Magnetization-induced second- and third-harmonic generation in magnetic thin films and nanoparticles
ABSTRACT The results of our recent experimental studies of magnetization-induced second- and third-order nonlinear optical effects in magnetic nanostructures are surveyed. Magnetization-induced variations of the intensity, the polarization state, and the relative phase of the second-harmonic wave are studied in magnetic nanogranular films, self-assembling films with garnet nanoparticles, thin magnetic metal films, and Langmuir-Blodgett films containing rare-earth ions. The nonlinear magneto-optical Kerr effect (NOMOKE) in second-harmonic generation (SHG) from thin magnetic and granular films is shown to exceed the linear magneto-optical Kerr effect by at least 1 order of magnitude. Magnetization-induced optical third-harmonic generation (THG) is observed in thin magnetic metal films and nanogranular films. The NOMOKE in THG from these magnetic nanostructures appears to be of the same order of magnitude as the second-order NOMOKE in SHG. The NOMOKE magnetic contrast in the THG intensity is up to ~0.1 in CoxAg(1-x) nanogranular films. For the THG wave, the magnetization-induced rotation of polarization is up to 10° in thin Fe(110) films, and the relative phase shift is up to 70° in thin Co films. The studies of the magnetization-induced quadratic and cubic nonlinear-optical effects show the interconnection between the magnetic, structural, and magneto-optical properties of magnetic nanomaterials.
- [show abstract] [hide abstract]
ABSTRACT: In recent years, optical second-harmonic generation has matured into a versatile and powerful technique for probing the electronic and structural properties of buried solid–solid interfaces. In particular Si/SiO2 interfaces have been studied extensively and significant progress has been made in understanding the sensitivity of second-harmonic generation to interface defects, steps, strain, roughness, electric fields, carrier dynamics, and chemical modifications. The macroscopic and microscopic aspects of the second-order nonlinear optical effects at buried semiconductor interfaces have been treated theoretically by first-principles calculations and semi-empirical models. It is the aim of this review article to present a comprehensive overview of recent accomplishments, current understandings and future directions in this field.Surface Science Reports 11/1999; 35(s 3–4):75–161. · 15.33 Impact Factor
- physica status solidi (a) 01/1999; 175(1):153-167. · 1.21 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: In this article previous and recent results of our nonlinear optical studies of low-dimensional structures are surveyed. Size effect in the optical second-harmonic generation (SHG) from Ag nanocrystals in island films and CdSe quantum dots in glass matrices as well as thermo- and DC-electric-field-induced effects in SHG from SiSiO2 multiple quantum wells (MQWs) on Si substrate are studied experimentally and theoretically. Essential (by several orders of magnitude) enhancement of quadratic optical response upon decrease in the particle size is observed for both Ag nanocrystals and CdSe quantum dots. Regular oscillations in the second-harmonic intensity measured as functions of temperature and applied DC electric field are observed for MQWs. It is shown that the size effect for metal nanocrystals can result from the fluctuations of the particle size breaking the local inversion symmetry. Another mechanism studied (based on concepts of dynamic chaos) describes the observed size effects for both metal and semiconductor particles. The dependence of the second-harmonic intensity on the SiO2 layer thickness in MQWs is described with taking into account the retardation of the second-harmonic radiation in MQWs, whereas the thermoinduced effect is interpreted as resulting from the optical interference in the MQWs substrate having thickness dependent on temperature (due to the thermal expansion). A possible approach to explaining the observed electroinduced effect in MQWs is also discussed.Surface Science 01/1995; · 1.84 Impact Factor
Magnetization-induced second- and
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
Department of Electrical and Electronic Engineering, Toyohashi University of Technology, Toyohashi 441-8580,
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.
polarization state, and the relative phase of the second-harmonic wave are studied in magnetic nanogranular
films, self-assembling films with garnet nanoparticles, thin magnetic metal films, and Langmuir–Blodgett
films containing rare-earth ions.The nonlinear magneto-optical Kerr effect (NOMOKE) in second-harmonic
generation (SHG) from thin magnetic and granular films is shown to exceed the linear magneto-optical Kerr
effect by at least 1 order of magnitude.Magnetization-induced optical third-harmonic generation (THG) is
observed in thin magnetic metal films and nanogranular films.
nanostructures appears to be of the same order of magnitude as the second-order NOMOKE in SHG.
NOMOKE magnetic contrast in the THG intensity is up to ?0.1 in CoxAg(1?x)nanogranular films.
THG 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 cubic
nonlinear-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.
Magnetization-induced variations of the intensity, the
The NOMOKE in THG from these magnetic
Optical second-harmonic generation (SHG) is one of the
most intensively studied phenomena in nonlinear optics
of nanostructures and microstructures over the past two
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.
high sensitivity comes about because SHG is forbidden in
the bulk of centrosymmetric materials in the electric di-
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 nonlinear
Another domain of the nonlinear optics of interfaces
and nanostructures appears as the break of the structural
inversion symmetry is combined with the broken time-
reversal symmetry in magnetic materials.
magnetization is an axial vector does not break the inver-
sion symmetry in centrosymmetric materials, but it does
break the time-reversal symmetry.
centrosymmetric magnetic material does not contribute to
the magnetization-induced SHG (MSHG) in the dipole ap-
proximation.However, the combination of the magneti-
zation with the lack of inversion symmetry creates the
nonlinear magneto-optical sources with proper localiza-
tion at surfaces and in nanostructures.
combination, MSHG becomes an extremely sensitive
probe of thin magnetic films and nanostructures.6–8
This pronounced surface sensitivity of the MSHG probe
kept magnetization-induced effects in third-order nonlin-
ear optical phenomena for a long time in shadow.
ever, third-harmonic generation (THG) and its magneto-
optical analog; magnetization-induced THG (MTHG),
seem to be very capable of probing magnetism and elec-
The fact that
Thus the bulk of a
Owing to this
138 J. Opt. Soc. Am. B/Vol. 22, No. 1/January 2005Aktsipetrov et al.
0740-3224/2005/010138-10$15.00© 2005 Optical Society of America
tronic properties in nanostructures.
MTHG probe provides complementary information for the
Study of nonlinear magneto-optics dates back to the
middle 1980s, when the MSHG was predicted for the
bulk9and surface10of magnetic materials.
mental observation of the MSHG dates to 1988, as the
nonlinear magneto-optical Kerr effect (NOMOKE) and
nonlinear-optical Faraday effect in MSHG were observed
in thin magnetic garnet films.11,12
from atomically clean surfaces of magnetic single crystals
was observed in Ref. 13. Later, other classes of magnetic
composite materials were involved in nonlinear magneto-
optics: MSHG in magnetic multilayer structures,14–16
magnetic nanogranular alloys,17,18and films containing
Recently MTHG was observed
magnetoresistance,20garnet magnetophotonic crystals,21
and thin garnet films.22
MSHG in garnet magnetophoto-
nic crystals was observed and studied in a series of
The SHG optical diffraction in magnetic
garnet films with the stripe structure (which can be con-
sidered, in some sense, as magnetophotonic crystals) was
also studied recently.28
Apart from studies of nanostructured and microstruc-
tured magnetic materials, magnetization-induced SHG
probes have found broad applications in the characteriza-
tion of bulk magnetic materials:
In this paper, the results of systematic studies of
magnetization-induced second- and third-order nonlinear
optical effects in magnetic nanostructures, such as nan-
ogranular magnetic films, self-assembled polymer films
containing yttrium iron-garnet nanoparticles, thin metal-
lic magnetic films, and Gd-containing Langmuir–Blodgett
films, 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.
sults of the experimental studies of nonlinear magneto-
optical effects in magnetic nanostructures.
NOMOKE in SHG
Section 3 contains the re-
2. PHENOMENOLOGICAL DESCRIPTION
A. Magnetization-Induced Nonlinear Susceptibilities
and Nonlinear Polarization
The description of the MSHG is based on the introduction
of magnetization-dependent second- and third-order sus-
ceptibilities, ? ˆ(2)/(3)(M), that can be divided into two
parts.The first one is an even function of the magneti-
zation M and coincides with the nonmagnetic crystallo-
? ˆ(2)/(3)even(M) ? ? ˆ(2)/(3)cryst.
second part of ? ˆ(2)/(3)(M) is an odd function of M:
? ˆ(2)/(3)odd(M) ? ?? ˆ(2)/(3)odd(?M).
polarization at the second-harmonic (SH) and third-
harmonic (TH) wavelengths, which are the sources of the
magnetization-induced SH and TH waves, are given, re-
Thus the nonlinear
PNL?2?, M? ? ?? ˆ?2?cryst? ? ˆ?2?odd?M??:E???E???,
PNL?3?, M? ? ?? ˆ?3?cryst
? ? ˆ?3?odd?M??]E???E???E???,
where E(?) is the fundamental wave with the frequency
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 material
that is forbidden in a nonmagnetic material for the proper
combination of polarizations of the fundamental and SH
waves. For example, nonmagnetic quadratic susceptibil-
ity [crystallographic term in Eq. (2.1) with even parity
with respect to magnetization] of in-plane isotropic mate-
rials possesses three independent nonzero components:
where in the sample coordinate frame x and y are in-plane
axes, the z axis is normal to the sample, and the zx plane
is the plane of incidence.These components are respon-
sible for the p-polarized nonmagnetic SH wave, Ep(2?).
Ep?2?? ? ?xzx
?2?crystEz???Ex??? ? ...,
where Ez(?) and Ex(?) are the corresponding compo-
nents of the p-polarized fundamental field.
the nonmagnetic s-polarized SH wave is not allowed in
isotropic materials. In contrast, a component of the
magnetization-dependent quadratic susceptibility, for ex-
ometry of magneto-optical Kerr effect, contributes to the
s-polarized component of the nonlinear polarization and
brings aboutthe appearance
magnetization-induced SH wave
(2)odd(M), which appears in the longitudinal ge-
Es?2?, M? ? Ey?2?, M? ? ?yzx
and, as a consequence, causes the NOMOKE polarization
rotation.Thus the rotation angle of the SH wave polar-
ization is given by
?2?? arctg?Es?2?, M?/Ep?2???
The ratio of the magnetization-induced and nonmagnetic
quadratic susceptibilities in Eq. (2.2) can be a noticeable
quantity, and ?2?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:
for opposite directions of the magnetization.
Contrary to the rotation of the SH wave polarization,
magnetization-induced variations in the SHG intensity
appear in the transversal geometry of the magneto-
optical Kerr effect. The SHG intensity in the far-field re-
gion from a magnetized noncentrosymmetric medium is
I2??M? ? ?Ecryst?2?? ? Eodd?2?, M??2,
are the SHG and THG intensities
Aktsipetrov et al.
Vol. 22, No. 1/January 2005/J. Opt. Soc. Am. B139
where Ecryst(2?) and Eodd(2?, M) are the SH fields gen-
erated by the nonmagnetic and the magnetization-
induced nonlinear polarizations, respectively.
cal interference of the nonmagnetic (crystallographic) and
magnetization-induced (odd) terms in Exp. (2.4) results in
the appearance of cross-product terms in the intensity of
the MSHG, which is odd in magnetization.
bution to the SHG intensity is not supposed to be small,
while odd terms in magnetization SH field, Eodd(2?, M),
are much smaller than the contribution from the crystal-
lographic susceptibility. This interference effect, called
internal homodyne effect,6,19can result in noticeable
magnetization-induced variations of the SHG and THG
The magnetic contrast ?2?/3?can appear in absorbing
media where the relative phase between the odd and crys-
tallographic components of the susceptibility, ?2?/3?, is
different from ?/2. In this case, and for a relatively small
value of the term of susceptibility, which is odd in magne-
tization, the magnetic contrast of the SHG intensity can
be expressed by
The relative value of the effective magnetic component of
the nonlinear susceptibility tensor, ? ˆeff
deduced from the SHG/THG interferometry measure-
ments when providing both the magnetic contrast ?2?/3?
and the relative phases ?2?/3?.
(2)/(3)odd(M), can be
B. Internal Homodyne Effect
In this section, the mechanism of the homodyne enhance-
ment is applied to intrinsically weak magnetization-
induced effects in SHG (or THG).
logical model of internal homodyne in magnetization-
interference of strong reference (crystallographic) SH
fields 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
A simple phenomeno-
I2?? ?ES?2?? ? EB?2???2,(2.6)
where ES(2?) and EB(2?) are the SH fields irradiated by
nonlinear polarizations localized at the surface and in the
bulk of the sample, respectively.
Subsection 2.A, the nonlinear polarization in magnetic
materials consists of nonmagnetic (crystallographic) and
magnetization-induced components, both of the surface
and the bulk localization.The ith components of the SH
fields generated by the surface and the bulk are given by
As was mentioned in
S?2?, M? ??
S?z?, 2?, M??G0?z, z??dz?
B?2?, M? ??
B?z?, 2?, M??dz?
magnetization-induced nonlinear polarizations and ten-
sor components of second-order susceptibilities, respec-
tively; ?S, ?Bare the relative phases between the corre-
polarizations; G0(z, z?) ? ? (z ? z?) and Gij(z, z?) are
the tensor Green functions for the surface and bulk non-
linear polarizations, respectively; ?z is the subsurface
layer where the surface nonlinear polarization is localized
and over which the integration is performed; g0is a nu-
merical factor that does not change the phase of the sur-
face SH field; the components of tensor Aˆ? ?Aij? are real
constants for a transparent film; ?k ? 2k?? k2?is the
phase mismatch; and k?and k2?are the fundamental
and SH wave vectors, respectively.
ometry of the MSHG experiment (NOMOKE measure-
ments) the phase mismatch is ??k? ? ?k??, and in trans-
mission geometry (nonlinear-optical Faraday effect) it is
??k? ? ?k??.In transparent films, as ?1? ?2? ?/2, Eq.
(2.6) for the MSHG intensity takes the form
S(2?, M), Pj
B(z?, 2?), Pj
(2)B(M) are the ith compo-
B(z?, 2?, M),
For the reflection ge-
??g0?ES?2?? ? iES?2?, M?? ?
? iEB?2?, M???
It follows from Eq. (2.8) that variations of the SHG in-
tensity with odd parity in magnetization are determined
by the interference of MSH fields, and those that are in-
dependent from magnetization are described by effective
these cross terms are supposed to be small, despite intrin-
(2)S(M), homodyne cross products.
140J. Opt. Soc. Am. B/Vol. 22, No. 1/January 2005Aktsipetrov et al.
sically small values of magnetization-induced suscepti-
bilities, whereas nonmagnetic (crystallographic) suscepti-
bilities are relatively large.
The internal homodyne effect has been considered here
for the two specific cases of MSHG and for semi-infinite
magnetic material.Generalization of this approach on
MTHG is straightforward; the bulk localized third-order
nonlinear polarization from Eq. (2.6) should be introduced
in the second part of Eq. (2.7), as one can ignore surface
contributions to MTHG.The tensor components Aijin
Eq. (2.8) are complex for films of a finite thickness or for
particles of finite size. The complexity of Aijwill bring
about the appearance of more cross-products, which are
odd in magnetization, than the two aforementioned.
A. Experimental Setup
Nonlinear-optical experiments are performed with an out-
put of a YAG:Nd?3laser at a 1064-nm wavelength, a
pulse duration of 15 ns, and a repetition rate of 25 Hz,
with the intensity per pulse being 1–10 MW/cm2.
SHG or THG radiation is detected in reflection from the
sample by a photomultiplier tube (PMT) and gated elec-
tronics.The fundamental and output polarizations are
set and checked by Glan prisms, and the SHG(THG) ra-
diation is filtered out by appropriate color filters, interfer-
ence filters, or a monochromator.
setup for the measurements of magnetization-induced
hyper-Rayleigh scattering (HRS) involves a Ti:sapphire
laser operating at a wavelength of 800 nm with a pulse
width of about 80 fs, a repetition rate of 82 MHz, and an
average power of 100 mW focused onto a spot of ?100 ?m
in diameter.For normalization of the SHG(THG) inten-
sity over the laser fluency, a reference channel with a
?-barium borate crystal as a reference SHG signal is
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 of
the nonlinear-optical scattering from the sample, i.e., to
check for the specularly reflected or diffuse nonlinear-
optical response, the HRS patterns are measured as the
detection 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 field
up to 2 kOe by means of an Fe–Nd permanent magnet.
Figures 1(b) and 1(c) show the geometry of the application
of the magnetic field for the transversal and the longitu-
dinal magneto-optical Kerr effect.
magnetic field is changed by the azimuthal rotation of
For study of the magnetization-induced shift of the
relative phase of the SH and TH waves, the interferomet-
ric measurements are performed with an experimental
scheme, shown in Fig. 1(a).
SHG(THG) signal detected by a PMT is determined by
the interference of the SH(TH) waves originated from the
sample and the reference. The reference of the SH(TH)
wave is a 30-nm-thick indium-tin-oxide (ITO) film on a
fused quartz substrate. The measurements are carried
out as translating the ITO film along the direction of
The direction of the
With this method, the
propagation of the fundamental wave.
pattern 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 and
phase shift of the SH(TH) waves from the sample can be
deduced from the relative shift of the interference pat-
terns measured for the opposite directions of the magnetic
B. MSHG and MTHG in Magnetic Thin-Metal Films
The studied samples are 200-nm-thick Co films, deposited
on glass ceramic substrates by evaporation of Co at the
residual pressure less than 10?4Pa, and Fe(110) films
100 nm and 200 nm thick epitaxially at the residual pres-
sure of 10?9Pa 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 of
both the SHG and THG intensity.10,20,21
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, ?2?/3?.
us to deduce the ratio of odd components in M and crys-
tallographic components of the nonlinear susceptibility in
accordance 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 the
SHG intensity calculated from these dependencies is ?2?
? 0.26, and the magnetization-induced shift of the SH
transversal and (c) longitudinal magneto-optical Kerr effect.
(a) Scheme of the interferometry measurements for
Scheme of the magnetic field application for (b)
Aktsipetrov et al.
Vol. 22, No. 1/January 2005/J. Opt. Soc. Am. B 141
interference patterns is ?10°.
mation of the ratio of magnetization-induced and crystal-
lographic components of the effective second-order sus-
ceptibility, ??(2)odd(M)?/?? ˆ(2)cryst? ? 0.18.
The interference patterns measured for the case of
THG are shown in Fig. 2(b).
induced phase shift up to 70° and a magnetic contrast of
the THG intensity ?3?? 0.09 are found for thin Co film,
which gives the ratio of the effective components of third-
order magnetization-induced and crystallographic suscep-
??(3)odd(M)?/??(3)cryst? ? 0.5.
The analogous experiments performed for thin Fe films
allow us to estimate the ratio of the effective second- and
third-order susceptibility components odd in M and crys-
tallographic second- and third-order susceptibility compo-
??(2)odd(M)?/??(2)cryst? ? 0.3
??(3)cryst? ? 0.09.The magnetization-induced rotation
angle of the TH wave polarization in Fe films is found to
It is worth noting that the observed NOMOKE in both
SHG and THG exceeds the linear magneto-optical analog
by at least 1 order of magnitude.
NOMOKE in SHG is discussed in Ref. 7 for magnetic
metal surfaces and is attributed to the surface nature of
the spin–orbit interaction.
plays the key role in large values of NOMOKE in THG for
Co and Fe surfaces.
This allows for the esti-
A large magnetization-
This enhancement of
The same effect apparently
C. MSHG and MTHG in Magnetic Nanogranular Films
The samples of CoxAg1?xgranular films of the composi-
tion 6 ? x ? 80 vol.% and of 400-nm thickness are de-
posited on glass ceramic substrates at room temperature
at the residual pressure 10?4Pa with a dual-electron-
beam deposition system as described elsewhere.34
composition of the films is characterized by energy disper-
sive x-ray analysis. The crystalline structure of the films
is studied with the Bragg–Brentano x-ray diffraction
technique and reveals the existence of the nanogranules
between 5 and 20 nm in size.
giant magnetoresistance (GMR) effect at room tempera-
ture. The GMR characterization is performed for the
transverse geometry of the applied magnetic field, the in-
plane electrical current being perpendicular to the mag-
netic field.The GMR coefficient is given by ?R/R
?? ?R(0) ? R(H)?/R(0), where R(H) is the resis-
tance of the film in the magnetic field H and R(0) is the
resistance for the demagnetized state. The dependencies
of ?R/R on the content of the magnetic component in
CoxAg1?xfilms are shown in the dashed curves of Fig. 3.
These structures exhibit
from Co thin films and measured for the opposite directions of
Interferometry patterns for the (a) SHG and (b) THG
wavelengths of 1064 nm and 800 nm; solid circles and triangles,
respectively; (b) NOMOKE contrast in THG (solid circles) and
SHG (open squares) for magnetic CoxAg(1?x)nanogranular films
as a function of the composition x.
tion of the composition x is shown as open circles; the dashed
curve is a guide to the eye.
(a) NOMOKE contrast in SHG for the fundamental
Magnetoresistance as a func-
142 J. Opt. Soc. Am. B/Vol. 22, No. 1/January 2005Aktsipetrov et al.
The increase of the GMR coefficient at a certain concen-
tration of the magnetic component (x ? 0.3 for CoxAg1?x
films) is connected with the existence of nanogranular
structure, which results in an enhancement of the spin-
dependent scattering of electrons under the application of
the magnetic field. Acorrelation between the magnetore-
sistance and NOMOKE in SHG from magnetic granular
structures, which manifests itself in a similar dependence
of the GMR and NOMOKE in SHG on the content of the
magnetic material in the film x was observed recently.18
Figure 3(a) shows the dependencies of the magnetic
contrast of the SHG intensity and the GMR coefficient on
the content of cobalt x in CoxAg1?xfilms.
contrast is measured for two wavelengths of the funda-
mental radiation, 800 and 1064 nm, for the p-in, p-out
combination of polarizations of the fundamental and SH
waves.For both fundamental waves, a clear maximum
of the NOMOKE contrast is observed at x for the range of
0.25–0.3, 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 the
?2?(x) is definitely observed for the Co concentrations x
? 0.4/0.5 where isolated Co nanogranules exist, and the
position of local maximum of the ?2?(x) is spectrally in-
Figure 3(b) shows ?2?(x) for another series of magnetic
CoxAg1?xfilms.These dependencies reveal a maximum
of the SHG(THG) magnetic contrast at x ? 0.3 for MSHG
and x ? 0.35 for MTHG, which is close to the concentra-
tion values corresponding to the maximum of the GMR
coefficient. This is again proof that the concentration de-
pendence of the NOMOKE contrast is spectrally indepen-
dent.A steep rise of ?2?/3?(x) in the vicinity of x
? 0.45 should be attributed to the formation of ferromag-
netic ordering in the granular structure at the percolation
The magnetization-induced phase shift for the THG
wave is found to be ?15° in Co0.31Ag0.69granular film,
which gives a ratio of the effective third-order compo-
nents, ??(3)odd(M)?/??(3)cryst? ? 0.16.
ments for the magnetization-induced SHG give the ratio
??(2)odd(M)?/??(2)cryst? ? 0.08.
To study the SHG mechanism in CoxAg1?xgranular
films, the SHG spectroscopic measurements are carried
out with the output of an optical-parametric-oscillator la-
ser system tuning in the wavelength range of 490–670
nm. Figure 4 shows the SHG intensity spectra measured
for the films of the compositions of x ? 0.19 and x
? 0.27. Both spectra reveal clear maxima in the vicinity
of 620–640 nm, the spectral position of the maximum of
the SHG intensity being redshifted for the film with
larger content of silver.These features of the SHG spec-
tra are probably caused by the excitation of local surface
plasmons in silver nanogranules at the Co–Ag interfaces.
The numerical calculations of local surface plasmons
spectra in CoxAg1?x granular films were performed
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.
surface plasmons in nanogranular CoxAg1?xfilms is re-
corded by means of the SHG spectroscopy, which perhaps
plays an important role in the correlation between GMR
and NOMOKE in SHG and THG.
The excitation of local
D. MSHG in Gd-Containing Langmuir–Blodgett Films
In this section, the nonlinear magneto-optical properties
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 of
Gd ions sandwiched between two monolayers of stearic
acetate.The superstructures consisting from 10 to 40
periods are composed with the Langmuir–Blodgett (LB)
technique from a water solution of Gd acetate.
5(a) shows a schematic view of the deposition procedure of
the LB films.
The structural and morphological properties of Gd-
containing LB films are characterized by x-ray diffraction
and the anisotropic SHG probe.
diffraction pattern that reveals sharp scattering peaks,
which confirm the periodicity of Gd layers across the
Figure 5(c) shows the azimuthal an-
gular dependence of the SHG intensity from the LB films
for the s-in, s-out combination of polarizations.
muthal dependence exhibits (i) anisotropic two-fold modu-
lation of the SHG intensity that is attributed to C2sym-
metry of LB superstructures and (ii) an isotropic
contribution independent from azimuthal angle. The lat-
ter contribution, forbidden in homogeneous films,36indi-
cates that the SHG is observed in the form of hyper-
Rayleigh scattering and is due to a random spatial
inhomogeneity of linear and nonlinear-optical properties
of Gd-containing LB films.Thus the SHG response from
Gd-containing LB superstructures consists of the sum of
coherent (anisotropic and specular) and incoherent (dif-
fuse) components. The random inhomogeneity of the LB
films is attributed to a two-dimensional islandlike mor-
phology of Gd3?ion aggregates in Gd layers sandwiched
between 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.
consisting of two-
Figure 5(b) shows x-ray
SHG spectra for Co0.27Ag0.73and Co0.19Ag0.81granular
Aktsipetrov et al.
Vol. 22, No. 1/January 2005/J. Opt. Soc. Am. B 143
Changing the direction of the applied magnetic field re-
sults in a rotation of the polarization plane of the SHG
wave to an angle of ?12° for the s-polarized fundamental
radiation.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 the
sample is set to the maximum of the SHG anisotropy,
which gave the maximum of the coherent SHG compo-
nent. In SHG interferometry measurements in partially
inhomogeneous films, interference involves only this com-
ponentof the SHwave
magnetization-induced phase shift of the SH wave from
the film is ?115°. The magnetization-induced effect in
the SHG intensity from Gd-containing LB films is not
Meanwhile, the observed magnetization-
induced variations of the polarization rotation angle and
the relative phase shift indicate a strong magnetic inter-
action and ordering in Gd aggregates induced by the ex-
ternal magnetic field. However, hysteresis-type behavior
is not observed for the polarization rotation angle and for
the phase shift as functions of magnetic field amplitude.
This implies that the magnetic order in Gd islands is close
to a superparamagnetic state that is confirmed by recent
magnetic studies of Gd-containing LB films.37
E. Magnetization-Induced Hyper-Rayleigh Scattering
from YIG Nanoparticles
This section presents the results of the experimental
studies of magnetization-induced SHG from the layer-by-
layer (LBL) self-assembled films containing yttrium iron
garnet (YIG) nanoparticles.
on the dependence of the SHG intensity on the number of
layers in LBL films as a discriminator between coherent
SHG and HRS.19
The LBL films containing nanoparticles of YIG and 32
nm in diameter are deposited by the self-assembling pro-
cedure.Glass substrates are immersed in poly(dial-
lyldimethylammonium chloride) (PDDA) and then in a
A special emphasis is made
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-out
combination of polarizations.
(a) Schematic view of the deposition procedure of Gd-
longitudinal NOMOKE and (b) MSHG interference patterns for
the transversal NOMOKE measured in Gd-containing LB films
for the opposite directions of the external magnetic field.
(a) Polarization diagrams of the SHG intensity for the
144 J. Opt. Soc. Am. B/Vol. 22, No. 1/January 2005 Aktsipetrov et al.
beaker containing the YIG suspension in water.
multilayers, the cycle of PDDA and YIG adsorption is re-
peated as many times as is necessary.
microscope image of the surface of LBL film is shown in
Fig. 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 of
the SHG intensity reveal the isotropy of both p- and
s-polarized SHG components.
of the s,s-prohibition rule36and is typical for HRS.
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 of
the 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.
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.
the dependencies of the SHG intensity on the number of
layers are close to a linear function, which is also an at-
tribute of HRS.
In the case of the s-polarized SHG, the intensity tends
to zero with a decreasing number of YIG-containing lay-
The atomic force
The latter is the violation
The latter is a mani-
In both cases,
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.
the contrary, the p-polarized SHG intensity tends to a
constant nonzero value, which should be attributed to the
contribution from the polymer sublayer and/or the sub-
strate. This contribution is responsible for the specular
SHG peak presented in Fig. 8.
nonlinear response of YIG nanoparticles is proved to be
incoherent SHG, i.e., hyper-Rayleigh scattering.
The magnetic properties of YIG nanoparticles are stud-
ied in the geometry of the transversal NOMOKE.
dependencies of the SHG intensity on the number of lay-
ers measured for the opposite directions of the magnetic
field are shown in the main panel of Fig. 8. These depen-
dencies appear to be close to linear functions.
magnetic 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 number
of layers in the LBL films.
experimental accuracy ?2?is constant, which stays in
agreement 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 I?(N) ? K?N
? IS, where the subscript ? ? 0, ? refers to different
polarities or to the absence of the magnetic field, and ISis
a coherent contribution of the polymer sublayer and the
interface.The linearity of the HRS intensity with re-
spect to N allows us to relate the SHG intensity with the
hyperpolarizability of an individual YIG nanoparticle ? ˆ,
? ˆ (M) ? ? ˆ0? ? ˆM(M), where ? ˆ0and ? ˆM(M) are the non-
magnetic and odd-in magnetization tensors of the hyper-
polarizability of an individual nanoparticle.
Thus the second-order
One can see that within the
ing pattern for the p-in, p-out combination of polarizations for
the 10-layer-thick LBL film containing YIG nanoparticles with
solid curve as a guide.
(a) Atomic force microscope image and (b) SHG scatter-
ticles without the external magnetic field (triangles) and for the
opposite directions of the magnetic field in the transversal
NOMOKE (circles) (main panel).
for H ? 0 for p-in, s-out SHG; Bottom inset; NOMOKE contrast
as a function of number of layers in LBL films containing YIG
SHG intensity in LBL films containing YIG nanopar-
Top inset, the SHG intensity
Aktsipetrov et al.
Vol. 22, No. 1/January 2005/J. Opt. Soc. Am. B145
with Eq. (2.5), the HRS magnetic contrast is ?2?
? 2? ˆM(M)/? ˆ0.This contrast stems from the assump-
tion that the HRS magnetic contrast is independent of the
number of layers. The latter stays in agreement with the
experimental data described above.
A nonzero magnetic contrast in the SHG intensity from
LBL films containing YIG nanoparticles indicates that a
relative phase between nonmagnetic and magnetization-
induced terms in Eq. (2.2) for these films is not equal to
90°. Apparently this is due to a resonance of the SH
wave with the absorption band in spectra of the YIG
nanoparticles. As a consequence, each of these terms has
real and imaginary contributions that result in the ap-
pearance of an odd term in the MSHG intensity owing to
the internal homodyne mechanism.
As a result of the
HRS? 0.15 and ? ˆM(M)/? ˆ0? 0.08.
In summary, the results of the performed experiments
show 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.
varieties of magnetic nanomaterials reveal significant
magnetization-induced effects in second- and third-order
nonlinear optical response.
Specific details of nonlinear magneto-optical response
are related to the structural features of nanostructures
and 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 LB
magnetization-induced HRS, is observed in nonlinear
magneto-optical studies of random arrays of magnetic
nanoparticles, such as self-assembling LBL films and Gd
islands 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 observation
of MTHG. Strong magnetization-induced effects in THG,
observed for the transversal NOMOKE in thin metal
films and in nanogranular systems, make the MTHG a
sensitive probe of the magnetic properties of nanostruc-
tures. It is shown that owing to a different localization of
THG as compared with the surface-sensitive SHG, MTHG
provides additional information about the behavior of the
spin system in the bulk of nanoparticles that is comple-
mentary to the characterization by the MSHG probe.
Moreover, a comparative analysis of NOMOKE in SHG
and THG seems to be accurate for the studies of the sur-
face spin–orbit interaction.
Observations of magnetization-induced effects in SHG
and THG with odd parity with respect to magnetization
show the fundamental role of internal homodyne mecha-
nism in magnitudes of nonlinear magneto-optical effects.
The authors gratefully acknowledge helpful and stimulat-
ing discussions with A. A. Nikulin.
mutov and N. Kotov for supplying the samples of LB and
We thank G. B. Kho-
sian Foundation for Basic Research (grants 04-02-16847,
04-02-17059, and 03-02-39010), the Presidential Grant for
Leading Russian Science Schools (1604.2003.2) and grant
03-51-3784 of the International Association for the Pro-
motion of Cooperation with Scientists from the Indepen-
dent States of the Former Soviet Union (INTAS).
This work is supported in part by the Rus-
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V. Murzina’s e-mail address is firstname.lastname@example.org.
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