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Swift heavy ion-beam induced amorphization and recrystallization of yttrium iron garnet
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 496001 (http://iopscience.iop.org/0953-8984/27/49/496001) View the table of contents for this issue, or go to the journal homepage for more
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 496001 (13pp)
doi:10.1088/0953-8984/27/49/496001
Swift heavy ion-beam induced amorphization and recrystallization of yttrium iron garnet Jean-Marc Costantini1, Sandrine Miro2, François Beuneu3 and Marcel Toulemonde4 1
CEA, DEN, SRMA, 91191 Gif-sur Yvette Cedex, France CEA, DEN, Service de Recherches de Métallurgie Physique, Laboratoire JANNUS, F-91191 Gif-sur-Yvette, France 3 LSI, CEA-CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France 4 CIMAP-GANIL, CEA-CNRS-ENSICAEN, Bd H. Becquerel, 14070 Caen, France 2
E-mail: [email protected] Received 12 June 2015, revised 20 October 2015 Accepted for publication 22 October 2015 Published 18 November 2015 Abstract
Pure and (Ca and Si)-substituted yttrium iron garnet (Y3Fe5O12 or YIG) epitaxial layers and amorphous films on gadolinium gallium garnet (Gd3Ga5O12, or GGG) single crystal substrates were irradiated by 50 MeV 32Si and 50 MeV (or 60 MeV) 63Cu ions for electronic stopping powers larger than the threshold value (~4 MeV μm−1) for amorphous track formation in YIG crystals. Conductivity data of crystalline samples in a broad ion fluence range (1011–1016 cm−2) are modeled with a set of rate equations corresponding to the amorphization and recrystallization induced in ion tracks by electronic excitations. The data for amorphous layers confirm that a recrystallization process takes place above ~1014 cm−2. Cross sections for both processes deduced from this analysis are discussed in comparison to previous determinations with reference to the inelastic thermal-spike model of track formation. Micro-Raman spectroscopy was also used to follow the related structural modifications. Raman spectra show the progressive vanishing and randomization of crystal phonon modes in relation to the ioninduced damage. For crystalline samples irradiated at high fluences (⩾1014 cm−2), only two prominent broad bands remain like for amorphous films, thereby reflecting the phonon density of states of the disordered solid, regardless of samples and irradiation conditions. The main band peaked at ~660 cm−1 is assigned to vibration modes of randomized bonds in tetrahedral (FeO4) units. Keywords: iron garnets, swift heavy ion irradiations, Raman spectroscopy, electrical conductivity (Some figures may appear in colour only in the online journal)
I. Introduction
showing such effects induced by electronic excitations, the so-called swift heavy ion-beam induced epitaxial crystallization (or SHIBIEC) effect, like in yttrium iron garnet (YIG) [2], fluorapatites (calcium phosphosilicates) [3, 4] or silicon carbide [5, 6]. Such mechanism should not be confused with the classical recrystallization process of cold-worked metals and alloys upon thermal annealing that is driven by the stored energy in strained materials [7]. We previously attempted to
Processes of amorphization and recrystallization of materials by swift heavy ion irradiations have recently become hot topics due to new molecular-dynamics simulations of the thermal spike induced by electronic excitations [1]. As a matter of fact, experimental evidence was already accumulated over the last 20 years on several ionic-covalent materials 0953-8984/15/496001+13$33.00
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© 2015 IOP Publishing Ltd Printed in the UK
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J. Phys.: Condens. Matter 27 (2015) 496001
were not satisfactorily modeled on the whole fluence range (1011–1016 cm−2) [10]. Therefore, we address this problem anew by performing conductivity modeling using contributions of the three phases on the whole fluence range on the basis of a set of rate equations including amorphization of nc-YIG. Conductivity data versus fluence are fairly well reproduced with a new set of amorphization cross-sections for two ion species that are compared with previous determinations and discussed on the basis of the TTM. Moreover, Raman scattering data are also reported for the first time to provide new experimental evidence of the damage induced by swift heavy ion irradiations in pure and substituted YIG.
address this issue for YIG on the basis of the so-called twotemperature model (TTM) of the inelastic thermal spike [8] by using two different approaches [9, 10]. The first one used a slow quench rate of the melt to generate recrystallized tracks [9], whereas the second one was based instead on a vaporization criterion of track formation [10]. Ferrimagnetic iron garnets doped with rare earths found a wide range of applications since the early 1970s for data storage with the so-called ‘magnetic bubble materials’ [11]. It was shown that YIG can be amorphized in tracks induced by heavy ion irradiations for electronic stopping power values Se = (−dE/dx)e above a threshold ~4 MeV μm−1 for energies in the 1 MeV u−1 range [12, 13]. Studies mainly focused on measurements of amorphous track-core radii for different Se values by Rutherford backscattering-channeling spectrometry (RBS/C) [14], x-ray diffraction (XRD) [2, 15], high-resolution transmission electron microscopy (HRTEM) [2, 15–18], saturation magnetization [12], Mössbauer spectroscopy [19, 20], and optical absorption data [21]. The effects of amorphous track formation on magnetic and magneto-optical properties [18–20, 22–27], as well as electrical properties [10, 14, 28–31] of pure and substituted YIG crystals were also thoroughly studied. It was shown that amorphous tracks could not only modify the coercitivity of ferromagnetic garnet films [23], but also pin Bloch walls after a proper chemical etching [27]. In the case of thin YIG epitaxial films, HRTEM has shown that the amorphous phase can suffer a recrystallization process into a nanostructured material after swift heavy ion irradiations at room temperature (RT) for large fluences [2]. Amorphous tracks were first produced then recrystallization set in for large track overlap. For high fluences (>1014 cm−2), HRTEM showed that the pristine single crystal (c-YIG) faded out, but the amorphous (a-YIG) and nanocrystalline (nc-YIG) phases were still coexisting. The recrystallization process was not totally completed up to 1016 cm−2 [2]. A possible chemical decomposition of the garnet into orthoferrite (YFeO3) and haematite (α-Fe2O3) was suggested, like for high-pressure and high-temperature conditions. A recrystallization process was also found for synthetic aluminate-ferrate garnets after 1.0 MeV Kr ion irradiation at 750 °C, near the critical amorphization temperature in the nuclear-collision regime, without chemical decomposition of the material [32]. A contrasted behavior occurred for some other ceramics like fayalite (γ-Fe2SiO4) that decomposed into magnetite (Fe2O4) and quartz (α-SiO2) in an amorphous matrix upon 1.5 MeV Kr ion irradiation at 600 °C [33]. However, in both cases, damage was mainly induced by atomic displacement cascades, and recrystallization occured at high temperatures. Electrical conductivity measurements of ion-irradiated YIG thin films were performed at RT to monitor the irradiationinduced phase changes versus fluence (φ) [10]. An effective medium approximation (2D-Bruggeman model) was used to model conductivity data in the case where the amorphization process dominates in the low-fluence range (φ 4 mW). Raman spectra were recorded in a broad wavenumber range, between 100 and 2000 cm−1. Several spectra were taken at different points of samples to ensure reproducibility of measurements. For highly damaged samples, longer accumulation times were needed to increase the signal/noise ratio. A depth-resolved spectrum was performed by steps of 0.1 μm in high-confocal mode, for the CaYIG film irradiated by 50 MeV Cu ions at 3.7 × 1012 cm−2. Optical transmission spectra for YIG and CaYIG films were also measured at RT with a Cary-17 double-beam spectrometer at normal incidence with a virgin GGG substrate on the reference beam.
The dc conductivity data (σ) are displayed for irradiated singlecrystal films showing two kinds of behaviors as a function of fluence (figure 2). Although some data may be scattered for heavily-doped CaYIG and SiYIG samples, σ exhibits a similar saturation for φs ~ 1012–1013 cm−2, regardless of crystal conductivity, then sharply increases with power-law dependence (~φ2) up to large values, above a threshold fluence φ0 ~ 1014 cm−2 (at the end of the plateau). By contrast, the undoped or lightly doped CaYIG samples with much lower conductivities exhibit a monotonous increase, and merge with the other data for large fluences. Similar plots are obtained regardless of ion species or doping for similar crystal conductivities. These results are consistent with data for irradiated a-YIG films also showing a plateau for φ φ0 (figure 2). First-order Raman spectra for virgin iron-garnet films and GGG substrate (figure 3) and irradiated films are shown up to 1000 cm−1 for increasing fluences up to 2 × 1015 cm−2 (figures 4(a)–(c)). Peaks are assigned to the Raman-active optical phonon modes that are labelled on the basis of the available data for YIG [36, 37] and yttrium aluminium garnet (Y3Al5O12, or YAG) [38–40]. Raman peaks for the three kinds of samples are consistent with literature data (table 2). Other second-order peaks were recorded above 1000 cm−1 (not shown). A small gap in the vibration modes probed by Raman spectroscopy appears for frequencies between ~600 and ~650 cm−1 for pure YIG. No major differences are found 3
J-M Costantini et al
J. Phys.: Condens. Matter 27 (2015) 496001
less reduced (figure 4(b)). For both ion species and all kinds of samples, similar spectra are obtained with two prominent spectral features at ~260 and ~670 cm−1 with full widths ~200–250 cm−1, growing on top of the crystal phonon peaks. Three other minor bands (tagged with arrows in figure 4(c)) are found at ~120, 150, and 200 cm−1. These broad bands are growing with fluence, but no significant spectral evolutions are found for φ > φ0, except some scattering background enhancement below 400 cm−1 (figure 4(c)). A similar spectrum is obtained for virgin a-YIG films with the same broad peaks (figure 4(d)). Irradiation of a-YIG does not change significantly the spectra, except also for some enhancement of scattered intensity below 400 cm−1 (figure 4(d)). In-depth mapping of the 1 μm thick CaYIG sample irradiated with 50 MeV Cu ions shows that damage is almost homogeneous across the film, in agreement with the stopping power depth profile (figures 5(a) and (b)). Although no absolute depth scale can easily be displayed in figures 5(a) and (b), the damaged depth is consistent with the film thickness (1 μm) after a correction using the refractive index of YIG (n = 2.416) for the wavelength of 509 nm [35]. Below this depth, spectra correspond to undamaged substrate by checking peaks at 273 and 417 cm−1 that are fingerprints of GGG, since these modes are clearly reduced with respect to pure YIG (figure 3 and table 2). This means that Raman spectra do not show any damage of the substrate, although GGG should be partly amorphized by irradiations above the threshold electronic stopping power (Se ~ 7 MeV μm−1) [41] (figure 1). The optical density at the wavelength of 500 nm for pure YIG and CaYIG films increases versus fluence for 50 MeV Cu ion irradiation up to the same saturation value corresponding to the amorphous state, for φ = φs ~ 1013 cm−2 (figure 6). Amorphous fractions are deduced from the optical density data by using a linear approximation with reference to the virgin-crystal value [21] (figure 6).
Figure 3. Micro-Raman spectra of virgin YIG, CaYIG films (thickness = 1 μm) and SiYIG film (thickness = 2.3 μm), and GGG substrate. Peaks tagged with arrows are strongly affected in intensity by substitutions in CaYIG and SiYIG with respect to pure YIG.
for Ca substitutions, except for the peak at 154 cm−1 (tagged with an arrow in figure 3) that is clearly enhanced with respect to pure YIG. Instead, peaks above 700 cm−1 (tagged with arrows in figure 3) are strongly affected by Si substitutions. The strongest peak at 352 cm−1 in YIG and CaYIG (and also GGG), is also very much reduced by Si substitutions, whereas some other smaller peaks between 400 and 700 cm−1 are clearly enhanced in SiYIG (tagged with arrows in figure 3). For the GGG substrate, a similar spectrum is found as for YIG films, yet some of these peaks are missing or have clearly different intensities (figure 3 and table 2). When irradiation proceeds, these crystal phonon peaks decrease in intensity and broaden significantly, then eventually vanish (figures 4(a)–(c)). Small residual peaks are still found for low fluences and disappear for φ > φ0, in agreement with increasing lattice disorder. The strong peaks at 353, 416, and 739 cm−1, and above 750 cm−1 are most affected by irradiation in pure YIG (figure 4(a)). A relative growth of peaks at 679 and 708 cm−1 is observed for 1.5 × 1012 S cm−2 with respect to virgin YIG sample. Smaller damage is found in CaYIG for the same fluences (figure 4(b)). However, for 1.5 × 1012 Cu cm−2, a decrease in intensity by a factor of ~80% is found for peaks at 271 and 353 cm−1 with respect to virgin CaYIG samples, whereas peaks below 200 cm−1 are
IV. Discussion IV.1. Raman scattering and optical absorption data IV.1.a. Virgin samples. Assignment of Raman-active phonon
modes in garnets gave rise to sharp controversies back in the late 1960s owing to the most complicated crystal structure of these oxides (Oh point group with 48 symmetry operations) [38]. In principle, 25 Raman-active and 17 IR-active phonon modes are expected, out of the 240 normal vibration modes, for the body-centered cubic garnet structure (Ia3d or O10 h space group), with 80 atoms per primitive unit cell. The 25 Raman-active gerade modes at the Brillouin zone (BZ) center (Γ point) were assigned to the A1g (3) Eg (8), and T2g (14) symmetry labels (or combinations of these modes) of the Oh point group for frequencies up to ~900 cm−1 [38–40]. The 17 IR-active ungerade modes were assigned to the T1u symmetry label in the same frequency range [42, 43]. Almost all of Raman-active modes are found in the present work (table 2). The high wave-number peaks (>500 cm−1) were assigned to some molecular-like internal vibration modes of the tetrahedral (AlO4) [39, 42] or octahedral (AlO6) building blocks 4
J-M Costantini et al
J. Phys.: Condens. Matter 27 (2015) 496001
Figure 4. (a) Micro-Raman spectra of YIG films (thickness = 1 μm): virgin and irradiated by 50 MeV S and 50 MeV Cu ions for various fluences. The amorphous fraction (fa) deduced from the optical density at 500 nm (figure 6) is given for each spectrum. (b) Micro-Raman spectra of CaYIG films (thickness = 1 μm): virgin and irradiated by 50 MeV Cu ions for various fluences. The amorphous fraction (fa) deduced from the optical density at 500 nm (figure 6) is given for each spectrum. (c) Micro-Raman spectra of SiYIG films (thickness = 2.3 μm): virgin and irradiated by 50 MeV Cu ions for various fluences. The broad peaks below 300 cm−1 are tagged with arrows. (d) Micro-Raman spectra of a-YIG films (thickness = 1 μm): virgin and irradiated by 60 MeV Cu ions for various fluences. 5
J-M Costantini et al
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Table 2. Wave numbers (in cm−1) of Raman peaks of virgin YIG, CaYIG and SiYIG thin films, and GGG substrate, with the respective assignments of phonon modes in reference to literature data for YAG [38–40] and YIG [36, 37].
YAG [38]
YAG [39]
YAG [40]
Eg
162 (s)
T2g T2g Eg
108 134 162
145 163
T2g
218 (s)
T2g
259 (s)
T2g T2g T2g
219 243 259
220 243 261
Eg Eg
310 (vw) T2g Eg 340 (s) Eg
296 310 340
A1g
373 (w)
Eg T2g
403 (s) 408 (s)
T2g
436 (vw)
YIG [36]
YIG [37]
T2g T2g Eg
130
T2g
131
175 193 237
T2g T2g T2g
174 194 238
295 310 340
T2g T2g T2g T2g T2g T2g Eg T2g Eg Eg Eg Eg + A1g
274 315 347
Eg + T2g Eg T2g Eg
274 319 324 346
T2g + A1g 370–373 370 372 Eg 403 402 T2g 408 406
A1g T2g T2g Eg T2g Eg + T2g
380
T2g
378
420
Eg T2g
416 419
T2g + A1g 449
T2g Eg A1g
445 456 504
T2g Eg Eg + T2g Eg + T2g A1g
592 624 685 692 704
438
T2g
Eg A1g Eg T2g A1g T2g
507
690 691 714–719 712 718
T2g Eg + A1g Eg T2g
698
Eg
757
754
Eg
740
Eg
531 (w)
A1g
561 (s)
T2g Eg
690 (w) T2g 714 (vw) Eg + T2g
T2g
719 (s)
Eg T2g A1g
530 544 564
523 536 545 559
A1g
783 (s)
A1g
794
783
A1g
T2g
857 (s)
T2g
856
857
T2g
593
A1g
T2g 711 A1g 736 Eg + T2g
YIG
CaYIG
SiYIG
GGG
110 (10) 128 (15) / 170 (30) 180 (20) 191 (50) 237 (40) / 271 (85)
110 (10) 128 (15) 154 (15) 170 (25) 180 (20) 191 (40) 237 (40) / 271 (70)
/ 127 (15) / 170 (25) / 191 (35) 237 (40) / 272 (65)
110 (10) / / 170 (15) 180 (20) / 239 (25) 261 (5) 273 (15)
323 / 353 (100) 376 (35)
323 / 353 (100) 377 (30)
323 340 (55) 353 (50) 376 (30)
/ / 353 (100) 381 (20)
391 (40) 415 (65)
391 (40) 415 (50)
392 (30) 391 (35) 416 (100) 417 (15)
432 (45) 448 (45) 451 (45) 504 (35) 525 (25) 587 (30) 598 (25)
432 (35) 448 (35) 451 (35) 504 (30) 525 (25) 587 (30) 598 (25)
/ / 453 (75) 504 (40) / 583 (30) /
431 (10) / 457 (5) / 524 (20) 583 (15) 598 (15)
679 (25)
680 (25)
688 (50)
/
708 (30)
710 (30)
/
/
739 (85)
739 (85)
736 (50)
740 (80)
786 (35) 820 (30) 858 (25) 896 (60) 924 950
786 (35) 820 (30) 858 (25) 896 (60) 924 954
786 (20) 819 (20) 860 (25) 896 (35) 925 /
786 (35) 820 (25) 858 896 (60) / 954
Note: Peak intensities are given in brackets: vs (very strong), s (strong), w (weak), and vw (very weak) for the literature data [38], and on a relative scale from 1 to 100 (maximum intensity peak marked in bold characters) for the present data. Missing or faint peaks are marked with a slash character (/).
[38] in YAG and rare-earth aluminum garnets. The low wavenumber peaks ( φ0 likely stem from randomization of bond angles and bond lengths in a-YIG, regardless of substitutions. Spectra for the different kinds of crystalline samples exhibit the same features as a-YIG films, regardless of irradiation conditions. Owing to the loss of selection rules based on the phonon wave-vector (q) in disordered solids, Raman spectra reflect the folded phonon DOS at the Γ point (for q = 0) [58–60]. Contributions to the spectra may arise from Ramanforbidden modes such as IR-active optical modes and even acoustical (TA/LA) modes, like for a-Ge or a-Si, and compounds like a-As2S3 [58, 59, 61]. Moreover, the decrease of phonon life time (viz. mean free path) due to lattice disorder and defects can also contribute to inhomogeneous peak broadening [59]. The increase of background below 150 cm−1 likely arises from contributions of low-frequency acoustical modes below 9.5 meV (~80 cm−1) [49, 62], that can become allowed by disorder. The shape of the main band at ~670 cm−1 extending towards lower wave numbers reflects contributions of other points of the BZ to the folded DOS in a range corresponding to the crystal phonon gap between ~600 and ~650 cm−1. This asymmetry may arise from overlap of randomized vibration modes from various directions in q-space. Indeed, calculations for Yb3Al5O12 display a peak in the one-phonon DOS at ~700 cm−1 along the [1 0 0] direction (Δ) [44]. As discussed above, main contributions in this frequency range arise from internal molecular modes of tetrahedral, as well as octahedral, building blocks. Actually, Mössbauer and x-ray absorption spectroscopy data have shown that (FeO4) and (FeO6) units are kept in the a-YIG and nc-YIG, with a decrease of tetrahedral sites in both phases with respect to c-YIG [20]. This is consistent with the clear decrease of the strong peaks at 353 and 416 cm−1 assigned to Eg modes of tetrahedral units. For a-YIG, the major band at ~660 cm−1 could arise from the weak (Eg + T2g) mode at ~680 cm−1 in YIG and CaYIG that is clearly enhanced by Si substitutions in tetrahedral (FeO4) units (figure 3). The IR-active mode at 655–677 cm−1 assigned to an overtone of the asymmetric stretching modes of (FeO4) units [43], may also become Raman-active due to disorder. The smaller band at ~260 cm−1 probably arises from the strong (Eg + T2g) mode at 271 cm−1, whereas the three minor bands likely also derive from the crystal phonon modes below 200 cm−1 (table 2). All the latter four weaker peaks can be assigned to translation modes of Y3+ ions in the disordered
Previous experimental studies of silicate garnets have also assigned Raman peaks above 400 cm−1 to Si–O stretching and rotational modes of (SiO4), and peaks below 400 cm−1 to mixed translational modes of (SiO4) and M cations [54]. This is consistent with other shell-model calculations showing that high-frequency vibration modes correspond to (SiO4) internal modes, and that mixing with M cation modes only occurs for lower frequencies ( φ0 (above the plateau), up to 2 × 1015 cm−2 (figure 4(a)). In principle, the small grain size (~10 nm) of nc-YIG, as seen by HRTEM [2, 15], might lead to (asymmetrical) Raman peak broadening due to phonon confinement, for optical phonon wavelength about the crystallite size [66, 67]. Such phonon confinement effect is generally noticeable only for grain sizes smaller than about 20 lattice parameter (i.e. ~20 nm for YIG [47]), and strong negative dispersion of the phonon branch away from Γ point, like for nc-ZnO [66]. For nc-TiO2 (anatase), the full width at half maximum (FWHM) increases from ~10 to ~20 cm−1 for the most intense peak at 144 cm−1, and from ~35 to ~80 cm−1 for the peak at 638 cm−1, when reducing the mean crystallite size from ~12 to ~6 nm [67]. However, the Raman scattered signal arising from nc-YIG may not be seen, since peak broadening arising from amorphization is likely more important. Moreover, it has to be borne in mind that peak intensities for damaged samples should be corrected for increasing selfabsorption of the scattered light, due to progressive opticalgap narrowing [21]. Therefore, quantitative assessment of fractions of the three phases cannot be reliably achieved from the present Raman spectra, giving qualitative trends only. We henceforth address the kinetics of the damage process with amorphization followed by recrystallization, and modelling of related dc-conductivity evolutions (figure 2).
dfc /dφ = −A fc (1) dfa /dφ = A fc + B fn − S fa (2) dfn /dφ = S fa − B fn (3)
where A is the amorphization cross-section of c-YIG, S is the recrystallization cross-section of a-YIG, and B is the amorphization cross-section of nc-YIG, with the conservation equation: fc + fa + fn =1 (4)
and initial conditions: fa (0) = fn (0) = 0, and fc (0) = 1. Solving equations (2) and (3), combined with equation (4), yields the following a-YIG and nc-YIG fractions:
fa = B /(B + S ) + [(A − B )/(B + S − A)] e−Aφ − {AS /[(B + S )(B + S − A)]} e –(B + S )φ
(5)
which is an increasing function tending to saturation (≠100%) for large fluences (fa → B/(B + S), for φ → +∞), and:
fn = S /(B + S ) − [S /(B + S − A)] e –Aφ + {AS /[(B + S )(B + S − A)]} e−(B + S )φ
(6)
which is also an increasing function tending to saturation (≠100%) for large fluences (fn → S/(B + S), for φ → +∞). According to this second model, the a-YIG fraction will not pass through a maximum value, by contrast to the first one [34]. However, conductivity data show that saturation of nc-YIG is not reached up to the highest fluence (figure 2). The c-YIG fraction deduced from equation (1) will decay to zero as: fc = e−Aφ. (7)
The variation of the effective medium conductivity (σ) with fluence can be derived on the basis of such kinetic equations. Previous modeling with the 2D-Bruggeman effective-medium theory of a mixture of c-YIG and a-YIG led to a second-degree equation with solutions being the effective-medium conductivity [34]. The A-values were deduced from least-squares fits of conductivity data versus Aφ, up to the saturation plateau (for φ ⩽ φs). The S-values were empirically deduced from the threshold fluences for recrystallization as 1/φ0. A power-law term (~φ2) was added to reproduce the high-fluence conductivity data that were not included in the fitting procedure. In the present case of a three-phase medium, we use a simple model of parallel resistors which is relevant when the applied electric field is set in the film plane, i.e. perpendicular to the track axis. This corresponds to the Wiener’s limit of mean-field theory where the electron mean free path is smaller than the inclusion size (i.e. track diameter) [68]. Such an approximation holds for hopping conductivity in wide bandgap crystalline insulating oxides or amorphous solids [69], like in the case of ion-irradiated YIG [12, 34]. This gives:
IV.2. Damage kinetics and conductivity modelling
Our modeling for damage kinetics of c-YIG was at first based on a set of rate equations with three variables, fc, fa, and fn, being the c-YIG, a-YIG, and nc-YIG volume fractions, respectively, as functions of φ, resulting from the two successive reactions c → a → nc [34]. In the present new model, we
σ = fc σc + fa σa + fn σn (8) 9
J-M Costantini et al
J. Phys.: Condens. Matter 27 (2015) 496001
Table 3. Data for single crystal YIG films irradiated with ions of energy E and mean electronic stopping power Se: dc conductivities of the starting single crystal (σc), amorphous (σa), and nanocrystalline (σn) phases, amorphization (A, B) and recrystallization (S) cross sections derived from conductivity data, and amorphization cross sections (ARBS) deduced from RBS/C data [14].
Material Ion CaYIG
32
S
Se σc E [MeV] [keV nm−1] [S cm−1] 50
63
Cu 50
SiYIG YIG a-YIG
32
S 50 S 50 63 Cu 50 32
7 7 11 11 7 7 11
2 × 10−9 1.5 × 10−4 7 × 10−5 3.5 × 10−5 3 × 10−5 2 × 10−10 /
σa [S cm−1]
σn [S cm−1] A [cm2]
B [cm2]
S [cm2]
ARBS [cm2]
3 × 10−10 1 × 10−7 1 × 10−7 1 × 10−10 3 × 10−10 3 × 10−10 1 × 10−7
1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4
1 × 10−18 2 × 10-18 2 × 10−18 2 × 10−18 2 × 10−18 1 × 10−17 1 × 10−17
1 × 10−16 1 × 10−17 1 × 10−17 1 × 10−17 1 × 10−17 1 × 10−18 3 × 10−17
3.2 × 10−14 3.2 × 10−14 5.3 × 10−13 5.3 × 10−13 3.2 × 10−14 3.5 × 10−14 /
3 × 10−13 1 × 10−12 2.5 × 10−12 2 × 10−12 2 × 10−12 3 × 10−13 /
where σc, σa and σn stand for the conductivities of c-YIG, a-YIG and nc-YIG, respectively. For high fluences (φ → +∞), σ → (B σa + S σn)/ (B + S). For a-YIG films, we use only equations (2) and (4) for fc = 0 that yield: fa (φ ) = [B /(B + S )] [1+(S /B )e−(B + S )φ] (9) fn (φ ) = [S /(B + S )] [1−e−(B + S )φ]. (10)
The same asymptotic value of σ for high fluences is found as for crystalline samples. By replacing equations (5)–(7) in equation (8), the dependence of σ versus φ was eventually used to fit the experimental data, for a given crystal conductivity (σc) (figure 2). Since all adjustable parameters (A, B, S, σa, and σn) could not be straightforwardly fitted at the same time, σa and σn were set to some reasonable values that were changed by a trial-and-error method. Since no saturation of high-fluence data is found, we had to use a guess value for σn (~10−4 S cm−1) that is compatible with all curves. For CaYIG films, σa was directly obtained from saturation values of the conductivity plateau (figure 2). For SiYIG films, where the fluence range of the plateau is smaller, it was deduced from the minimum conductivity value. Similar values were also used for undoped YIG films. These values are consistent with measurements done on virgin a-YIG films with σa ~ 10−7 S cm−1. Conductivity values are displayed together with the cross-section data, as obtained from trial-and-error calculations (table 3). For A-values, large deviations are found from values (ARBS) deduced from RBS/C data [14] (table 3). Smaller deviations (for A/ARBS φ0 stems from the secondorder development of equation (8) for 1/A φ 1/(B + S). Discrepancies with previous values partly arise from the broad fluence range (5 order-of-magnitude scale) and conductivity range (7 order-of-magnitude scale) for the fitting procedure.
Figure 7. Track radii (this work: open red circles; previous data [10]: full red circles) and recrystallized track radii (this work: open blue stars, previous data [10]: full blue stars) (R) versus mean electronic stopping power (Se) in YIG films deduced from conductivity data. Values deduced from RBS/C (full red squares) [14], optical absorption (full blue up-triangles) [21], saturation magnetization (full black down-triangles) [30], HRTEM (open diamonds) [2], and XRD data (open squares) [2, 15] are also displayed. Red dashed line is a fit of data of magnetically-oriented track radii (a) [16]. Black (b) and blue (c) solid lines are TTM calculations corresponding to amorphous track formation by 1 MeV u−1 and 5 MeV u−1 ions respectively, with the melting criterion (for λ = 5 nm). Black dashed (d) and dotted (e) lines are TTM calculations of recrystallized track formation for 1 MeV u−1 ions with the vaporizing criterion (for λ = 3.3 nm), for vaporizing energies of 1.3 eV at−1 and 2.2 eV at−1, respectively. Dash–dotted line (f) corresponds to TTM calculations for 5 MeV u−1 ions and vaporizing energy of 2.2 eV at−1.
However, consistent sets of parameters are obtained for such a wide range of conductivities. Track radii deduced from average A-values (table 3) and previous values [34] are plotted (figure 7) versus the mean electronic stopping power in the films deduced from depth profiles (figure 1). Values derived from saturation magnetization [29], RBS/C [14], HRTEM [2], XRD [2, 15], and optical absorption data [21], for various projectiles are also plotted (figure 7). The present values are quite larger than these latter values for the same stopping power values. By contrast, recrystallized track radii deduced from S-values (table 3) are 10
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J. Phys.: Condens. Matter 27 (2015) 496001
clearly lower than previous values corresponding to 1/φ0 [34] that are also plotted (figure 7). The possible decomposition of the iron garnet into nanocrystalline orthoferrite and haematite with different conductivities might account for the discrepancies on A values [10, 19]. However, the most intense Raman lines of α-Fe2O3 at 409 and 612 cm−1 [64] are not seen in our spectra. Moreover, such chemical decomposition did not occur in natural garnets, for high-temperature irradiations [32, 33], or in gallium garnets under high pressure and high temperature conditions [70]. These deviations might actually stem from the extra contributions of track outer shells (the so-called ‘track-halos’) to the conductivity, yielding much larger track radii, like the optical absorption data for high stopping power (figure 7) that may include contributions of point defects. As shown for LuAG (Lu3Al5O12), oxygen vacancies (F and F+ centers) and interstitials were generated in track halos by 2.15 GeV U ion irradiation (Se > 30 MeV μm−1) for non-overlapping tracks (fluence of 1012 cm−2) [71]. Several absorption bands of those point defects were recorded in the UV-visible range for this wide band gap insulator (Eg ~ 8 eV). A similar kind of track structure with a defective cubic-fluorite shell surrounding the amorphous track core was found for pyrochlores (Gd2Ti2O7) irradiated by swift heavy ions for high Se values (>14 MeV μm−1) [72, 73]. Such large track radii for YIG are consistent with the large radii of the magnetically-oriented outer shells deduced from Mössbauer spectra after swift heavy ion irradiations [16]. Magnetization rotation in these track outer shells arises from stresses induced by the difference in atomic density between the amorphous track core and the surrounding crystal (magneto-elastic effect) [20]. A fitted curve of the latter outer shell data [16] shown in figure 7 is in rather good agreement with the present track radii, by taking into account large standard deviations (±20%) for the trialand-error fitting process of conductivity data (figure 2). These point defects in the track halos also generate defectrelated local levels in the crystal band gap, thereby increasing the carrier density, like for the case of doping species [69]. This will lead to an increase of the RT extrinsic (electronic) conductivity of the outer shells (σsc) with respect to the virgin crystal (σc). The contribution of tracks (fa σa) deduced from the fits of the effective conductivity (σ) with equation (8) is in fact the sum of the real contribution of amorphous cores ( f ′aσa) and the stressed crystal shells (fsc σsc). The latter fraction (fsc) is likely much smaller than the amorphous track fraction ( f ′a) and should show a maximum value versus fluence due to track overlap, as for pyrochlores [72]. For large track overlap (φ > φs), fsc → 0 and σ → σa, but for smaller track overlap (φ φs), σ will depend on fsc. As a result, the real fraction of amorphous tracks ( f ′a = fa − fsc σsc/σa) is likely smaller than fa (for σsc > σa), and hence the real amorphization cross sections (A′) smaller than the present A values.
to lattice atoms by the electron–phonon interactions on the ps time scale. This process is stopped when the electronic temperature (Te) gets lower than the atomic temperature (Ta). The super-heated atomic subsystem is then cooled down rapidly from temperatures larger than the melting temperature, and quenched into a solid phase. For such high cooling rates, an out-of-equilibrium amorphous phase can be produced at RT. Details on the equations and assumptions of this model can be found in earlier papers [8]. More recent calculations have been carried out since then, using experimental data for swift heavy ion and atomic cluster irradiations in a wide range of electronic stopping power and energy [74]. In the latter calculations for YIG, the latent heat of fusion (300 ± 100 J g−1 = 0.12 ± 0.4 eV at−1) [75] was included, as opposed to older ones [9, 76]. This allowed a better estimation of the electron–phonon mean free path (λ = 5 ± 0.3 nm), which is a key-parameter in these calculations. Calculations of the amorphization cross-section (or amorphous track-core radius) as a function of stopping power were carried out for ion energies ranging between 1 and 15 MeV u−1. Calculated values for 1 and 5 MeV u−1 ions are displayed with experimental data that are consistent with thresholds ~4 and ~6 MeV μm−1 respectively (figure 7). A good agreement is found, except for the present conductivity data that are much larger, maybe due to the contribution of point defects in track halos, as mentioned above. As regards the recrystallization process, the electron– phonon coupling must be stronger in a-YIG than in c-YIG, due to atomic disorder [9]. This results in a greater localization of energy in the lattice inducing higher Ta in a-YIG than in c-YIG for the same electronic energy loss (i.e. for the same Te). As a result, a reduced λ value (
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Swift heavy ion-beam induced amorphization and recrystallization of yttrium iron garnet
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 496001 (13pp)
doi:10.1088/0953-8984/27/49/496001
Swift heavy ion-beam induced amorphization and recrystallization of yttrium iron garnet Jean-Marc Costantini1, Sandrine Miro2, François Beuneu3 and Marcel Toulemonde4 1
CEA, DEN, SRMA, 91191 Gif-sur Yvette Cedex, France CEA, DEN, Service de Recherches de Métallurgie Physique, Laboratoire JANNUS, F-91191 Gif-sur-Yvette, France 3 LSI, CEA-CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France 4 CIMAP-GANIL, CEA-CNRS-ENSICAEN, Bd H. Becquerel, 14070 Caen, France 2
E-mail: [email protected] Received 12 June 2015, revised 20 October 2015 Accepted for publication 22 October 2015 Published 18 November 2015 Abstract
Pure and (Ca and Si)-substituted yttrium iron garnet (Y3Fe5O12 or YIG) epitaxial layers and amorphous films on gadolinium gallium garnet (Gd3Ga5O12, or GGG) single crystal substrates were irradiated by 50 MeV 32Si and 50 MeV (or 60 MeV) 63Cu ions for electronic stopping powers larger than the threshold value (~4 MeV μm−1) for amorphous track formation in YIG crystals. Conductivity data of crystalline samples in a broad ion fluence range (1011–1016 cm−2) are modeled with a set of rate equations corresponding to the amorphization and recrystallization induced in ion tracks by electronic excitations. The data for amorphous layers confirm that a recrystallization process takes place above ~1014 cm−2. Cross sections for both processes deduced from this analysis are discussed in comparison to previous determinations with reference to the inelastic thermal-spike model of track formation. Micro-Raman spectroscopy was also used to follow the related structural modifications. Raman spectra show the progressive vanishing and randomization of crystal phonon modes in relation to the ioninduced damage. For crystalline samples irradiated at high fluences (⩾1014 cm−2), only two prominent broad bands remain like for amorphous films, thereby reflecting the phonon density of states of the disordered solid, regardless of samples and irradiation conditions. The main band peaked at ~660 cm−1 is assigned to vibration modes of randomized bonds in tetrahedral (FeO4) units. Keywords: iron garnets, swift heavy ion irradiations, Raman spectroscopy, electrical conductivity (Some figures may appear in colour only in the online journal)
I. Introduction
showing such effects induced by electronic excitations, the so-called swift heavy ion-beam induced epitaxial crystallization (or SHIBIEC) effect, like in yttrium iron garnet (YIG) [2], fluorapatites (calcium phosphosilicates) [3, 4] or silicon carbide [5, 6]. Such mechanism should not be confused with the classical recrystallization process of cold-worked metals and alloys upon thermal annealing that is driven by the stored energy in strained materials [7]. We previously attempted to
Processes of amorphization and recrystallization of materials by swift heavy ion irradiations have recently become hot topics due to new molecular-dynamics simulations of the thermal spike induced by electronic excitations [1]. As a matter of fact, experimental evidence was already accumulated over the last 20 years on several ionic-covalent materials 0953-8984/15/496001+13$33.00
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J. Phys.: Condens. Matter 27 (2015) 496001
were not satisfactorily modeled on the whole fluence range (1011–1016 cm−2) [10]. Therefore, we address this problem anew by performing conductivity modeling using contributions of the three phases on the whole fluence range on the basis of a set of rate equations including amorphization of nc-YIG. Conductivity data versus fluence are fairly well reproduced with a new set of amorphization cross-sections for two ion species that are compared with previous determinations and discussed on the basis of the TTM. Moreover, Raman scattering data are also reported for the first time to provide new experimental evidence of the damage induced by swift heavy ion irradiations in pure and substituted YIG.
address this issue for YIG on the basis of the so-called twotemperature model (TTM) of the inelastic thermal spike [8] by using two different approaches [9, 10]. The first one used a slow quench rate of the melt to generate recrystallized tracks [9], whereas the second one was based instead on a vaporization criterion of track formation [10]. Ferrimagnetic iron garnets doped with rare earths found a wide range of applications since the early 1970s for data storage with the so-called ‘magnetic bubble materials’ [11]. It was shown that YIG can be amorphized in tracks induced by heavy ion irradiations for electronic stopping power values Se = (−dE/dx)e above a threshold ~4 MeV μm−1 for energies in the 1 MeV u−1 range [12, 13]. Studies mainly focused on measurements of amorphous track-core radii for different Se values by Rutherford backscattering-channeling spectrometry (RBS/C) [14], x-ray diffraction (XRD) [2, 15], high-resolution transmission electron microscopy (HRTEM) [2, 15–18], saturation magnetization [12], Mössbauer spectroscopy [19, 20], and optical absorption data [21]. The effects of amorphous track formation on magnetic and magneto-optical properties [18–20, 22–27], as well as electrical properties [10, 14, 28–31] of pure and substituted YIG crystals were also thoroughly studied. It was shown that amorphous tracks could not only modify the coercitivity of ferromagnetic garnet films [23], but also pin Bloch walls after a proper chemical etching [27]. In the case of thin YIG epitaxial films, HRTEM has shown that the amorphous phase can suffer a recrystallization process into a nanostructured material after swift heavy ion irradiations at room temperature (RT) for large fluences [2]. Amorphous tracks were first produced then recrystallization set in for large track overlap. For high fluences (>1014 cm−2), HRTEM showed that the pristine single crystal (c-YIG) faded out, but the amorphous (a-YIG) and nanocrystalline (nc-YIG) phases were still coexisting. The recrystallization process was not totally completed up to 1016 cm−2 [2]. A possible chemical decomposition of the garnet into orthoferrite (YFeO3) and haematite (α-Fe2O3) was suggested, like for high-pressure and high-temperature conditions. A recrystallization process was also found for synthetic aluminate-ferrate garnets after 1.0 MeV Kr ion irradiation at 750 °C, near the critical amorphization temperature in the nuclear-collision regime, without chemical decomposition of the material [32]. A contrasted behavior occurred for some other ceramics like fayalite (γ-Fe2SiO4) that decomposed into magnetite (Fe2O4) and quartz (α-SiO2) in an amorphous matrix upon 1.5 MeV Kr ion irradiation at 600 °C [33]. However, in both cases, damage was mainly induced by atomic displacement cascades, and recrystallization occured at high temperatures. Electrical conductivity measurements of ion-irradiated YIG thin films were performed at RT to monitor the irradiationinduced phase changes versus fluence (φ) [10]. An effective medium approximation (2D-Bruggeman model) was used to model conductivity data in the case where the amorphization process dominates in the low-fluence range (φ 4 mW). Raman spectra were recorded in a broad wavenumber range, between 100 and 2000 cm−1. Several spectra were taken at different points of samples to ensure reproducibility of measurements. For highly damaged samples, longer accumulation times were needed to increase the signal/noise ratio. A depth-resolved spectrum was performed by steps of 0.1 μm in high-confocal mode, for the CaYIG film irradiated by 50 MeV Cu ions at 3.7 × 1012 cm−2. Optical transmission spectra for YIG and CaYIG films were also measured at RT with a Cary-17 double-beam spectrometer at normal incidence with a virgin GGG substrate on the reference beam.
The dc conductivity data (σ) are displayed for irradiated singlecrystal films showing two kinds of behaviors as a function of fluence (figure 2). Although some data may be scattered for heavily-doped CaYIG and SiYIG samples, σ exhibits a similar saturation for φs ~ 1012–1013 cm−2, regardless of crystal conductivity, then sharply increases with power-law dependence (~φ2) up to large values, above a threshold fluence φ0 ~ 1014 cm−2 (at the end of the plateau). By contrast, the undoped or lightly doped CaYIG samples with much lower conductivities exhibit a monotonous increase, and merge with the other data for large fluences. Similar plots are obtained regardless of ion species or doping for similar crystal conductivities. These results are consistent with data for irradiated a-YIG films also showing a plateau for φ φ0 (figure 2). First-order Raman spectra for virgin iron-garnet films and GGG substrate (figure 3) and irradiated films are shown up to 1000 cm−1 for increasing fluences up to 2 × 1015 cm−2 (figures 4(a)–(c)). Peaks are assigned to the Raman-active optical phonon modes that are labelled on the basis of the available data for YIG [36, 37] and yttrium aluminium garnet (Y3Al5O12, or YAG) [38–40]. Raman peaks for the three kinds of samples are consistent with literature data (table 2). Other second-order peaks were recorded above 1000 cm−1 (not shown). A small gap in the vibration modes probed by Raman spectroscopy appears for frequencies between ~600 and ~650 cm−1 for pure YIG. No major differences are found 3
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less reduced (figure 4(b)). For both ion species and all kinds of samples, similar spectra are obtained with two prominent spectral features at ~260 and ~670 cm−1 with full widths ~200–250 cm−1, growing on top of the crystal phonon peaks. Three other minor bands (tagged with arrows in figure 4(c)) are found at ~120, 150, and 200 cm−1. These broad bands are growing with fluence, but no significant spectral evolutions are found for φ > φ0, except some scattering background enhancement below 400 cm−1 (figure 4(c)). A similar spectrum is obtained for virgin a-YIG films with the same broad peaks (figure 4(d)). Irradiation of a-YIG does not change significantly the spectra, except also for some enhancement of scattered intensity below 400 cm−1 (figure 4(d)). In-depth mapping of the 1 μm thick CaYIG sample irradiated with 50 MeV Cu ions shows that damage is almost homogeneous across the film, in agreement with the stopping power depth profile (figures 5(a) and (b)). Although no absolute depth scale can easily be displayed in figures 5(a) and (b), the damaged depth is consistent with the film thickness (1 μm) after a correction using the refractive index of YIG (n = 2.416) for the wavelength of 509 nm [35]. Below this depth, spectra correspond to undamaged substrate by checking peaks at 273 and 417 cm−1 that are fingerprints of GGG, since these modes are clearly reduced with respect to pure YIG (figure 3 and table 2). This means that Raman spectra do not show any damage of the substrate, although GGG should be partly amorphized by irradiations above the threshold electronic stopping power (Se ~ 7 MeV μm−1) [41] (figure 1). The optical density at the wavelength of 500 nm for pure YIG and CaYIG films increases versus fluence for 50 MeV Cu ion irradiation up to the same saturation value corresponding to the amorphous state, for φ = φs ~ 1013 cm−2 (figure 6). Amorphous fractions are deduced from the optical density data by using a linear approximation with reference to the virgin-crystal value [21] (figure 6).
Figure 3. Micro-Raman spectra of virgin YIG, CaYIG films (thickness = 1 μm) and SiYIG film (thickness = 2.3 μm), and GGG substrate. Peaks tagged with arrows are strongly affected in intensity by substitutions in CaYIG and SiYIG with respect to pure YIG.
for Ca substitutions, except for the peak at 154 cm−1 (tagged with an arrow in figure 3) that is clearly enhanced with respect to pure YIG. Instead, peaks above 700 cm−1 (tagged with arrows in figure 3) are strongly affected by Si substitutions. The strongest peak at 352 cm−1 in YIG and CaYIG (and also GGG), is also very much reduced by Si substitutions, whereas some other smaller peaks between 400 and 700 cm−1 are clearly enhanced in SiYIG (tagged with arrows in figure 3). For the GGG substrate, a similar spectrum is found as for YIG films, yet some of these peaks are missing or have clearly different intensities (figure 3 and table 2). When irradiation proceeds, these crystal phonon peaks decrease in intensity and broaden significantly, then eventually vanish (figures 4(a)–(c)). Small residual peaks are still found for low fluences and disappear for φ > φ0, in agreement with increasing lattice disorder. The strong peaks at 353, 416, and 739 cm−1, and above 750 cm−1 are most affected by irradiation in pure YIG (figure 4(a)). A relative growth of peaks at 679 and 708 cm−1 is observed for 1.5 × 1012 S cm−2 with respect to virgin YIG sample. Smaller damage is found in CaYIG for the same fluences (figure 4(b)). However, for 1.5 × 1012 Cu cm−2, a decrease in intensity by a factor of ~80% is found for peaks at 271 and 353 cm−1 with respect to virgin CaYIG samples, whereas peaks below 200 cm−1 are
IV. Discussion IV.1. Raman scattering and optical absorption data IV.1.a. Virgin samples. Assignment of Raman-active phonon
modes in garnets gave rise to sharp controversies back in the late 1960s owing to the most complicated crystal structure of these oxides (Oh point group with 48 symmetry operations) [38]. In principle, 25 Raman-active and 17 IR-active phonon modes are expected, out of the 240 normal vibration modes, for the body-centered cubic garnet structure (Ia3d or O10 h space group), with 80 atoms per primitive unit cell. The 25 Raman-active gerade modes at the Brillouin zone (BZ) center (Γ point) were assigned to the A1g (3) Eg (8), and T2g (14) symmetry labels (or combinations of these modes) of the Oh point group for frequencies up to ~900 cm−1 [38–40]. The 17 IR-active ungerade modes were assigned to the T1u symmetry label in the same frequency range [42, 43]. Almost all of Raman-active modes are found in the present work (table 2). The high wave-number peaks (>500 cm−1) were assigned to some molecular-like internal vibration modes of the tetrahedral (AlO4) [39, 42] or octahedral (AlO6) building blocks 4
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Figure 4. (a) Micro-Raman spectra of YIG films (thickness = 1 μm): virgin and irradiated by 50 MeV S and 50 MeV Cu ions for various fluences. The amorphous fraction (fa) deduced from the optical density at 500 nm (figure 6) is given for each spectrum. (b) Micro-Raman spectra of CaYIG films (thickness = 1 μm): virgin and irradiated by 50 MeV Cu ions for various fluences. The amorphous fraction (fa) deduced from the optical density at 500 nm (figure 6) is given for each spectrum. (c) Micro-Raman spectra of SiYIG films (thickness = 2.3 μm): virgin and irradiated by 50 MeV Cu ions for various fluences. The broad peaks below 300 cm−1 are tagged with arrows. (d) Micro-Raman spectra of a-YIG films (thickness = 1 μm): virgin and irradiated by 60 MeV Cu ions for various fluences. 5
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Table 2. Wave numbers (in cm−1) of Raman peaks of virgin YIG, CaYIG and SiYIG thin films, and GGG substrate, with the respective assignments of phonon modes in reference to literature data for YAG [38–40] and YIG [36, 37].
YAG [38]
YAG [39]
YAG [40]
Eg
162 (s)
T2g T2g Eg
108 134 162
145 163
T2g
218 (s)
T2g
259 (s)
T2g T2g T2g
219 243 259
220 243 261
Eg Eg
310 (vw) T2g Eg 340 (s) Eg
296 310 340
A1g
373 (w)
Eg T2g
403 (s) 408 (s)
T2g
436 (vw)
YIG [36]
YIG [37]
T2g T2g Eg
130
T2g
131
175 193 237
T2g T2g T2g
174 194 238
295 310 340
T2g T2g T2g T2g T2g T2g Eg T2g Eg Eg Eg Eg + A1g
274 315 347
Eg + T2g Eg T2g Eg
274 319 324 346
T2g + A1g 370–373 370 372 Eg 403 402 T2g 408 406
A1g T2g T2g Eg T2g Eg + T2g
380
T2g
378
420
Eg T2g
416 419
T2g + A1g 449
T2g Eg A1g
445 456 504
T2g Eg Eg + T2g Eg + T2g A1g
592 624 685 692 704
438
T2g
Eg A1g Eg T2g A1g T2g
507
690 691 714–719 712 718
T2g Eg + A1g Eg T2g
698
Eg
757
754
Eg
740
Eg
531 (w)
A1g
561 (s)
T2g Eg
690 (w) T2g 714 (vw) Eg + T2g
T2g
719 (s)
Eg T2g A1g
530 544 564
523 536 545 559
A1g
783 (s)
A1g
794
783
A1g
T2g
857 (s)
T2g
856
857
T2g
593
A1g
T2g 711 A1g 736 Eg + T2g
YIG
CaYIG
SiYIG
GGG
110 (10) 128 (15) / 170 (30) 180 (20) 191 (50) 237 (40) / 271 (85)
110 (10) 128 (15) 154 (15) 170 (25) 180 (20) 191 (40) 237 (40) / 271 (70)
/ 127 (15) / 170 (25) / 191 (35) 237 (40) / 272 (65)
110 (10) / / 170 (15) 180 (20) / 239 (25) 261 (5) 273 (15)
323 / 353 (100) 376 (35)
323 / 353 (100) 377 (30)
323 340 (55) 353 (50) 376 (30)
/ / 353 (100) 381 (20)
391 (40) 415 (65)
391 (40) 415 (50)
392 (30) 391 (35) 416 (100) 417 (15)
432 (45) 448 (45) 451 (45) 504 (35) 525 (25) 587 (30) 598 (25)
432 (35) 448 (35) 451 (35) 504 (30) 525 (25) 587 (30) 598 (25)
/ / 453 (75) 504 (40) / 583 (30) /
431 (10) / 457 (5) / 524 (20) 583 (15) 598 (15)
679 (25)
680 (25)
688 (50)
/
708 (30)
710 (30)
/
/
739 (85)
739 (85)
736 (50)
740 (80)
786 (35) 820 (30) 858 (25) 896 (60) 924 950
786 (35) 820 (30) 858 (25) 896 (60) 924 954
786 (20) 819 (20) 860 (25) 896 (35) 925 /
786 (35) 820 (25) 858 896 (60) / 954
Note: Peak intensities are given in brackets: vs (very strong), s (strong), w (weak), and vw (very weak) for the literature data [38], and on a relative scale from 1 to 100 (maximum intensity peak marked in bold characters) for the present data. Missing or faint peaks are marked with a slash character (/).
[38] in YAG and rare-earth aluminum garnets. The low wavenumber peaks ( φ0 likely stem from randomization of bond angles and bond lengths in a-YIG, regardless of substitutions. Spectra for the different kinds of crystalline samples exhibit the same features as a-YIG films, regardless of irradiation conditions. Owing to the loss of selection rules based on the phonon wave-vector (q) in disordered solids, Raman spectra reflect the folded phonon DOS at the Γ point (for q = 0) [58–60]. Contributions to the spectra may arise from Ramanforbidden modes such as IR-active optical modes and even acoustical (TA/LA) modes, like for a-Ge or a-Si, and compounds like a-As2S3 [58, 59, 61]. Moreover, the decrease of phonon life time (viz. mean free path) due to lattice disorder and defects can also contribute to inhomogeneous peak broadening [59]. The increase of background below 150 cm−1 likely arises from contributions of low-frequency acoustical modes below 9.5 meV (~80 cm−1) [49, 62], that can become allowed by disorder. The shape of the main band at ~670 cm−1 extending towards lower wave numbers reflects contributions of other points of the BZ to the folded DOS in a range corresponding to the crystal phonon gap between ~600 and ~650 cm−1. This asymmetry may arise from overlap of randomized vibration modes from various directions in q-space. Indeed, calculations for Yb3Al5O12 display a peak in the one-phonon DOS at ~700 cm−1 along the [1 0 0] direction (Δ) [44]. As discussed above, main contributions in this frequency range arise from internal molecular modes of tetrahedral, as well as octahedral, building blocks. Actually, Mössbauer and x-ray absorption spectroscopy data have shown that (FeO4) and (FeO6) units are kept in the a-YIG and nc-YIG, with a decrease of tetrahedral sites in both phases with respect to c-YIG [20]. This is consistent with the clear decrease of the strong peaks at 353 and 416 cm−1 assigned to Eg modes of tetrahedral units. For a-YIG, the major band at ~660 cm−1 could arise from the weak (Eg + T2g) mode at ~680 cm−1 in YIG and CaYIG that is clearly enhanced by Si substitutions in tetrahedral (FeO4) units (figure 3). The IR-active mode at 655–677 cm−1 assigned to an overtone of the asymmetric stretching modes of (FeO4) units [43], may also become Raman-active due to disorder. The smaller band at ~260 cm−1 probably arises from the strong (Eg + T2g) mode at 271 cm−1, whereas the three minor bands likely also derive from the crystal phonon modes below 200 cm−1 (table 2). All the latter four weaker peaks can be assigned to translation modes of Y3+ ions in the disordered
Previous experimental studies of silicate garnets have also assigned Raman peaks above 400 cm−1 to Si–O stretching and rotational modes of (SiO4), and peaks below 400 cm−1 to mixed translational modes of (SiO4) and M cations [54]. This is consistent with other shell-model calculations showing that high-frequency vibration modes correspond to (SiO4) internal modes, and that mixing with M cation modes only occurs for lower frequencies ( φ0 (above the plateau), up to 2 × 1015 cm−2 (figure 4(a)). In principle, the small grain size (~10 nm) of nc-YIG, as seen by HRTEM [2, 15], might lead to (asymmetrical) Raman peak broadening due to phonon confinement, for optical phonon wavelength about the crystallite size [66, 67]. Such phonon confinement effect is generally noticeable only for grain sizes smaller than about 20 lattice parameter (i.e. ~20 nm for YIG [47]), and strong negative dispersion of the phonon branch away from Γ point, like for nc-ZnO [66]. For nc-TiO2 (anatase), the full width at half maximum (FWHM) increases from ~10 to ~20 cm−1 for the most intense peak at 144 cm−1, and from ~35 to ~80 cm−1 for the peak at 638 cm−1, when reducing the mean crystallite size from ~12 to ~6 nm [67]. However, the Raman scattered signal arising from nc-YIG may not be seen, since peak broadening arising from amorphization is likely more important. Moreover, it has to be borne in mind that peak intensities for damaged samples should be corrected for increasing selfabsorption of the scattered light, due to progressive opticalgap narrowing [21]. Therefore, quantitative assessment of fractions of the three phases cannot be reliably achieved from the present Raman spectra, giving qualitative trends only. We henceforth address the kinetics of the damage process with amorphization followed by recrystallization, and modelling of related dc-conductivity evolutions (figure 2).
dfc /dφ = −A fc (1) dfa /dφ = A fc + B fn − S fa (2) dfn /dφ = S fa − B fn (3)
where A is the amorphization cross-section of c-YIG, S is the recrystallization cross-section of a-YIG, and B is the amorphization cross-section of nc-YIG, with the conservation equation: fc + fa + fn =1 (4)
and initial conditions: fa (0) = fn (0) = 0, and fc (0) = 1. Solving equations (2) and (3), combined with equation (4), yields the following a-YIG and nc-YIG fractions:
fa = B /(B + S ) + [(A − B )/(B + S − A)] e−Aφ − {AS /[(B + S )(B + S − A)]} e –(B + S )φ
(5)
which is an increasing function tending to saturation (≠100%) for large fluences (fa → B/(B + S), for φ → +∞), and:
fn = S /(B + S ) − [S /(B + S − A)] e –Aφ + {AS /[(B + S )(B + S − A)]} e−(B + S )φ
(6)
which is also an increasing function tending to saturation (≠100%) for large fluences (fn → S/(B + S), for φ → +∞). According to this second model, the a-YIG fraction will not pass through a maximum value, by contrast to the first one [34]. However, conductivity data show that saturation of nc-YIG is not reached up to the highest fluence (figure 2). The c-YIG fraction deduced from equation (1) will decay to zero as: fc = e−Aφ. (7)
The variation of the effective medium conductivity (σ) with fluence can be derived on the basis of such kinetic equations. Previous modeling with the 2D-Bruggeman effective-medium theory of a mixture of c-YIG and a-YIG led to a second-degree equation with solutions being the effective-medium conductivity [34]. The A-values were deduced from least-squares fits of conductivity data versus Aφ, up to the saturation plateau (for φ ⩽ φs). The S-values were empirically deduced from the threshold fluences for recrystallization as 1/φ0. A power-law term (~φ2) was added to reproduce the high-fluence conductivity data that were not included in the fitting procedure. In the present case of a three-phase medium, we use a simple model of parallel resistors which is relevant when the applied electric field is set in the film plane, i.e. perpendicular to the track axis. This corresponds to the Wiener’s limit of mean-field theory where the electron mean free path is smaller than the inclusion size (i.e. track diameter) [68]. Such an approximation holds for hopping conductivity in wide bandgap crystalline insulating oxides or amorphous solids [69], like in the case of ion-irradiated YIG [12, 34]. This gives:
IV.2. Damage kinetics and conductivity modelling
Our modeling for damage kinetics of c-YIG was at first based on a set of rate equations with three variables, fc, fa, and fn, being the c-YIG, a-YIG, and nc-YIG volume fractions, respectively, as functions of φ, resulting from the two successive reactions c → a → nc [34]. In the present new model, we
σ = fc σc + fa σa + fn σn (8) 9
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Table 3. Data for single crystal YIG films irradiated with ions of energy E and mean electronic stopping power Se: dc conductivities of the starting single crystal (σc), amorphous (σa), and nanocrystalline (σn) phases, amorphization (A, B) and recrystallization (S) cross sections derived from conductivity data, and amorphization cross sections (ARBS) deduced from RBS/C data [14].
Material Ion CaYIG
32
S
Se σc E [MeV] [keV nm−1] [S cm−1] 50
63
Cu 50
SiYIG YIG a-YIG
32
S 50 S 50 63 Cu 50 32
7 7 11 11 7 7 11
2 × 10−9 1.5 × 10−4 7 × 10−5 3.5 × 10−5 3 × 10−5 2 × 10−10 /
σa [S cm−1]
σn [S cm−1] A [cm2]
B [cm2]
S [cm2]
ARBS [cm2]
3 × 10−10 1 × 10−7 1 × 10−7 1 × 10−10 3 × 10−10 3 × 10−10 1 × 10−7
1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4 1 × 10−4
1 × 10−18 2 × 10-18 2 × 10−18 2 × 10−18 2 × 10−18 1 × 10−17 1 × 10−17
1 × 10−16 1 × 10−17 1 × 10−17 1 × 10−17 1 × 10−17 1 × 10−18 3 × 10−17
3.2 × 10−14 3.2 × 10−14 5.3 × 10−13 5.3 × 10−13 3.2 × 10−14 3.5 × 10−14 /
3 × 10−13 1 × 10−12 2.5 × 10−12 2 × 10−12 2 × 10−12 3 × 10−13 /
where σc, σa and σn stand for the conductivities of c-YIG, a-YIG and nc-YIG, respectively. For high fluences (φ → +∞), σ → (B σa + S σn)/ (B + S). For a-YIG films, we use only equations (2) and (4) for fc = 0 that yield: fa (φ ) = [B /(B + S )] [1+(S /B )e−(B + S )φ] (9) fn (φ ) = [S /(B + S )] [1−e−(B + S )φ]. (10)
The same asymptotic value of σ for high fluences is found as for crystalline samples. By replacing equations (5)–(7) in equation (8), the dependence of σ versus φ was eventually used to fit the experimental data, for a given crystal conductivity (σc) (figure 2). Since all adjustable parameters (A, B, S, σa, and σn) could not be straightforwardly fitted at the same time, σa and σn were set to some reasonable values that were changed by a trial-and-error method. Since no saturation of high-fluence data is found, we had to use a guess value for σn (~10−4 S cm−1) that is compatible with all curves. For CaYIG films, σa was directly obtained from saturation values of the conductivity plateau (figure 2). For SiYIG films, where the fluence range of the plateau is smaller, it was deduced from the minimum conductivity value. Similar values were also used for undoped YIG films. These values are consistent with measurements done on virgin a-YIG films with σa ~ 10−7 S cm−1. Conductivity values are displayed together with the cross-section data, as obtained from trial-and-error calculations (table 3). For A-values, large deviations are found from values (ARBS) deduced from RBS/C data [14] (table 3). Smaller deviations (for A/ARBS φ0 stems from the secondorder development of equation (8) for 1/A φ 1/(B + S). Discrepancies with previous values partly arise from the broad fluence range (5 order-of-magnitude scale) and conductivity range (7 order-of-magnitude scale) for the fitting procedure.
Figure 7. Track radii (this work: open red circles; previous data [10]: full red circles) and recrystallized track radii (this work: open blue stars, previous data [10]: full blue stars) (R) versus mean electronic stopping power (Se) in YIG films deduced from conductivity data. Values deduced from RBS/C (full red squares) [14], optical absorption (full blue up-triangles) [21], saturation magnetization (full black down-triangles) [30], HRTEM (open diamonds) [2], and XRD data (open squares) [2, 15] are also displayed. Red dashed line is a fit of data of magnetically-oriented track radii (a) [16]. Black (b) and blue (c) solid lines are TTM calculations corresponding to amorphous track formation by 1 MeV u−1 and 5 MeV u−1 ions respectively, with the melting criterion (for λ = 5 nm). Black dashed (d) and dotted (e) lines are TTM calculations of recrystallized track formation for 1 MeV u−1 ions with the vaporizing criterion (for λ = 3.3 nm), for vaporizing energies of 1.3 eV at−1 and 2.2 eV at−1, respectively. Dash–dotted line (f) corresponds to TTM calculations for 5 MeV u−1 ions and vaporizing energy of 2.2 eV at−1.
However, consistent sets of parameters are obtained for such a wide range of conductivities. Track radii deduced from average A-values (table 3) and previous values [34] are plotted (figure 7) versus the mean electronic stopping power in the films deduced from depth profiles (figure 1). Values derived from saturation magnetization [29], RBS/C [14], HRTEM [2], XRD [2, 15], and optical absorption data [21], for various projectiles are also plotted (figure 7). The present values are quite larger than these latter values for the same stopping power values. By contrast, recrystallized track radii deduced from S-values (table 3) are 10
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J. Phys.: Condens. Matter 27 (2015) 496001
clearly lower than previous values corresponding to 1/φ0 [34] that are also plotted (figure 7). The possible decomposition of the iron garnet into nanocrystalline orthoferrite and haematite with different conductivities might account for the discrepancies on A values [10, 19]. However, the most intense Raman lines of α-Fe2O3 at 409 and 612 cm−1 [64] are not seen in our spectra. Moreover, such chemical decomposition did not occur in natural garnets, for high-temperature irradiations [32, 33], or in gallium garnets under high pressure and high temperature conditions [70]. These deviations might actually stem from the extra contributions of track outer shells (the so-called ‘track-halos’) to the conductivity, yielding much larger track radii, like the optical absorption data for high stopping power (figure 7) that may include contributions of point defects. As shown for LuAG (Lu3Al5O12), oxygen vacancies (F and F+ centers) and interstitials were generated in track halos by 2.15 GeV U ion irradiation (Se > 30 MeV μm−1) for non-overlapping tracks (fluence of 1012 cm−2) [71]. Several absorption bands of those point defects were recorded in the UV-visible range for this wide band gap insulator (Eg ~ 8 eV). A similar kind of track structure with a defective cubic-fluorite shell surrounding the amorphous track core was found for pyrochlores (Gd2Ti2O7) irradiated by swift heavy ions for high Se values (>14 MeV μm−1) [72, 73]. Such large track radii for YIG are consistent with the large radii of the magnetically-oriented outer shells deduced from Mössbauer spectra after swift heavy ion irradiations [16]. Magnetization rotation in these track outer shells arises from stresses induced by the difference in atomic density between the amorphous track core and the surrounding crystal (magneto-elastic effect) [20]. A fitted curve of the latter outer shell data [16] shown in figure 7 is in rather good agreement with the present track radii, by taking into account large standard deviations (±20%) for the trialand-error fitting process of conductivity data (figure 2). These point defects in the track halos also generate defectrelated local levels in the crystal band gap, thereby increasing the carrier density, like for the case of doping species [69]. This will lead to an increase of the RT extrinsic (electronic) conductivity of the outer shells (σsc) with respect to the virgin crystal (σc). The contribution of tracks (fa σa) deduced from the fits of the effective conductivity (σ) with equation (8) is in fact the sum of the real contribution of amorphous cores ( f ′aσa) and the stressed crystal shells (fsc σsc). The latter fraction (fsc) is likely much smaller than the amorphous track fraction ( f ′a) and should show a maximum value versus fluence due to track overlap, as for pyrochlores [72]. For large track overlap (φ > φs), fsc → 0 and σ → σa, but for smaller track overlap (φ φs), σ will depend on fsc. As a result, the real fraction of amorphous tracks ( f ′a = fa − fsc σsc/σa) is likely smaller than fa (for σsc > σa), and hence the real amorphization cross sections (A′) smaller than the present A values.
to lattice atoms by the electron–phonon interactions on the ps time scale. This process is stopped when the electronic temperature (Te) gets lower than the atomic temperature (Ta). The super-heated atomic subsystem is then cooled down rapidly from temperatures larger than the melting temperature, and quenched into a solid phase. For such high cooling rates, an out-of-equilibrium amorphous phase can be produced at RT. Details on the equations and assumptions of this model can be found in earlier papers [8]. More recent calculations have been carried out since then, using experimental data for swift heavy ion and atomic cluster irradiations in a wide range of electronic stopping power and energy [74]. In the latter calculations for YIG, the latent heat of fusion (300 ± 100 J g−1 = 0.12 ± 0.4 eV at−1) [75] was included, as opposed to older ones [9, 76]. This allowed a better estimation of the electron–phonon mean free path (λ = 5 ± 0.3 nm), which is a key-parameter in these calculations. Calculations of the amorphization cross-section (or amorphous track-core radius) as a function of stopping power were carried out for ion energies ranging between 1 and 15 MeV u−1. Calculated values for 1 and 5 MeV u−1 ions are displayed with experimental data that are consistent with thresholds ~4 and ~6 MeV μm−1 respectively (figure 7). A good agreement is found, except for the present conductivity data that are much larger, maybe due to the contribution of point defects in track halos, as mentioned above. As regards the recrystallization process, the electron– phonon coupling must be stronger in a-YIG than in c-YIG, due to atomic disorder [9]. This results in a greater localization of energy in the lattice inducing higher Ta in a-YIG than in c-YIG for the same electronic energy loss (i.e. for the same Te). As a result, a reduced λ value (
