magnetization-induced second- and third-harmonic generation in magnetic thin films and nanoparticles

138 J. Opt. Soc. Am. B/Vol. 22, No. 1 /January 2005 Aktsipetrov et al.

Magnetization-induced second- andthird-harmonic generation

in magnetic thin films and nanoparticles

Oleg A. Aktsipetrov, Tatyana V. Murzina, Evgeniya M. Kim, Ruslan V. Kapra, and Andrey A. Fedyanin

Department of Physics, Moscow State University, 119992 Moscow, Russia

Mitsuteru Inoue

Department of Electrical and Electronic Engineering, Toyohashi University of Technology, Toyohashi 441-8580,Japan

Anatoliy F. Kravets

Institute of Magnetism, National Academy of Sciences of Ukraine, Kiev, 03680 Ukraine

Svetlana V. Kuznetsova, Mikhail V. Ivanchenko, and Victor G. Lifshits

Institute of Automation and Control Processes, 690041 Vladivostok, Russia

Received June 4, 2004; revised manuscript received September 13, 2004; accepted September 13, 2004

The results of our recent experimental studies of magnetization-induced second- and third-order nonlinear op-tical effects in magnetic nanostructures are surveyed. Magnetization-induced variations of the intensity, thepolarization state, and the relative phase of the second-harmonic wave are studied in magnetic nanogranularfilms, self-assembling films with garnet nanoparticles, thin magnetic metal films, and Langmuir–Blodgettfilms containing rare-earth ions. The nonlinear magneto-optical Kerr effect (NOMOKE) in second-harmonicgeneration (SHG) from thin magnetic and granular films is shown to exceed the linear magneto-optical Kerreffect by at least 1 order of magnitude. Magnetization-induced optical third-harmonic generation (THG) isobserved in thin magnetic metal films and nanogranular films. The NOMOKE in THG from these magneticnanostructures appears to be of the same order of magnitude as the second-order NOMOKE in SHG. TheNOMOKE magnetic contrast in the THG intensity is up to ;0.1 in CoxAg(12x) nanogranular films. For theTHG wave, the magnetization-induced rotation of polarization is up to 10° in thin Fe(110) films, and the rela-tive phase shift is up to 70° in thin Co films. The studies of the magnetization-induced quadratic and cubicnonlinear-optical effects show the interconnection between the magnetic, structural, and magneto-optical prop-erties of magnetic nanomaterials. © 2005 Optical Society of America

OCIS codes: 190.4350, 160.3820, 190.3270.

1. INTRODUCTIONOptical second-harmonic generation (SHG) is one of themost intensively studied phenomena in nonlinear opticsof nanostructures and microstructures over the past twodecades.1–3 Interest in SHG stems from a unique sensi-tivity of this probe to structural, electronic, magnetic, fer-roelectrics, etc. properties of surfaces, buried interfaces,nanostructures, and microstructures. This unusuallyhigh sensitivity comes about because SHG is forbidden inthe bulk of centrosymmetric materials in the electric di-pole approximation.4 On the other hand, the lack of in-version symmetry at interfaces and in nanostructures al-lows us to probe them by means of second-order nonlinearoptical effects, such as SHG and sum-frequencygeneration.5

Another domain of the nonlinear optics of interfacesand nanostructures appears as the break of the structuralinversion symmetry is combined with the broken time-

0740-3224/2005/010138-10$15.00 ©

reversal symmetry in magnetic materials. The fact thatmagnetization is an axial vector does not break the inver-sion symmetry in centrosymmetric materials, but it doesbreak the time-reversal symmetry. Thus the bulk of acentrosymmetric magnetic material does not contribute tothe magnetization-induced SHG (MSHG) in the dipole ap-proximation. However, the combination of the magneti-zation with the lack of inversion symmetry creates thenonlinear magneto-optical sources with proper localiza-tion at surfaces and in nanostructures. Owing to thiscombination, MSHG becomes an extremely sensitiveprobe of thin magnetic films and nanostructures.6–8

This pronounced surface sensitivity of the MSHG probekept magnetization-induced effects in third-order nonlin-ear optical phenomena for a long time in shadow. How-ever, third-harmonic generation (THG) and its magneto-optical analog; magnetization-induced THG (MTHG),seem to be very capable of probing magnetism and elec-

2005 Optical Society of America

Aktsipetrov et al. Vol. 22, No. 1 /January 2005 /J. Opt. Soc. Am. B 139

tronic properties in nanostructures. Moreover, theMTHG probe provides complementary information for theMSHG characterization.

Study of nonlinear magneto-optics dates back to themiddle 1980s, when the MSHG was predicted for thebulk9 and surface10 of magnetic materials. The experi-mental observation of the MSHG dates to 1988, as thenonlinear magneto-optical Kerr effect (NOMOKE) andnonlinear-optical Faraday effect in MSHG were observedin thin magnetic garnet films.11,12 NOMOKE in SHGfrom atomically clean surfaces of magnetic single crystalswas observed in Ref. 13. Later, other classes of magneticcomposite materials were involved in nonlinear magneto-optics: MSHG in magnetic multilayer structures,14–16

magnetic nanogranular alloys,17,18 and films containingmagnetic nanoparticles.19 Recently MTHG was observedin nanogranular films exhibiting giantmagnetoresistance,20 garnet magnetophotonic crystals,21

and thin garnet films.22 MSHG in garnet magnetophoto-nic crystals was observed and studied in a series ofpapers.23–27 The SHG optical diffraction in magneticgarnet films with the stripe structure (which can be con-sidered, in some sense, as magnetophotonic crystals) wasalso studied recently.28

Apart from studies of nanostructured and microstruc-tured magnetic materials, magnetization-induced SHGprobes have found broad applications in the characteriza-tion of bulk magnetic materials: rare-earth garnets,29

rare-earth manganites,30 Cr2O3 ,31 NiO,32 etc.In this paper, the results of systematic studies of

magnetization-induced second- and third-order nonlinearoptical effects in magnetic nanostructures, such as nan-ogranular magnetic films, self-assembled polymer filmscontaining yttrium iron-garnet nanoparticles, thin metal-lic magnetic films, and Gd-containing Langmuir–Blodgettfilms, are presented. The paper is organized as follows.Section 2 is devoted to general aspects of the phenomeno-logical description of the nonlinear magneto-optical re-sponse in magnetic materials. Section 3 contains the re-sults of the experimental studies of nonlinear magneto-optical effects in magnetic nanostructures.

2. PHENOMENOLOGICAL DESCRIPTIONA. Magnetization-Induced Nonlinear Susceptibilitiesand Nonlinear PolarizationThe description of the MSHG is based on the introductionof magnetization-dependent second- and third-order sus-ceptibilities, x (2)/(3)(M), that can be divided into twoparts. The first one is an even function of the magneti-zation M and coincides with the nonmagnetic crystallo-graphic susceptibility: x (2)/(3)even(M) 5 x (2)/(3)cryst. Thesecond part of x (2)/(3)(M) is an odd function of M:x (2)/(3)odd(M) 5 2x (2)/(3)odd(2M). Thus the nonlinearpolarization at the second-harmonic (SH) and third-harmonic (TH) wavelengths, which are the sources of themagnetization-induced SH and TH waves, are given, re-spectively, by

PNL~2v, M! 5 @ x~2 !cryst 1 x~2 !odd~M !#:E~v!E~v!,

PNL~3v, M! 5 @ x~3 !cryst

1 x~3 !odd~M !#]E~v!E~v!E~v!,

(2.1)

where E(v) is the fundamental wave with the frequencyv.

To explain a strong Faraday and Kerr rotation of polar-ization of the SH wave, one should consider an appear-ance of the s-polarized SH wave in magnetized materialthat is forbidden in a nonmagnetic material for the propercombination of polarizations of the fundamental and SHwaves. For example, nonmagnetic quadratic susceptibil-ity [crystallographic term in Eq. (2.1) with even paritywith respect to magnetization] of in-plane isotropic mate-rials possesses three independent nonzero components:

xzzz~2 !cryst , xzxx

~2 !cryst 5 xzyy~2 !cryst , xxzx

~2 !cryst 5 xyzy~2 !cryst ,

where in the sample coordinate frame x and y are in-planeaxes, the z axis is normal to the sample, and the zx planeis the plane of incidence. These components are respon-sible for the p-polarized nonmagnetic SH wave, Ep(2v).For example,

Ep~2v! } xxzx~2 !crystEz~v!Ex~v! 1 ...,

where Ez(v) and Ex(v) are the corresponding compo-nents of the p-polarized fundamental field. Meanwhile,the nonmagnetic s-polarized SH wave is not allowed inisotropic materials. In contrast, a component of themagnetization-dependent quadratic susceptibility, for ex-ample xyzx

(2)odd(M), which appears in the longitudinal ge-ometry of magneto-optical Kerr effect, contributes to thes-polarized component of the nonlinear polarization andbrings about the appearance of the s-polarizedmagnetization-induced SH wave

Es~2v, M ! 5 Ey~2v, M ! } xyzx~2 !odd~M !Ez~v!Ex~v!,

and, as a consequence, causes the NOMOKE polarizationrotation. Thus the rotation angle of the SH wave polar-ization is given by

u2v 5 arctg@Es~2v, M !/Ep~2v!#

' 2arctg@xyzx~2 !odd~M !/xxzx

~2 !cryst#. (2.2)

The ratio of the magnetization-induced and nonmagneticquadratic susceptibilities in Eq. (2.2) can be a noticeablequantity, and u2v is typically more than 1 order of magni-tude larger than the linear magneto-optical Kerr rotation.

Intensity effects in MSHG and MTHG are character-ized quantitatively by the NOMOKE contrast:

r2v/3v 5 ~I2v/3v1M 2 I2v/3v

2M !/~I2v/3v1M 1 I2v/3v

2M !, (2.3)

where I2v/3v1M and I2v/3v

2M are the SHG and THG intensitiesfor opposite directions of the magnetization.

Contrary to the rotation of the SH wave polarization,magnetization-induced variations in the SHG intensityappear in the transversal geometry of the magneto-optical Kerr effect. The SHG intensity in the far-field re-gion from a magnetized noncentrosymmetric medium isgiven by

I2v~M! } uEcryst~2v! 1 Eodd~2v, M!u2, (2.4)


where Ecryst(2v) and Eodd(2v, M) are the SH fields gen-erated by the nonmagnetic and the magnetization-induced nonlinear polarizations, respectively. The opti-cal interference of the nonmagnetic (crystallographic) andmagnetization-induced (odd) terms in Exp. (2.4) results inthe appearance of cross-product terms in the intensity ofthe MSHG, which is odd in magnetization. This contri-bution to the SHG intensity is not supposed to be small,while odd terms in magnetization SH field, Eodd(2v, M),are much smaller than the contribution from the crystal-lographic susceptibility. This interference effect, calledinternal homodyne effect,6,19 can result in noticeablemagnetization-induced variations of the SHG and THGintensities.

The magnetic contrast r2v/3v can appear in absorbingmedia where the relative phase between the odd and crys-tallographic components of the susceptibility, w2v/3v , isdifferent from p/2. In this case, and for a relatively smallvalue of the term of susceptibility, which is odd in magne-tization, the magnetic contrast of the SHG intensity canbe expressed by

r2v,3v ' @2xeff~2 !/~3 !odd~M !cos~w2v/3v!#/xeff

~2 !/~3 !cryst .(2.5)

The relative value of the effective magnetic component ofthe nonlinear susceptibility tensor, xeff

(2)/(3)odd(M), can bededuced from the SHG/THG interferometry measure-ments when providing both the magnetic contrast r2v/3v

and the relative phases w2v/3v .

B. Internal Homodyne EffectIn this section, the mechanism of the homodyne enhance-ment is applied to intrinsically weak magnetization-induced effects in SHG (or THG). A simple phenomeno-logical model of internal homodyne in magnetization-induced effects in SHG takes into account theinterference of strong reference (crystallographic) SHfields and magnetization-induced SH fields, each gener-ated in the bulk and at the surface of a magnetic material.The SHG intensity in the far-field region from a semi-infinite medium is given by

I2v } uES~2v! 1 EB~2v!u2, (2.6)

where ES(2v) and EB(2v) are the SH fields irradiated bynonlinear polarizations localized at the surface and in thebulk of the sample, respectively. As was mentioned inSubsection 2.A, the nonlinear polarization in magneticmaterials consists of nonmagnetic (crystallographic) andmagnetization-induced components, both of the surfaceand the bulk localization. The ith components of the SHfields generated by the surface and the bulk are given by

EiS~2v, M ! } E

Dz@Pi

S~z8, 2v!

1 PiS~z8, 2v, M !#G0~z, z8!dz8

5 g0@x ijk~2 !S 1 exp~iw S!x ijk

~2 !S~M !#Ej~v!Ek~v!,

EiB~2v, M ! 5 E

0

`

Gij~z, z8!@PjB~z8, 2v!

1 PjB~z8, 2v, M !#dz8

5i

DkAij@x jkl

~2 !B

1 exp~iw B!x jkl~2 !B~M !#Ek~v!El~v!,

(2.7)

where PiS(2v), Pi

S(2v, M), PjB(z8, 2v), Pj

B(z8, 2v, M),and x ijk

(2)S , x ijkl(2)S(M), x jkl

(2)B , x jklm(2)B (M) are the ith compo-

nents of the surface and bulk, nonmagnetic, andmagnetization-induced nonlinear polarizations and ten-sor components of second-order susceptibilities, respec-tively; f S, f B are the relative phases between the corre-sponding nonmagnetic and magnetization-inducedpolarizations; G0(z, z8) ; d (z 2 z8) and Gij(z, z8) arethe tensor Green functions for the surface and bulk non-linear polarizations, respectively; Dz is the subsurfacelayer where the surface nonlinear polarization is localizedand over which the integration is performed; g0 is a nu-merical factor that does not change the phase of the sur-face SH field; the components of tensor A 5 iAiji are realconstants for a transparent film; Dk 5 2kv 2 k2v is thephase mismatch; and kv and k2v are the fundamentaland SH wave vectors, respectively. For the reflection ge-ometry of the MSHG experiment (NOMOKE measure-ments) the phase mismatch is uDku ; ukvu, and in trans-mission geometry (nonlinear-optical Faraday effect) it isuDku ! ukvu. In transparent films, as w1 5 w2 5 p/2, Eq.(2.6) for the MSHG intensity takes the form

I2v~M!`uE~2v, M!u2

5 Ug0@ES~2v! 1 iES~2v, M!# 1i

DkA@EB~2v!

1 iEB~2v, M!#U2

} UH g0@x ikl~2 !S 1 ix ikl

~2 !S~M !# 1i

DkAij@x jkl

~2 !B

1 ix jkl~2 !B~M !#J Ek~v!El~v!U2

. (2.8)

It follows from Eq. (2.8) that variations of the SHG in-tensity with odd parity in magnetization are determinedby the interference of MSH fields, and those that are in-dependent from magnetization are described by effectivesurface–bulk, ;xeff

(2)Sxeff(2)B(M), and surface–surface,

;xeff(2)Sxeff

(2)S(M), homodyne cross products. Neither ofthese cross terms are supposed to be small, despite intrin-


sically small values of magnetization-induced suscepti-bilities, whereas nonmagnetic (crystallographic) suscepti-bilities are relatively large.

The internal homodyne effect has been considered herefor the two specific cases of MSHG and for semi-infinitemagnetic material. Generalization of this approach onMTHG is straightforward; the bulk localized third-ordernonlinear polarization from Eq. (2.6) should be introducedin the second part of Eq. (2.7), as one can ignore surfacecontributions to MTHG. The tensor components Aij inEq. (2.8) are complex for films of a finite thickness or forparticles of finite size. The complexity of Aij will bringabout the appearance of more cross-products, which areodd in magnetization, than the two aforementioned.

3. EXPERIMENTA. Experimental SetupNonlinear-optical experiments are performed with an out-put of a YAG:Nd13 laser at a 1064-nm wavelength, apulse duration of 15 ns, and a repetition rate of 25 Hz,with the intensity per pulse being 1–10 MW/cm2. TheSHG or THG radiation is detected in reflection from thesample by a photomultiplier tube (PMT) and gated elec-tronics. The fundamental and output polarizations areset and checked by Glan prisms, and the SHG(THG) ra-diation is filtered out by appropriate color filters, interfer-ence filters, or a monochromator. The experimentalsetup for the measurements of magnetization-inducedhyper-Rayleigh scattering (HRS) involves a Ti:sapphirelaser operating at a wavelength of 800 nm with a pulsewidth of about 80 fs, a repetition rate of 82 MHz, and anaverage power of 100 mW focused onto a spot of ;100 mmin diameter. For normalization of the SHG(THG) inten-sity over the laser fluency, a reference channel with ab-barium borate crystal as a reference SHG signal isused.

The azimuthal angular dependencies of the SHG(THG)intensity are measured by rotation of the sample with re-spect to the normal to its surface. For characterization ofthe nonlinear-optical scattering from the sample, i.e., tocheck for the specularly reflected or diffuse nonlinear-optical response, the HRS patterns are measured as thedetection system (PMT and related optical components)are rotated around the sample in the plane of incidence.

The magnetic measurements are performed under ap-plication to the samples of an in-plane dc magnetic fieldup to 2 kOe by means of an Fe–Nd permanent magnet.Figures 1(b) and 1(c) show the geometry of the applicationof the magnetic field for the transversal and the longitu-dinal magneto-optical Kerr effect. The direction of themagnetic field is changed by the azimuthal rotation ofmagnets.

For study of the magnetization-induced shift of therelative phase of the SH and TH waves, the interferomet-ric measurements are performed with an experimentalscheme, shown in Fig. 1(a). With this method, theSHG(THG) signal detected by a PMT is determined bythe interference of the SH(TH) waves originated from thesample and the reference. The reference of the SH(TH)wave is a 30-nm-thick indium-tin-oxide (ITO) film on afused quartz substrate. The measurements are carriedout as translating the ITO film along the direction of

propagation of the fundamental wave. The interferencepattern appears as a result of the relative phase shift be-tween the SH(TH) waves from the sample and the refer-ence owing to a dispersion of air at the fundamental andSH(TH) wavelengths.33 The magnetization-inducedphase shift of the SH(TH) waves from the sample can bededuced from the relative shift of the interference pat-terns measured for the opposite directions of the magneticfield.

B. MSHG and MTHG in Magnetic Thin-Metal FilmsThe studied samples are 200-nm-thick Co films, depositedon glass ceramic substrates by evaporation of Co at theresidual pressure less than 1024 Pa, and Fe(110) films100 nm and 200 nm thick epitaxially at the residual pres-sure of 1029 Pa grown on a Si(111) or GaAs substrate.The NOMOKE in SHG and THG is studied for the trans-versal magnetic field. In this case, the change of the di-rection of the dc-magnetic field can result in variations ofboth the SHG and THG intensity.10,20,21 The SHG(THG)interferometry patterns measured for the opposite direc-tions of the magnetic field provide both the magnetic con-trast in SHG(THG) intensity and the magnetization-induced shift of the relative phase, f2v/3v . This allowsus to deduce the ratio of odd components in M and crys-tallographic components of the nonlinear susceptibility inaccordance with Eq. (2.5).

Figure 2(a) shows the SHG interference patterns mea-sured for the opposite directions of the transversal mag-netic field for thin Co film and for the p-in, p-out combi-nation of polarizations. The magnetic contrast of theSHG intensity calculated from these dependencies is r2v

' 0.26, and the magnetization-induced shift of the SH

Fig. 1. (a) Scheme of the interferometry measurements forSHG(THG). Scheme of the magnetic field application for (b)transversal and (c) longitudinal magneto-optical Kerr effect.


interference patterns is ;10°. This allows for the esti-mation of the ratio of magnetization-induced and crystal-lographic components of the effective second-order sus-ceptibility, ux (2)odd(M)u/ux (2)crystu . 0.18.

The interference patterns measured for the case ofTHG are shown in Fig. 2(b). A large magnetization-induced phase shift up to 70° and a magnetic contrast ofthe THG intensity r3v ' 0.09 are found for thin Co film,which gives the ratio of the effective components of third-order magnetization-induced and crystallographic suscep-tibilities: ux (3)odd(M)u/ux (3)crystu . 0.5.

The analogous experiments performed for thin Fe filmsallow us to estimate the ratio of the effective second- andthird-order susceptibility components odd in M and crys-tallographic second- and third-order susceptibility compo-nents, ux (2)odd(M)u/ux (2)crystu . 0.3 and ux (3)odd(M)u/ux (3)crystu . 0.09. The magnetization-induced rotationangle of the TH wave polarization in Fe films is found tobe ;10°.

It is worth noting that the observed NOMOKE in bothSHG and THG exceeds the linear magneto-optical analogby at least 1 order of magnitude. This enhancement ofNOMOKE in SHG is discussed in Ref. 7 for magneticmetal surfaces and is attributed to the surface nature ofthe spin–orbit interaction. The same effect apparentlyplays the key role in large values of NOMOKE in THG forCo and Fe surfaces.

Fig. 2. Interferometry patterns for the (a) SHG and (b) THGfrom Co thin films and measured for the opposite directions ofthe magnetization.

C. MSHG and MTHG in Magnetic Nanogranular FilmsThe samples of CoxAg12x granular films of the composi-tion 6 , x , 80 vol. % and of 400-nm thickness are de-posited on glass ceramic substrates at room temperatureat the residual pressure 1024 Pa with a dual-electron-beam deposition system as described elsewhere.34 Thecomposition of the films is characterized by energy disper-sive x-ray analysis. The crystalline structure of the filmsis studied with the Bragg–Brentano x-ray diffractiontechnique and reveals the existence of the nanogranulesbetween 5 and 20 nm in size. These structures exhibitgiant magnetoresistance (GMR) effect at room tempera-ture. The GMR characterization is performed for thetransverse geometry of the applied magnetic field, the in-plane electrical current being perpendicular to the mag-netic field. The GMR coefficient is given by DR/R5 2 @R(0) 2 R(H)#/R(0), where R(H) is the resis-tance of the film in the magnetic field H and R(0) is theresistance for the demagnetized state. The dependenciesof DR/R on the content of the magnetic component inCoxAg12x films are shown in the dashed curves of Fig. 3.

Fig. 3. (a) NOMOKE contrast in SHG for the fundamentalwavelengths of 1064 nm and 800 nm; solid circles and triangles,respectively; (b) NOMOKE contrast in THG (solid circles) andSHG (open squares) for magnetic CoxAg(12x) nanogranular filmsas a function of the composition x. Magnetoresistance as a func-tion of the composition x is shown as open circles; the dashedcurve is a guide to the eye.


The increase of the GMR coefficient at a certain concen-tration of the magnetic component (x ' 0.3 for CoxAg12xfilms) is connected with the existence of nanogranularstructure, which results in an enhancement of the spin-dependent scattering of electrons under the application ofthe magnetic field. A correlation between the magnetore-sistance and NOMOKE in SHG from magnetic granularstructures, which manifests itself in a similar dependenceof the GMR and NOMOKE in SHG on the content of themagnetic material in the film x was observed recently.18

Figure 3(a) shows the dependencies of the magneticcontrast of the SHG intensity and the GMR coefficient onthe content of cobalt x in CoxAg12x films. The NOMOKEcontrast is measured for two wavelengths of the funda-mental radiation, 800 and 1064 nm, for the p-in, p-outcombination of polarizations of the fundamental and SHwaves. For both fundamental waves, a clear maximumof the NOMOKE contrast is observed at x for the range of0.25–0.3, which stays in a good agreement with the maxi-mum of the Co-content dependence of the GMR coeffi-cient. These data show that the local maximum of ther2v(x) is definitely observed for the Co concentrations x, 0.4/0.5 where isolated Co nanogranules exist, and theposition of local maximum of the r2v(x) is spectrally in-dependent.

Figure 3(b) shows r2v(x) for another series of magneticCoxAg12x films. These dependencies reveal a maximumof the SHG(THG) magnetic contrast at x ' 0.3 for MSHGand x ' 0.35 for MTHG, which is close to the concentra-tion values corresponding to the maximum of the GMRcoefficient. This is again proof that the concentration de-pendence of the NOMOKE contrast is spectrally indepen-dent. A steep rise of r2v/3v(x) in the vicinity of x' 0.45 should be attributed to the formation of ferromag-netic ordering in the granular structure at the percolationthreshold.

The magnetization-induced phase shift for the THGwave is found to be ;15° in Co0.31Ag0.69 granular film,which gives a ratio of the effective third-order compo-nents, ux (3)odd(M)u/ux (3)crystu . 0.16. Similar measure-ments for the magnetization-induced SHG give the ratioux (2)odd(M)u/ux (2)crystu . 0.08.

Fig. 4. SHG spectra for Co0.27Ag0.73 and Co0.19Ag0.81 granularfilms.

To study the SHG mechanism in CoxAg12x granularfilms, the SHG spectroscopic measurements are carriedout with the output of an optical-parametric-oscillator la-ser system tuning in the wavelength range of 490–670nm. Figure 4 shows the SHG intensity spectra measuredfor the films of the compositions of x ' 0.19 and x' 0.27. Both spectra reveal clear maxima in the vicinityof 620–640 nm, the spectral position of the maximum ofthe SHG intensity being redshifted for the film withlarger content of silver. These features of the SHG spec-tra are probably caused by the excitation of local surfaceplasmons in silver nanogranules at the Co–Ag interfaces.The numerical calculations of local surface plasmonsspectra in CoxAg12x granular films were performedrecently.18 The SHG spectra in Fig. 4 are in good agree-ment with the calculated ones.

Thus the NOMOKE in magnetic nanogranules is ob-served in both SHG and THG. The excitation of localsurface plasmons in nanogranular CoxAg12x films is re-corded by means of the SHG spectroscopy, which perhapsplays an important role in the correlation between GMRand NOMOKE in SHG and THG.

D. MSHG in Gd-Containing Langmuir–Blodgett FilmsIn this section, the nonlinear magneto-optical propertiesof magnetic superstructures consisting of two-dimensional layers of Gd ions in organic matrix are stud-ied by NOMOKE in SHG. The studied samples are su-perstructures, each period being formed by a monolayer ofGd ions sandwiched between two monolayers of stearicacetate. The superstructures consisting from 10 to 40periods are composed with the Langmuir–Blodgett (LB)technique from a water solution of Gd acetate. Figure5(a) shows a schematic view of the deposition procedure ofthe LB films.

The structural and morphological properties of Gd-containing LB films are characterized by x-ray diffractionand the anisotropic SHG probe. Figure 5(b) shows x-raydiffraction pattern that reveals sharp scattering peaks,which confirm the periodicity of Gd layers across thesuperstructures.35 Figure 5(c) shows the azimuthal an-gular dependence of the SHG intensity from the LB filmsfor the s-in, s-out combination of polarizations. This azi-muthal dependence exhibits (i) anisotropic two-fold modu-lation of the SHG intensity that is attributed to C2 sym-metry of LB superstructures and (ii) an isotropiccontribution independent from azimuthal angle. The lat-ter contribution, forbidden in homogeneous films,36 indi-cates that the SHG is observed in the form of hyper-Rayleigh scattering and is due to a random spatialinhomogeneity of linear and nonlinear-optical propertiesof Gd-containing LB films. Thus the SHG response fromGd-containing LB superstructures consists of the sum ofcoherent (anisotropic and specular) and incoherent (dif-fuse) components. The random inhomogeneity of the LBfilms is attributed to a two-dimensional islandlike mor-phology of Gd31 ion aggregates in Gd layers sandwichedbetween stearic acetate monolayers.

Figure 6(a) shows the MSHG polarization diagrams,i.e., the dependencies of the SHG intensity on the azi-muthal angle of the analyzer, measured for the longitudi-nal NOMOKE Gd-containing LB films of 10 periods thick.


Changing the direction of the applied magnetic field re-sults in a rotation of the polarization plane of the SHGwave to an angle of ;12° for the s-polarized fundamentalradiation. Figure 6(b) shows the SHG interference pat-terns measured in the longitudinal NOMOKE for the s-in,s-out polarization combination and for the opposite direc-tions of the magnetic field. The azimuthal position of thesample is set to the maximum of the SHG anisotropy,which gave the maximum of the coherent SHG compo-nent. In SHG interferometry measurements in partiallyinhomogeneous films, interference involves only this com-ponent of the SH wave from the sample. Themagnetization-induced phase shift of the SH wave fromthe film is ;115°. The magnetization-induced effect inthe SHG intensity from Gd-containing LB films is notpronounced.35 Meanwhile, the observed magnetization-induced variations of the polarization rotation angle andthe relative phase shift indicate a strong magnetic inter-action and ordering in Gd aggregates induced by the ex-

Fig. 5. (a) Schematic view of the deposition procedure of Gd-containing Langmuir–Blodgett films; (b) x-ray diffraction pat-tern from 50-layer-thick Gd-containing LB film; and (c) azi-muthal dependence of the SHG intensity for the s-in, s-outcombination of polarizations.

ternal magnetic field. However, hysteresis-type behavioris not observed for the polarization rotation angle and forthe phase shift as functions of magnetic field amplitude.This implies that the magnetic order in Gd islands is closeto a superparamagnetic state that is confirmed by recentmagnetic studies of Gd-containing LB films.37

E. Magnetization-Induced Hyper-Rayleigh Scatteringfrom YIG NanoparticlesThis section presents the results of the experimentalstudies of magnetization-induced SHG from the layer-by-layer (LBL) self-assembled films containing yttrium irongarnet (YIG) nanoparticles. A special emphasis is madeon the dependence of the SHG intensity on the number oflayers in LBL films as a discriminator between coherentSHG and HRS.19

The LBL films containing nanoparticles of YIG and 32nm in diameter are deposited by the self-assembling pro-cedure. Glass substrates are immersed in poly(dial-lyldimethylammonium chloride) (PDDA) and then in a

Fig. 6. (a) Polarization diagrams of the SHG intensity for thelongitudinal NOMOKE and (b) MSHG interference patterns forthe transversal NOMOKE measured in Gd-containing LB filmsfor the opposite directions of the external magnetic field.


beaker containing the YIG suspension in water. To formmultilayers, the cycle of PDDA and YIG adsorption is re-peated as many times as is necessary. The atomic forcemicroscope image of the surface of LBL film is shown inFig. 7(a), demonstrating the existence of individual par-ticles and their agglomerates of a size less than 100 nm.

The measurements of the azimuthal dependencies ofthe SHG intensity reveal the isotropy of both p- ands-polarized SHG components. The latter is the violationof the s,s-prohibition rule36 and is typical for HRS. Fig-ure 7(b) shows a diffuse SHG scattering pattern for a p-in,p-out combination of polarizations for 10-layered YIG-containing LBL film. This dependence shows a peak ofthe SHG intensity in the direction of the specular reflec-tion from the film and a broad peak with a maximum cen-tered at the normal to the sample. The latter is a mani-festation of HRS.

The dashed curve in Fig. 8, main panel, shows the de-pendence of the nonmagnetic SHG intensity on the num-ber of layers of LBL YIG-containing film for p-in and p-and s-out combinations of polarizations. In both cases,the dependencies of the SHG intensity on the number oflayers are close to a linear function, which is also an at-tribute of HRS.

In the case of the s-polarized SHG, the intensity tendsto zero with a decreasing number of YIG-containing lay-

Fig. 7. (a) Atomic force microscope image and (b) SHG scatter-ing pattern for the p-in, p-out combination of polarizations forthe 10-layer-thick LBL film containing YIG nanoparticles withsolid curve as a guide.

ers, which indicates that SHG originates only from YIG-containing layers, i.e., that there is no SHG (or HRS) sig-nal from the PDDA layers and from the substrate. Onthe contrary, the p-polarized SHG intensity tends to aconstant nonzero value, which should be attributed to thecontribution from the polymer sublayer and/or the sub-strate. This contribution is responsible for the specularSHG peak presented in Fig. 8. Thus the second-ordernonlinear response of YIG nanoparticles is proved to beincoherent SHG, i.e., hyper-Rayleigh scattering.

The magnetic properties of YIG nanoparticles are stud-ied in the geometry of the transversal NOMOKE. Thedependencies of the SHG intensity on the number of lay-ers measured for the opposite directions of the magneticfield are shown in the main panel of Fig. 8. These depen-dencies appear to be close to linear functions. The HRSmagnetic contrast is calculated from these linear depen-dencies for the p-in, p-out combination of polarizations,shown in Fig. 8, bottom inset, as a function of the numberof layers in the LBL films. One can see that within theexperimental accuracy r2v is constant, which stays inagreement with the expectations for the magnetic con-trast of HRS; this relative parameter is expected to be in-dependent from the number of scatterers.

The SHG intensity from YIG-containing films in the di-rection of specular reflection is given by Ia(N) 5 KaN1 IS , where the subscript a 5 0, 6 refers to differentpolarities or to the absence of the magnetic field, and IS isa coherent contribution of the polymer sublayer and theinterface. The linearity of the HRS intensity with re-spect to N allows us to relate the SHG intensity with thehyperpolarizability of an individual YIG nanoparticle g,g (M) ' g0 1 gM(M), where g0 and gM(M) are the non-magnetic and odd-in magnetization tensors of the hyper-polarizability of an individual nanoparticle. By analogy

Fig. 8. SHG intensity in LBL films containing YIG nanopar-ticles without the external magnetic field (triangles) and for theopposite directions of the magnetic field in the transversalNOMOKE (circles) (main panel). Top inset, the SHG intensityfor H 5 0 for p-in, s-out SHG; Bottom inset; NOMOKE contrastas a function of number of layers in LBL films containing YIGnanoparticles.


with Eq. (2.5), the HRS magnetic contrast is r2vHRS

} 2gM(M)/g0 . This contrast stems from the assump-tion that the HRS magnetic contrast is independent of thenumber of layers. The latter stays in agreement with theexperimental data described above. As a result of themeasurements, r2v

HRS . 0.15 and gM(M)/g0 . 0.08.A nonzero magnetic contrast in the SHG intensity from

LBL films containing YIG nanoparticles indicates that arelative phase between nonmagnetic and magnetization-induced terms in Eq. (2.2) for these films is not equal to90°. Apparently this is due to a resonance of the SHwave with the absorption band in spectra of the YIGnanoparticles. As a consequence, each of these terms hasreal and imaginary contributions that result in the ap-pearance of an odd term in the MSHG intensity owing tothe internal homodyne mechanism.

4. SUMMARYIn summary, the results of the performed experimentsshow the efficiency and the potentials of the nonlinear op-tical probes, MSHG and MTHG, for studying the magne-tism in magnetic thin films and nanostructures. Broadvarieties of magnetic nanomaterials reveal significantmagnetization-induced effects in second- and third-ordernonlinear optical response.

Specific details of nonlinear magneto-optical responseare related to the structural features of nanostructuresand to the type of magnetic ordering in their spin sys-tems; e.g., the ferromagnetic state of Co and Fe thin films,or super paramagnetic ordering in prepercolation granu-lar Co–Ag films and Gd islands in the Gd-containing LBfilms. Incoherent magnetization-induced SHG, i.e.,magnetization-induced HRS, is observed in nonlinearmagneto-optical studies of random arrays of magneticnanoparticles, such as self-assembling LBL films and Gdislands in the Gd-containing LB films.

Extension of conventional nonlinear magneto-optics re-stricted for decades to the MSHG studies, to the third-order nonlinear-optical effects, results in an observationof MTHG. Strong magnetization-induced effects in THG,observed for the transversal NOMOKE in thin metalfilms and in nanogranular systems, make the MTHG asensitive probe of the magnetic properties of nanostruc-tures. It is shown that owing to a different localization ofTHG as compared with the surface-sensitive SHG, MTHGprovides additional information about the behavior of thespin system in the bulk of nanoparticles that is comple-mentary to the characterization by the MSHG probe.Moreover, a comparative analysis of NOMOKE in SHGand THG seems to be accurate for the studies of the sur-face spin–orbit interaction.

Observations of magnetization-induced effects in SHGand THG with odd parity with respect to magnetizationshow the fundamental role of internal homodyne mecha-nism in magnitudes of nonlinear magneto-optical effects.

ACKNOWLEDGMENTSThe authors gratefully acknowledge helpful and stimulat-ing discussions with A. A. Nikulin. We thank G. B. Kho-mutov and N. Kotov for supplying the samples of LB and

LBL films. This work is supported in part by the Rus-sian Foundation for Basic Research (grants 04-02-16847,04-02-17059, and 03-02-39010), the Presidential Grant forLeading Russian Science Schools (1604.2003.2) and grant03-51-3784 of the International Association for the Pro-motion of Cooperation with Scientists from the Indepen-dent States of the Former Soviet Union (INTAS).

O. A. Aktsipetrov’s e-mail address is [email protected]; T.V. Murzina’s e-mail address is [email protected].

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magnetization-induced second- and third-harmonic generation in magnetic thin films and nanoparticles

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