Resonant enhancement of the transversal Kerr effect in the InMnAs layers

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2010 J. Phys.: Condens. Matter 22 396002

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IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 22 (2010) 396002 (9pp) doi:10.1088/0953-8984/22/39/396002

Resonant enhancement of the transversalKerr effect in the InMnAs layersE A Gan’shina1,5, L L Golik2,5, V I Kovalev2, Z E Kun’kova2,A G Temiryazev2, Yu A Danilov3, O V Vikhrova3, B N Zvonkov3,A D Rubacheva1, P N Tcherbak1, A N Vinogradov1

and O M Zhigalina4

1 Department of Physics, Moscow State University, Moscow 119992, Russia2 Institute of Radio Engineering and Electronics (Fryazino Branch), RAS, VvedenskiiSquare 1, Fryazino 141190, Russia3 Physicotechnical Research Institute, Nizhny Novgorod State University, Gagarin Prospekt23/3, Nizhny Novgorod 603950, Russia4 Institute of Crystallography, RAS, Leninskii Prospekt 59, Moscow 119333, Russia

E-mail: eagan@mail.ru and llg@ms.ire.rssi.ru

Received 4 June 2010, in final form 16 August 2010Published 14 September 2010Online at stacks.iop.org/JPhysCM/22/396002

AbstractSpectral dependences of the transversal Kerr effect (TKE) as well as of the real and imaginaryparts of the permittivity of InMnAs layers were studied. Pulsed laser ablation of Mn and InAstargets was used to form the layers on GaAs(100) substrates. Spectra of the optical constantsand TKE depended substantially on layer fabrication conditions and testified to the presence ofMnAs inclusions in the samples. The cross-sectional transmission electron microscopy revealedthe presence of inclusions of size 10–40 nm in the layers. At room temperature a strong resonantband was observed in the TKE spectra of the InMnAs layers in the energy range of 0.5–2.2 eV.In this band the TKE was comparable in magnitude but opposite in sign to that in the strongferromagnetic MnAs. The resonant character of the TKE spectra was explained by excitation ofsurface plasmons in the MnAs nanoclusters embedded in the InMnAs semiconductor host.Modelling the TKE spectra for (InAs)1−X :(MnAs)X nanocomposites in the effective-mediumapproximation (Maxwell–Garnett approximation) confirmed the assumption on the plasmonmechanism of the resonant enhancement of the transversal Kerr effect in the InMnAs layers.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Diluted magnetic semiconductors (DMS) (III, Mn)V, inparticular In1−x Mnx As, are the subject of intensive researchsince they are considered as prospective materials forsemiconductor spintronics [1]. The Curie temperature (TC)of the In1−x Mnx As layers fabricated by low-temperaturemolecular-beam epitaxy (LT-MBE) is 90 K [2], while the TC

value of the layers grown with the use of metal–organic vapourphase epitaxy (MOVPE) is higher than room temperature(∼330 K) [3]. The high-temperature ferromagnetism in theIn1−x Mnx As layers (x = 0.03–0.08) has been attributed by the

5 Authors to whom any correspondence should be addressed.

authors of [4, 5] to the presence of atomic scale clusters of Mn(dimers and trimers) in the InMnAs lattice.

The issue of the relation of magnetic properties, especiallyhigh Curie temperatures in some DMS, to the presence ofnanoscale regions with essentially differing concentrationsof magnetic ions (particularly inclusions of nanoclusters ofother magnetic phases) is actively discussed now [6, 7]. Thepresence of ferromagnetic nanoclusters in a semiconductorhost leads also to the occurrence of some interesting properties.It was reported [8] that low concentrations of the secondarymagnetic phase (MnAs nanoclusters) in the (Ga, Mn)Asfilms enhanced the coercivity by a factor up to ∼100. Theconsiderable increase of the Faraday rotation and magneticcircular dichroism (MCD) [9, 10], as well as of the

0953-8984/10/396002+09$30.00 © 2010 IOP Publishing Ltd Printed in the UK & the USA1

J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

Table 1. Growth conditions and some parameters of the samples.

SampleTechnologyparameter, YMn

InMnAs layerthickness, d (nm)

Share of MnAsvolume fraction, XMnAs

Layer thickness,dell (nm) (ellipsometry)

#0 0 (InAs) 190 0 200 ± 1#1 0.05 120 0.03 130 ± 1#2 0.09 120 0.055 ± 0.005 103 ± 1#3 0.13 130 0.055 ± 0.005 111 ± 1#4 0.2 220 – –#5 0.26 270 – –#6 1 (MnAs) 320 1 –

transversal [11] and polar [12] Kerr effects was observed in theGaAs:MnAs granular layers at room temperature. These layerswere fabricated by thermal annealing of the Ga1−x MnxAslayers grown by the LT-MBE method. The values of themagneto-optical effects in such layers were comparable tothose observed in bulk MnAs, while the proportion of MnAsvolume fraction in the granular layers was only a few percent. On this basis the conclusion of a substantial enhancementof the magneto-optical effects in the GaAs:MnAs granularfilms was made. These films are considered as promisingmaterial for magneto-optical devices [10], but the nature ofthe strong magneto-optical effects in them is not clarified.The similar enhancement of the MCD was observed in theIn0.52Al0.48As:MnAs films with 12% content of Mn in thespectral range E = 1.2–2.4 eV [13].

The InMnAs layers, being ferromagnetic at roomtemperature, have been fabricated by pulsed-laser ablationof solid targets (Mn and InAs) in a flow of hydrogen andarsine [14, 15]. The Mn quantity in the layers has beencontrolled by changing the ratio of sputtering times of the Mnand InAs targets (YMn = tMn

tMn+tInAs) and substrate temperature

(Tg). An anomalous Hall effect with a hysteresis loop has beenobserved in the layers at T = 295 K [15]. The properties ofsuch layers are of considerable interest.

Magneto-optical (MO) spectroscopy is an effectivemethod to obtain the unique information on the electronic andmagnetic structure of inhomogeneous ferromagnetics. Onecan expect that MO study of the InMnAs layers will allow usto reveal the specific features, which are due to the presenceof MnAs inclusions and Mn ions in different site positions,as well as to a change of the electronic structure with Mndoping. In [16] we have explored the InMnAs layers grownby laser ablation at Tg = 280–320 ◦C, YMn = 0.25 and 0.33using magneto-optical (the transversal Kerr effect) and optical(spectral ellipsometry) techniques. Several bands causedby electronic transitions in the MnAs inclusions have beendetected in the TKE spectra of these layers. With decreasingYMn a number of changes have been observed in the TKEand permittivity spectra, which have been explained by MnAscontent reduction and competition of contributions from theIn1−x Mnx As host and MnAs inclusions.

This paper presents the results of a study of the evolutionof the transversal Kerr effect and permittivity spectra forInMnAs layers, grown by the laser ablation technique at lowerYMn values than in [16]. A resonant enhancement of thetransversal Kerr effect was observed in some InMnAs layers.We suppose that this TKE enhancement is caused by excitation

of surface plasmons in the MnAs nanoclusters embedded in theIn1−xMnx As semiconductor host.

2. Samples and experimental methods

The InMnAs layers were grown on GaAs(100) substrates byNd:YAG pulsed-laser ablation of the InAs and Mn targets ina flow of hydrogen and arsine at YMn = 0.05–0.26 and Tg =320 ◦C. Fabrication conditions and thickness of these layers(samples #1–#5) are shown in table 1. The parameters forInAs (#0) and MnAs (#6) reference samples fabricated by laserablation of the InAs and Mn targets (respectively) in a flow ofarsine are also specified in table 1. Electrical, magnetic andmagneto-transport properties of the InMnAs layers, grown inthe same conditions as samples #1–#5, were studied in [15, 17].According to the x-ray diffraction data all the layers had goodcrystal quality, and in samples #4, #5 inclusions of the MnAshexagonal phase were found [15].

The transversal Kerr effect (TKE) consists in an intensityvariation of the p-polarization light reflected by the sampleunder magnetization. The value

δ = [I (H ) − I (0)]/I (0), (1)

where I (H ) and I (0) are the reflected light intensities in thepresence and absence of a magnetic field, respectively, wasdirectly measured in the experiment. The alternating magneticfield up to 3 kOe was aligned parallel to the sample surfaceand perpendicular to the light incidence plane. The sensitivityof the apparatus was 10−5. The TKE spectra were recorded inthe energy range of 0.5–4.4 eV. In most cases a light incidenceangle was about 70◦. The temperature range for the studies wasT = 30–310 K.

The spectral ellipsometry technique, atomic forcemicroscopy and magnetic force microscopy, and alsotransmission electron microscopy, were used to characterizethe layers under study. Spectra of the ellipsometry parameters,tan � and cos � [18], were measured in the energy rangeE = 1.43–4.7 eV at T = 293 K employing the automaticexperimental set-up [19]. The lower range limit of themeasurements was determined by the GaAs absorption edge,because interference arising in the substrate made difficulta selection of sample models used in the ellipsometry dataprocessing. The measurement accuracy of the tan � and cos �

values was 2 × 10−5 and 5 × 10−5, respectively.Atomic force microscopy (AFM) and magnetic force

microscopy (MFM) allowed us to derive data about surface

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J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

topography and microscopic magnetic structure of the layersat room temperature. A SmartSPM™-1000 scanning probemicroscope6 was applied. The tip was magnetized vertically(along the needle) with a permanent magnet. The magneticimages were recorded using a two-pass procedure. First, thesurface topography was determined with the use of the tappingmode. Then the needle followed the same path, keeping aconstant height above the surface (lift mode). When usingthis procedure the surface geometry image and magnetic imagewere obtained simultaneously. A phase shift of cantilevervibrations induced by the magnetic interaction between themagnetized tip and the sample was measured.

Transmission electron microscopy (TEM) gave informa-tion on the structure of the InMnAs layers. Cross-sectionalTEM specimens were prepared by a standard method of me-chanical polishing followed by Ar ion thinning. Conventionaland high-resolution observations were performed on a TecnaiG230ST electron microscope (equipped with a device forenergy-dispersive analysis) operating at an accelerating voltageof 300 kV.

3. Results and discussion

3.1. Spectral ellipsometry

The spectra of the ellipsometry parameters, tan �(E) andcos �(E), for the InAs and InMnAs layers measured at 70◦angle of incidence are shown in figures 1(a) and (b). Thespectra for samples #2 and #3 are almost the same, thereforethey are displayed for sample #2 only. Increase of theYMn value leads to increasing the ellipsometry parameters forsamples #1–# 5 compared with those for the InAs sample (#0).The well-marked maximum at the tan �(E) dependence in therange E ≈ 2.4–3 eV results from optical transitions near thecritical L point of the Brillouin zone in InAs. In the rangeE ≈ 1.4–2.2 eV the less intensive bands are observed, themaximum location depending on the layer thickness. The latterpoints to an interference origin of the low-energy bands.

The ellipsometry data were processed with the samplemodel, which included the substrate and two-layer mediumcomposed of the InMnAs layer and a damaged surface layer(mixture of the InAs oxides and an air void). In the selectionof model parameters the InMnAs layer was considered as amixture of InAs and MnAs. The Bruggeman effective-mediumapproximation and spectral dependences of the refraction nand extinction k indices for InAs, GaAs [20], MnAs [21]and InAs oxides [22] were used. We used the data [21]for MnAs, because a strong surface roughness of our MnAslayers hampered a determination of the optical constants frommeasured spectra. The characteristics of the layer irregularitiesobtained by the AFM measurements were taken into account inthe model construction. The selected parameters of the double-layer model for samples #0 and #1–#3 are given in table 2.

The tan �(E) and cos �(E) spectra simulated with theseparameters for samples #0, #1 and #2 are shown in figures 1(a)and (b) as solid curves. As seen in the figure, the calculatedspectra well approximate the experimental ones, but the

6 www.aist-nt.com.

Figure 1. Spectral dependences of the ellipsometry parameters,tan �(E) (a) and cos �(E) (b), for the InAs (#0) and InMnAs(#1–#5) layers, and also those calculated for the 130 nm thick InAslayer using the tabulated data [20] (the curves ‘tab’). T = 293 K.The spectra simulated for samples #0, #1 and #2 using theparameters given in table 2 are shown by solid lines. In (a) thespectra for samples #1 and #2 are shifted up by 0.03 and the righty axis corresponds to the curves for samples #4 and #5.

doublet structure of the maximum, which is clearly defined atthe calculated tan �(E) curves, is smeared in the experimentalspectra for samples #1 and #2. The exploitation of the tabulateddata for the undoped InAs semiconductor [20] instead ofreal characteristics of the InMnAs layers, which contain highconcentrations of Mn impurities and structural defects, couldbe the reason for the observed discrepancy. The interferencefringes in the experimental spectra (E ≈ 1.4–2.2 eV) forsamples #0 and #1–#3 have allowed us to estimate a thickness(dell) of the layers. The obtained dell values are given intable 1. One can see they differ insignificantly from thethickness evaluations derived using the calibration curves ofthe technological process. For samples #4 and #5 satisfactorycoincidence of the calculated and measured tan �(E) andcos �(E) spectra was reached using multilayer models (withminimal number of layers N = 4). It points to inhomogeneity

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J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

Table 2. Parameters of the sample models used.

Sample #1 #2 #3 #0

Parametersof the first layer

Composition:InAs oxides (50%)+ void (50%)Thickness = 3.5 nm

Composition:InAs oxides (50%)+ void (50%)Thickness = 6.5 nm

Composition:InAs oxides (50%)+ void (50%)Thickness = 4.5 nm

Composition:InAs oxides (50%)+ void (50%)Thickness = 3 nm

Parameters of thesecond layer

Composition:InAs (97 ± 0.5)%+ MnAs (3 ± 0.5)%Thickness = 130 ± 1 nm

Composition:InAs (94.5 ± 0.5)%+ MnAs (5.5 ± 0.5)%Thickness = 103 ± 1 nm

Composition:InAs (94.5 ± 0.5)%+ MnAs (5.5 ± 0.5)%Thickness = 111 ± 1 nm

Composition:InAs (100%)Thickness = 200 ± 1 nm

Substrate GaAs GaAs GaAs GaAs

of samples #4 and #5 through the thickness and, in particular,to increased MnAs content near their surface. A largenumber of adjustable parameters did not allow us to apply themultilayer models for processing the ellipsometry spectra ofthese samples. For this reason we used the double-layer modelfor samples #4 and #5 also. The resulting optical constantsare effective characteristics of the non-uniform layers. Notethat the ellipsometry data point to the presence of the MnAsphase in all samples #1–#5. The estimations for a share of theMnAs volume fraction (XMnAs) in samples #1–#3 are shown intable 1.

The derived ε1(E) and ε2(E) spectra for the InMnAs andInAs layers are displayed in figures 2(a) and (b). The ε1(E)

and ε2(E) spectra plotted with the tabulated data for InAs [20]are shown by dotted lines. As seen in figure 2, the obtaineddependences for the InAs layer (#0) practically coincide withthe tabulated spectra for InAs. The peaks corresponding to theoptical transitions near critical points of the Brillouin zone inthe InAs parent compound are well marked in the ε2(E) spectrafor the InMnAs layers (#1–#3). It is evidence of the goodcrystal quality of these layers. An increase of host imperfectionwith the Mn doping and the presence of the MnAs inclusionsare possible reasons for decreasing the maxima, smearing thedoublet (E ≈ 2.5–2.8 eV) and increase of the ε2 values in theregion E < 2 eV in the spectra of samples #1–#3. Along withthe mentioned reasons the more essential transformation of theε1(E) and ε2(E) spectra for samples #4 and #5 is explained bythe interference caused by the inhomogeneity of these layersthrough the thickness, which is ignored in the double-layermodel.

3.2. AFM and MFM data

All InMnAs samples revealed some magnetic contrast atroom temperature. Topography of the surface and magneticforce microscopy (MFM) images of the same surface regions,obtained for samples #4 and #5, are displayed in figure 3.When the YMn parameter decreases, the magnetic contrastfor samples #4–#1 becomes weaker, and at the same timeits characteristic sizes are changed slightly. The strongestmagnetic contrast but with the smaller inhomogeneity sizeswas observed for sample #5. Since the lateral sizes of thesurface irregularities for sample #5 are appreciably larger thanthose for sample #4 (figures 3(a) and (b)), one cannot associatethe magnetic structure of the InMnAs layers with the surfaceirregularities. The MFM images for samples #1–#4 are similar

(a)

(b)

Figure 2. Spectral dependences of the real ε1 (a) and imaginary ε2

(b) parts of the diagonal components of the permittivity tensor for theInMnAs (#1–#5) and InAs (#0, ‘tab’) layers. (The spectra forsamples #2 and #3 are almost the same.) T = 293 K.

to those for the GaAs:MnAs layers containing the hexagonalMnAs clusters with sizes of 10–20 nm [23].

3.3. TEM data

Cross-sectional TEM images have been obtained for theInMnAs samples #1 and #2. The diffraction patterns of these

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J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

Figure 3. Topography of the surface ((a), (b)) and MFM images ((c),(d)) of the same surface regions for samples #4 ((a), (c)) and #5 ((b),(d)). Spatial resolution of the MFM images is approximately 100 nm.

samples are characteristic for cubic crystal structure of the zincblende type. They do not contain any additional reflectionsand testify to high crystal perfection of the samples. Roundedinclusions of the size 10 and 40 nm are visible in the TEMimage of sample #2, which is presented in figure 4. Misfitdislocations near the border with the GaAs substrate are alsoseen in the figure. In sample #2 the presence of In, As andMn was detected, the Mn and As content increasing near to thesample surface. Any inclusions were not revealed in the TEMimages of the explored regions for sample #1. A lower densityof inclusions could be the cause of their absence in the TEMimages for this sample.

3.4. Transversal Kerr effect

The TKE spectral dependences for the InMnAs (#1–#5) andMnAs (#6) samples measured at T = 293 K and T = 30 K areshown in figures 5(a) and (b). Two positive bands are seen inthe spectrum for the MnAs sample (#6) at T = 293 K. Theseare the strong low-energy (LE) band with a maximum at E1 ≈2.4 eV and the weaker high-energy (HE) band at E2 ≈ 3.5 eV.As seen in figure 5(b), the magnitude of the TKE increaseswith a decrease in the sample temperature and two peaks withE1a ≈ 2.0 eV and E1b ≈ 2.6 eV become spectrally resolved inthe energy range of the LE band. According to [24, 25] theobserved peculiarities can be associated with the transitionsbetween fully and partly occupied spin-up sub-bands formedby the 3d states of Mn and 4p states of As, respectively.

In our previous study [16] these features were observedin the TKE spectra of the InMnAs layers fabricated at Tg =280–320◦C, YMn = 0.25 and 0.33. It was evidence forthe presence of the MnAs inclusions in the layers. Themagnitude of the TKE in the InMnAs layers decreased withdecrease of the YMn value. This decrease was stronger in theHE band than in the LE band, the peak at E1b ≈ 2.6 eVdisappearing. In addition, the low-energy TKE peak (at E1a ≈

Figure 4. Cross-sectional TEM image of the border region forsample #2. Two inclusions of the rounded form (with the moirepattern) are visible.

Figure 5. The TKE spectral dependences, δ(E), for the InMnAs andMnAs layers measured at T : (a) 293 K and (b) 30 K. Inset: the TKEspectrum of the GaAs:MnAs sample, T = 293 K [11].

2.0 eV) exhibited a shift towards the lower energies (to E ≈1.6–1.8 eV).

The TKE spectra for sample #5 (YMn = 0.26) displaysimilar behaviour, as is evident from figure 5. The peak withEmax ≈ 1.75 eV and the wide band in the region E > 2.5 eV,which were observed in [16], are well defined in the spectra.At the same time the δ(E) dependences for this sample are

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J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

different from the spectra reported in [16] by the presence ofthe band with Emax ≈ 0.85 eV. In samples #4–#1, as the YMn

value decreases, the TKE magnitude appreciably decreases inthe region E > 2.2 eV and the pronounced TKE band consist-ing of one positive and one negative component appears in therange 0.5–2.2 eV. As a result of such changes the TKE spectrafor samples #4–#1 acquire the resonant character. In the regionof the new band the TKE sign is opposite to that in the MnAslayer. In the resonance region the TKE signal decreases withdecreasing the YMn parameter, but in all samples #4–#1 theTKE values are comparable to those in ferromagnetic MnAs.Under cooling the TKE signal is enhanced, but the spectralshape of the resonant band does not vary.

Temperature dependences, δ(T ), were measured nearto a maximum of the positive peak of the TKE resonantband for samples #1–#4 and in the region of the largerpeak (E = 1.67 eV) for sample #5. For MnAs (#6) thetemperature dependence was measured in the HE band region(E = 3.49 eV), since spectral resolution of the LE bandscan influence on δ(T ) behaviour. For samples #1, #3–#6the δ(T ) dependences are of monotonic behaviour with oneregion of the abrupt rise, T1 ≈ 310–250 K. For sample #2,besides this region the abrupt rise of the δ value is alsoobserved at T2 < 80 K. Figure 6 shows the normalizeddependences, δ(T )norm = δ(T )/δT =80 K, for the InMnAsand MnAs layers. The δ(T )norm curves for samples #1 and#4 coincide with those for samples #5 and #3, accordingly.Therefore, the former curves are not displayed in the figure.Except for the low-temperature region for sample #2, thetemperature dependences, δ(T )norm, for the InMnAs layersare similar to the normalized M(T )/Mo dependences ofthe magnetization for MnAs and GaAs:MnAs (here Mo—the saturation magnetization), which have been reproducedfrom the data [26, 12, 27]. On this basis it is possible toconclude that the high-temperature ferromagnetic behaviour inall explored InMnAs layers is caused by the presence of theMnAs inclusions.

The δ(T ) curve for sample #2, having two regions ofthe sharp rise, is characteristic for a medium containingtwo magnetic phases. The similar behaviour of the M(T )

dependence was observed in the Ga1−x MnxAs layers withembedded MnAs nanoclusters [28]. The authors explainedthe low-temperature region of the sharp magnetization riseby the ferromagnetic ordering of the semiconductor host.Apparently, the low-temperature region of the rise at theδ(T ) curve for sample #2 (T < 80 K) is also due to thecontribution of the In1−xMnx As ferromagnetic host to theTKE. It is known that the presence of free holes is the necessarycondition for the ferromagnetic ordering in the (III, Mn)Vsemiconductors. According to the results of the magneto-transport measurements performed on the samples of thisseries, namely in sample #2, the highest concentration of freecarriers (holes) was detected [15].

3.5. On the nature of the enhancement of the magneto-opticalresponse in the (III, Mn)As:MnAs granular layers

The detection of the resonant band (E ≈ 0.5–2.2 eV),which has not been observed in magneto-optical spectra

Figure 6. The normalized temperature dependences, δ(T )norm, forthe InMnAs and MnAs layers. E , eV: 1.08 (#2); 1.06 (#3); 1.67 (#5)and 3.49 (#6).

of InMnAs layers earlier, is the most interesting amongthe obtained results. The resonant band is located in thesame spectral region, where the strong bands have beenobserved in the MO spectra of the GaAs:MnAs [9–12]and In0.52Al0.48As:MnAs [13] granular layers containing theMnAs nanoclusters. According to our data (the δ(T )

dependences, ellipsometry spectra, MFM and TEM data) theMnAs nanoclusters are also present in the investigated InMnAslayers.

The physical mechanisms responsible for the strongmagneto-optical effects in the (III, V):MnAs granularlayers are not ascertained now. Since the enhancementof the magneto-optical effects in the GaAs:MnAs andIn0.52Al0.48As:MnAs layers occurred in the spectral regionnear to the absorption edge of their semiconductor hosts, theauthors [9, 13] assumed that the MCD signal coming from theMnAs clusters was enhanced by an optical transition of freecarriers at the energy gap of the semiconductor host. The insetin figure 5(a) shows the TKE spectrum for the GaAs:MnAsgranular film (XMnAs ≈ 0.03) containing the MnAs clusterswith an average diameter of 6 nm [11]. It is seen that theshape and energy position of the TKE bands are close for theGaAs:MnAs and InMnAs (#1–#4) layers, so one can assumethat these bands are of the same nature. However, in contrast toGaAs:MnAs the TKE band for the InMnAs samples is locatedin the fundamental absorption region of the semiconductorhost, and the assumption [9] cannot explain the resonantcharacter and high values of the TKE in the InMnAs layers.

In [11] excitation of the plasmons in the MnAsnanoclusters was specified among the possible causes of theTKE enhancement in the GaAs:MnAs granular films. Theabsorption band with Emax ≈ 0.9 eV was detected inthe GaAs:MnAs films in [29] and the authors related thisband to excitation of the surface plasmons in the MnAs

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J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

clusters. A possibility of the enhancement of magneto-optical response in the composite medium, consisting offerromagnetic nanoparticles embedded into a dielectric host,by exciting the surface plasmons in the particles was showntheoretically in [30, 31]. In our opinion, it is this mechanismthat is responsible for the resonance character of the TKEspectrum in the studied InMnAs layers.

It is known that the surface plasma oscillations in sphericalmetal clusters embedded in a transparent dielectric host can beexcited at the photon energy, Esr, satisfying to the followingcondition [32]:

ε1m(Esr) = −2ε10(Esr). (2)

Here ε1m and ε10 are the real parts of the diagonal componentsof the permittivity tensor for the metallic particles and the host,accordingly. For the solution of equation (2) we used the ε1(E)

dependence for α-MnAs given in [21]7. The ε1(E) dependencefor InAs [20] was used as ε01(E) for the host. The obtainedenergy of the spherical plasmon resonance, Esr ≈ 0.8 eV,conforms to the low-energy part of the experimental resonantTKE band in the InMnAs layers. Note that the expression (2)is valid for a transparent dielectric host. In our case, theresonant band is in the fundamental absorption region of thehost (Eg ≈ 0.37 eV for InAs). Therefore the obtained value,Esr ≈ 0.8 eV, is evaluated for InMnAs. Use of equation (2) todefine the Esr value is more valid for the GaAs:MnAs granularlayers (Eg ≈ 1.43 eV for GaAs). The graphical solutionof equation (2) with the use of the ε1(E) dependence forGaAs [33] gives the value Esr ≈ 0.9 eV for GaAs:MnAs. Thenegligible distinction of the Esr values derived for InAs:MnAsand GaAs:MnAs is a consequence of the small difference in theε10 magnitudes for the InAs and GaAs hosts in the consideredspectral range. The small distinction of the Esr values explainsthe close spectral location of the TKE bands for the InMnAs(#1–#4) and GaAs:MnAs [11] layers (figure 5(a)).

For sample #5 the character of the TKE spectrumdiffers from the resonant one. In the energy region E >

2 eV the relatively intensive band due to the interbandtransitions in MnAs is observed. In the low-energy rangetwo maxima are clearly visible. Analysing the ellipsometryspectra we concluded that there was a high content of MnAsinclusions near the surface of sample #5. On this basis itis possible to explain the TKE spectrum in the low-energyregion by a superposition of a contribution originating fromrelatively large (‘bulk’) near-surface inclusions of MnAs and asmaller contribution from the surface plasmons in the MnAsnanoclusters. Possibly, the change in dimensions of theinhomogeneities in the magnetic image for sample #5 isalso related to the presence of the ‘bulk’ near-surface MnAsinclusions.

3.6. TKE spectra calculation for (In As)1−X :(Mn As)X

composites: comparison with the experiment

To check the assumption on the plasmon mechanism ofthe TKE resonant enhancement in the InMnAs layers we

7 The spectral range of our ellipsometry set-up does not include the resonanceregion. For this reason, here and below we use the reported spectraldependences of the optical constants for InAs, GaAs and MnAs.

have calculated the δ(E) spectra for (InAs)1−X :(MnAs)X

composites. At first, the diagonal (εe = ε1e − iε2e) andoff-diagonal (ε′

e = ε′1e − iε′

2e) components of the effectivepermittivity tensor, εeff:

εeff =(

εe iε′e 0

−iε′e εe 0

0 0 εe

)(3)

for (InAs)1−X :(MnAs)X have been calculated. To calculate theεeff components we have used the equations obtained within thelimits of the Maxwell–Garnett approximation (MGA), whichrelate the εe and ε′

e to the components of the permittivitytensors for the nonmagnetic (ε0)

ε0 =(

ε0 0 00 ε0 00 0 ε0

)(4)

and magneto-active (εm)

εm =(

εm iε′m 0

−iε′m εm 0

0 0 εm

)(5)

constituents of the composite medium [34]:

εe = ε0

[1 + X

εm − ε0

ε0 + (εm − ε0)(Lm − X L0)

], (6)

ε′e = ε′

m X

[ε0 + (εm − ε0)(Lm − X L0)]2. (7)

Equations (6) and (7) are valid under the conditions ε′m � εm

and X � 1, where X is a share of the volume fraction of themagneto-active inclusions. The case when an internal ellipsoid(with a form factor Lm) is the magnetic component and anexternal ellipsoid (with a form factor L0) is the nonmagneticone is considered.

In the calculations we have used the spectral dependencesfor the real and imaginary parts of the diagonal components ofthe permittivity tensor for InAs (ε0 = ε10 − iε20) and MnAs(εm = ε1m − iε2m) given in [20, 21]. The spectra of theconstituents of the off-diagonal components (ε′

m = ε′1m − iε′

2m)have been calculated using the following formulae [35]:

δ = aε′1m + bε′

2m, (8)

a =(

2A

A2 + B2

)sin 2ϕ,

b =(

2B

A2 + B2

)sin 2ϕ,

(9)

A = ε2m(2ε1m cos2 ϕ − 1

),

B = (ε2

2m − ε21m

)cos2 ϕ + ε1m − sin2 ϕ

(10)

and the δ1,2(E) spectra for MnAs, which were measured by usat two angles of light incidence (ϕ1,2). Then the obtained εe(E)

and ε′e(E) dependences of the effective permittivity tensor

components and the formulae (8)–(10) were used to calculateδ(E) spectra for the (InAs)1−X :(MnAs)X composites.

7

J. Phys.: Condens. Matter 22 (2010) 396002 E A Gan’shina et al

Figure 7. The calculated δ(E) dependences for the(InAs)1−X :(MnAs)X composites: ϕ = 70◦, Lm = 0.53, L0 = 0.33.The experimental δ(E) curve for sample #2 is also shown.

The derived TKE spectral dependences for threeconcentrations of the magnetic phase (X = 0.03, 0.05 and0.1) are shown in figure 7, where the experimental spectrumfor sample #2 is also presented. As follows from the figurethere is a clearly visible maximum at the calculated δ(E)

dependences. This maximum is shifted towards smallerenergies by approximately 0.2 eV in comparison with theexperimental curve. The negative peak at Emin ≈ 1.8 eV isnot observed at all the calculated curves.

The difference between the calculated and experimentalenergy of the maximum can be due to the inequalityof the dimensions and shapes of the nanoclusters. Theuse of the ε0(E) dependences for InAs instead of thosefor the In1−xMnx As real host and insufficient accuracy ofdetermination of the optical constants for MnAs can alsoincrease the error. (The ε1(E) and ε2(E) spectra for MnAspublished by different authors differ considerably [21, 29].) Inour opinion, the absence of the negative peak in the vicinityof 1.8 eV is caused by a competition of two contributionsin the TKE in the considered spectral range. The negativecontribution arises from the surface plasmon resonance of freecarriers and the positive one is due to the interband transitionsin MnAs with the energy E ≈ 2 eV. The excitation of thesurface plasmon resonance in the nanoclusters should resultin an essential attenuation of the light intensity penetratinginto the clusters, and consequently in a decrease of theinterband contribution in the TKE. Perhaps the approximationused takes into account this process to an insufficient degreeand the interband contribution, which provides the positiveTKE signal, prevails at the calculated δ(E) dependences inthe range E ≈ 1.5–2.2 eV. Considering the large numberof approximations, one can believe that the calculated δ(E)

dependences agree closely with the experimental TKE spectrafor the InMnAs layers (#1–#4).

4. Conclusions

Spectra of the transversal Kerr effect and permittivity of theInMnAs layers fabricated by laser ablation have been studied.

The MnAs inclusions have been detected in all layers. Atthe same time the ellipsometry spectra and derived spectra ofthe permittivity components testify to a high crystal qualityof the semiconductor host of the layers with the proportionof the MnAs volume fraction XMnAs ≈ 0.03–0.06 (YMn =0.05−0.13). The ferromagnetic behaviour and transversal Kerreffect in the InMnAs layers at room temperature are due to thepresence of the MnAs inclusions, the shape of the TKE spectradepending on the MnAs content.

In the TKE spectra of the InMnAs layers with XMnAs �0.06 the resonant band has been detected in the energyrange E ≈ 0.5–2.2 eV. In this band region the TKEis comparable in magnitude but opposite in sign to thatin bulk ferromagnetic MnAs. The resonant behaviour ofthe TKE spectra has been explained by the excitation ofthe surface plasmons in the MnAs nanoclusters embeddedin the In1−xMnx As semiconductor host. The TKE spectraof the (InAs)1−X :(MnAs)X composites calculated using theeffective-medium approximation demonstrate the resonantbehaviour in the same spectral region where the experimentalresonant TKE bands are observed. It substantiates theassumption of the plasmon mechanism of the resonantenhancement of the transversal Kerr effect in the InMnAslayers. This mechanism may be the cause of the strongmagneto-optical effects observed in other (III, V):MnAs layersat room temperature [9–13].

Acknowledgments

The work was supported by the Program of the Presidiumof RAS no. 27, the Russian Foundation for Basic Research(grants 08-02-00548 and 08-0297038), the Ministry ofEducation of Russian Federation (projects 2.2.2.2/4297 and2.1.1/2833) and CRDF (grant BP4M01).

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