Intensive research has been ongoing to determinethermoannealing processes in metallic glasses byuse of traditional structural methods.1–3 All theexisting methods are sensitive to structural rear-rangement but, based on a simple consideration,one can expect an essential contribution fromelectron-quasi-phonon interaction. In previouspapers4–6 we have shown that optical photoinducedsecond-harmonic generation ~PISHG! is more sen-sitive to rearrangement or phase transition.PISHG is sensitive to the existence of electron-charge density noncentrosymmetry caused bystrong electron-quasi-phonon interaction. Photo-induced beams generate both electron-free carriersas well as electrostrictive acoustical quasi-phonons,which effectively contributes to the output opticalresponse functions. Nunzi et al.7 have shown thatrelaxation of excited photocarriers that are due toanisotropy of ambipolar diffusion can cause photo-induced noncentrosymmetry in randomly oriented
The authors are with the Solid State Department, Institute ofPhysics, Czestochowa Wyzsza Szkola Pedagogiczna, al. Armii Kra-jowej 13y15, Czestochowa PL-42201, Poland. The e-mail addressor I. V. Kityk is [email protected].
Received 22 January 1999; revised manuscript received 29 April1999.
5162 APPLIED OPTICS y Vol. 38, No. 24 y 20 August 1999
media because of nonequilibrium conditions of pho-toexcited carrier decay in the direction of light prop-agation even for unpolarized photoinduced beams.Therefore photoexcited quanta gain weak electron-quasi-phonon bound states with an increase ofelectron-charge density noncentrosymmetry. Theobserved effects are also a result of magnetoelectro-striction.8 Therefore, additional use of externalmagnetic fields is preferred for observation ofPISHG output signals. As a consequence simul-taneous operation with external magnetic andphotoexcited fields can be used to vary the noncen-trosymmetry detected by the probing light beams.Most of the traditional methods ~electron micros-copy, photoelectron and x-ray electron spectroscopy,transport phenomena, etc.! are not directly sensi-tive to the observed phenomena, and only nonlinearthird-order optical methods ~particularly SHG!emit output signals that are sensitive to electron-charge density noncentrosymmetry.
With regard to the influence of surface states, allthe measurements were taken for the same specimensurface. Therefore, surface background is elimi-nated automatically and only the field-inducedchanges are monitored. Moreover, the proposedmethod has additional advantages connected withcontactless features, for example, the possibility oflow-dimensional range detection such as light beamspots as large as 60 mm!.
The main goals of this study are as follows:
0bceam
P
exploration of PISHG sensitivity to thermoannealingin Fe–Co–Si–B metallic glasses,
fulfillment of the phase synchronism condition fornear-surface states,
study of the influence of the external magnetic fieldon PISHG, and
clarification of the microscopic mechanisms that areused to determine the observed PISHG.
In Section 2 we present the experimental setup forperforming PISHG. Experimental data and theo-retical simulations are presented in Section 3.
2. Experimental
We produced the specimens at the Institute of Mate-rials Engineering of Warsaw Technical University byusing the melt-spin method described in Ref. 9. Thespecimens measured 10 mm 3 10 mm 3 5 mm.Photoinduced light beams were generated with aQ-switched nitrogen laser ~l 5 377 nm! with approx-imately 25-MW power and a pulse width that variedbetween 400 and 980 ps; see Fig. 1. The pulse du-ration value depended on how much overheating ofthe specimen could be avoided. Rotating Fresnelprisms were obtained with special rotating mechan-ical equipment for operation of incident light polar-ization. The incident angle varied between 8° and12°. Such a wide range of angle variation was nec-essary to achieve a maximal output PISHG signal.Below we show that phase synchronism has a centralrole in our experiments with a PISHG signal. Thediameter of the light beam spot varied between 85and 1240 mm and, depending on the surface quality,the light spot diameter was varied to achieve themaximal output PISHG signal. Moreover the setupallowed us to scan the beam through the surface ofthe specimen. The beam has a Gaussian-like shapewith a dispersion half-width of approximately 78%.
Fig. 1. Principal experimental setup for measurement of thePISHG: S, synchronizer for the laser power; BS1, BS2, quartzbeam splitters; P1, P2, Glan–Thompson polarizers; specimens,magnetic camera for the specimens; PM, PM2, photomultipliers;BC, boxcar; MN, grating monochromator; DL, delay line.
The stability of laser generation was not worse than
0.1%. Generation of the photoinduced nitrogen la-ser was synchronized by generating a probingYAG:Nd laser. We used an unfocused YAG:Nd ~l 51.06-mm! laser beam with a spot diameter of 0.2–13.6mm, laser power of 6–14 MW, and a pulse duration of1.3–1850 ps. Pulse repetition was synchronized forphotoinduced and probe laser beams for as long as 0.9ps. For polarization of the photoinduced and probebeams we used Glan–Thompson polarizers with adegree of polarizability of approximately 99.998~7!%.Electro-optically operated delay lines from Li2B4O7single crystals have been used for time delay. Thisallows us to vary the delay time with a resolution ofnot worse than 0.6 ps. To justify the laser beams,the lasers were supplied with low power He–Ne la-sers, which allowed us to correct any imbalance thatmight exist between laser beams. For each speci-men the measurements were taken for more than 80points to obtain reliable statistical averaging withinthe x2 Student distribution that was not worse than0.02.
Photodetection was carried out with digital high-resolution multipliers, RCA-121 and FE-124-H, con-nected by boxcar with the gate at approximately 480ps. The SPM-3 grating monochromator with a spec-tral resolution of approximately 7 nmymm was usedto separate the green double-frequency signal ~l 5.53 mm! from the probe YAG:Nd laser ~l 5 1.06-mm!ackground. Both pump and probe signals wereontrolled by the bonded synchronized photomultipli-rs. Specimens were placed in the magnetic fieldnd directed through the specimen surface. Theagnetic field varied between 0.1 and 1.5 T.
3. Results and Discussion
Figure 2 shows typical angular dependencies ofPISHG versus applied magnetic fields directedthrough the specimen surfaces ~the angle is depictedin Fig. 1!. One can see that the maximal output
ISHG signal is observed at angles between 57° and
Fig. 2. Typical angular dependencies of the PISHG for differentapplied magnetic fields directed through the specimen surfaces.
20 August 1999 y Vol. 38, No. 24 y APPLIED OPTICS 5163
iiocap
ds
n
5
60°. The absolute value of the output PISHG signalwas approximately 1026 compared with the incidentbeam power. We observed the essential output sig-nal only for parallel polarization of the photoinducedand probe beams. When noncollinearity was higherthan 7°, the output PISHG vanished drastically ~atleast by as much as 2 orders of magnitude!. Nonho-mogeneity of the output PISHG signal distributionthrough the specimen surface is approximately 6%.Therefore, we present all the data in arbitrary units.
With increased magnetic field strength ~see Fig. 2!one can see an increase of the output PISHG signaland a slight shift of the maximum toward higherangles ~from 48° to 54°!. For magnetic fields higherthan 0.75 T, we saturated the output PISHG and thiscorrelates well with the saturation of the glass mag-netization. The observed drastic narrowing of thePISHG signal for magnetic field strengths of approx-imately 0.50 T is caused by the occurrence of mag-netic reoriented regions that essentially changephase synchronism conditions. The precision of thePISHG measurement allows one to determine theoutput PISHG signal with a relative error of less than0.8%. Therefore the observed enhancement of theoutput PISHG signal ~as much as 7%! is absolutelyreliable.
To explain the observed dependence it is conve-nient to present the considered system as a superpo-sition of clusters a-Fe and CoB2. The structural andHall investigations have shown9 that thermoanneal-ng stimulates formation of such types of cluster andncreased grain sizes. To clarify the origin of thebserved phenomena, we performed a quantumhemical simulation of thermoannealing using the-Fe and CoB2 clusters. The GAUSSIAN 94 computerrogram10 for simulation of the thermoannealing pro-
cess was used. Ab initio restricted Hartree–Fockcalculations were used for geometry optimizationwithin the molecular dynamics simulation. Thepresence of 3d orbitals in Fe and Co atoms indicatesthe appearance of a region with higher spin densitybetween the mentioned fragments ~see Fig. 3!. The
ata reflect the more probable geometry and corre-ponding spin density distribution for a-Fe:CoB2
structural fragments before the external magneticfield was applied. After we applied the externalmagnetic fields, the simulations indicated the ap-pearance of noncentrosymmetry ~see Fig. 4!. Thenoncentrosymmetry on the border between these twofragments has electron-quasi-phonon coupling. Thestronger quasi-phonon mode at 2100 cm21 that con-tributes to the output optical response is indicated byarrows. The final cluster could be presented as astructural fragment with local symmetry C2, which isconfirmed by nonzero third-order SHG tensor compo-nents x222, x123, x332, x312, x321. It is necessary toemphasize that the applied external magnetic field isadvantageous for increased grain sizes. Calcula-tions of the matrix dipole moments are presented inthe Table 1 and confirm the essential increase of thetotal dipole moment that is due to the clustering ofparticular fragments.
164 APPLIED OPTICS y Vol. 38, No. 24 y 20 August 1999
To check the symmetry of the thermoannealedclusters, we conducted optically polarized measure-ments under the influence of an external magneticfield. We adopted the applied magnetic field as aneffective axis direction. As shown in Figs. 3 and 4,because of spin-polarized Fe and Co ions, one canexpect the mentioned clusters to be oriented in themagnetic field. According to our calculations, onecan predict the creation of larger grains, which is inagreement with the experimental data reported inRef. 9. It is well known that a disordered systemstimulates the appearance of a large number of trap-ping levels. On the other hand, such electron levelsare advantageous for long-lived, quasi-metastablestates that essentially prolong the output PISHG op-tical response. To check this prediction we investi-gated the time-resolved dependencies of the PISHGsignal; see Fig. 5. We achieved the maximal outputPISHG signal for a time delay of an approximately
Fig. 3. Simulated molecular dynamics of the spin density distri-bution in Fe–CoB2 clusters before application of the external mag-
etic field.
Fig. 4. Appearance of noncentrosymmetry in the electron-chargedensity distribution within the Fe–CoB2 clusters after applicationof the approximately 0.6-T external magnetic field. The arrowsindicate the strongest quasi-phonon anharmonic modes at 2100cm21 that stimulate the observed noncentrosymmetry.
mtomt
lp
Table 1. Calculated Matrix Dipole Moments of Specific Clusters Before and After Connection
1.2-ps probe light beam toward the photoexcitedstate. For comparison x-ray diffractograms are pre-sented in Fig. 6. A good correlation is shown be-tween the structural ordering and decreasedrelaxation time of the PISHG. This unambiguouslyconfirms our previous prediction and can be used forindependent control of disorder in Fe–Co–Si–Bglasses.
Another important aspect is the problem of phasesynchronism that plays a central role in nonlinearoptics ~see, for example, Ref. 11!. The individual
agnetic clusters are presented as chromophoreshat are responsible for PISHG. The total intensityf the PISHG in disordered materials was deter-ined by statistical averaging of particular clus-
ers.12,13 Total intensity I of PISHG by an assemblyof N magnetic grains is expressed as
I 5 @k~2v!Iv~2!gv
(2)#y~32p2cε03!
3 U(j
(ijklmn
N
PijklmneiejekVlVmVn exp~iDkRj!U2
, (1)
where Pijklmn is the effective externally induced non-inear optical susceptibility caused by electrostrictivehotoorientation and a magnetically induced contri-
Fig. 5. Dependence of the relaxation time on PISHG versus theapplied magnetic field.
a-Fe Point change 20.95Sp hybrida 0.25Pd hybrida 20.13Sum 0.82
CoB2 Point change 2.11Sp hybrida 0.07Pd hybrida 20.27Sum 1.92
aThe interaction between S and P or p and d orbitals is represe
bution; ei ej ek are unit polarization vectors of thephotoinduced and probe beams directed along indicesi, j, and k, respectively; Vl Vm Vn are intensities of thephotostimulated and magnetically stimulated elec-trostrictive long-wave quasi-phonons that effectivelycontribute to the output PISHG susceptibility; v isthe laser probe frequency; gv
~2! is the degree of second-order coherence; Dk 5 2k~v! 2 k~2v!; and Rj representsthe vector positions of the j chromophores. It is im-
Fig. 6. X-ray diffractogram that indicate ordering of the Fe–Co–Si–B glasses during thermoannealing.
20 August 1999 y Vol. 38, No. 24 y APPLIED OPTICS 5165
tat
mptc
ctsttwsfnd
5
portant to point out that the wavevector mismatch isapproximated on the assumption of long-wave pho-non behavior.
An effective externally induced nonlinear opticalsusceptibility Pijklmn based on the above definitionshould have two main parts, the first of which ismagnetically induced static electric polarizationp~v,0!
i:
p~v,0!i 5 Mijk
~v,0!Ej~v!Hk
~0!, (2)
where Mijk~v,0! is the magnetoelectric axially symmetric
hird rank tensor that corresponds to light-inducednd magnetically induced contributions to polariza-ion vector p~v,0!
i, connecting the external static mag-netic field with the electromagnetic light componentsEj
~v! and glass polarization p~v,0!i. The values of the
axial tensor are fully determined by asymmetry of theelectron-charge density distribution shown in Fig. 4.From this equation one can easily imagine the exper-imentally observed saturation of the output PISHG.Within the phenomenological approach the latter cor-responds to magnetic saturation of the given clustersin the external magnetic field. The generated non-compensated magnetically induced field causes con-ventional electrostriction as described by theexpression
slm~0! 5 pi
~v,0!ihilm (3)
for the low power field, where s~0!lm represents the
echanical stress induced by electrostriction. Thishenomenon is simultaneously responsible for acous-ic phonons that contribute to the output PISHG ac-ording to Eq. ~1!.
In the case of photo-orientation there are two con-tributions: the first of which corresponds to the cre-ation of photoexcited static polarization p~0!
i asdescribed by
p~0!i 5 aijk
~v,0!Ej~v!mk
~0!, (4)
where mk~0! is a static dipole moment of the individual
magnetic clusters, aijk is macropolarizability as de-termined by the glass elasticity, reoriented tempera-ture, local electric field screening, and by the spacederivation of the corresponding electrostatic poten-tial. The phenomenological aspect for the followingphoto-oriented electrostriction is similar to the onespresented in Eq. ~2!.
Special attention should be paid to the phase syn-hronism conditions described by the exponentlikeerm in Eq. ~1!. In this case fulfillment of the phaseynchronism conditions can be achieved because ofhe existence of grains with an average diameter be-ween approximately 5 and 15 nm that increaseshen the magnetic field strength is enhanced. Ab-
orption of the photoinduced beam causes diffractionrom the two neighboring layers. The first origi-ates from the two near-surface grain layers and isescribed by the double wavevector k~v! and the sec-
ond corresponds to the wavevector k~2v!. As a resultof diffraction, conditions similar to the ferroelectricdomains are fulfilled.14 One can achieve the maxi-
166 APPLIED OPTICS y Vol. 38, No. 24 y 20 August 1999
mum output of the PISHG signal by varying the in-cident angle. Therefore the observed PISHGdependencies are a result of agreement with the cor-responding phase synchronism conditions. We per-formed the mathematical simulations of the existinggrain sizes. The corresponding dependencies arepresented in Fig. 7. Several differences in the de-gree of angle-dependent asymmetry are probably in-dicative of nonhomogeneous distribution of grainsizes for real specimens. However, the basic fea-tures are similar, which is confirmation that the pro-posed model can be used efficiently.
The method we have presented can be used as aneffective tool for investigation of hyperfine magneticordering within spin glasses. The main advantageof the method compared with the traditional struc-tural studies such as x-ray diffractometry and elec-tron microscopy consists of relatively highersensitivity of the optical methods to magnetically in-duced electron-charge density noncentrosymmetry.A drawback of the proposed method is that it is nec-essary to have a high-quality surface in order to de-tect reliable output of the PISHG signal.
4. Conclusions
Sensitivity of the PISHG to thermoanneled orderingof Fe–Co–Si–B glasses has been shown. An in-creased magnetic field applied through the specimensurface leads to increased output of the PISHG sig-nal. The appearance of a long-range crystallineorder was achieved by the formation of a-Fe–CoB2spin-polarized magnetic clusters. The latter leadsthrough magnetoelectrostriction to structural rear-rangement and to creation of electron-charge densitynoncentrosymmetry detected by nonlinear opticalmethods, which in our case is second-harmonic gen-eration. A magnetic field additionally stimulatesnoncentrosymmetry, an increase of grain sizes, andtends toward saturation of the observed PISHG.Preliminary fulfillment of phase synchronism condi-tions is due to light diffraction from the two near-surface grain layers. The proposed method can beused for nondestructive control of structural rear-rangements in metallic glasses that contain 3d and4d metals.
Fig. 7. Theoretically calculated angular dependence of thePISHG for different grain sizes.
8. A. K. Bhatangar, B. Seshu, G. V. Sudhakar Rao, and N. R.
References1. Y. Yoshizawa, S. Ogura, and K. Yamaguchi, “Thermoannea-
lilng processes in the Fe-Si-B-Cu-Nb glasses,” J. Appl. Phys.64, 6044–6049 ~1988!.
2. K. Suzuki, N. Kataoka, A. Inoue, A. Makino, and T. Masumoto,“Thermostabilisation in the Fe-Zr-B glasses,” Mater. Trans.JIM 32, 743–747 ~1990!.
3. Y. Ueda, S. Ikeda, and T. Sakaguchi, “Permeability and a-Feprecipitated in Fe-Si-B-Cu-Nb amorphous alloys,” IEEETrans. J. Magn. Jpn 9, 39–45 ~1994!.
4. E. Golis, I. V. Kityk, J. Wasylak, and J. Kasperczyk, “Nonlin-ear optical properties of lead-bismuth-gallium glasses,” Mater.Res. Bull. 31, 1057–1065 ~1996!.
5. I. V. Kityk, “Photoinduced second-harmonic generation ofYBa2Cu3Ox single crystals,” Phys. Condens. Matter 6, 4119–4128 ~1994!.
6. J. Wasylak, J. Kucharski, I. V. Kityk, and B. Sahraoui, “Pho-toinduced effects in the Sb2Se3-BaCl2-PbCl2 glasses,” J. Appl.Phys. 85, 425–431 ~1999!.
7. J.-M. Nunzi, F. Charra, S. Delysse, P. Lefin, and N. Pfeffer,“Limits of the use of polymer thin films for spatial light mod-ulation,” in Second International Conference on Optical Infor-mation Processing, Z. I. Alferov, A. F. Ioffe, Y. V. Gulyaev, andD. R. Pope, eds., Proc. SPIE 2969, 138–144 ~1996!.
Munirathnam, “Mossbauer measurements of amorphousFe722xNi101x2yMoyB16Si2,” J. Non-Cryst. Solids 204~3!, 305–308 ~1996!.
9. E. Jakubczyk, Z. Mandecki, and J. Filipecki, “Quantum-chemical estimations of Fe-Co-Si-B metallic glasses,” J. Non-Cryst. Solids 192–193, 509–513 ~1995!.
10. M. J. Frisch, G. W. Trucks, H. W. Schlegel, P. M. W. Gill, B. G.Johnson, M. W. Wong, J. B. Foresman, M. A. Robb, M. Head-Gordon, E. S. Replogle, R. Gomperts, J. L. Andres, K. Ragh-vachari, J. S. Binkley, C. Gonzales, R. L. Martin, D. J. Fox,D. J. Defrees, J. Baker, J. J. P. Steart, and J. A. Pople, GAUS-SIAN 94, Rev. C3 ~Gaussian, Inc., Pittsburgh, Pennsylvania,1994!.
11. R. Boyd, Nonlinear Optics ~Academic, New York, 1992!.12. P. Allcock and D. L. Andrews, “Six-wave mixing secular reso-
nances in a higher-order mechanism for second-harmonic gen-eration,” J. Phys. B 30, 3731–3742 ~1997!.
13. D. L. Andrews, “Modern nonlinear optics,” Adv. Chem. Phys.85, 545–552 ~1993!.
14. I. V. Kityk, M. Matusiewicz, J. Kasperczyk, and M. Piasecki,“Nonlinear optical investigations of domains in Hg-Ba-Ca-Cu-O crystals,” Ferroelectrics 191, 147–151 ~1997!.
20 August 1999 y Vol. 38, No. 24 y APPLIED OPTICS 5167
