- Email: [email protected]
Nonlinear magneto-optics in magnetic nanoparticles
Colloids and Surfaces A: Physicochemical and Engineering Aspects 202 (2002) 165– 173 www.elsevier.com/locate/colsurfa
Nonlinear magneto-optics in magnetic nanoparticles O.A. Aktsipetrov * Department of Physics, Moscow State Uni6ersity, 119899 Moscow, Russia Received 7 December 2000; accepted 22 March 2001
Abstract In this paper, the results of our recent studies of the magnetization-induced nonlinear optical effects in magnetic nanoparticles are surveyed. There are three aspects of nonlinear magneto-optics of nanoparticles, which attract attention in this review being interdisciplinary in terms of magnetism, low-dimensionality, nonlinear and coherent optics. The first is the fact that the nonlinear magneto-optical Kerr effect (NOMOKE), i.e. magnetization-induced second-harmonic generation (MSHG), exists in magnetic nanogranular films simultaneously with giant magnetoresistance effect (GMR). Moreover, the NOMOKE contrast attains maximum at the same content of magnetic component in magnetic nanogranular films as the maximum of GMR coefficient. Up to now nonlinear magneto-optics was concentrated on the regular magnetic systems and as a consequence described a coherent nonlinear response. On the contrary, in recent studies an attention is turned to the random magnetic nanostructures and, in particular, to the random two-dimensional arrays of magnetic nanoparticles fabricated by Self-Assembly techniques. Thus, an incoherent analog of MSHG, which can be called: magnetization-induced hyper-Rayleigh scattering, is observed. And finally a general issue of intrinsic weakness of magnetization-induced nonlinear optical effects governed by the fine structure parameter is discussed in terms of internal homodyne effect as one of the mechanisms of an enhancement of the magnetic effects in nonlinear optics. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnetization-induced second-harmonic generation; Nonlinear magneto-optical Kerr effect; Hyper-Rayleigh scattering; Internal homodyne effect; Giant magnetoresistance; Magnetic granular films; Self assembling films containing magnetic nanoparticles PACS numbers: 75.70.Ak; 75.70.Cn; 42.65. 78.66.Bz; 42.65.Ky; 78.20.Ls; 75.70.-1
1. Introduction This paper is devoted to the review of recent studies of the magnetization-induced nonlinear optical effects in magnetic nanoparticles [1 – 3].
* http://www.shg.ru. E-mail address: [email protected] (O.A. Aktsipetrov)
The optical second-harmonic generation (SHG) has been one of the most intensively studied phenomena in optics of surfaces and nanostructures for the last two decades [4–6]. The interest in SHG stems from its unique sensitivity to the structural, electronic, magnetic, ferroelectric, and etc. properties of surfaces, interfaces and nanostructures. This unusually high surface/interfacesensitivity comes about because, in the electric
0927-7757/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 1 ) 0 1 0 7 6 - 7
166
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
dipole approximation, SHG is forbidden in the bulk of materials with inversion symmetry [7]. However, the inversion symmetry is always broken at an interface because of the discontinuity of the (crystalline) structure. Related nonlinear sources of SHG are localized in a thin (several nanometers thick) surface layer of the particles. Experimental nonlinear optics of metal and semiconductor nanoparticles traces back to min-1980s as the size effects in SHG from the Ag and CdSe nanocrystals were observed [8]. Another domain of nonlinear optics of surfaces and nanostructures appears as the breakdown of the structural inversion symmetry is combined with the broken time reversal symmetry due to the magnetization of a magnetic material. DC-magnetic field being an axial vector does not break inversion symmetry in centrosymmetric materials whereas breaks time reversal symmetry instead. Thus, the bulk of centrosymmetric magnetized material does not contribute to the magnetizationinduced SHG (MSHG) in dipole approximation. However, the combination of the bulk (or surface) magnetization with surface lack of inversion symmetry creates the MSHG sources with precise surface localization. Due to this combination magnetization-induced SHG becomes an extremely sensitive probe of magnetism of surfaces and nanostructures [9]. Experimental studies of MSHG trace back to the 1988s when nonlinear magneto-optical Kerr effect (NOMOKE)1 and nonlinear-optical Faraday effect (NFE) were observed in thin magnetic garnet films [11,12]. These experiments were initiated by the 1985s paper by N.N. Akhmediev, A.K. Zvezdin and co-workers where these effects have been predicted [13]. Then revolutionary experimental step has been done by J. Kirshner and co-workers [14] and E. Matthias and co-workers [15] who observed NOMOKE from atomically clean surfaces of magnetic single crystals under UHV conditions. 1
The description NOMOKE which has been introduced in recent papers [10] is somewhat misleading since it could be related to the nonlinear dependence of an angle of the linear magneto-optical Kerr (MOKE) rotation on the magnitude of a DC-magnetic field.
Finally, the latter group has developed time-resolved MSHG as a probe for the studies of dynamics of surface magnetic phenomena with femtosecond time resolution [16,17]. Later another class of magnetic materials was involved in nonlinear magneto-optics: MSHG in planar layered magnetic structures has been intensively studied by Th. Rasing and co-workers [18– 21]. A number of these papers devoted to NOMOKE in magnetic superlattices should have been transformed to the idea of the correlation between the MSHG effect and giant magnetoresistance, which also exists in magnetic superlattices. Meanwhile, this idea came to light recently [22] after the observation of giant NOMOKE in magnetic granular films [23] which belong to the another than multilayers, class of magnetic nanocomposites exhibiting GMR [24]. Apart from the interest in fundamental relations between nonlinear magneto-optics and magneto-transport phenomena this transition of experimentalist’s attention from regular planar structures to the granular films has taken from the shadow the broad family of materials promising for magneto-optical memories based on the self assembling films containing magnetic nanoparticles. Moreover, these structures with random distribution of nanoparticles open a new chapter in nonlinear magneto-optical studies: the studies of magnetic effects in incoherent second-harmonic generation, i.e. magnetization-induced hyper-Rayleigh scattering. Aforementioned issue of coherency (or/and incoherence) of nonlinear response has another fundamental aspect in nonlinear magneto-optics which related to the internal homodyne mechanism of enhancement of these intrinsically weak phenomena. The key idea of this mechanism is the appearance of cross terms in the intensity of the interfering SHG fields originating from weak magnetization-induced and strong magneto-independent (crystallographic) sources. Internal homodyne effect being interference process of two coherent optical fields results in appearance of the product of two factors, the weak and strong nonlinearities, which is not supposed to be weak. This homodyne ‘amplifier’ of magnetization-induced effects in SHG shows the importance of interdisci-
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
plinary links between nonlinear and coherent optics. Thus, in this paper three aspects of nonlinear magneto-optics of magnetic nanoparticles are considered: (i) correlation between GMR and NOMOKE is experimentally approved [1]; (ii) magnetization-induced hyper-Rayleigh scattering is observed [2], and (iii) internal homodyne mechanism for weakly nonlinear processes is suggested [2,3].
2. Nonlinear magneto-optical Kerr effect in granular films exhibiting giant magnetoresistance Magnetic nanostructures such as magnetic superlattices and granular films have received considerable attention recently because of new magnetic phenomena observed in these systems: the oscillatory coupling through the nonmagnetic spacers, spin-dependent electron scattering and tunneling, etc. Moreover, these nanostructures possess GMR effect, which attracts considerable attention recently due to its promising applications. The simultaneous experimental characterization of the Cox Ag1 − x films by the GMR and NOMOKE is discussed below. A set of magnetic granular films of the Cox Ag1 − x composition (x is the volume fraction) is prepared (A.F. Kravets and co-workers [24]) by co-deposition of Co and Ag in a dual electronbeam evaporator at the room temperature and residual pressure of 10 − 4 Pa on glass ceramic substrates. The composition of the films is determined by means of the ESXA technique. The concentration of Co in the set of the Cox Ag1 − x films ranges from 0.09 to 0.72. The thickness of all films is approximately 400 nm. The crystalline structure is studied by X-ray diffraction and transmission electron microscopy. The diffraction allows to estimate roughly that the mean size of Co granules in the annealed films ranges approximately from 2 to 6 nm as content of magnetic component varies within the interval indicated above. The Cox Ag1 − x magnetic granular films exhibit the pronounced GMR effect. The electrical resistance of the films is measured using four point AC
167
technique in temperature range from 77 to 300 K. The room temperature magneroresistance is measured in magnetic field up to 8.2 kOe for in plane current configuration and three configurations of external magnetic field application. The dot line in Fig. 1 shows the non-monotony dependence of the GMR coefficient on the content of a magnetic component with a pronounced maximum at x = 0.3. The nonlinear-optical studies are performed using (i) the unfocused output of a Q-switched YAG:Nd + 3 laser at a wavelength of 1064 nm with a pulse width of about 15 ns, a repetition rate of 12.5 Hz and an intensity of 2 MW cm − 2 and (ii) the output of a Ti:Sapphire laser at a wavelength of 800 nm with a pulse width of about 30 fs, a repetition rate of 82 MHz, an average power of 100 mW focused onto a spot of about 100 micron in a diameter. An angle of incidence was 45°. The second-harmonic (SH) signal generated in reflection is detected by a PMT and gated electronics in the case of impulse YAG:Nd + 3 laser and photon counter for Ti:Sapphire laser. In the studies of magnetization-induced effects in SHG a DC-magnetic field up to 2.5 kOe is
Fig. 1. Dependences of the NOMOKE magnetic contrast on the concentration x of Co in the Cox Ag1 − x films at the fundamental wavelengths of 1064 and 800 nm, solid and dashed lines, respectively. The dot line is the dependence of the GMR coefficient on the concentration x for the Cox Ag1 − x films.
168
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
applied in the transversal configuration. NOMOKE is characterized quantitatively by the NOMOKE magnetic contrast z2 =(IM + (2v) − IM − (2v))/(IM + (2 ) +IM − (2 )), where IM + (2 ) and IM − (2 ) is the SHG intensity for opposite directions of the magnetization, M. The solid and dashed lines in Fig. 1 show the dependence of the NOMOKE magnetic contrast on the content of the magnetic component in the Cox Ag1 − x films at the fundamental wavelengths of 1064 and 800 nm, respectively. The NOMOKE magnetic contrast reveals a wavelength independent maximum at approximately the same Co concentration as the maximum of the GMR coefficient. Then the NOMOKE magnetic contrast reveals a pronounced rise in the vicinity of x = 0.45 − 0.5 where the percolation threshold is observed [24]. The simultaneous measurements of the magnetization-induced effects both in DC-conductivity (resistivity) and SHG give a preliminary answer to a question whether a correlation between the two phenomena, GMR and NOMOKE, occurs in magnetic granular films. Namely, the maximum in the dependence of the NOMOKE magnetic contrast on x weakly depends on the fundamental wavelength and is attained at almost the same x as the maximum in the concentration dependence of the magnetoresistance (Fig. 1). This is apparently due to the fact that both the spin-dependent electron scattering (determining the magnitude of the magnetoresistivity) and the magnetization-induced SHG are driven by the same quantity: the local value of the magnetization, M. On the other hand, at x \0.4 (i.e. above the percolation threshold) the behavior of the NOMOKE magnetic contrast and that of the magnetoresistance become quite different: the ferromagnetic ordering of the magnetic moments in the granules leads to a significant increase in the NOMOKE magnetic contrast but suppresses the spin-dependent electron scattering and, as a result, the magnetoresistance. Summarizing up this Section, the electronic and magnetic properties of the Cox Ag1 − x granular films experimentally studied by means of nonlinear-optical magnetic Kerr effect in the combination with the giant magnetoresistance reveal a correlation in the mechanisms of these phenom-
ena which both are sensitive to the quality of buried granular-host material interfaces [1].
3. Magnetization-induced hyper-Rayleigh scattering from layer-by-layer assembled films of YIG nanoparticles Yttrium iron garnet (YIG) Y3Fe5O12 and related Bi-doped compounds have received considerable attention because of their prominent magneto-optical properties. They exhibit the largest known Verdet constants responsible for the rotation of light polarization in the Faraday effect and magneto-optical Kerr effect. Thin films of YIG are widely studied with the aim of production of magneto-optical elements for integrated optoelectronics [25]. Moreover, concerning nonlinear optics, it was in these materials that magnetization-induced nonlinear optical effects were discovered [11,12]. Apart from basic concern nonlinear optics promises the development of new read-out methods of high-density magneto-optical memories based on YIG materials [26]. New preparation techniques allow the construction of thin nanostructured YIG films with characteristics being optimal for the design of a new generation of magneto-optical devices. This motivates us to subject YIG nanoparticles to nonlinear magneto-optical studies, previously having been carried out for the bulk YIG material [11,12,27,28]. An additional momentum to these studies is given by the fact that, in regard to nanocomposite materials, NOMOKE has been observed only in Co–Cu an Co –Ag granular films and only for coherent SHG, without any evidence for magnetization-induced hyper-Rayleigh scattering (HRS), i.e. incoherent MSHG (see Section 2). Coherent SHG and HRS from the bulk of a film much thinner than the fundamental radiation wavelength can be distinguished by the dependence of the SHG intensity on the film thickness, quadratic and linear, respectively. In this Section, we study magnetization-induced SHG in layer-by-layer (LBL) assembled films of YIG nanoparticles with special emphasis on the dependence of the SHG intensity on the number of layers in LBL films as a discriminator between
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
coherent SHG and HRS. For identification of NOMOKE in hyper-Rayleigh scattering we use by analogy to a coherent MSHG (Section 2) a magnetic-contrast technique based on measuring the values IM + (2 ) and IM − (2 ) of the intensity of the SH radiation being generated by the studied system at two values of the applied DC magnetic field, the same in magnitude (well above the magnetization saturation threshold) and opposite in direction. This is worth noting that the difference in IM + (2 ) and IM − (2 ) occurs exactly due to the aforementioned internal homodyne mechanism. This mechanism will be discussed in Section 4 in more details. Anyway, shortly this difference is due to appearance of the cross-term in the interference of (2) even and (2) odd, the constituents of the quadratic susceptibility (2) that are even and odd with respect to the static magnetization, M, respectively: IM 9(2 ) 8 (2) even9 (2) odd 2 = (2) even 2 + (2) odd 2 92Re( (2)* even (2) odd). Layer-by-layer assembled films were deposited on glass substrates by the procedure developed by N.A. Kotov and co-workers [29]. YIG nanoparticles were of 32 nm an average size agglomerated to the substructures of the size less than 100 nm. For the SHG measurements the output of a TISSA-100 Ti:Sapphire laser at the wavelength of 760 nm with a repetition rate of 82 MHz, an average power of approximately 400 mW, a pulse duration of 80 fs is focused onto the sample to a spot of approximately 100 micron in diameter. The angle of incidence of the p-polarized fundamental radiation is 45°. A DC-magnetic field of an amplitude up to 2.5 kOe is applied in the transversal geometry. The angular aperture of the gathering system is approximately 10 − 1 sr which allows to gather both specular signal of coherent SHG and diffuse signal of incoherent HRS. The polar diagram in Fig. 2(a) shows a typical dependence of the SHG intensity on the azimuthal angle. The SHG response is isotropic, which indicates the in-plane isotropy of the studied films within the laser spot area. Fig. 2(b) shows the dependence of the s-polarized SHG response on the number of layers in the LBL assembled films for p-polarized fundamental wave. The intensity of s-polarized SHG is sensi-
169
tive to the homogeneity (or, as a consequence, to inhomogeneity) of the isotropic films. This sensitivity comes about of the polarization selection rules which forbidden the generation of coherent s-polarized second harmonic from homogeneous isotropic film [30]. The whole s-polarized SHG signal in Fig. 2(b) can be attributed to the incoherent SHG (in other words, HRS). Fig. 2(c) shows the dependences of the SHG intensity for p-in, p-out combination of polarization of the SHG and fundamental waves on number of layers N measured at magnetic field H= 0 and H= 9 2.5 kOe. These dependences, I0(N), I 9 (N) can be approximated as linear functions of N: Ia(N)= KaN+ IS, where a=0, 9 and the constant IS is interpreted as a contribution of polymer from the film-air and film-substrate interface with the lack of inversion symmetry discussed above. Linearity in N is an attribute of hyperRayleigh scattering, which distinguish incoherent HRS process from coherent SHG which intensity thickness dependence (dependence on number of layers) must be quadratic. The model of magnetization-induced HRS developed by A.A. Nikulin [2] allows to estimate from the HRS magnetic contrast, z(2 ), the magnetic and nonmagnetic hyperpolarizabilities of an individual YIG particle, kM and k0, respectively: kM[kMM]H = 2.5 kOe/ k 0 z/2: 0.07. Summarizing up this section (i) nonlinear magneto-optical Kerr effect(NOMOKE) in hyperRayleigh scattering from self-assembling films of YIG nanoparticles has been observed for the first time; (ii) a noticeable magnetic contrast of the NOMOKE has been observed as a manifestation of an internal homodyne mechanism; (iii) the ratio of the magnetization-induced and nonmagnetic quadratic hyperpolarizabilities of YIG nanoparticles is estimated from the value of the magnetic contrast and is 0.1 [2].
4. Internal homodyne mechanism in the enhancement of magnetization-induced second-harmonic generation The role which interference of coherent waves plays in nonlinear-optical phenomena is well-
170
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
Fig. 2. Dependence of the p-in, p-out SHG intensity from a six layered LBL assembled YIG-nanoparticle containing film on azimuthal angle: panel (a). Dependence of the p-in, s-out SHG intensity from the LBL assembled YIG-nanoparticle containing films on the number of layers: panel (b). Dependences of the p-in, p-out SHG intensity on the number of layers measured at magnetic field H = 0 and H= 92.5 kOe: panel (c).
known. As an example, the optical interference between the spectral background and resonant contribution to the third-order nonlinear susceptibility brings about a spectral shift of resonance wavelengths which is observed in a coherent antiStokes Raman spectroscopy (CARS) [31]. The optical interference between contributions from first-order and quadratic susceptibilities stresses the appearance of weak absorption bands in spontaneous down-conversion spectroscopy [32]. The latter shows an example while the interference serves as an amplifier for the weak nonlinearoptical effects. All these examples of interference between the waves from different linear and nonlinear sources
can be interpreted in terms of homodyne effect: interference of signal and reference waves which could be constructive or destructive in certain particular case. If the source of reference wave is localized internally in the sample one can call about internal homodyne effect. Such a constructive interference of the weak signal wave with strong wave from internal reference can be considered as an internal homodyne enhancement mechanism of weak effects in SHG and received recently significant attention in DC-electricfield induced SHG [33]. In this paper we extend this idea to the homodyne enhancement of intrinsically weak magnetization-induced effects in SHG [2,3].
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
In the following a simple phenomenological model of internal homodyne in MSHG effects is considered which takes into account an interference of the strong reference (crystallographic) SH fields and magnetization-induced SH fields, both generated in the bulk and at the surface of particles. The SHG intensity in the far-field region from a semiinfinite medium is given by: I2 8 E S(2 ) + E B(2 ) 2,
(1)
where E S(2 ) and E B(2 ) are the SH fields generated by surface and bulk nonlinear polarizations, respectively. Generally, in a magnetic medium they contain nonmagnetic (crystallographic) and magnetization-induced components. In the following only components of the quadratic susceptibility (2) will be considered (see (2) odd in Section 3 which posses the odd parity with respect to magnetization, M, i.e. that change their sign under the inversion (2)M of M: (2)M ijkl (M) = − ijkl ( −M). The ith component of the SH field generated by the surface, E S(2 ), is given by: E Si (2 )8
&
Dz
8 (2)Sd ijk E j E k +e SCr i
(2)SdM E ijkl j E k Ml,
SM i
&
0
Gij (z, z%)P Bj (z%, 2 )dz%
E + e i2 (2)BdM jklm k (z)E l (z)Mm )
(3)
where P B(z%, 2 ) is the bulk nonlinear polarization; G(z, z%) is Green function of the wave equation for the bulk polarization; (2)Bd , (2)BdM are the dipole jkl jklm bulk nonmagnetic and magnetic susceptibilities (which are real quantities in a transparent media), respectively, and 2 is the phase shift between them; Dk = 2k − k2 is the phase mismatch; k and k2 and are the fundamental and SH wave vectors, respectively. For the reflection geometry of the MSHG experiment (NOMOKE measurements) the phase mismatch Dk k , and in transmission NFE geometry Dk k . For a transparent film Aij are real constants. Thus, Eq. (1) for the MSHG intensity takes the form: I2 E( (2 ) 2 = E Sd(2 )+ iE SdM(2 , M) + iK. (E Bd(2 )+ iE BdM(2 , M) 2 2 − Kij (2)BdM Mm )E jklm j Ek
(2)
where P (2 ) and P (2 , M) are the i-th components of the surface, nonmagnetic and magnetization-induced nonlinear polarizations, respectively; (2)Sd and (2)SdM are the dipole surface, ijk ijkl nonmagnetic and magnetic susceptibilities, respectively, and 1 is the phase shift between them; E j is the component of a fundamental field; G0 is the Green function for the surface nonlinear sources, the integration is over the subsurface layer Dz. It is important that G0 gives only a numerical factor g0 in the nonlinear polarization and does not change the phase of the SH fields generated by the surface nonlinear polarizations. In a transparent magnetic material 1 =p/2 off-resonance conditions. The bulk i-th component of the SH field is given by: E Bi (2 )=
i E Aij ( (2)Bd jkl k (z)E l (z) Dk
8 (2)Sd + i (2)SdM Ml + iKij (2)Bd ijk ijkl jkl
(P SCr (2 ) +P SM i i (2 , M))G0dz% i1
8
171
(4)
where Kij are real constants for a transparent film. It follows from Eq. (4) that at off-resonance, as 1 = 2 = p/2, odd in magnetization changes of the SHG intensity are determined by the interference of magnetization-induced SH fields and those independent from magnetization and, as a consequence, are described by surface-bulk homodyne cross(2)BdM (2)BdM terms: ( (2)Sd Mm ) and ( (2)Sd Ml ). ijk jklm ijk jklm Both these products are not supposed to be small in spite of the small factor of magnetic susceptibility as a factor of nonmagnetic (crystallographic) susceptibility is large. At pre-resonant or resonant conditions, as 1 " p/2 and 2 " p/2, a number of magnetic/nonmagnetic homodyne cross-terms can appear in Eq. (4). In this case the reference SH fields from the noncentrosymmetric bulk of the film are supposed to be dominate contribution to the MSHG intensity, and the largest contribution to odd in magnetization changes of the SHG response are described by the large homodyne cross-term ( (2)Bd (2)BdM Ml ). jkl ijkl
172
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
This is worth noting that for the sake of simplicity the internal homodyne MSHG effect has been considered in this model for a semi-infinite magnetic medium. For films of a finite thickness or for particles of finite size, the tensor elements Aij and Kij in Eqs. (3) and (4) should be complex. It will bring about the appearance of additional homodyne cross-terms in Eq. (4) both at a resonance and off-resonance fundamental wavelength.
lation between GMR and NOMOKE has appeared. I thank T.V. Murzina, A.A. Nikulin, N.A. Kotov, J. Gu¨ dde, G. Marowsky and A.F. Kravets for the long-term collaboration in this area and the opportunity to use the results of collaborative research in this review. This reviewing work was partly supported by NATO grants PST.ARW.977033 and PST.CLG.975264, the Russian Foundation of Basic Research grants 0002-16253 and 01-02-17524, and grant for Leading Russian Science Schools 00-15-96555.
5. Summery of review The electronic and magnetic properties of Co nanoparticles in the Cox Ag1 − x granular films are experimentally studied by means of SH generation and NOMOKE in the combination with giant magnetoresistance measurements. The giant magnetoresistance coefficient and the NOMOKE contrast non-monotonously depend on the content of magnetic component in the granular films. The maximum of the NOMOKE magnetic contrast is attained at the magnetic component concentration value that weakly depends on the fundamental wavelength and is close to that for the maximum of the giant magnetoresistance. This observation is the manifestation of the basic links between these two phenomena [1]. Magnetization-induced SH generation in layerby-layer assembled films containing YIG nanoparticles is observed. The SHG intensity, including its magnetization-induced component, linearly increases with the number of self-assembling layers, which indicates that SHG occurs in its incoherent form: hyper-Rayleigh scattering [2]. The NOMOKE in HRS has a noticeable magnetic contrast brought about by the internal homodyne mechanism. The phenomenological model of the internal homodyne mechanism of the enhancement of intrinsically weak magnetization-induced effects is considered for magnetic nanoparticles [3].
Acknowledgements I gratefully acknowledge Professor E. Matthias for fruitful discussions in which the idea of corre-
References [1] T.V. Murzina, T.V. Misuryaev, A.F. Kravets, J. Gu¨ dde, D. Schuhmacher, G. Marowsky, A.A. Nikulin, O.A. Aktsipetrov, Surf. Sci. 482 – 485 (2001) 1101. [2] T.V. Murzina, A.A. Nikulin, O.A. Aktsipetrov, J.W. Ostrander, A.A. Mamedov, N.A. Kotov, M.A.C. Devillers, J. Roark, Appl. Phys. Lett. 79 (2001) 1309. [3] T.V. Murzina, A.A. Fedyanin, T.V. Misuryaev, G.B. Khomutov, O.A. Aktsipetrov, Appl. Phys. B 68 (1999) 537. [4] G. Lu¨ pke, Surf. Sci. Rep. 35 (1999) 75. [5] J.F. McGilp, Phys. Stat. Sol. A 175 (1999) 153. [6] O.A. Aktsipetrov, P.V. Elyutin, A.A. Fedyanin, A.A. Nikulin, A.N. Rubtsov, Surf. Sci. 325 (1995) 343. [7] T.F. Heinz, in: H.-E. Ponath, G.I. Stegeman (Eds.), Nonlinear Surface Electromagnetic Phenomena, North Holland, Amsterdam, 1991, p. 355. [8] O.A. Aktsipetrov, P.V. Elyutin, A.A. Nikulin, E.A. Ostrovskaya, Phys. Rev. B 51 (1995) 17591. [9] R.-P. Pan, H.D. Wie, Y.R. Shen, Phys. Rev. B 39 (1989) 1229. [10] T. Rasing, J. Magn. Magn. Mater. 165 (1997) 35. [11] O.A. Aktsipetrov, O.V. Braginskii, D.A. Esikov, Sov. J. Quantum Electron. 20 (1990) 259. [12] O.A. Aktsipetrov, O.V. Braginskii, D.A. Esikov, In: Proceedings of ICONO-13, Minsk, USSR, 1988, Vol. 2, pp. 142. [13] N.N. Akhmediev, S.B. Borisov, A.K. Zvezdin, I.L. Lyubchanskii, Y.V. Melnikov, Sov. Physics-Solid State 27 (1985) 650. [14] J. Reif, J.C. Zink, C.-M. Schneider, J. Kirschner, Phys. Rev. Lett. 67 (1991) 2878. [15] J. Reif, C. Rau, E. Matthias, Phys. Rev. Lett. 71 (1993) 1931. [16] J. Hohlfeld, E. Matthias, R. Knorren, K.H. Bennemann, Phys. Rev. Lett. 78 (1997) 4861. [17] J. Gu¨ dde, U. Conrad, V. Jaehnke, J. Hohlfeld, E. Matthias, Phys. Rev. B 59 (1999) R6608. [18] G. Spierings, V. Koutsos, H.A. Wierenga, M.W.J. Prins, D. Abraham, T. Rasing, Surf. Sci. 287 – 288 (1993) 747.
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173 [19] G. Spierings, V. Koutsos, H.A. Wierenga, M.W.J. Prins, D. Abraham, T. Rasing, J. Magn. Magn. Mater. 121 (1993) 109. [20] B. Koopmans, M.G. Koerkamp, T. Rasing, H. van den Berg, Phys. Rev. Lett. 74 (1995) 3692. [21] A. Kirilyuk, Th. Rasing, B. Doudin, J.-P. Ansermet, J. Appl. Phys. 81 (1997) 4723. [22] Discussion with Professor E. Matthias. [23] T.V. Murzina, E.A. Ganshina, V.S. Guschin, T.V. Misuryaev, O.A. Aktsipetrov, Appl. Phys. Lett. 73 (1998) 3769. [24] Yu.G. Pogorelov, G.N. Kakazei, J.B. Sousa, A.F. Kravets, N.A. Lesnik, M.M. Pereira de Azevedo, M. Malinowska, P. Panissod, Phys. Rev. B 60 (1999) 12200. [25] R. Wolfe, Thin Solid Films 216 (1992) 184. [26] O.A. Aktsipetrov, A.A. Fedyanin, A.V. Melnikov, E.D. Mishina, T.V. Murzina, Jpn. J. Appl. Phys. 36 (1998) 48.
173
[27] R.V. Pisarev, B.B. Krichevtsov, V.N. Gridnev, V.P. Klin, D. Frohlich, C. Pahlke-Lerch, J. Phys. 5 (1993) 8621. [28] V.V. Pavlov, R.V. Pisarev, A. Kirilyuk, T. Rasing, Phys. Rev. Lett. 78 (1997) 2004. [29] J.W. Ostrander, A.A. Mamedov, N.A. Kotov, J. Am. Chem. Soc. 123 (2001) 1101. [30] O.A. Aktsipetrov, I.M. Baranova, Y.A. Ilinskii, Sov. Phys. JETP 64 (1986) 167. [31] N.I. Koroteev, M. Endemann, R.L. Byer, Phys. Rev. Lett. 43 (1979) 398. [32] O.A. Aktsipetrov, G.M. Georgiev, I.V. Mityusheva, A.G. Mikhailovskii, A.N. Penin, Sov. Physics-Solid State 17 (1975) 1324. [33] O.A. Aktsipetrov, A.A. Fedyanin, A.V. Melnikov, E.D. Mishina, A.N. Rubtsov, M.H. Anderson, P.T. Wilson, M. ter Beek, X.F. Hu, J.I. Dadap, M.C. Downer, Phys. Rev. B 60 (1999) 8924.
Nonlinear magneto-optics in magnetic nanoparticles O.A. Aktsipetrov * Department of Physics, Moscow State Uni6ersity, 119899 Moscow, Russia Received 7 December 2000; accepted 22 March 2001
Abstract In this paper, the results of our recent studies of the magnetization-induced nonlinear optical effects in magnetic nanoparticles are surveyed. There are three aspects of nonlinear magneto-optics of nanoparticles, which attract attention in this review being interdisciplinary in terms of magnetism, low-dimensionality, nonlinear and coherent optics. The first is the fact that the nonlinear magneto-optical Kerr effect (NOMOKE), i.e. magnetization-induced second-harmonic generation (MSHG), exists in magnetic nanogranular films simultaneously with giant magnetoresistance effect (GMR). Moreover, the NOMOKE contrast attains maximum at the same content of magnetic component in magnetic nanogranular films as the maximum of GMR coefficient. Up to now nonlinear magneto-optics was concentrated on the regular magnetic systems and as a consequence described a coherent nonlinear response. On the contrary, in recent studies an attention is turned to the random magnetic nanostructures and, in particular, to the random two-dimensional arrays of magnetic nanoparticles fabricated by Self-Assembly techniques. Thus, an incoherent analog of MSHG, which can be called: magnetization-induced hyper-Rayleigh scattering, is observed. And finally a general issue of intrinsic weakness of magnetization-induced nonlinear optical effects governed by the fine structure parameter is discussed in terms of internal homodyne effect as one of the mechanisms of an enhancement of the magnetic effects in nonlinear optics. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnetization-induced second-harmonic generation; Nonlinear magneto-optical Kerr effect; Hyper-Rayleigh scattering; Internal homodyne effect; Giant magnetoresistance; Magnetic granular films; Self assembling films containing magnetic nanoparticles PACS numbers: 75.70.Ak; 75.70.Cn; 42.65. 78.66.Bz; 42.65.Ky; 78.20.Ls; 75.70.-1
1. Introduction This paper is devoted to the review of recent studies of the magnetization-induced nonlinear optical effects in magnetic nanoparticles [1 – 3].
* http://www.shg.ru. E-mail address: [email protected] (O.A. Aktsipetrov)
The optical second-harmonic generation (SHG) has been one of the most intensively studied phenomena in optics of surfaces and nanostructures for the last two decades [4–6]. The interest in SHG stems from its unique sensitivity to the structural, electronic, magnetic, ferroelectric, and etc. properties of surfaces, interfaces and nanostructures. This unusually high surface/interfacesensitivity comes about because, in the electric
0927-7757/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 1 ) 0 1 0 7 6 - 7
166
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
dipole approximation, SHG is forbidden in the bulk of materials with inversion symmetry [7]. However, the inversion symmetry is always broken at an interface because of the discontinuity of the (crystalline) structure. Related nonlinear sources of SHG are localized in a thin (several nanometers thick) surface layer of the particles. Experimental nonlinear optics of metal and semiconductor nanoparticles traces back to min-1980s as the size effects in SHG from the Ag and CdSe nanocrystals were observed [8]. Another domain of nonlinear optics of surfaces and nanostructures appears as the breakdown of the structural inversion symmetry is combined with the broken time reversal symmetry due to the magnetization of a magnetic material. DC-magnetic field being an axial vector does not break inversion symmetry in centrosymmetric materials whereas breaks time reversal symmetry instead. Thus, the bulk of centrosymmetric magnetized material does not contribute to the magnetizationinduced SHG (MSHG) in dipole approximation. However, the combination of the bulk (or surface) magnetization with surface lack of inversion symmetry creates the MSHG sources with precise surface localization. Due to this combination magnetization-induced SHG becomes an extremely sensitive probe of magnetism of surfaces and nanostructures [9]. Experimental studies of MSHG trace back to the 1988s when nonlinear magneto-optical Kerr effect (NOMOKE)1 and nonlinear-optical Faraday effect (NFE) were observed in thin magnetic garnet films [11,12]. These experiments were initiated by the 1985s paper by N.N. Akhmediev, A.K. Zvezdin and co-workers where these effects have been predicted [13]. Then revolutionary experimental step has been done by J. Kirshner and co-workers [14] and E. Matthias and co-workers [15] who observed NOMOKE from atomically clean surfaces of magnetic single crystals under UHV conditions. 1
The description NOMOKE which has been introduced in recent papers [10] is somewhat misleading since it could be related to the nonlinear dependence of an angle of the linear magneto-optical Kerr (MOKE) rotation on the magnitude of a DC-magnetic field.
Finally, the latter group has developed time-resolved MSHG as a probe for the studies of dynamics of surface magnetic phenomena with femtosecond time resolution [16,17]. Later another class of magnetic materials was involved in nonlinear magneto-optics: MSHG in planar layered magnetic structures has been intensively studied by Th. Rasing and co-workers [18– 21]. A number of these papers devoted to NOMOKE in magnetic superlattices should have been transformed to the idea of the correlation between the MSHG effect and giant magnetoresistance, which also exists in magnetic superlattices. Meanwhile, this idea came to light recently [22] after the observation of giant NOMOKE in magnetic granular films [23] which belong to the another than multilayers, class of magnetic nanocomposites exhibiting GMR [24]. Apart from the interest in fundamental relations between nonlinear magneto-optics and magneto-transport phenomena this transition of experimentalist’s attention from regular planar structures to the granular films has taken from the shadow the broad family of materials promising for magneto-optical memories based on the self assembling films containing magnetic nanoparticles. Moreover, these structures with random distribution of nanoparticles open a new chapter in nonlinear magneto-optical studies: the studies of magnetic effects in incoherent second-harmonic generation, i.e. magnetization-induced hyper-Rayleigh scattering. Aforementioned issue of coherency (or/and incoherence) of nonlinear response has another fundamental aspect in nonlinear magneto-optics which related to the internal homodyne mechanism of enhancement of these intrinsically weak phenomena. The key idea of this mechanism is the appearance of cross terms in the intensity of the interfering SHG fields originating from weak magnetization-induced and strong magneto-independent (crystallographic) sources. Internal homodyne effect being interference process of two coherent optical fields results in appearance of the product of two factors, the weak and strong nonlinearities, which is not supposed to be weak. This homodyne ‘amplifier’ of magnetization-induced effects in SHG shows the importance of interdisci-
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
plinary links between nonlinear and coherent optics. Thus, in this paper three aspects of nonlinear magneto-optics of magnetic nanoparticles are considered: (i) correlation between GMR and NOMOKE is experimentally approved [1]; (ii) magnetization-induced hyper-Rayleigh scattering is observed [2], and (iii) internal homodyne mechanism for weakly nonlinear processes is suggested [2,3].
2. Nonlinear magneto-optical Kerr effect in granular films exhibiting giant magnetoresistance Magnetic nanostructures such as magnetic superlattices and granular films have received considerable attention recently because of new magnetic phenomena observed in these systems: the oscillatory coupling through the nonmagnetic spacers, spin-dependent electron scattering and tunneling, etc. Moreover, these nanostructures possess GMR effect, which attracts considerable attention recently due to its promising applications. The simultaneous experimental characterization of the Cox Ag1 − x films by the GMR and NOMOKE is discussed below. A set of magnetic granular films of the Cox Ag1 − x composition (x is the volume fraction) is prepared (A.F. Kravets and co-workers [24]) by co-deposition of Co and Ag in a dual electronbeam evaporator at the room temperature and residual pressure of 10 − 4 Pa on glass ceramic substrates. The composition of the films is determined by means of the ESXA technique. The concentration of Co in the set of the Cox Ag1 − x films ranges from 0.09 to 0.72. The thickness of all films is approximately 400 nm. The crystalline structure is studied by X-ray diffraction and transmission electron microscopy. The diffraction allows to estimate roughly that the mean size of Co granules in the annealed films ranges approximately from 2 to 6 nm as content of magnetic component varies within the interval indicated above. The Cox Ag1 − x magnetic granular films exhibit the pronounced GMR effect. The electrical resistance of the films is measured using four point AC
167
technique in temperature range from 77 to 300 K. The room temperature magneroresistance is measured in magnetic field up to 8.2 kOe for in plane current configuration and three configurations of external magnetic field application. The dot line in Fig. 1 shows the non-monotony dependence of the GMR coefficient on the content of a magnetic component with a pronounced maximum at x = 0.3. The nonlinear-optical studies are performed using (i) the unfocused output of a Q-switched YAG:Nd + 3 laser at a wavelength of 1064 nm with a pulse width of about 15 ns, a repetition rate of 12.5 Hz and an intensity of 2 MW cm − 2 and (ii) the output of a Ti:Sapphire laser at a wavelength of 800 nm with a pulse width of about 30 fs, a repetition rate of 82 MHz, an average power of 100 mW focused onto a spot of about 100 micron in a diameter. An angle of incidence was 45°. The second-harmonic (SH) signal generated in reflection is detected by a PMT and gated electronics in the case of impulse YAG:Nd + 3 laser and photon counter for Ti:Sapphire laser. In the studies of magnetization-induced effects in SHG a DC-magnetic field up to 2.5 kOe is
Fig. 1. Dependences of the NOMOKE magnetic contrast on the concentration x of Co in the Cox Ag1 − x films at the fundamental wavelengths of 1064 and 800 nm, solid and dashed lines, respectively. The dot line is the dependence of the GMR coefficient on the concentration x for the Cox Ag1 − x films.
168
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
applied in the transversal configuration. NOMOKE is characterized quantitatively by the NOMOKE magnetic contrast z2 =(IM + (2v) − IM − (2v))/(IM + (2 ) +IM − (2 )), where IM + (2 ) and IM − (2 ) is the SHG intensity for opposite directions of the magnetization, M. The solid and dashed lines in Fig. 1 show the dependence of the NOMOKE magnetic contrast on the content of the magnetic component in the Cox Ag1 − x films at the fundamental wavelengths of 1064 and 800 nm, respectively. The NOMOKE magnetic contrast reveals a wavelength independent maximum at approximately the same Co concentration as the maximum of the GMR coefficient. Then the NOMOKE magnetic contrast reveals a pronounced rise in the vicinity of x = 0.45 − 0.5 where the percolation threshold is observed [24]. The simultaneous measurements of the magnetization-induced effects both in DC-conductivity (resistivity) and SHG give a preliminary answer to a question whether a correlation between the two phenomena, GMR and NOMOKE, occurs in magnetic granular films. Namely, the maximum in the dependence of the NOMOKE magnetic contrast on x weakly depends on the fundamental wavelength and is attained at almost the same x as the maximum in the concentration dependence of the magnetoresistance (Fig. 1). This is apparently due to the fact that both the spin-dependent electron scattering (determining the magnitude of the magnetoresistivity) and the magnetization-induced SHG are driven by the same quantity: the local value of the magnetization, M. On the other hand, at x \0.4 (i.e. above the percolation threshold) the behavior of the NOMOKE magnetic contrast and that of the magnetoresistance become quite different: the ferromagnetic ordering of the magnetic moments in the granules leads to a significant increase in the NOMOKE magnetic contrast but suppresses the spin-dependent electron scattering and, as a result, the magnetoresistance. Summarizing up this Section, the electronic and magnetic properties of the Cox Ag1 − x granular films experimentally studied by means of nonlinear-optical magnetic Kerr effect in the combination with the giant magnetoresistance reveal a correlation in the mechanisms of these phenom-
ena which both are sensitive to the quality of buried granular-host material interfaces [1].
3. Magnetization-induced hyper-Rayleigh scattering from layer-by-layer assembled films of YIG nanoparticles Yttrium iron garnet (YIG) Y3Fe5O12 and related Bi-doped compounds have received considerable attention because of their prominent magneto-optical properties. They exhibit the largest known Verdet constants responsible for the rotation of light polarization in the Faraday effect and magneto-optical Kerr effect. Thin films of YIG are widely studied with the aim of production of magneto-optical elements for integrated optoelectronics [25]. Moreover, concerning nonlinear optics, it was in these materials that magnetization-induced nonlinear optical effects were discovered [11,12]. Apart from basic concern nonlinear optics promises the development of new read-out methods of high-density magneto-optical memories based on YIG materials [26]. New preparation techniques allow the construction of thin nanostructured YIG films with characteristics being optimal for the design of a new generation of magneto-optical devices. This motivates us to subject YIG nanoparticles to nonlinear magneto-optical studies, previously having been carried out for the bulk YIG material [11,12,27,28]. An additional momentum to these studies is given by the fact that, in regard to nanocomposite materials, NOMOKE has been observed only in Co–Cu an Co –Ag granular films and only for coherent SHG, without any evidence for magnetization-induced hyper-Rayleigh scattering (HRS), i.e. incoherent MSHG (see Section 2). Coherent SHG and HRS from the bulk of a film much thinner than the fundamental radiation wavelength can be distinguished by the dependence of the SHG intensity on the film thickness, quadratic and linear, respectively. In this Section, we study magnetization-induced SHG in layer-by-layer (LBL) assembled films of YIG nanoparticles with special emphasis on the dependence of the SHG intensity on the number of layers in LBL films as a discriminator between
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
coherent SHG and HRS. For identification of NOMOKE in hyper-Rayleigh scattering we use by analogy to a coherent MSHG (Section 2) a magnetic-contrast technique based on measuring the values IM + (2 ) and IM − (2 ) of the intensity of the SH radiation being generated by the studied system at two values of the applied DC magnetic field, the same in magnitude (well above the magnetization saturation threshold) and opposite in direction. This is worth noting that the difference in IM + (2 ) and IM − (2 ) occurs exactly due to the aforementioned internal homodyne mechanism. This mechanism will be discussed in Section 4 in more details. Anyway, shortly this difference is due to appearance of the cross-term in the interference of (2) even and (2) odd, the constituents of the quadratic susceptibility (2) that are even and odd with respect to the static magnetization, M, respectively: IM 9(2 ) 8 (2) even9 (2) odd 2 = (2) even 2 + (2) odd 2 92Re( (2)* even (2) odd). Layer-by-layer assembled films were deposited on glass substrates by the procedure developed by N.A. Kotov and co-workers [29]. YIG nanoparticles were of 32 nm an average size agglomerated to the substructures of the size less than 100 nm. For the SHG measurements the output of a TISSA-100 Ti:Sapphire laser at the wavelength of 760 nm with a repetition rate of 82 MHz, an average power of approximately 400 mW, a pulse duration of 80 fs is focused onto the sample to a spot of approximately 100 micron in diameter. The angle of incidence of the p-polarized fundamental radiation is 45°. A DC-magnetic field of an amplitude up to 2.5 kOe is applied in the transversal geometry. The angular aperture of the gathering system is approximately 10 − 1 sr which allows to gather both specular signal of coherent SHG and diffuse signal of incoherent HRS. The polar diagram in Fig. 2(a) shows a typical dependence of the SHG intensity on the azimuthal angle. The SHG response is isotropic, which indicates the in-plane isotropy of the studied films within the laser spot area. Fig. 2(b) shows the dependence of the s-polarized SHG response on the number of layers in the LBL assembled films for p-polarized fundamental wave. The intensity of s-polarized SHG is sensi-
169
tive to the homogeneity (or, as a consequence, to inhomogeneity) of the isotropic films. This sensitivity comes about of the polarization selection rules which forbidden the generation of coherent s-polarized second harmonic from homogeneous isotropic film [30]. The whole s-polarized SHG signal in Fig. 2(b) can be attributed to the incoherent SHG (in other words, HRS). Fig. 2(c) shows the dependences of the SHG intensity for p-in, p-out combination of polarization of the SHG and fundamental waves on number of layers N measured at magnetic field H= 0 and H= 9 2.5 kOe. These dependences, I0(N), I 9 (N) can be approximated as linear functions of N: Ia(N)= KaN+ IS, where a=0, 9 and the constant IS is interpreted as a contribution of polymer from the film-air and film-substrate interface with the lack of inversion symmetry discussed above. Linearity in N is an attribute of hyperRayleigh scattering, which distinguish incoherent HRS process from coherent SHG which intensity thickness dependence (dependence on number of layers) must be quadratic. The model of magnetization-induced HRS developed by A.A. Nikulin [2] allows to estimate from the HRS magnetic contrast, z(2 ), the magnetic and nonmagnetic hyperpolarizabilities of an individual YIG particle, kM and k0, respectively: kM[kMM]H = 2.5 kOe/ k 0 z/2: 0.07. Summarizing up this section (i) nonlinear magneto-optical Kerr effect(NOMOKE) in hyperRayleigh scattering from self-assembling films of YIG nanoparticles has been observed for the first time; (ii) a noticeable magnetic contrast of the NOMOKE has been observed as a manifestation of an internal homodyne mechanism; (iii) the ratio of the magnetization-induced and nonmagnetic quadratic hyperpolarizabilities of YIG nanoparticles is estimated from the value of the magnetic contrast and is 0.1 [2].
4. Internal homodyne mechanism in the enhancement of magnetization-induced second-harmonic generation The role which interference of coherent waves plays in nonlinear-optical phenomena is well-
170
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
Fig. 2. Dependence of the p-in, p-out SHG intensity from a six layered LBL assembled YIG-nanoparticle containing film on azimuthal angle: panel (a). Dependence of the p-in, s-out SHG intensity from the LBL assembled YIG-nanoparticle containing films on the number of layers: panel (b). Dependences of the p-in, p-out SHG intensity on the number of layers measured at magnetic field H = 0 and H= 92.5 kOe: panel (c).
known. As an example, the optical interference between the spectral background and resonant contribution to the third-order nonlinear susceptibility brings about a spectral shift of resonance wavelengths which is observed in a coherent antiStokes Raman spectroscopy (CARS) [31]. The optical interference between contributions from first-order and quadratic susceptibilities stresses the appearance of weak absorption bands in spontaneous down-conversion spectroscopy [32]. The latter shows an example while the interference serves as an amplifier for the weak nonlinearoptical effects. All these examples of interference between the waves from different linear and nonlinear sources
can be interpreted in terms of homodyne effect: interference of signal and reference waves which could be constructive or destructive in certain particular case. If the source of reference wave is localized internally in the sample one can call about internal homodyne effect. Such a constructive interference of the weak signal wave with strong wave from internal reference can be considered as an internal homodyne enhancement mechanism of weak effects in SHG and received recently significant attention in DC-electricfield induced SHG [33]. In this paper we extend this idea to the homodyne enhancement of intrinsically weak magnetization-induced effects in SHG [2,3].
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
In the following a simple phenomenological model of internal homodyne in MSHG effects is considered which takes into account an interference of the strong reference (crystallographic) SH fields and magnetization-induced SH fields, both generated in the bulk and at the surface of particles. The SHG intensity in the far-field region from a semiinfinite medium is given by: I2 8 E S(2 ) + E B(2 ) 2,
(1)
where E S(2 ) and E B(2 ) are the SH fields generated by surface and bulk nonlinear polarizations, respectively. Generally, in a magnetic medium they contain nonmagnetic (crystallographic) and magnetization-induced components. In the following only components of the quadratic susceptibility (2) will be considered (see (2) odd in Section 3 which posses the odd parity with respect to magnetization, M, i.e. that change their sign under the inversion (2)M of M: (2)M ijkl (M) = − ijkl ( −M). The ith component of the SH field generated by the surface, E S(2 ), is given by: E Si (2 )8
&
Dz
8 (2)Sd ijk E j E k +e SCr i
(2)SdM E ijkl j E k Ml,
SM i
&
0
Gij (z, z%)P Bj (z%, 2 )dz%
E + e i2 (2)BdM jklm k (z)E l (z)Mm )
(3)
where P B(z%, 2 ) is the bulk nonlinear polarization; G(z, z%) is Green function of the wave equation for the bulk polarization; (2)Bd , (2)BdM are the dipole jkl jklm bulk nonmagnetic and magnetic susceptibilities (which are real quantities in a transparent media), respectively, and 2 is the phase shift between them; Dk = 2k − k2 is the phase mismatch; k and k2 and are the fundamental and SH wave vectors, respectively. For the reflection geometry of the MSHG experiment (NOMOKE measurements) the phase mismatch Dk k , and in transmission NFE geometry Dk k . For a transparent film Aij are real constants. Thus, Eq. (1) for the MSHG intensity takes the form: I2 E( (2 ) 2 = E Sd(2 )+ iE SdM(2 , M) + iK. (E Bd(2 )+ iE BdM(2 , M) 2 2 − Kij (2)BdM Mm )E jklm j Ek
(2)
where P (2 ) and P (2 , M) are the i-th components of the surface, nonmagnetic and magnetization-induced nonlinear polarizations, respectively; (2)Sd and (2)SdM are the dipole surface, ijk ijkl nonmagnetic and magnetic susceptibilities, respectively, and 1 is the phase shift between them; E j is the component of a fundamental field; G0 is the Green function for the surface nonlinear sources, the integration is over the subsurface layer Dz. It is important that G0 gives only a numerical factor g0 in the nonlinear polarization and does not change the phase of the SH fields generated by the surface nonlinear polarizations. In a transparent magnetic material 1 =p/2 off-resonance conditions. The bulk i-th component of the SH field is given by: E Bi (2 )=
i E Aij ( (2)Bd jkl k (z)E l (z) Dk
8 (2)Sd + i (2)SdM Ml + iKij (2)Bd ijk ijkl jkl
(P SCr (2 ) +P SM i i (2 , M))G0dz% i1
8
171
(4)
where Kij are real constants for a transparent film. It follows from Eq. (4) that at off-resonance, as 1 = 2 = p/2, odd in magnetization changes of the SHG intensity are determined by the interference of magnetization-induced SH fields and those independent from magnetization and, as a consequence, are described by surface-bulk homodyne cross(2)BdM (2)BdM terms: ( (2)Sd Mm ) and ( (2)Sd Ml ). ijk jklm ijk jklm Both these products are not supposed to be small in spite of the small factor of magnetic susceptibility as a factor of nonmagnetic (crystallographic) susceptibility is large. At pre-resonant or resonant conditions, as 1 " p/2 and 2 " p/2, a number of magnetic/nonmagnetic homodyne cross-terms can appear in Eq. (4). In this case the reference SH fields from the noncentrosymmetric bulk of the film are supposed to be dominate contribution to the MSHG intensity, and the largest contribution to odd in magnetization changes of the SHG response are described by the large homodyne cross-term ( (2)Bd (2)BdM Ml ). jkl ijkl
172
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173
This is worth noting that for the sake of simplicity the internal homodyne MSHG effect has been considered in this model for a semi-infinite magnetic medium. For films of a finite thickness or for particles of finite size, the tensor elements Aij and Kij in Eqs. (3) and (4) should be complex. It will bring about the appearance of additional homodyne cross-terms in Eq. (4) both at a resonance and off-resonance fundamental wavelength.
lation between GMR and NOMOKE has appeared. I thank T.V. Murzina, A.A. Nikulin, N.A. Kotov, J. Gu¨ dde, G. Marowsky and A.F. Kravets for the long-term collaboration in this area and the opportunity to use the results of collaborative research in this review. This reviewing work was partly supported by NATO grants PST.ARW.977033 and PST.CLG.975264, the Russian Foundation of Basic Research grants 0002-16253 and 01-02-17524, and grant for Leading Russian Science Schools 00-15-96555.
5. Summery of review The electronic and magnetic properties of Co nanoparticles in the Cox Ag1 − x granular films are experimentally studied by means of SH generation and NOMOKE in the combination with giant magnetoresistance measurements. The giant magnetoresistance coefficient and the NOMOKE contrast non-monotonously depend on the content of magnetic component in the granular films. The maximum of the NOMOKE magnetic contrast is attained at the magnetic component concentration value that weakly depends on the fundamental wavelength and is close to that for the maximum of the giant magnetoresistance. This observation is the manifestation of the basic links between these two phenomena [1]. Magnetization-induced SH generation in layerby-layer assembled films containing YIG nanoparticles is observed. The SHG intensity, including its magnetization-induced component, linearly increases with the number of self-assembling layers, which indicates that SHG occurs in its incoherent form: hyper-Rayleigh scattering [2]. The NOMOKE in HRS has a noticeable magnetic contrast brought about by the internal homodyne mechanism. The phenomenological model of the internal homodyne mechanism of the enhancement of intrinsically weak magnetization-induced effects is considered for magnetic nanoparticles [3].
Acknowledgements I gratefully acknowledge Professor E. Matthias for fruitful discussions in which the idea of corre-
References [1] T.V. Murzina, T.V. Misuryaev, A.F. Kravets, J. Gu¨ dde, D. Schuhmacher, G. Marowsky, A.A. Nikulin, O.A. Aktsipetrov, Surf. Sci. 482 – 485 (2001) 1101. [2] T.V. Murzina, A.A. Nikulin, O.A. Aktsipetrov, J.W. Ostrander, A.A. Mamedov, N.A. Kotov, M.A.C. Devillers, J. Roark, Appl. Phys. Lett. 79 (2001) 1309. [3] T.V. Murzina, A.A. Fedyanin, T.V. Misuryaev, G.B. Khomutov, O.A. Aktsipetrov, Appl. Phys. B 68 (1999) 537. [4] G. Lu¨ pke, Surf. Sci. Rep. 35 (1999) 75. [5] J.F. McGilp, Phys. Stat. Sol. A 175 (1999) 153. [6] O.A. Aktsipetrov, P.V. Elyutin, A.A. Fedyanin, A.A. Nikulin, A.N. Rubtsov, Surf. Sci. 325 (1995) 343. [7] T.F. Heinz, in: H.-E. Ponath, G.I. Stegeman (Eds.), Nonlinear Surface Electromagnetic Phenomena, North Holland, Amsterdam, 1991, p. 355. [8] O.A. Aktsipetrov, P.V. Elyutin, A.A. Nikulin, E.A. Ostrovskaya, Phys. Rev. B 51 (1995) 17591. [9] R.-P. Pan, H.D. Wie, Y.R. Shen, Phys. Rev. B 39 (1989) 1229. [10] T. Rasing, J. Magn. Magn. Mater. 165 (1997) 35. [11] O.A. Aktsipetrov, O.V. Braginskii, D.A. Esikov, Sov. J. Quantum Electron. 20 (1990) 259. [12] O.A. Aktsipetrov, O.V. Braginskii, D.A. Esikov, In: Proceedings of ICONO-13, Minsk, USSR, 1988, Vol. 2, pp. 142. [13] N.N. Akhmediev, S.B. Borisov, A.K. Zvezdin, I.L. Lyubchanskii, Y.V. Melnikov, Sov. Physics-Solid State 27 (1985) 650. [14] J. Reif, J.C. Zink, C.-M. Schneider, J. Kirschner, Phys. Rev. Lett. 67 (1991) 2878. [15] J. Reif, C. Rau, E. Matthias, Phys. Rev. Lett. 71 (1993) 1931. [16] J. Hohlfeld, E. Matthias, R. Knorren, K.H. Bennemann, Phys. Rev. Lett. 78 (1997) 4861. [17] J. Gu¨ dde, U. Conrad, V. Jaehnke, J. Hohlfeld, E. Matthias, Phys. Rev. B 59 (1999) R6608. [18] G. Spierings, V. Koutsos, H.A. Wierenga, M.W.J. Prins, D. Abraham, T. Rasing, Surf. Sci. 287 – 288 (1993) 747.
O.A. Aktsipetro6 / Colloids and Surfaces A: Physicochem. Eng. Aspects 202 (2002) 165–173 [19] G. Spierings, V. Koutsos, H.A. Wierenga, M.W.J. Prins, D. Abraham, T. Rasing, J. Magn. Magn. Mater. 121 (1993) 109. [20] B. Koopmans, M.G. Koerkamp, T. Rasing, H. van den Berg, Phys. Rev. Lett. 74 (1995) 3692. [21] A. Kirilyuk, Th. Rasing, B. Doudin, J.-P. Ansermet, J. Appl. Phys. 81 (1997) 4723. [22] Discussion with Professor E. Matthias. [23] T.V. Murzina, E.A. Ganshina, V.S. Guschin, T.V. Misuryaev, O.A. Aktsipetrov, Appl. Phys. Lett. 73 (1998) 3769. [24] Yu.G. Pogorelov, G.N. Kakazei, J.B. Sousa, A.F. Kravets, N.A. Lesnik, M.M. Pereira de Azevedo, M. Malinowska, P. Panissod, Phys. Rev. B 60 (1999) 12200. [25] R. Wolfe, Thin Solid Films 216 (1992) 184. [26] O.A. Aktsipetrov, A.A. Fedyanin, A.V. Melnikov, E.D. Mishina, T.V. Murzina, Jpn. J. Appl. Phys. 36 (1998) 48.
173
[27] R.V. Pisarev, B.B. Krichevtsov, V.N. Gridnev, V.P. Klin, D. Frohlich, C. Pahlke-Lerch, J. Phys. 5 (1993) 8621. [28] V.V. Pavlov, R.V. Pisarev, A. Kirilyuk, T. Rasing, Phys. Rev. Lett. 78 (1997) 2004. [29] J.W. Ostrander, A.A. Mamedov, N.A. Kotov, J. Am. Chem. Soc. 123 (2001) 1101. [30] O.A. Aktsipetrov, I.M. Baranova, Y.A. Ilinskii, Sov. Phys. JETP 64 (1986) 167. [31] N.I. Koroteev, M. Endemann, R.L. Byer, Phys. Rev. Lett. 43 (1979) 398. [32] O.A. Aktsipetrov, G.M. Georgiev, I.V. Mityusheva, A.G. Mikhailovskii, A.N. Penin, Sov. Physics-Solid State 17 (1975) 1324. [33] O.A. Aktsipetrov, A.A. Fedyanin, A.V. Melnikov, E.D. Mishina, A.N. Rubtsov, M.H. Anderson, P.T. Wilson, M. ter Beek, X.F. Hu, J.I. Dadap, M.C. Downer, Phys. Rev. B 60 (1999) 8924.