broeder,and J. J. De Vries, Reports on Progress in Physics , 1409(1996). K.-S. Ryu, S.-H. Yang, L. Thomas, and S. S. P. Parkin,Nature Communications , 3910 (2014). H. Yang, A. Thiaville, S. Rohart, A. Fert, and M. Chshiev,Phys. Rev. Lett. , 267210 (2015). R. M. Rowan-Robinson, A. A. Stashkevich, Y. Roussigné,M. Belmeguenai, S.-M. Chérif, A. Thiaville, T. P. A. Hase,A. T. Hindmarch, and D. Atkinson, Scientific Reports ,16835 (2017). W. T. Eeles and A. L. Sutton, Acta Crystallographica ,575 (1963). A. M. Beesley, M. F. Thomas, A. D. F. Herring, R. C. C.Ward, M. R. Wells, S. Langridge, S. D. Brown, S. W. Zo-chowski, L. Bouchenoire, W. G. Stirling, et al., Journal ofPhysics: Condensed Matter , 8491 (2004). R. Springell, S. W. Zochowski, R. C. C. Ward, M. R. Wells,S. D. Brown, L. Bouchenoire, F. Wilhelm, S. Langridge,W. G. Stirling, and G. H. Lander, Journal of Physics: Con-densed Matter , 215229 (2008). Appendix A: Further x-ray data for Fe and Nisamples
X-ray reflectivity measurements were taken on all sam-ples in the Ni-U series, in a similar way to the datashown in the main text for the Fe series. The reflectivitydata could be well fitted with the GenX software, givingrise to roughness values, σ U and σ Ni , for the U and Nilayers, respectively. These roughness values are shownversus d U in Fig .
12. At relatively low d U the rough-ness changes significantly, and there are some similari-ties between the form of the roughness when comparedwith that of the anisotropy. However, a higher thick-ness, where the roughness is more consistent, there is lesssimilarity to the form of the anisotropy. This suggeststhat while the roughness may influence the anisotropy atlower thicknesses, it is not the mechanism which gives theanisotropy its non-monotonic form at greater thicknesses. FIG. 12. [Color online] Interfacial roughness for the Ni/Uinterface (red squares) and the U/Nb interface (blue circle)extracted from the GenX fitting to the x-ray reflectivity data,for various d U . Grazing incidence x-ray diffraction (GIXRD) scanswere also carried out for representative samples in theFe and Ni-based series. These data are shown in Figs . ω ,while the detector rotates. As θ , the angle between theincident and diffracted beam increases, the angle of thescattering vector shifts so that it always bisects the anglebetween the incident and detected waves. Thus, while the diffraction peaks are not necessarily parallel to thesurface, the diffraction observed for small ω is still domi-nated by the largest component of the scattering vector,which is the normal to the thin film. Hence GIXRD pro-vides useful information on the crystallographic textureof the samples.The GIXRD scans were carried out over a range of ω = 0.5 ◦ - 10.0 ◦ . Fits to the data are composed of aquadratic background, and a Gaussian fits to each peak.The broad uranium peak is expected to be composed ofthree α -uranium peaks; (110) at 34.8 ◦ (021) at 35.5 ◦ ,and (002) at 36.3 ◦ [Ref . d U [Refs .
43, 44].
FIG. 13. [Color online] GIXRD data (blue) for the Fe bilayerseries with d U = 3 . nm. In this scan, ω = 1 ◦ . The redline is the sum of a fourth order polynomial, to represent thebackground (dominated by the glass substrate), and Gaussianpeaks. FIG. 14. [Color online] GIXRD data (blue) for the Fe bilayerseries with d U = 6 . nm. In this scan, ω = 1 ◦◦