Magnetism and Metal-Insulator Transition in III-V Based DilutedMagnetic Semiconductors

S. Katsumoto1,2, T. Hayashi1, Y. Hashimoto1, Y. Iye1,2

Y. Ishiwata1, M. Watanabe3, R. Eguchi1, T. Takeuchi4, Y. Harada3, S. Shin1,3

and K. Hirakawa2,5

1Institute for Solid State Physics, University of Tokyo,

5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

2CREST, Japan Science and Technology Corporation,

Mejiro, Tokyo 171-0031, Japan

3RIKEN, Sayo-gun, Hyogo 679-5143, Japan

4Department of Applied Physics, Science University of Tokyo

Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

5Institute of Industrial Science, University of Tokyo,

7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan

abstract

We report experiments on the magnetism and the transport in III-V based diluted mag-netic semiconductors (Ga,Mn)As and (In,Mn)As. Heat treatment (annealing) at compara-tively low temperatures (slightly above the growth temperature) is unexpectedly found tobe effective to improve the ferromagnetism and the metallic conduction. Infrared opticalconductivity measurements and soft x-ray absorption spectroscopy reveal that the doubleexchange model is convenient to describe the ferromagnetism. The transport in the vicinityof metal-insulator critical point was studied in detail by using the low-temperature annealingmethod.

§1 Introduction

Diluted magnetic semiconductors (DMS’s) synthesized byintroduction of magnetic ions into semiconductors are nowexpanding a new horizon of “spin-electronics”. Espe-cially III-V based DMS’s (In,Mn)As and (Ga,Mn)As haveattracted much attention. They undergo ferromagnetictransition at comparatively high temperatures and havehigh connectivity to sophisticated III-V artificial super-structures. A remarkable feature of the ferromagnetismis that it is mediated by the doped holes, which factwas demonstrated by illumination-driven ferromagnetictransition3) and by disappearance of the ferromagnetismby counter doping4).

However the physical mechanism of the ferromagnetismis still under discussion. In a II-IV DMS, it is claimedthat the Ruderman-Kittel-Kasuya-Yosida (RKKY) inter-action is the origin of the transient ferromagnetism5). Thetransport and the response to external magnetic field in(Ga,Mn)As were analyzed along similar interpretation6).This interpretation, however, has an essential difficultythat the estimated amplitude of the exchange constanttends to exceed the Fermi energy. While interpretationsto solve this inconsistency were attempted7), a calcula-tion of band structure8) in (In,Mn)As suggested double-exchange (DE) mechanism is more plausible. Though theresult of the band-calculation is also getting experimentalsupports9), decisive evidence has not appeared yet. In asense, these two pictures describe limiting cases and the

reality should exist between them. It would be meaning-ful, however, to examine which picture is convenient todescribe the experiments.

These materials also shows exotic properties intransport10). Increasing Mn concentration (x) from thedilute limit, they undergo an insulator-to-metal transi-tion (the first MIT). The ferromagnetism appears at aMn concentration slightly lower than the first MI criticalpoint. Further increase in x causes a metal-to-insulatorre-entrant transition (the second MIT).

One of the problems in these materials for researchesand applications is that the qualities of the grown crystalsare too sensitive to the growth conditions because the con-ditions are very far from equilibrium11). In this article, wereport that annealing (heat treatment) at comparativelylow temperatures partly solve the problem. We apply thismethod to explore the picture for the ferromagnetism, andthe nature of the second MIT. Owing to limited space, wemainly discuss the case of (Ga,Mn)As.

§2 Experiment

(Ga,Mn)As films were grown by low temperature molec-ular beam epitaxy (LT-MBE) onto semi-insulating (001)GaAs substrates. The growth temperature was around230C, and the V/III ratio was about 5. These parame-ters were optimized so as to obtain highest TC for eachMn concentration. The nominal Mn concentrations weredetermined from (004) diffraction of x-ray in the as-grown

1

samples.The effect of low-temperature annealing was examined

mainly at x = 0.05. The as-grown wafer was cleaved intosquares of 4×4 mm2. The annealing was performed inN2 gas flow without any coverage of the surfaces12). Theannealing time was fixed to 15 minutes.

The transport above 2K was measured by a conventionalAC bridge with van der Pauw method in a He circulationcryostat. Below 2K, we prepared samples with a Hall-barshape by mesa-etching, which were cooled down to 50mKby a 3He-4He dilution refrigerator.

For infrared conductivity measurement, the wafers werecleaved into pieces of 5×5 mm2 in a He gas flow cryo-stat. The conductivities were measured in a transmission-geometry by using a Fourier transform spectrometer. Theoptical absorption coefficient α(ω) of the epitaxial film(Ga,Mn)As is expressed by the transmission spectrum ofthe insulating GaAs substrate tGaAs and that of the filmtGaMnAs as

α(ω) = log

(

tGaAs

tGaMnAs

)

/d, (1)

where d is the thickness of the film. The transmissionspectra are also connected to the optical conductivity σ(ω)through

tGaAs

tGaMnAs=

∣

∣

∣

∣

1 +σ(ω)d

Y0 + Ys

∣

∣

∣

∣

2

, (2)

wher Y0 and Ys are the admittances of the vacuum andGaAs, respectively.

The x-ray absorption spectroscopy (XAS) was per-formed by using a soft-x-ray spectrometer installed at theundulator beamline BL-2C in Photon Factory of KEK.Synchrotron radiation was monochromatized using a var-ied line spacing plane grating, whoes energy resolution wasless than 0.1 eV at 650eV. The spectra were taken at roomtemperatures.

The growth conditions for (In,Mn)As were the same for(Ga,Mn)As besides the growth temperature, which were30 degrees higher than that for (Ga,Mn)As.

§3 Effect of annealing on the transport

and magnetism

The Mn concentration dependence of the Curie tempera-ture (TC) in as-grown samples was similar to that reportedpreviously10, 13) when the growth conditions are optimizedto maximize TC. However slight difference in the condi-tions results in severe degradation in transport and mag-netism especially around the second MIT. For example,10 degree difference in the growth temperature makes theconduction from metallic to insulating even though thegrowth mode observed by refractive high energy electrondiffraction (RHEED) does not change11). This high sen-sitivity arises from the fact that the growth is very farfrom the equilibrium. This would be an obstacle for re-search and application of these materials. In the followingwe show that low-temperature annealing after the growthwould be a key to solve this problem.

as grown

220C

260C

=310C

(Ga,Mn)As

(K)

Res

isti

vity

(Ω

cm)

T

Ta

10 100

10-2

10-1

100

Figure 1: Temperature dependence of resistivity in as-grownand annealed (Ga,Mn)As films.

Figure 1 shows the temperature dependence of resistiv-ity in (Ga,Mn)As with nominal Mn concentration of 5%.The as-grown sample shows strongly insulating behaviorwith a hump structure around 30K. This hump is known toappear around TC. As demonstrated in Fig.1, by the an-nealing at comparatively low temperature (slightly abovethe growth temperature), the resistivity was lowered andthe hump moved to higher temperatures. This is surpris-ing because it was reported that the annealing at highertemperatures results in the clustering of MnAs14) and evenat comparatively low temperatures the annealing causesdegradation in the transport and the magnetism15).

We summarize the effect of the annealing in Fig.2. TC

and the hole concentration p, which was estimated fromroom temperature Hall coefficient, show maxima aroundthe annealing temperature (Ta) of 260 C while the latticeconstant a decreases monotonically with Ta. The decreasein a is steeper for the higher Ta. For this decrease in a,it is hardly conceivable that Mn atoms ran away from thesubstrate considering the inherent vapor pressure. Therewas no increase in full width at half maximum of the X-ray diffraction peak, which manifests that the annealingcaused no significant inhomogeneity in the films. On theother hand, what is remarkable is that TC reaches 95K,which is highest among so far reported for (Ga,Mn)As di-rectly grown onto GaAs. A more important experimentalfact, which cannot be seen in Fig.2, is that the highestTC obtained by the annealing does not strongly dependon Ta. That is, even if Ta is lower than 260 C, longerannealing time enhances TC to the highest value obtainedfor Ta =260 C in the end. This means that by adoptingthe low-temperature annealing, we can overcome the dif-ficulty due to the sensitivity of the crystalline quality to

2

the growth parameters16).

220 240 260 280 300

5.672

5.674

5.676

70

80

90

100

(C)C (K

)

( 10

19 c

m-3

)(A

)p

Ta

a

T

5

6

7

Figure 2: Material parameters in Ga0.95Mn0.05As (lattice con-stant a, Curie temperature TC, and hole concentration p) as afunction of annealing temperature Ta.

A natural question is what happens in the annealingprocess. Because x of 5% is close to the second MI transi-tion, one might suspect that precipitation of MnAs occursduring annealing and the decrease in the effective Mn con-centration caused the increase in TC and the conductivity.However this is not only simply eliminated by the fact thatTC reaches higher value than those obtained in as-grownsamples but also denied by the dependence of TC

16).Hence answering the above question would be a key to

clarify more essential issue, i.e., the mechanism of the fer-romagnetism.

The annealing technique also gives us a means to controlmaterial parameters finely in a single wafer. We can thusobtain, e.g., a sample which is very close to the MI criticalpoint. In the following sections we discuss our presentunderstanding of these issues based on the experimentson infrared absorption and soft X-ray absorption.

§4 Infrared absorption spectra

Figure 3 shows optical conductivity spectrum σ(ω) of ametallic sample with x = 4.6%17). The gap in the spectrais due to the Reststrahlen band of GaAs. σ(ω) is almostindependent of ω at high temperatures, indicating veryshort scattering time of holes. At 5K, σ(ω) increases withincreasing ω. This behavior is suggestive of hopping trans-port rather than usual metallic Drude conduction.

It also suggests us to reconsider the “metallic” DC con-duction in (Ga,Mn)As10). In the samples with x in therange from 3.5% to 4.8%, the temperature dependence of

0 1000 2000 3000 4000 5000 6000 0.000

0.002

0.004

0.006

0.008 10K

150K

GaMnAs (Mn content = 4%) T

c = 90 K

T s = 225 o C

d = 200 nm

She

et C

ondu

ctiv

ity (

S)

Frequency (cm -1 )

Figure 3: Optical conductivity spectrum σ(ω) of a metallic(Ga,Mn)As sample with x = 4.6%. The parameter is temper-ature varying from down to top as 150, 120, 90, 60, 30, 10K.

the DC resistivity is obviously metallic. However the meanfree path estimated from Hall mobility assuming simpleDrude model, is around 10A, which is extremely short asheavily doped semiconductors. And this mean free pathis, again according to the Drude theory, comparable withthe Fermi wavelength, which result tells that the Drudepicture is totally broken down. Instead of propagation ofholes conserving momentum, we should consider conduc-tion through wavefunctions with strong spatial modula-tion due to disorder. Hence in high energy region, thetransport should be more or less hopping-like in accor-dance with σ(ω) spectra. It seems rather unnatural, then,to apply the picture of RKKY interaction, in which thebasic assumptions are local moments and free electrons(holes) scattered by them.

In order to obtain further information, we investigatedα(ω) in higher frequency range. Figures 4 (a) and (b) showthe α(ω) spectra obtained for semiconducting and metallicsamples respectively. The semiconducting one is as-grownwhile the metallic one is obtained by LT-annealing. Whileα(ω) of the insulating and semiconducting samples vanishin the zero-frequency limit for low temperatures, that ofthe metallic sample remains finite for ω → 0, indicatingthe existence of delocalized holes. The most pronouncedfeature in these spectra is the broad conductivity peak ataround 200meV.

Besides the peak, a remarkable characteristic is the en-hancement in α(ω) with decreasing T in the region below400meV. The enhancement sets in just at TC and is mostpronounced for the metallic sample. According to the sumrule in the oscillator strength, there should be some trans-fer of the spectral weight which corresponds to the en-hancement. Such spectral transfer below TC in a wide

3

energy range is characteristic to DE-driven ferromagnets.Hence the observed transfer in the spectral weight of α(ω)suggests that the double-exchange (together with p − dexchange) is the dominant mechanism for the ferromag-netism.

0 200 400 600 800 0.00

0.01

0.02

0.03

4.2K

300K

(a)

GaMnAs Mn = 5.2 % Ts = 220C, as-grown

Opt

ical

Con

duct

ivity

(S

/ m

)

Photon Energy (meV)

0 200 400 600 800 0.00

0.01

0.02

0.03

(b)

4.2K

300K

GaMnAs Mn = 5.2 % T

s = 220 C, annealed

Opt

ical

Con

duct

ivity

(S

/ m

)

Photon Energy (meV)

Figure 4: Absorption coefficient α(ω) spectra obtained forsemiconducting (a) and metallic (b) samples respectively. Thesemiconducting one is as-grown while the metallic one is ob-tained by LT-annealing. The temperature was varied fromdown to top as 300, 250, 200, 150, 120, 100, 80, 60, 40, 20,10 and 4.2K.

Also for the peak structure around 200meV, an inter-pretation along the DE mechanism is possible. The latticeconfiguration around Mn atom must be distorted by theJahn-Teller effect and a hopping of a hole between Mnsites is associated with annihilation and creation of smallpolarons. When considerable amount of holes are localizedforming small polarons, α(ω) is expected to have a broadpeak at about 2Esp, where Esp is the formation energy ofa small polaron and estimated to be about 100meV from

Fig.4. On the other hand, the linewidth is predicted to be4(Esphωph)1/2 for kBT < hωph, where hωph is the relevantphonon energy. Substituting hωph with the GaAs phononenergy near the Brillouin zone boundary (∼ 30meV), weobtain a line width of 200meV, which reasonably agreeswith the results in Fig.4.

The DE model has been said to describe several man-ganites such as (La,Sr)MnO3, in which steep decrease ofresistivity below TC is observed. This is reminiscent ofthe resistivity humps shown in Fig.1. In previous reports,they are attributed to critical scattering of holes6, 18) atthe transition temperature. However, as discussed above,the picture of “almost localized holes” seems to be moreappropriate than such “scattering of free holes” pictureto describe the present system. Especially the coherenceof holes between scatterings by magnetic moments is es-sential for the critical scattering effect. It is thus naturalto attribute the decrease of the resistivity below TC tothe delocalization of holes which gain the kinetic energyby the DE mechanism. The simplest DE model does notdescribe the temperature dependence above TC, thoughit is known that the combination of the DE Hamiltonianand electron-phonon coupling via the Jahn-Teller effectexplains the “peak” feature around TC

19).In the case of (In,Mn)As, clear Drude tailing to the

low frequency limit appears in contrast to (Ga,Mn)As,though “dirtiness” of the DC conduction is comparable.The transfer in the spectral weight is also much clearer in-dicating the double exchange picture works well. However,this transfer starts at a temperature much higher thanTC. This transfer is probably related to the superparam-agnetism, which appears at very high (∼ 100K) tempera-tures.

§5 Soft X-ray absorption spectra

As seen in the previous section, it is more important toexplore the local electronic structure around Mn ions inorder to clarify the origin of the ferromagnetism. For thispurpose, local probes of Mn atoms such as core level x-ray photoemission spectroscopy (XPS)9) would be suit-able. Here we report a study of local electronic structure in(Ga,Mn)As by using Mn 2p x-ray absorption spectroscopy(XAS)20).

Figure 5(a) shows the XAS spectra of as-grown samples,while those of annealed samples are shown in Fig.5(b).The structures around 640eV and 651eV correspond toL3 and L2 levels respectively. The main peak (L3) in theas-grown samples has a doublet structure, which consistsof peaks at 639.5eV and 640eV. On the other hand in theannealed samples, only a single peak at 640eV appearsfor L3 except in the sample with x =0.032. This “single-peak” spectrum is very similar to a Mn 2p XAS calcula-tion based on atomic multiplet theory for Mn2+ (d5) intetrahedral (Td) co-ordination for the case with crystal-field strength (10Dq)=0.5eV21), manifesting Mn is in Td

symmetry (Fig.6(a)).This doublet→ singlet transition by annealing indicates

4

x

x

x

x

x

!" "!# $&% '( ')+*&),- ./10 ,243

x 5 6879

x

x

x

x

: ;8<

Figure 5: Mn 2p XAS spectra for (a) as-grown and (b) LT-annealed (Ga,Mn)As.

= >? @>AB? CD EFGHI>B ? AJ

K L8M NPOOQNR QSUTVNXWZY [ \ ]^`_8WZY W a bZcXd

e fg

^`_8h ij8kl jml kn o pPq

r st usvwt xy z|~sw v

& U& 8+

8 1V W Y [ \ ] ^1_ WZY W a b cd ¡¢£¥¤ ¦ §¨ª©«¬­®°¯ ± ²³µ´

Figure 6: (a) Comparison between Mn 2p XAS spectra forannealed GaMnAs with x=4.7% and the calculation based onatomic multiplet theory for Mn2+ (d5) in Td co-ordination for10Dq=0.5eV21). (b) An example of spectrum decomposed intotwo spectra. Solid line is the spectrum for as-grown samplewith x=4.7%. The dashed and the dotted lines are spectrumA and B respectively.

that two types of Mn ions exist in as-grown samples, oneof which is transformed into the other type by annealing.Assuming that the spectrum for the annealed sample withx =0.047 is purely from one species, we decompose theother spectra into spectrum A and B (Fig.6(b)). Figure 7displays intensities of these spectra and TC as a functionof x. It is apparent that TC has close correlation with theintensity of spectrum A. Hence it is suggested that thespecies of Mn which produces the spectrum A generatesthe ferromagnetism.

The simplest interpretation of the annealing process, isdisposal of excess As atoms through the evaporation fromthe surface. Such excess As atoms are known to work asdeep donors and to compensate holes. Hence the anneal-ing increases the concentration of 4p holes. We tentativelyassume that Mn which produce spectrum A are those nor-mally replaced the Ga sites22) and have four nearest neigh-bor As atoms. Since XAS gives site projected partial den-sity of states, such a Mn is assigned to be Mn-h (As 4phole) complex.

¶

· ¸ ¹ · ¸

º » ¼

¶

· ¸ ¹ · ¸

º ½ ¼

∆¾À¿ªÁ à Ä

à Š∆¾Æ¿ªÁ+Ç È É Ê Ë ÌÈ

∆¾ÆÍÍ ∆¾

¶

· ¸ ¹

º Î ¼

¶

· ¸ ¹

º Ï ¼· ¸ ¹

· ¸ ¹

à Š∆¾Æ¿ªÁ+Ç ¾PÐ

à Š∆¾À¿ªÁÒÑ È É Ê Ë Ì È Ó ¾ Ð

∆¾ÆÍ8Í ∆¾

Figure 7: A possible energy level scheme of (Ga,Mn)As. Solidarrows stand for electrons while dotted arrows are for holes inAs 4p orbital. The diagrams are shown for the cases in whichthe magnetic moments of Mn-h complex and free Mn2+ ionare (a) parallel or (b) antiparallel, and two Mn-h complexesare (c) parallel or (d) antiparallel. Here Jp−d is assumed to benegative.

If we further assume that the Mn for spectrum B alsohave the same atomic configuration and the annealing onlychanges the compensation, the two kinds of Mn statesare assigned to d5L and d5 configurations respectively forspectrum A and B, where L represents a hole in the lig-and As. The energy difference (0.5eV) between d5L and d5

estimated from the difference in the spectra can be under-stood from the electronic structure parameters obtainedby Mn 2p core-level photo-emission spectra9).

In the concluding part of these two sections, we discussa possible mechanism for the ferromagnetism. Now it isclear that the holes almost localized around Mn2+ ionsmediate the ferromagnetism. Possible schematic energy

5

diagrams are shown in Fig.8, where the p − d exchangeinteraction (Jpd) is negative (anti-ferromagnetic). Thesediagrams explain that in order to gain the kinetic energyof 4p holes, hopping between two Mn sites should be “al-lowed”, which leads to the ferromagnetic order of d-spinsthrough the p − d hybridization Jpd. This is a kind ofDE mechanism and naturally explains the present obser-vations.

§6 Metal-insulator transition

Here we show an example of the application of the an-nealing technique to basic research. MI transition (MIT)is one of the central issues in solid state physics23). Thesimplest mechanism of MI transition in doped semicon-ductors is the overlapping of donor (acceptor) wavefunc-tions and the formation of impurity bands. Actual MIT’sare, however, considered to be dominated by other mech-anisms especially in the vicinity of the critical points. An-derson localization is one of such mechanisms. Thus far,the MIT’s in doped semiconductors have been consideredin the context of Anderson localization plus Coulomb re-pulsion in the presence of disorder24). On the other hand,in “strongly correlated” systems, Mott-type transition isoften the central mechanism for the MIT’s.

! #"$ &%('

Figure 8: Temperature dependence of conductivity in thevicinity of the MIT critical point. The external magnetic fieldwas varied from 0.2T to 1.8T with the step width of 0.01T.The abscissa is plotted as T 1/4.

The MIT’s in (Ga,Mn)As and (In,Mn)As have uniquecharacteristics. The critical Mn concentration is very farfrom the Mott’s criterion23), which manifests that theseMIT’s are so different from those of ordinal doped semi-conductors. On the other hand, DE mechanism for ferro-magnetism is associated with a MIT. However these mate-rials undergo ferromagnetic transition even in the insulat-ing phase. The disorder should thus play an important rolein the MIT’s. More remarkably, they showed the secondMIT’s when the Mn concentration is further increased. Inthese second MIT’s, the disorder should be more impor-tant.

It is crucial to approach the critical points in the studyof phase transitions though in the case of MIT’s, therelevant parameter is often difficult to be varied in asingle specimen. Here we tuned the resistivity of the(Ga,Mn)As sample (x =0.05) by repeated short-time an-nealing at 260 C to just insulating side of the secondMIT. Then by applying external magnetic field, the giantmagnetoresitance10) can bring the sample into the metallicside through the MIT critical point.

Figure 8 shows temperature dependence of the conduc-tivity for various external magnetic field. The abscissa isplotted in T 1/4. The data points are in lines whose offsetsat absolute zero cross zero-conductance indicating thatσ ∝ T 1/4 approximates the experiment around the crit-ical point. The temperature dependence of T 1/2 is oftenobserved at MIT’s in compensated semiconductors. Thismeans that in the present case, the temperature depen-dence dσ/dT becomes steeper with lowering temperaturecompared with ordinal compensated semiconductors. Thisis qualitatively interpreted as follows. Just below TC, theordering of Mn spins is favorable for conduction throughthe DE mechanism. However at lower temperatures thefreezing of magnetic moments pointing random directions,would enhance effective degree of disorder and acceleratequenching of conduction.

Fortunately we can examine whether the conductancescales on H (magnetic field) and T consistently regardlessof the detailed contents of the theoretical model throughtwo-parameter scaling form24);

σ(H,T ) ∝ T xf(|H/Hc − 1|/T y), (3)

where f is a scaling function, x and y are parameters,giving the critical exponent ν = x/y, which is defined bythe critical behavior as

σ(H, 0) ∝ (H −Hc)ν . (4)

We found that by adopting f as a third order polynomial,the data around the critical point can be aligned alongthe scaling curve as shown in Fig.10. The fitting givesthe value of the critical exponent of the conductivity ν =1.6± 0.2.

The exponents for temperature and the magnetic fieldare uncommon to those reported so far in MIT’s. Thisis not so surprising, however, considering that both theelectron correlation and the disorder are important in the

6

present MIT. In such cases, it is known that even thechoice of the parameter to approach to the critical pointchanges the universality class of the system25). It shouldbe noted that the value of ν is close to the results of nu-merical scaling in non-interacting systems26).

!

"#$%&'

(*)+ ,.-/ 0213,.-54 687 9;:

Figure 9: Two parameter scaling plot of the data shown inFig.8. The formula is shown in the text.

It is hardly believed that the Coulomb repulsion is ir-relevant in the present system. However the external fieldis considered to vary almost purely the degree of disorderbecause the effect of the external field is negligible besidesordering of random magnetic moments. And that wouldbe the reason we got the value close to the result in non-interacting systems27).

This work is partly supported by Grant-in-Aid for Sci-entific Research on the Priority Area ”Spin ControlledSemiconductor Nanostructures” from the Ministry of Ed-ucation, Science, Sports and Culture, Japan.

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7