Figure 1a shows an example of the X-ray reflectivity (XRR) of a typical YIG sample before and after annealing (see Table 1 for parameters). For the unnealed sample the electron densities of both the substrate and YIG are about 5% less than the bulk. After annealing the total thickness is diminished but the important point is that we cannot obtain the best fit for these data without including an additional layer at the interface. The indication that there may be diffusion at the interface is that although a good fit was obtained using only a YIG layer (goodness of fit (GOF) of 0.05), the fitted density of the GGG was only 91% that of bulk GGG. A much better fit is obtained by using a trilayer system of GGG/~50–60 Å of Gd3Fe5O12/YIG where the interface layer has a density that is reduced by about 13%. In the light of additional structural information (see TEM results below), we now model this interface as a mixed layer of YIG and Gd (YIG1 and Gd in Table 1). This illustrates that we are not relying on a particular crystal structure (GdIG, for example) to explain the results. The interface layer is modelled by allowing the total thickness to approach that of the dead layer (6 nm) found in magnetometry and significant roughness and grading in the layer. The roughness in this fit is modelled as a Gaussian with the full width at half maximum representing the standard deviation of an effective roughness. The roughness is that produced by terraces or steps, for example, whereas grading is represents interdiffusion. However, since we are only in the specular regime, it is not possible to distinguish between a chemically graded interface and physical roughness18. Nevertheless, the parameters returned by the fit for this layer are as we expected - roughness and grading that is nearly equal to the thickness of the layer and much reduced densities. In this way we can represent a somewhat disordered interface layer. The roughness at the other interfaces are reasonable and given that the x-rays illuminate the entire sample, 4 Å roughness on the YIG surface agrees quite well with the RMS roughness of the atomic force microscopy (AFM) results. The thickness of the interface region varies from 5–6 nm between samples. The GOF for this fit is 0.04 and importantly, the densities for the YIG and GGG are within 1% of the bulk values giving us confidence that the top layer is stoichiometrically correct.
Figure 1b presents the X-ray diffraction (XRD) data for three samples of YIG with thicknesses 30, 50 and 250 nm. These data show the evolution of a peak that, for the thickest sample, has a lattice constant of 12.496 ± 0.002 Å. This shows that the YIG film is close to the (111) crystalline orientation of the GGG substrate with a lattice constant of 12.383 Å for the (444) planes (seen at 51.05°). The diffraction peak width is 0.0120 ± 0.0001 degrees confirming the high quality of the films. To assess the roughness of the YIG surface, AFM has been performed in tapping mode over a range of 5 microns. As can be seen from the image in Fig. 1(c), the surface appears smooth over this range and the rms roughness of a series of films in the 6–70 nm thickness range (panel d) have surface roughness of 1–3 Å.
The magnetic properties of YIG films were studied at 295 K using a vibrating sample magnetometer (VSM) by applying an in-plane magnetic field. Figure 2(a) shows the hysteresis loops for different YIG film thicknesses ranging from 10–50 nm. The data shows that the coercivity is similar across this range of samples with a value of 0.30 ± 0.05 Oe. In order to determine the magnetisation of our samples we have plotted the magnetic moment per unit area a function of thickness. The results are shown in Fig. 2(b). From these data it is clear that the relationship is linear and that the data does not extrapolate to zero for zero thickness. Thus there is a single value of the magnetisation that describes these data (144 ± 6 emc/cc) which compares well with the bulk value of 140 emu/cc19. In addition, at room temperature, there is a magnetic dead layer of about ~6 nm. As is common in magnetic thin films, dead layers are usually found at the sample/substrate interface and in this case this thickness corresponds remarkably well to the diffusion region identified by the reflectivity and the structural analysis (see below). The interpretation thus far is that Gd and Y have interdiffused into the interface region but at room temperature it is paramagnetic because 295 K is above the Curie temperature of the Gd-doped region. Panel (c) of Fig. 2, shows the Curie temperature of a 100 nm sample fitted with a Bloch T3/2 law illustrating that the value of ~550 K is close to the bulk value of 559 K.
In order to obtain direct confirmation of interdiffusion, we carried out an atomic-scale investigation of the GGG/YIG interface using aberration-corrected scanning transmission electron microscopy (STEM) (see the methods section for technical details). High-angle annular-dark-field (HAADF) images of the interface observed along the  zone axis reveal a gradual transition of the intensity from the GGG substrate to the film: a representative example is shown in Fig. 3a, with identical observations along the entire interface. Given the sensitivity of this imaging mode to the average atomic number, Z, of the material (the HAADF contrast scales to a good approximation as Z1.7)20, this alone suggests a chemically-diffuse, rather than sharp, interface, in good agreement with the XRR measurements. Electron energy loss spectroscopy (EELS) provides further proof of the interdiffusion of the various cations across the interface: chemical maps of Ga, Gd, O, Y and Fe were recorded across the interface region delimited by the white rectangle in Fig. 3a. Averaged composition profiles obtained by integrating these maps across the interface show a 6.5 nm wide region of mixed chemical composition, while the compositions on either side of this region correspond (within the measurement accuracy: see methods section) to the expected bulk values for YIG and GGG: Fig. 3b. This interdiffusion layer is delimited, as a guide to the eye, by dotted lines on Fig. 3b and on the HAADF image acquired simultaneously with the EELS (Fig. 3c). The shape of the EELS element intensity profiles shown in Fig. 3c are consistent with diffusion of Gd and Ga from the GGG substrate into the deposited YIG layer. For Yttrium and Iron the element intensity profile is inverted, which most likely infers diffusion of vacancies from within the YIG layer (presumably arising as a result of deposition) to the original GGG/YIG boundary (which acts as a vacancy sink) and hence diffusion of Y and Fe away from the boundary. This would then ultimately result in a Gd- and Ga-doped YIG interlayer some 6 nm thick. Images and chemical maps obtained at higher spatial sampling provide an atomic-scale picture of the interface, although due to tight packing in this orientation, it is difficult to confirm the exact lattice position of the interdiffused cations: Fig. 3d. Nevertheless, it is clear from these results that the extent and chemical nature of the interdiffusion is in remarkable agreement with the conclusions drawn from the other techniques. It is known that Gd and Y are diffusion pairs in the GGG/YIG system21 diffusing with similar coefficients through the (c) sublattice. An interdiffusion distance of width of 6 nm implies a diffusion lengthscale of ∼3 nm either side of the original boundary. From the annealing conditions (2 hours at 850 °C), we estimate a diffusion coefficient of ∼1.25 × 10−17 cm2 s−1. This compares favourably with an extrapolated diffusion coefficient for Y in YIG at 850 °C of between 10−17 and 10−18 cm2 s−1 (from Fig. 8 in ref.22). We note that Gallagher et al.23 show a STEM/EDX profile across a similar YIG/GGG interface which exhibited an interfacial transition regions of ca. 5 nm (for Gd and Fe). They attributed this to delocalisation of the X-ray emission due to probe broadening and inelastic delocalisation rather than elemental interdiffusion; however, this delocalisation appeared to vary between different elements. We believe our current STEM/EELS results, which were taken from a large number of separate regions along the interface, do not suffer such problems with delocalisation and can be attributed to chemical intermixing matching the structural data from the other techniques.
It would seem that the room temperature magnetic properties of YIG do not reveal any influence of the Gd diffusion but, as a function of temperature, the magnetic ordering of the Gd-diffused layer is immediately evident in the magnetisation. To better understand the magnetic behaviour in this complex material we require a depth-resolved technique. Polarised neutron reflectivity (PNR) is ideally suited and measurements were performed on the Polref beamline at the ISIS neutron source of the Rutherford Laboratory where there is the availability of a range of temperatures and applied magnetic fields. We measured the temperature dependence of the magnetisation, M(T), from 385 K down to 1.8 K using a SQUID-VSM in an applied field of 30 mT and have analysed these in combination with the PNR measurements as a function of temperature on the same samples. Figure 4(a) and (c) show the temperature dependent spin-polarised neutron reflectivity data and their fits for an 80nm-thick YIG sample. Derived from these data is the spin asymmetry (SA), shown in panels (b) and (d), which is given by:
The fits for the reflectivity and SA are obtained by using Gen-X24 and a two layer model for YIG and Gd-doped YIG. The PNR model has a rough substrate (∼1.2 nm) and then a layer of 6–7 nm for the interdiffusion region. Recall we see the average scattering length density so we cannot make the elemental distinction. However Gd is one of the few elements with a significant neutron absorption cross-section which makes us more sensitive to it. The absorption is included in the neutron model and has to be there for the model to fit the data reliably. From the model we obtain the scattering length densities (see Methods section) plotted as a function of distance and temperature in panel (e) of Fig. 4. The z-axis represents distance through the vertical direction of the sample where z = 0 indicates the GGG/YIG interface. At 250 K the SLD near z = 0 indicates a region that is paramagnetic but as the sample is cooled, this region becomes magnetic and orders anti-parallel to the rest of the YIG: indicated by a negative SLD. The total thickness is given by the Kiessig fringes and the model returns a thickness of ∼6 nm for the Gd-diffusion region which agrees well with the X-ray, the superSTEM and the room temperature magnetometry. The integrated SLD is proportional to the magnetisation of the sample and these data are plotted on the independently measured M(T) in 3(f). It is obvious that the data agree well. The moment in YIG is due to antiferromagnetic superexchange mediated by the O2− between the Fe3+ ions on the A and D sites. This is the strongest of the interactions, which is why Gd-doping does not change Tc. Gd substitutes for Y on the C sites and orders antiparallel to the net moment of the A + D sites. This explains the observed PNR results. In Gd-doped compounds where the concentration of Gd exceeds 24%, there is a compensation temperature where the total moment passes through zero and interestingly, the Gd-YIG system rotates coherently as the compensation temperature is passed19.
Informed by the PNR results, we developed a mean field model for the YIG system based on two layers where:
where B is the Brillouin function, My and Mg are the saturation magnetisations of the YIG and Gd-YIG layers respectively.
where t is the thickness of the total layer, tg is the thickness of the Gd-layer, taken to be 6 nm for all samples, Hy and Hg are the Weiss fields for YIG and the Gd-layer and are fitting parameters. Mm(T) is the measured value of the magnetisation. The spin quantum numbers for the two layers were taken to be: Jy = 5/2 and Jg = 7/2.
Figure 5 shows the temperature dependence of the saturation magnetisation where below 100 K there is the decrease in M(T) where the extent of the decrease depends on the thickness of the YIG. In the upper panels are the M(T) measurements for various thicknesses of the samples and the solid line represents the fit using the two-layer mean field model. The lower panels show the two individual layer magnetisations where a negative sign indicates an antiparallel moment. The fits return values of the saturation magnetisation for YIG that are close to the accepted value. The behaviour of the Gd-layer varies slightly across the samples, since we have taken a fixed thickness of 6 nm for this layer, the difference is due to the Weiss field fitting parameter. We note that it is very difficult for the fitting routine to find an acceptable Gd-layer result for the thickest samples as there is no decrease in M(T) - without this, a single layer fit will suffice. We have kept the thickness of the Gd-layer constant as that is what is found in the other techniques but we don’t know the concentration of the elements in the diffusion layer. We have assumed from the profile of the diffusion elements (Fig. 2c) that vacancies might be implicated. It is possible that the concentration of vacancies after annealing depends on the thickness of the YIG layer such that the thinner samples have a higher concentration.
It may have taken four films to get there, but the DC Extended Universe has finally produced a good old-fashioned superhero. Sure, previous entries in the Warner Bros. assembly line have given us sporadically successful, demythified takes on Batman and Superman, but they’ve all seemed skeptical, if not downright hostile, toward the sort of unabashed do-gooderism that DC Comics’ golden-age heroes exemplified. Never prone to stewing in solitude, and taking more notes from Richard Donner than from Christopher Nolan, Patty Jenkins’ “Wonder Woman” provides a welcome respite from DC’s house style of grim darkness — boisterous, earnest, sometimes sloppy, yet consistently entertaining — with star Gal Gadot proving an inspired choice for this avatar of truth, justice and the Amazonian way.
Although Gadot’s Diana Prince had a decent chunk of screentime in last year’s “Batman v. Superman,” “Wonder Woman” assumes no foreknowledge of any previous franchise entry — or of the character herself, for that matter. With most of the film’s presumptive audience too young to remember TV Wonder Woman Lynda Carter, Gadot and Jenkins have an unusually broad license to introduce the character to filmgoers, and they remain largely faithful to her comics origins while also crafting a hero who is both thoroughly internationalist and refreshingly old-school. In her earliest iterations, Wonder Woman was an all-American figure with a mythical background; here, she’s an essentially mythical force who just happens to fight for America.
Like far too many films before it, “Wonder Woman” offers yet another origin story, but at least it’s one we haven’t already seen several times onscreen. And perhaps more importantly, it’s almost entirely free of the distracting cameos and seeding of future films’ plotlines that so often keep modern comic-book films from functioning as satisfying standalone stories.
After a brief prologue in modern-day Paris, the action whisks us away to the secluded island of Themyscira, home to the all-female society of Amazons. Drawn in lush, misty colors, the island is a sanctuary for the tribe, sheltered by Zeus, whom they helped in fighting off a coup from the war god Ares. On guard against Ares’ possible return, the Amazons have all dedicated themselves to the arts of combat.
All, that is, except young princess Diana (Lilly Aspell at age 8, Emily Carey at 12), who’s the only child on the island. Yearning to learn the ways of her fellow Amazons, Diana is shielded from combat training by her mother Hippolyta (Connie Nielsen). Fortunately, her aunt Antiope (Robin Wright, cutting an imposing figure and affecting a strange accent) is the tribe’s chief field general, and she agrees to train the girl in secret. By the time she’s reached adulthood, Diana (Gadot) is ready to take on all comers, her traditional battle skills augmented by supernatural abilities of which she’s only partially aware.
Themyscira seems a realm outside of time, but the film’s 1918 setting abruptly announces itself in the form of a crippled German warplane that crash-lands in the ocean just beyond the island’s shores. Diana swoops in to rescue the pilot, an American soldier named Steve Trevor (Chris Pine). Once under the influence of the Amazons’ lasso of truth — a potentially silly device from the comic’s lore that the film adapts admirably — Steve reveals he was undercover with the Germans as a double agent, dispatched to collect intel on their experimental new weapon: a powerful poison gas developed by sadistic general Ludendorff (Danny Huston) and his facially scarred star chemist, nicknamed Dr. Poison (Elena Anaya).
When Diana hears Steve describe the Great War raging outside their protected enclave, she immediately suspects Ares has returned, and resolves to head to the front lines to confront him. She and Steve sail to London, and the film takes an unexpected, largely successful detour into light comedy, evoking shades of “Encino Man” as Diana stumbles wide-eyed through the big city, her rapport with Steve growing closer all the while. (Steve is the first man Diana has ever seen, and the film acknowledges the elephant in the room with some choice volleys of double-entendre.) The plot snaps back into focus when Steve and Diana learn Dr. Poison’s gas will soon be ready to launch at soldiers and civilians alike, and finding little help from military brass, they take off to the Western front themselves to intervene.
It says quite a lot about the general tenor of the DC cinematic universe that a film set in the trenches of WWI, with a plot revolving around the development of chemical warfare, is nonetheless its most cheerful and kid-friendly entry. But while “Wonder Woman” may dabble in moments of horror, it never revels in the vicissitudes of human depravity quite like its predecessors. A huge factor in its ability to convey a note of inherent goodness lies in Gadot, whose visage radiates dewy-eyed empathy and determination — and whose response to the iniquity of human nature isn’t withdrawn cynicism but rather outrage.
“Wonder Woman” is the first major studio superhero film directed by a woman, and it shows in a number of subtle, yet important ways. As skimpy as Gadot’s outfits may get, for example, Jenkins’ camera never leers or lingers gratuitously — Diana is always framed as an agent of power, rather than its object. When she finally unleashes her full fighting potential in an extended battle sequence on the front lines, the movie comes alive in a genuinely exhilarating whirl of slow-motion mayhem, and Diana’s personality is never lost amid all the choreography.
From this high point, the film begins to falter a bit in its final act, with some credulity-straining staging — a thunderous mano-a-mano battle appears to take place in full view of dozens of German troops, all of whom continue to blithely load cargo — and a final assault that lapses into the type of deadening CGI overkill that the film admirably avoids in the earlygoing. Approaching 2½ hours in length, “Wonder Woman” does fall victim to a fair bit of blockbuster bloat, and a trio of comic-relief comrades (Said Taghmaoui, Ewen Bremner, Eugene Brave Rock) don’t add nearly enough to justify their long-windup introduction.
Pine plays second-banana with a great deal of good humor: making little attempt to de-modernize his diction, he nonetheless registers as a noble yet sometimes lunkish jarhead, and it’s clear why Diana might find him attractive while also failing to be particularly impressed by him. None of the film’s villains get much of a chance to distinguish themselves, though Lucy Davis makes a good impression as saucy sidekick Etta Candy.
It’s an open question how much of the tone and aesthetic of “Wonder Woman” will extend to the innumerable future films in which her character is set to appear; subject to an exhausting amount of both kneejerk second-guessing and kneejerk over-praise, the DC Extended Universe has been figuring out just what it wants to be in fits and starts. But for once, it’s easy to stop the armchair executive producing and simply enjoy the moment.
Film Review: 'Wonder Woman'
Reviewed at AMC Burbank 16, May 24, 2017. MPAA rating: PG-13. Running time: 141 MIN.
Production: A Warner Bros. Pictures release and presentation in association with Ratpac-Dune Entertainment, Tencent Pictures, Wanda Pictures of an Atlas Entertainment/Cruel and Unusual production. Produced by Charles Roven, Deborah Snyder, Zack Snyder, Richard Suckle. Executive producers, Geoff Johns, Jon Berg, Wesley Coller, Rebecca Steel Roven, Stephen Jones.
Crew: Directed by Patty Jenkins. Screenplay: Allan Heinberg, from a story by Heinberg, Zack Snyder, Jason Fuchs, based on DC’s Wonder Woman created by William Moulton Marston. Camera (color): Matthew Jensen. Editor, Martin Walsh. Music: Rupert Gregson-Williams.
With: Gal Gadot, Chris Pine, Connie Nielsen, Robin Wright, Danny Huston, David Thewlis, Said Taghmaoui, Ewen Bremner, Eugene Brave Rock, Lucy Davis, Elena Anaya
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