Ferromagnetism in semiconductors and oxides: prospects from a ten years' perspective
FFerromagnetism in semiconductors and oxides: prospects from a ten years’ perspective
Tomasz Dietl
1, 2, ∗ Institute of Physics, Polish Academy of Science,al. Lotnik´ow 32/46, PL-02-668 Warszawa, Poland Institute of Theoretical Physics, University of Warsaw, PL-00-681 Warszawa, Poland (Dated: August 15, 2011)Over the last decade the search for compounds combining the resources of semiconductors and fer-romagnets has evolved into an important field of materials science. This endeavour has been fuelledby continual demonstrations of remarkable low-temperature functionalities found for ferromagneticstructures of (Ga,Mn)As, p-(Cd,Mn)Te, and related compounds as well as by ample observationsof ferromagnetic signatures at high temperatures in a number of non-metallic systems. In this pa-per, recent experimental and theoretical developments are reviewed emphasising that, from the onehand, they disentangle many controversies and puzzles accumulated over the last decade and, onthe other, offer new research prospects.
PACS numbers: 75.50.Pp
Introduction
Advances in the epitaxy of semiconductor compoundshave made it possible to fabricate quantum structures inwhich confined electrons or photons exhibit outstandingproperties and functionalities. Similarly, the atomic pre-cision of metal and oxide film deposition has allowed tomaster a number of striking spin transport phenomena.The discovery of ferromagnetism in p-type Mn-doped IV-VI (ref. 1), III-V (refs 2–4), and II-VI (refs 5,6) com-pounds has opened a road towards the development ofmultifunctional materials systems bridging the resourcesof semiconductor quantum structures and ferromagneticmultilayers as well as has enabled the study of collectivemagnetic phenomena as a function of the spin and carrierdensities.Over the last ten years or so the field of ferromag-netism in dilute magnetic semiconductors (DMSs) anddilute magnetic oxides (DMOs) has evolved into an im-portant branch of materials science. The comprehensiveresearch on these systems has been stimulated by con-tinual demonstrations of outstanding low-temperaturefunctionalities in (Ga,Mn)As, p-(Cd,Mn)Te, and re-lated structures , some examples being spin-injection ,electric-field and electric-current control of mag-netism, tunneling anisotropic magnetoresistance in pla-nar junctions and in the Coulomb blockade regime ,as well as current-induced domain displacement withoutthe assistance of a magnetic field . These findings haveput into focus the interplay of magnetization texture anddynamics with carriers’ population and currents, a broadtopic of today’s physics of spintronic materials. At thesame time, since the first report on (Ti,Co)O (ref. 16),the persistence of spontaneous magnetization to abovethe room temperature has been found for a number ofDMOs and DMSs, and even for materials nominally con-taining no transition metal (TM) impurities.However, despite the massive investigations, the originand control of ferromagnetism in DMSs and DMOs is, ar-guably, the most controversial research topic in today’s materials science and the condensed matter physics. Asemphasized here, the abundance of contradicting viewshas resulted from intertwined theoretical and experimen-tal challenges, requiring the application of cutting edgecomputational and materials nanocharacterisation meth-ods, often becoming available only now. In this way,DMSs and DMOs emerge as an outstanding playgroundto test our understanding of unanticipated relationshipsbetween growth conditions and a self-organized alloystructure as well as between quantum localization, car-rier correlation, and ferromagnetism, and constitute anactive research direction .We begin this review by recalling the foundations ofthe p − d Zener model, proposed a decade ago to de-scribe the origin and properties of ferromagnetism in p-type Mn-doped semiconductors . A crucial role of theAnderson-Mott localization in the physics of these sys-tems is then discussed in the context of other models putforward to explain outstanding findings which have beenaccumulated over the recent years for (Ga,Mn)As. It isshown that the p − d Zener model describes a number ofthermodynamic and micromagnetic properties of III-Vand II-VI DMSs as well as continues to constitute a goodstarting point to address the question about prospectsof research on hole-mediated ferromagnetic semiconduc-tors. The second part of the review is devoted to theorigin and control of high temperature ferromagnetismin DMSs and DMOs. We argue, exploiting results of ex-tensive nanocharacterisation works, that puzzling prop-erties of these compounds reflect a highly non-randomdistribution of magnetic cations. While a number of ap-pealing functionalities has already been demonstrated forthese ferrmagnetic/semiconductor nanocomposites, weare only at the beginning of the road to demonstratedevice structures of these emerging materials systems. a r X i v : . [ c ond - m a t . m t r l - s c i ] A ug THE p − d ZENER MODEL
In view of the progress in materials fabrication byepitaxial methods it was timely a decade ago tounderstand the ferromagnetism in DMSs as well as toask whether the Curie temperature T C can be raisedto above 300 K from the 110 K observed at that timein (Ga,Mn)As containing only 5% of Mn (ref. 22).Photoemission as well as optical studies in the singleimpurity limit demonstrated that Mn provides both lo-calised spins and itinerant holes mutually coupled by a p − d exchange interaction. Zener first proposed themodel of ferromagnetism driven by the exchange inter-action between band carriers and localized spins. In thecase of semiconductors, the Zener model is equivalentto the approach developed by Ruderman, Kittel, Kasuya,and Yosida (RKKY), in which the Friedel oscillations ofthe spin density are taken into account .In the proposed implementation of the Zener model thestructure of the valence subbands was described by theKohn-Luttinger six bands’ kp hamiltonian, taking thespin-orbit interaction into account . Thermodynamiccharacteristics were then evaluated in the mean-field ap-proximation. At the same time, arguments were pre-sented why the model is valid even on the insulator side ofthe Anderson-Mott metal-to-insulator transition (MIT),provided that the holes remain weakly localised.This approach was found to constitute an appropri-ate minimal theory, capable to describe adequately themagnitude of T C and of magnetic anisotropy fields in-duced by biaxial strains in (Ga,Mn)As and p-(Zn,Mn)Te(ref. 21). It was also pointed out that GaN and ZnOcontaining appropriately high concentrations of both Mnspins ( x (cid:38) p (cid:38) . · cm − ) might supportthe ferromagnetic order to above the room temperature.It was underlined, however, that prior to the verificationof this prediction, important issues of solubility limitsand self-compensation as well as of the transition to astrong-coupling case with the decreasing lattice constantneed to be addressed experimentally . A GUIDE THROUGH OTHER MODELS
Extensive studies over last ten years have made clearthat ferromagnetic DMSs and DMOs form two distinctclasses. The first class comprises p-type Mn-based DMSs,in which the ferromagnetism is associated with the pres-ence of holes. Here, step by step improvements in growthprotocols and in post-grown processing have made it pos-sible to increase the Mn and hole densities, particularlyin (Ge,Mn)Te (ref. 28) and (Ga,Mn)As (ref. 29–31), inwhich the magnitudes of T C ’s approach now 190 K at avalue of the effective Mn concentration x eff below 10%,as implied by the magnitude of saturation magnetization(see Fig. 1). While this evolution of T C is consistentwith the p − d Zener model, its basic foundation, namely that in the concentration range relevant to ferromag-netism the holes reside in the valence band in (Ga,Mn)Asand related systems has been objected by two schools ofthoughts: • Following pioneering ab initio work carried out for(In,Mn)As (ref. 32), it has been argued based on theoutcome of available first principles methods thatthe holes reside in band-gap states derived from theTM d levels, so that the relevant spin-spin couplingmechanism is the double-exchange . • A series of findings from optical and transport stud-ies, and hard to reconcile with expectations for theholes moving in a weakly perturbed valence band,have been taken as an evidence for the location ofthe Fermi energy within a Mn-acceptor impurityband detached from the valence band or retainingthe d character of Mn dopants even in the region,where they overlap with the valence band on themetallic side of the MIT .To the second class of ferromagnetic systems belongsa broad range of semiconductors, oxides, and carbonderivatives, showing ferromagnetic-like features persist-ing to above room temperature without the presence ofitinerant holes or, in some cases, even without intentionaldoping by TM impurities . A number of divergingmodels has been proposed to explain the origin of thisintriguingly robust ferromagnetism:First, in a long series of ab initio works a ferromag-netic ground state has been found for dilute TM spinseven in the absence of band carriers . Following pio-neering contributions , the effect has been assigned tothe ferromagnetic superexchange or, more frequently,to the double exchange that turns up, within the em-ployed computation methodologies, if the states derivedfrom the TM d levels are partly occupied for one spindirection .Second, it is supposed that electrons either residingin the conduction band or forming bound magneticpolarons mediate ferromagnetic couplings between di-lute TM spins. Alternatively, the presence of these cou-plings is assigned to carriers residing on defects, such asvacancies or on residual impurities, such as hydrogen .Third, the ferromagnetic response is related to spins ofelectrons residing on point or extended defects and cou-pled by an exchange interaction. Within this so-called d model of high temperature ferromagnetism, the presenceof magnetic impurities is either unnecessary or servesmerely to bring the Fermi level to the relevant defectstates .Finally, it has been persistently suggested that thelimited solubility of TMs’ impurities in particular hostsmay result in the formation of nanoscale regions contain-ing a large density of magnetic cations and, thus, speci-fied by a high spin ordering temperature. M agne t i z a t i on ( e m u / c m ) Ge Mn x Te x = 0.08 Ga Mn x As Saturation magnetization (emu/cm ) C u r i e t e m pe r a t u r e ( K ) FIG. 1: Experimental data for p-type DMSs films showingthe Curie temperature T C approaching 200 K at the effectiveMn concentration x eff below 10%. Upper panel: temperaturedependence of magnetization in (Ge,Mn)Te with high (circles)and low (triangles) hole concentrations (after ref. 28); Lowerpanel: T C as a function of saturation magnetization M Sat forannealed (Ga,Mn)As films grown in various molecular beamepitaxy (MBE) systems (after ref. 30).
WHERE DO THE HOLES RESIDE IN (Ga,Mn)As?
According to the double exchange scenario , theanti-crossing picture , and the impurity bandmodels , the hole states retain impurity band charac-teristics in the density regime relevant to the ferromag-netism of (Ga,Mn)As. For a comprehensive presentationof arguments in favour of such a scenario we remit thereaders to ref. 35.Another view, shared by the present author and ex-posed in detail elsewhere , is that similarly to otherdoped semiconductors the carrier localization in p-typeDMSs results from a collective effect of randomly dis-tributed scattering centres upon the Fermi liquid ofstrongly correlated band carriers . Guided by pre-vious extensive studies of non-magnetic semiconductors, we may anticipate that rather than absolute values, onlycertain scaling characteristics of d.c., a.c., and tunnelingconductivity tensors can be presently interpreted theoret-ically near the MIT, at least at temperatures below themomentum relaxation rate. This is in contrast to ther-modynamic properties, such as electronic specific heat,which are virtually unperturbed by disorder and elec-tronic correlation at the localization boundary .Empirically, the Anderson-Mott MIT occurs for thecarrier concentration p c at which the magnitude of thekinetic energy per band carrier, E kin ≈ (3 / E F , calcu-lated with no disorder diminishes to about one third ofthe single impurity binding energy E I (ref. 55). In Fig. 2the experimental values of E I for Mn acceptors in vari-ous III-V semiconductors are shown . As seen, E I and,thus, p c is enhanced rather dramatically comparing tonon-magnetic acceptors, particularly on going from an-timonides to nitrides through arsenides and phosphides.This shift is caused by the p − d hybridisation, whoseimportance grows with the decreasing cation-anion bondlength, ultimately resulting in a transition to the strongcoupling limit, where the hole binding is dominated bythe p − d interaction . I n S b A l S b G a S b I n A s I n P G a A s A l A s G a P A l P I n N G a N E ne r g y ( e V ) Lattice constant (nm)
FIG. 2: Experimental energies of Mn levels in the gap of III-V compounds with respect to the valence-band edges (afterref. 56).
According to the scaling theory and relevantexperiments , the Anderson-Mott MIT is continuous.Hence, the carrier localization length ξ decreases rathergradually from infinity at the MIT towards the impurityBohr radius in the strongly localised regime, so that ata length scale smaller that ξ , the wave function retainsan extended character. Such band-like carriers, whosequantum diffusivity vanishes at the MIT, were originallythought to mediate the long-range interactions betweenthe TM spins in DMSs in the whole density regime rele-vant to ferromagnetism .In agreement with this view temperature dependentquantum corrections to the conductance and the char-acter of tunneling DOS are consistent in (Ga,Mn)Aswith the expectations for Anderson-Mott localization ofholes in the GaAs valence band. In particular, scanningtunneling microscopy data , though affected presum-ably by the proximity to the surface, point rather directlyto the crucial importance of both disorder and carrier cor-relation in the relevant range of Mn concentrations. Atthe same time, the direct visualisation of spatial fluctu-ations in local DOS provides a support to the view thatthe disappearance of ferromagnetism with carrier local-ization proceeds via an intermediate superparamagnetic-like phase.Within the Anderson-Mott localization model, theeffects of disorder and carrier correlation appear assome broadening and Landau’s renormalisation of va-lence band thermodynamic DOS at E F , ρ F which deter-mines T C within the p − d Zener model (refs 21,26,59).In this context, thermoelectric power S at high tem-peratures is relevant, as it is a good measure of ρ F , sothat its magnitude may tell between the valence bandand impurity band pictures. Recent measurements of S in compensated (Ga,Mn)As were interpreted in termsof the anti-crossing model treating broadening of theimpurity band as an adjustable parameter . In thisway, a rather small difference between the magnitudesof S for (Ga,Mn)As and GaAs:Be at given hole densi-ties was explained. We note, however, that the Mottformula S = ( π / e ) k T ∂ E F ln σ ( E F ) with ρ F of theGaAs valence band describes quantitatively not onlythe data for GaAs:Be but also for (Ga,Mn)As assumingthat the energy dependence of the apparent hole mobility µ = σ/ep changes from the value expected for acousticphonon scattering, µ ∼ E − / , to the one specific forionised impurity scattering, µ ∼ E / , when the degreeof compensation increases.Furthermore, within the impurity-band models, themagnitude of T C is predicted to reach a maximum, whenthe Fermi level is shifted across the peak in the den-sity of the impurity states. The accumulated data for(Ga,Mn)As show that the value of T C decreases mono-tonically when diminishing the hole concentration bygating or by increasing the concentration of compen-sating donors . On the other hand, it was foundin recent studies that the magnitude of T C actually in-creases by co-doping with Si donors and, moreover, itgoes through a maximum as a result of the modulationdoping by Be acceptors . As underlined in these works,the findings are consistent with the impurity band sce-nario. However, the presented data reveal that the in-crease of T C in Si-doped samples and its decrease in theBe case is associated with, respectively, an enlargementand a reduction of the saturation value of magnetizationand, thus, of the Mn concentration x eff that determinesthe magnitude of T C . The results can, therefore, beexplained by the known anticorrelation between x eff and the density of holes during the epitaxy, here reduced by Si donors or ”siphoned off” from the Be-doped bar-rier into the grown quantum well .At the same time, low values of µ (below 10 cm /Vs),taken as an evidence for the large magnitude of an ef-fective hole mass , can be explained by the prox-imity to the MIT, where charge diffusion is much re-duced by quantum localization effects. Furthermore, re-ferring to a shift of an a.c. conductivity maximum withthe hole density , which contradicts the expectations ofthe Drude-Boltzmann theory, we emphasise that the fre-quency dependent conductance near the MIT, at least upto frequencies of the order of the momentum relaxationrate, is dominated by quantum localization effects ,whose presence may account for the observed anomalies. CURIE TEMPERATURE FORCARRIER-MEDIATED FERROMAGNETISM INIII-V DMSs
In Fig. 3 the highest values of T C found to date in p-type Mn-based III-V DMSs are reported , andcompared to the early predictions of the p − d Zenermodel for fixed values of the Mn and hole concen-trations. We see that the theory reproduces the chemi-cal trends and describes semi-quantitatively the absolutevalues of T C . The observed trend reflects a decrease ofthe p − d exchange energy for larger cation-anion dis-tances as well as an enhanced role of the competingspin-orbit interaction in materials with heavier anions.At the same time, the dependence of T C on the effec-tive Mn concentration and the density of itinerantholes, changed in (Ga,Mn)As by Mn concentration, donorcompensation or by gating , is consistent with the p − d Zener model. Furthermore, the model describesproperly the magnitude of the strain-induced magneticanisotropy .Unfortunately, a more detailed comparison betweentheory and experiment is hampered by the lack of in-formation on short-range antiferromagnetic interactions,which become progressively more important when theMn concentration increases, as well as by enduring diffi-culties in the accurate determination of the Mn and holedensities. According to 3D atom probe investigations ,Mn ions are distributed randomly in (Ga,Mn)As withina 1 nm resolution. Nevertheless, from previous channel-ing studies we know that because of self-compensation,a considerable portion of Mn ions occupies interstitialpositions, and hence they act as double donors , com-pensating partly holes as well as Mn spins, due to a sup-posedly antiferromagnetic coupling between interstitialand substitutional Mn pairs. Furthermore, a large frac-tion of Mn, particularly in annealed samples, reside in anear-to-the-surface MnO layer.The applicability of the p − d Zener model for(Ga,Mn)As and related systems has been confirmed by ab initio studies in which inaccuracies of the LSDA arepartly compensated by the LSDA + U approach or by
10 100
InSb InAsGaSb GaP GaAs
Curie temperature (K)
Computed T C x Mn = 0.05 p = 0.35 nm -3
10 100
InSb InAsGaSb GaP GaAs
Curie temperature (K)
Highest T C reported forp-type (III,Mn)V FIG. 3: Predictions of the p − d Zener model compared to ex-perimental data for p-type (III,Mn)V DMSs. Upper panel:computed values of the Curie temperature T C for variousp-type semiconductors containing 5% of Mn and 3 . × holes per cm (after ref. 21; the value for (In,Mn)Sb is takenfrom ref. 69). Lower panel: the highest reported valuesfor (Ga,Mn)P (ref. 65); (Ga,Mn)As (ref. 29,30); (In,Mn)As(ref. 66); (Ga,Mn)Sb (ref. 67); (In,Mn)Sb (ref. 68). self-interaction corrections . Furthermore, a number offerromagnetism models, tailored to DMSs without holesin the valence band, have been put forward, as reviewedelsewhere . It is still unclear, however, whether a longrange ferromagnetic order can settle, say, above 10 K, ifholes are bound to individual Mn acceptors in DMSs (thestrongly localized regime), so that the exchange interac-tion decays exponentially with the distance between spinpairs. So-far, a ferromagnetic coupling between isolatednearest neighbor Mn pairs was revealed be scanning tun-neling microscopy in GaAs:Mn, and analyzed successfullyin terms of a tight binding model .It is instructive to compare (Ga,Mn)As, (Ga,Mn)P,and (Ga,Mn)N containing the same concentration of Mn,say, 6%, as in these three material systems E I differs C u r i e t e m pe r a t u r e TM concentration, DOS strong couplingstrong couplingweak couplingweak couplingVCAVCA
MITMIT
FIG. 4: Schematic dependence of T C on the concentration ofmagnetic impurities and density of hole states at the Fermilevel for a weak and a strong coupling. Higher values of T C are predicted within the virtual crystal and molecular fieldapproximation for the strong coupling. However, the region,where the holes are localized and do not mediate the spin-spininteraction is wider in the strong coupling case (after ref. 57). significantly, according to the data collected in Fig. 2.The (Ga,Mn)As films containing 6% of Mn and typicallyabove 10 holes per cm are on the metallic side of theMIT . In the case of Ga . Mn . P the magnitude of E I is large enough to result in hole localization. How-ever, the magnitude of the conductance activation energy(ref. 65), a factor of ten smaller than E I for GaP:Mn, in-dicates that the holes are only weakly localised. Accord-ingly, also in this case the p − d Zener model can serveto explain the origin of ferromagnetic correlations.In contrast, no information on hole transport is avail-able for the MBE-grown Ga . Mn . N film , indicatingthat the strongly localised regime is reached. In line withthe notion that itinerant holes are necessary to observea coupling between diluted spins, the observed T C is aslow as 8 K. In terms of a schematic drawing presented inFig. 4, (Ga,Mn)N represents the strong coupling case,where the holes remain localised over a wide rage ofMn concentrations, in contrast to both Ga − x Mn x As, forwhich the MIT appears already below x = 2% for weaklycompensated samples , and (Ga,Mn)P representing anintermediate case.It is worth noting that there are indications of a non-random Mn distribution in another (Ga,Mn)N film grownby MBE (ref. 78). This may suggest that T C = 8 K con-stitutes actually an upper limit for T C in Ga . Mn . N.These findings demonstrate, therefore, that the cur-rent ab initio theory , predicting T C ≈
60 K forGa . Mn . N, still overestimates the significance of fer-romagnetic couplings in the case of DMSs with no valenceband holes.
COMPETING INTERACTIONS IN p-TYPE II-VIDMSs
In II-VI compounds, where Mn is an isoelectronic im-purity, it is possible to control independently the spin andthe carrier density. However, at given Mn and hole con-centrations, T C is much lower in II-VI DMSs, comparingto III-V compounds, owing to a destructive influence ofthe short-range antiferromagnetic superexchange. Thiseffect is less relevant in III-V DMSs, where Mn cen-tres are negatively charged, so that the enhanced holedensity at closely lying Mn pairs compensates, at leastpartly, short-range antiferromagnetic interactions .Following theoretical prediction , carrier-induced fer-romagnetism was revealed in modulation doped p-type(Cd,Mn)Te/(Cd,Zn,Mn)Te:Mg heterostructures employ-ing photoluminescence spectroscopy . The characterof magnetic anisotropy as well as the magnitude of T C and its evolution with the hole density, controlled by theelectric field and illumination, were found to be consis-tent with the p − d Zener model, adapted for this lowdimensionality system. Interestingly, however, no mag-netic hystereses have been detected below T C . Accordingto extensive Monte-Carlo simulations, the effect reflectsfast magnetization dynamics, generated by the antiferro-magnetic interactions at the borders of the hole layer .Ferromagnetic signatures were also found in epi-layers of p-type (Zn,Mn)Te:N (refs 6,80) and n-type(Zn,Mn)O:Al (ref. 81). As shown in Fig. 5, under thehigh density of carriers, the low-temperature resistanceacquires a hysteretic behaviour. This points to the ap-pearance of a ferromagnetic order as well as demonstratesdirectly the existence of a strong coupling between car-riers and Mn spins. The temperature dependence of thecoercive force, together with magnetic susceptibility mea-surements above 2 K, point to a magnetic ordering tem-perature T C = 1 .
45 K in the case of Zn . Mn . Te:Ncontaining 1 . · holes per cm . This value is in agree-ment with the predictions of the p − d Zener model, pro-vided that the aforementioned antiferromagnetic inter-actions and the spin-orbit interaction are taken carefullyinto account . A similar experimental procedure leadsto T C = 160 mK in the case of Zn . Mn . O:Al con-taining 1 . · electrons per cm (ref. 81). Taking thedifferences in relevant parameters and, in particular, athree times larger amplitude of the p − d exchange in-tegral comparing to the s − d case, the experimentallyobserved difference in the T C values between p-type andn-type materials can be readily explained. PROSPECTS FOR HIGHER T C IN DMSs
A number of authors has reported the observation ofroom temperature ferromagnetism in various semicon-ductors and oxides containing supposedly randomly dis-tributed localised spins. However, it is probably fair tosay that so-far none of these findings has been confirmed nature materials the magnitude of T C and its evolution with the hole density, which are controlled by the electric field and the illumination, was found to be consistent with the p – d Zener model adapted for this low-dimen-sionality system. Interestingly, however, no magnetic hystereses have been detected below T C . According to extensive Monte Carlo simu-lations, the effect reflects fast magnetization dynamics generated by the antiferromagnetic interactions at the borders of the hole layer .Ferromagnetic signatures were also found in epilayers of p-type (Zn,Mn)Te:N (refs 6, 80) and n-type (Zn,Mn)O:Al (ref. 81). As shown in Fig. 5, for a high carrier density the low-temperature resistance becomes hysteretic. This points to the appearance of ferromagnetic order and directly demonstrates the existence of a strong coupling between carriers and Mn spins. The temperature dependence of the coercive force, together with magnetic susceptibility measurements above 2 K, point to a magnetic ordering temperature of T C = 1.45 K in the case of Zn Mn Te:N with 1.2 × holes cm −3 . This value is in agreement with the predictions of the p – d Zener model, pro-vided that the aforementioned antiferromagnetic interactions and the spin–orbit interaction are taken carefully into account . A simi-lar experimental procedure shows that T C = 160 mK in the case of Zn Mn O:Al with 1.4 × electrons cm −3 (ref. 81). Given the difference between relevant parameters and, in particular, the three-fold-greater amplitude of the exchange integral in the p – d case than in the s – d case, the experimentally observed difference in the T C values between p-type and n-type materials can be readily explained. Carrier-mediated ferromagnetism with higher T C A number of authors have reported the observation of room-temperature ferromagnetism in various semiconductors and oxides containing supposedly randomly distributed localized spins. However, it is probably fair to say that so far none of these findings has been confirmed by other groups and none has resulted in the demonstration of a device structure working at room temperature. As I will argue in the following sections, if this robust ferromagnet-ism is not an experimental artefact it can be explained by assuming a non-random distribution of the magnetic ions.It seems that despite ten years of extensive investigations, the conditions under which room-temperature ferromagnetism was predicted for nitrides and oxides have not yet been experimentally met. In particular, no (Ga,Mn)N, (Zn,Mn)O or related compound containing a few per cent of randomly distributed magnetic cations and a few 10 delocalized or weakly localized holes per cubic centi-metre has so far been synthesized. However, in annealed (Ga,Mn)As the effective Mn concentration, as judged from the saturation mag-netization, now approaches 10%, although T C remains below 200 K.Can, therefore, carrier-mediated, indirect spin–spin coupling produce ferromagnetic ordering that is stable up to room tempera-ture? I note that a variant of the p–d Zener model explains the ori-gin of ferromagnetism in double-perovskite compounds, such as Sr CrReO , where T C can reach 625 K (ref. 82) despite the distance between localized spins being as large as 0.6–0.7 nm. This shows the potential of this mechanism to support high-temperature ferromag-netism possibly also in DMSs, where, in GaN and ZnO, the distance between second-nearest-neighbour cations is less than 0.5 nm.However, the obvious difficulty is to synthesize a p-type, wide-bandgap DMS system in which the hole density is large enough to result in a MIT even in the strong-coupling case, as sketched in Fig. 4. It has been suggested —but not yet verified experimen-tally—that once the MIT is reached, and the bound states therefore washed out by many-body screening, high values of T C (expected in the virtual-crystal and molecular-field approximations ) should emerge. Various methods allowing us to enlarge the hole density −0.05 0.00 0.05Magnetic field (T)−0.5 0.0 0.5Magnetic field (T) 05101520 n–(Zn,Mn)Op–(Zn,Mn)Te:N 50 mK0.1 K 60 mK0.2 K 75 mK0.3 K 100 mK0.45 K 125 mK0.6 K 150 mK0.8 K 200 mK1 K100500 ∆ R xx ( Ω ) a bFigure | resistive indications of ferromagnetism in p-Zn mn te:n and n-Zn mn o:al. a , The temperature dependence of the hysteresis widths at low temperatures and the magnetic susceptibility measurements above 2 K indicate that T C = 1.45 ± 0.05 K in p-Zn Mn Te:N with a hole concentration of 1.2 × 10 cm −3 . b , The temperature and field scales are an order of magnitude smaller in n-Zn Mn O:Al with an electron concentration of 1.4 × 10 cm −3 , where T C = 160 ± 20 mK. Solid lines show changes of longitudinal resistivity in the magnetic field, D R xx , as measured for decreasing (blue arrows) and increasing (red arrows) the field. Curves obtained at different temperatures are vertically shifted for clarity. The width of the hysteresis loops is seen to increase on lowering the temperature. Figures reproduced with permission from: a , ref. 80, © 2001 APS; b , ref. 81, © 2001 Springer. review article NATure MATerIAls
Doi: 10.1038/nmat2898 nmat_2898_DEC10.indd 969 10/11/10 16:09:57 © 20 Macmillan Publishers Limited. All rights reserved10
FIG. 5: Resistive indications of ferromagnetism in p-Zn . Mn . Te:N and n-Zn . Mn . O:Al. The temper-ature dependence of the hystereses width at low tempera-tures as well as magnetic susceptibility measurements above2 K point to T C = 1 . ± .
05 K in p-Zn . Mn . Te:Nwith the hole concentration 1 . · cm − . The temper-ature and field scales are an order of magnitude smallerin n-Zn . Mn . O:Al with the electron concentration 1 . · cm − , where T C = 160 ±
20 mK (adapted from refs. 80and 81). by other groups as well as none has resulted in the demon-stration of a device structure working at room temper-ature. As we will argue in the following sections, if notrepresenting an experimental artifact, this robust ferro-magnetism can be explained assuming a non -random dis-tribution of the magnetic ions.It appears that despite ten years of extensive investiga-tions the conditions under which the room temperatureferromagnetism was predicted for nitrides and oxides have not yet been experimentally met. In particular, no(Ga,Mn)N, (Zn,Mn)O, or a related compound containinga few percent of randomly distributed magnetic cations and a few 10 delocalised or weakly localised holes percm has so-far been synthesised. On the other hand, inannealed (Ga,Mn)As the effective Mn concentration, asjudged from the magnitude of the saturation magnetiza-tion, approaches now 10% but T C remains below 200 K.Can, therefore, carrier mediated indirect spin-spin cou-pling produce a ferromagnetic ordering stable up to theroom temperature? We note that a variant of the p − d Zener model explains the origin of ferromagnetism indouble perovskite compounds, such as Sr CrReO , wherethe magnitudes of T C attain 625 K (ref. 82), despite thatthe distance between localized spins is as large as 0.6 –0.7 nm. This shows a potential of this mechanism to sup-port high-temperature ferromagnetism, possibly also inDMSs, where the distance between second nearest neigh-bour cations is smaller than 0.5 nm in GaN and ZnO.However, the obvious difficulty is to synthesise a p-type wide band gap DMS systems, in which the holedensity is large enough to result in a MIT, even in thestrong coupling case, as sketched in Fig. 4. It has beensuggested —but not yet verified experimentally—thatonce the MIT is reached, which means that the boundstates are washed out by many body screening, high val-ues of T C , expected within the VCA and MFA , shouldemerge. Various methods allowing to enlarge the holedensity above 10 cm − without increasing the degreeof disorder, such as gating as well as doping in a mod-ulated fashion or by exploiting interfacial electric fields,may constitute the appropriate road towards achievinga semiconductor showing high and tunable T C values.We note that the enduring progress in the gate oxidedeposition allows one to achieve an interfacial chargedensity of the order of 3 · cm − , that is up to about3 · per cm . ORIGIN OF HIGH TEMPERATUREFERROMAGNETISM
Perhaps the most surprising development of the lastdecade in the science of magnetic materials is abundantobservations of spontaneous magnetization persisting upto above room temperature in semiconductors and ox-ides, in which no ferromagnetism at any temperature hasbeen expected, particularly within the p − d Zener model.These findings have offered prospects for a spread of spin-tronic functionalities much wider than it could initiallybe anticipated. At the same time, they have generateda considerable theoretical effort resulting in proposals ofseveral novel mechanisms of exchange interactions be-tween diluted spins, designed to interpret robust ferro-magnetism in magnetically doped or even magneticallyundoped systems. Nevertheless, it appears that there isno visible convergence between particular experimentalfindings and theoretical models.Over the last years we start to realize that open d shells of magnetic impurities in non-magnetic solids notonly provide localised spins but via hybridisation withband states contribute significantly to the cohesive en-ergy, particularly if TM impurities occupy neighboringsites. The resulting attractive force between magneticcations leads to their aggregation invalidating the mainparadigm of the DMS and DMO physics concerning therandom distribution of TM spins. It may be anticipatedthat the magnetic nanocrystals formed in this way as-sume the crystallographic form imposed by the matrix.Accordingly, the properties of these condensed magneticsemiconductors (CMSs) may be not yet included in ma-terials compendia, so that it is a priori unknown whetherthey are metallic or insulating as well as whether they ex-hibit ferromagnetic, ferrimagnetic or antiferromagneticspin order. However, due to a large concentration ofthe magnetic constituent within the CMSs nanocrystals,their spin ordering temperature is expected to be rela-tively high, typically above the room temperature.As seen today, the experimental detection of a non-random spin distribution and possible contamination hasbeen highly challenging in DMSs research . Only re- cently the actual spatial distribution of TM cations insome DMSs has been established by some groups, ow-ing to the application of state-of-the-art element-specificnanocharacterisation tools. While in some cases onedeals with elemental ferromagnetic metal nanoparticles,the case of Co in ZnO (ref. 83), usually TM compoundsare involved. Taking (Ga,Fe)N as an example, we notethat according to standard laboratory high-resolution x-ray diffraction (HRXRD), the incorporation of Fe sim-ply leads to a broadening of the GaN-related diffrac-tion maxima without revealing any secondary phases .In contrast, a much brighter synchrotron source has al-lowed to identify the presence of precipitates in the samesamples, as shown in Fig. 6, a counterpart of MnAsnanocrystals in GaAs (ref. 85,86). The appearance ofcrystallographic phase separation in (Ga,Fe)N is sup-ported by near-edge x-ray absorption fine-structure (EX-AFS) studies . The dominant ferromagnetic precipitatewas identified as Fe N but in some cases nanocrystalsin the form of an elemental ferromagnetic metal, Fe inthis case, are also visible . At the same time, transmis-sion electron microscopy (TEM) with appropriate massand strain contrast as well as electron dispersive spec-troscopy (EDS), not only corroborated the outcome ofsynchrotron XDR, but revealed also the aggregation ofmagnetic cations without distorting the host wurtzitestructure under certain growth conditions . This chem-ical phase separation is known in the DMS literatureas spinodal decomposition, independently of the micro-scopic mechanism leading to the aggregation of the TMcations.The application of TEM with EDS allowed toevidence the chemical phase separation in annealed(Ga,Mn)As (ref. 86,89), (Zn,Cr)Te (ref. 90), (Al,Cr)N,and (Ga,Cr)N (ref. 91), whereas according to the re-sults summarised in Fig. 6, hexagonal nanocrystals weredetected in (Ga,Mn)N. Finally, we mention the case of(Ge,Mn), where under suitable growth conditions quasi -periodically arranged nanocolumns are observed , asshown in Fig. 7. Actually, a tendency to nanocolumnformation was also reported for (Al,Cr)N (ref. 91) and(Zn,Cr)Te (ref. 93). This demonstrates that growth con-ditions can assist in controlling the nanocrystals shape.Interestingly, these two kinds of nanocrystal forms werereproduced by Monte-Carlo simulations . Furthermore,a strict correlation between ferromagnetic features andthe presence of CMS nanocrystals has been demonstratedfor these systems. However, the identification of the dom-inant microscopic mechanisms leading to robust spin or-dering, that is to a large magnitude of T C and magneticanisotropy, awaits for detailed experimental and theo-retical studies for particular combinations of CMSs andhosts.As expected, the lowering of the growth temperatureand/or the increase of the growth rate hampers theaggregation of magnetic cations. Moreover, it has beensuggested that it is possible to change the TM chargestate and, therefore, the aggregation energy by co-doping HIGH [Mn]
Mn pile-up
Mn-K β Mn-K α Ga-K β Ga escape peak
Ga-K α ENERGY (keV) FL U O R ES C E NC E LOW [Mn]
Mn pile-up
Mn-K β Mn-K α Ga-K β Ga escape peak
Ga-K α ENERGY (keV)
X ( μ m) P R O F I L ES Ga-K α μ m Mn Ga Scattering
Mn-K α FIG. 6: Evidence for crystallographic and chemical phaseseparations in DMSs. Upper panel: synchrotron XRDand TEM results for (Ga,Fe)N showing the precipitation ofhexagonal (cid:15) -Fe N nanocrystals (after ref. 88). Lower panel:element-specific synchrotron radiation micro-probe analysis of(Ga,Mn)N showing aggregation of Mn cations (after ref. 78). with shallow donors or acceptors . This way of af-fecting the TM valency stems from the presence of bandgap states derived from the d orbitals. These statestrap carriers supplied by shallow impurities, altering thecharge state of the magnetic cations and, hence, modi-fying their mutual interactions. Accordingly, co-dopingof DMSs and DMOs with shallow acceptors or donors,during either growth or post-growth processing, modifiesthe valence providing a powerful mean for the controlof the magnetic cation aggregation. These predictionsare corroborated by experimental finding for (Ga,Mn)N(ref. 39), (Zn,Cr)Te (ref. 90), and (Ga,Fe)N (ref. 88),where remarkable changes in the ferromagnetic charac-teristics upon co-doping with shallow impurities havebeen found and correlated with the TM distribution. FIG. 6: Evidence for crystallographic and chemical phaseseparations in DMSs. Upper panel: synchrotron XRDand TEM results for (Ga,Fe)N showing the precipitation ofhexagonal ǫ -Fe N nanocrystals (after ref. 88). Lower panel:element-specific synchrotron radiation micro-probe analysis of(Ga,Mn)N showing aggregation of Mn cations (after ref. 78). suggested that it is possible to change the TM chargestate and, therefore, the aggregation energy by co-dopingwith shallow donors or acceptors . This way of af-fecting the TM valency stems from the presence of bandgap states derived from the d orbitals. These statestrap carriers supplied by shallow impurities, altering thecharge state of the magnetic cations and, hence, modi-fying their mutual interactions. Accordingly, co-dopingof DMSs and DMOs with shallow acceptors or donors,during either growth or post-growth processing, modifiesthe valence providing a powerful mean for the controlof the magnetic cation aggregation. These predictions FIG. 7: Formation of nanocolumns in DMS by aggregation ofMn cations. Upper panel: Mn-rich nanocolumns in (Ge,Mn)evidenced by: (a) HRTEM plane view and (b) Mn chemicalmaps (after ref. 92). Lower panel: Monte Carlo simulation ofchemical phase separation in (Zn,Cr)Te with seeding to initi-ate the growth of nanocolumns and control of their diameterby Cr flux (after ref. 94). are corroborated by experimental finding for (Ga,Mn)N(ref. 39), (Zn,Cr)Te (ref. 90), and (Ga,Fe)N (ref. 88),where remarkable changes in the ferromagnetic charac-teristics upon co-doping with shallow impurities havebeen found and correlated with the TM distribution.Finally, we note that depending on the growth condi-tions CMS nanocrystals can be distributed randomly oraccumulate either at the interface with the buffer or atthe film surface. Furthermore, TM impurities may deco-rate or diffuse along extended defects such as dislocationsor grain boundaries . This appears to explain an inversecorrelation between samples’ quality and the appearanceof high T C ferromagnetism, noted by some authors in thecase of oxides . SOME MODELING
The above qualitative considerations are supported by ab initio studies. For instance, the computed energychange associated with bringing two Ga-substitutionalMn atoms to the nearest neighbor cation position is E d = −
120 meV in GaAs and −
300 meV in GaN,and reaches −
140 and −
350 meV in the case of acation-substitutional Cr nearest neighbor pair in ZnTeand GaN, respectively . In contrast, there is virtu-ally no energy change associated with bringing two Zn-substitutional Mn atoms to the nearest neighbor cationsites in (Zn,Mn)Te, where E d = 21 meV (ref. 90). Thiscan be associated to the fact that the Mn d states lit-tle perturb the sp tetrahedral bonds as both the lower FIG. 7: Formation of nanocolumns in DMS by aggregation ofMn cations. Upper panel: Mn-rich nanocolumns in (Ge,Mn)evidenced by: (a) HRTEM plane view and (b) Mn chemicalmaps (after ref. 92). Lower panel: Monte Carlo simulation ofchemical phase separation in (Zn,Cr)Te with seeding to initi-ate the growth of nanocolumns and control of their diameterby Cr flux (after ref. 94).
Finally, we note that depending on the growth condi-tions CMS nanocrystals can be distributed randomly oraccumulate either at the interface with the buffer or atthe film surface. Furthermore, TM impurities may deco-rate or diffuse along extended defects such as dislocationsor grain boundaries . This appears to explain an inversecorrelation between samples’ quality and the appearanceof high T C ferromagnetism, noted by some authors in thecase of oxides . SOME MODELING
The above qualitative considerations are supported by ab initio studies. For instance, the computed energychange associated with bringing two Ga-substitutionalMn atoms to the nearest neighbor cation position is E d = −
120 meV in GaAs and −
300 meV in GaN,and reaches −
140 and −
350 meV in the case of acation-substitutional Cr nearest neighbor pair in ZnTeand GaN, respectively . In contrast, there is virtu-ally no energy change associated with bringing two Zn-substitutional Mn atoms to the nearest neighbor cationsites in (Zn,Mn)Te, where E d = 21 meV (ref. 90). Thiscan be associated to the fact that the Mn d states lit-tle perturb the sp tetrahedral bonds as both the lower d (donor) and the upper d (acceptor) Hubbard levelsare respectively well below and above the band edges inII-VI compounds , so that there is no considerable dif-ference between the band hybridisation involving Zn orMn. This conclusion is consistent with a large solubility (Zn,Cr)Te (Ga,Cr)As P a i r i ng ene r g y ( m e V ) Number of holes in d -shell FIG. 8: Computed energy change E d resulting from bringingtwo Cr impurities to the nearest neighbor cation positions inZnTe and GaAs depending on the number of holes in the Cr d shell (adapted from ref. 102). of Mn in II-VI compounds and the apparently randomdistribution of Mn in these systems .To model the effect of co-doping, we note that the en-ergy of the screened Coulomb interaction between two el-ementary charges residing on the nearest neighbor cationsites in the GaAs lattice is E d = −
280 meV. This valueindicates that a change in the charge state can affect theaggregation significantly, as the gain of energy associatedwith bringing two Mn atoms close by is E d = −
120 meV,as quoted above . Accordingly, a surplus of charge onTM ions, comparing to non-magnetic cations, broughtby co-doping with shallow dopants can overweight thegain of energy stemming from p − d hybridization andimpede the nanocrystal assembling . This picture isconfirmed by ab initio computations within the LSDAfor (Ti,Cr)O (ref. 96) and (Zn,Cr)Te (refs 90 and 102).As shown in Fig. 8, the value of E d attains a minimumin ZnTe when the two Cr cations are in the 2+ chargestate ( d configuration). However, the computationresults shown in the same plot indicate that also in GaAs, E d goes through a minimum for the Cr case, ratherthan in the case of Cr pairs, as might be expected forIII-V compounds. FROM DILUTE TO NANOCOMPOSITESYSTEMS
In view of the above discussion, the incorporation ofTM impurities to semiconductors not only bridges ferro-magnetic and semiconductor capabilities but also offersa way to develop a new kind of nanocomposite systemsconsisting of ferromagnetic and metallic nanocrystals co-herently buried in a semiconductor host. The applica-tion of embedded metallic and semiconducting nanocrys-tals is known to be on the way to revolutionise the per- formance of various commercial devices, such as flashmemories, low current semiconductor lasers, and singlephoton emitters. Similarly far reaching can be the useof nanocomposite semiconductor/ferromagnetic systemsdue to their unique capabilities and to the possibility ofcontrolling the shape (nanodots vs. nanocolumns) andsize by growth parameters and co-doping during the epi-taxial process.It has already been demonstrated that these nonocom-posites show strong magnetotrasport and magnetoopti-cal effects , that could possibly allow these systemsto be exploited as magnetic field sensors as well as inmagnetooptical devices. In particular, a combination ofa strong magnetic circular dichroism specific to ferromag-netic metals and weak losses characterising the semicon-ductor hosts suggest possible functionalities as opticalisolators as well as three-dimensional (3D) tunable pho-tonic crystals and spatial light modulators for advancedphotonic applications. As an interesting recent develop-ment one can quote a spin battery effect demonstratedfor the GaAs:MnAs system in a magnetic field .As shown in Fig. 7, the controlled growth ofnanocolumns of a ferromagnetic metal can allow to fab-ricate in-situ , e.g. , a dense array of magnetic tunneljunctions or Coulomb blockade devices. Thus, themedia in question can be employed for low-power high-density magnetic storage, including spin-torque magneticrandom access memories and race-track 3D domain-wallbased memories. If sufficiently high tunneling magnetore-sistance (TMR) will be found, one can envisage the appli-cation for field programmable logic (TMR-based connect-ing/disconnecting switches) and even for all-magneticlogic, characterised by low power consumption and radi-ation hardness. Furthermore, embedded metallic nanos-tructures may serve as building blocks for all-metallicnanoelectronics and for high quality nanocontacts in na-noelectronics, optoelectronics, and plasmonics as wellas constitute media for thermoelectric applications .Worth mentioning is also the importance of hybrid semi-conductor/ferromagnetic systems in various proposals ofscalable quantum processors. d FERROMAGNETISM AND BEYOND
Organic ferromagnets and quantum Hall ferromagnetsare a proof that ferromagnetism is possible in materialswithout magnetic ions, albeit the corresponding T C ’s areso-far rather low, typically below 20 K. It has also beensuggested that a robust ferromagnetism can appear incertain zinc-blende metals like CaAs, and be driven by aStoner instability in the narrow heavy hole band ,a prediction awaiting for an experimental confirmation.It has been known for a long time that a number ofdefects or non-magnetic impurities form localised para-magnetic centers in various hosts. Some of these statesmight show a large intra-center correlation energy U thatcould ensure an adequate stability of the spins, even if0their density increases or the material is co-doped withshallow impurities. It is, therefore, tempting to relatethe presence of unexpected high-temperature ferromag-netism in various oxides and carbon derivates to mag-netic moments residing rather on nonmagnetic defects orimpurities than on open d shells of TMs .As shown theoretically , a sizable exchange interac-tion takes place between valence-band holes residing onnon-magnetic acceptors and electrons in the conductionband. This demonstrates that band carriers can mediatea Zener-type coupling between spins localised on defectcenters. Furthermore, if the spin concentration increases,so that either the Hubbard-Mott or the Anderson-Motttransition is reached, the double exchange or Stoner-likemechanism might appear . However, in each of thesecases a clear correlation between magnetic and trans-port properties should be visible, analogous to the oneobserved routinely in manganites, (Ga,Mn)As, and p -(Zn,Mn)Te. In particular, the fabrication of a spintronicstructure – like a magnetic tunnel junction – working upto high temperatures, would constitute a strong confir-mation of the existence of spin transport in these chal-lenging systems. Alternatively, defects and impurities,similarly to TM dopants, could form high spin aggre-gates in certain hosts. In this case, the presence offerromagnetic-like features should correlate with the ex-istence of defect agglomerations that can be revealed byemploying state-of-the-art nanocharacterisation tools.To date, suggestions concerning defect-related high-temperature ferromagnetism come only from global mag-netization measurements. Therefore, it appears morenatural to assume at this stage that a small numberof magnetic nanoparticles – that escaped from the de-tection procedure – account for the high-temperatureferromagnetic-like behaviour of nominally nonmagneticinsulators and semiconductors. Such nanoparticles couldbe introduced during the synthesis or post-growth pro-cessing, and can reside in the sample volume, at disloca-tions or grain boundaries but also at the surface, interfaceor in the substrate. An instructive example is providedby the case of porous silicon . SUMMARY
Where are we then after these ten years? With nodoubt (Ga,Mn)As and related compounds have consid-erably strengthen their position as an outstanding play- ground to develop and test novel functionalities uniqueto a combination of ferromagnetic and semiconductorsystems. Many of the concepts , like spin-injection,electric-field control of the T C magnitude and magneti-zation direction, tunneling anisotropic magnetoresistancein planar junctions and in the Coulomb blockade regime,current-induced domain displacement without assistanceof a magnetic field, are being now developed in devicesinvolving ferromagnetic metals, which may function atambient temperatures. Obviously, however, a further in-crease of T C , over the current record value of 190 K,continues to be a major goal in the field of DMSs.At the same time, investigations of magnetically dopedsemiconductors and oxides have faced us with unexpect-edly challenging issues, intractable by conventional ma-terials characterisation, computational, and theoreticaltools. In addition to an interplay between phenomenaspecific to strongly correlated and disordered systems,encountered in doped semiconductors and manganites,DMSs and DMOs show a fundamentally new ingredientbrought about by a not anticipated correlation in themagnetic ion distribution. We are now learning how tovisualise and control the magnetic ion aggregation in or-der to develop methods allowing to obtain lateral and ver-tical distributions as well as shapes of magnetic nanocrys-tals on demand. The ferromagnetic metal/semiconductornanocomposites fabricated in this way offer a spectrumof so-far unexplored possibilities in various fields of ma-terials science and device physics.Are there only two classes of magnetically doped semi-conductors and oxides showing ferromagnetic features,say, above 10 K? Are ferromagnetic correlation mediatedby valence band holes and embedded magnetic nanocrys-tals the only sources of spontaneous magnetization inthese systems? We will see in the years to come. Acknowledgments
The author’s works described here were supported bythe FunDMS Advanced Grant of the European ResearchCouncil within the ”Ideas” 7th Framework Programmeof the EC, and earlier by ERATO project of Japan Sci-ence and Technology Agency and Humboldt Foundation.The fruitful and enjoyable collaboration with the groupsof Alberta Bonanni, Shinji Kuroda, Hideo Ohno, andMaciej Sawicki is gratefully acknowledged. ∗ Electronic address: [email protected] Story, T., Galazka, R. R., Frankel, R. B. & Wolff, P. A.Carrier-concentration–induced ferromagnetism in PbSn-MnTe.
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