Magnetic order of intermetallic FeGa Ge studied by µSR and 57Fe Mo¨ssbauer 3−y y spectroscopy J. Munevar,1, M. Cabrera-Baez,2 M. Alzamora,3 J. Larrea,4 E. M. Bittar,4 E. ∗ Baggio-Saitovitch,4 F. J. Litterst,4,5 R. A. Ribeiro,6 M. A. Avila,6 and E. Morenzoni1 1Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 2CCNH, Universidade Federal do ABC (UFABC), Santo Andr´e, SP 09210-580, Brazil 3Universidade Federal do Rio de Janeiro, Campus Xer´em, RJ 25245-390, Brazil 4Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, RJ 22290-180, Brazil 5Technische Universita¨t Braunschweig, 38106 Braunschweig, Germany 7 6CCNH, Universidade Federal do ABC, Santo Andr´e, SP 09210-580, Brazil 1 (Dated: January 9, 2017) 0 Temperature dependent magnetization, muon spin rotation and 57Fe M¨ossbauer spectroscopy 2 experiments performed on crystals of intermetallic FeGa3 yGey (y = 0.11,0.14,0.17,0.22,0.27, n 0.29,0.32) are reported. Whereas at y = 0.11 even a sensit−ive magnetic microprobe such as µSR a doesnotdetectmagnetism,allothersamplesdisplayweakferromagnetismwithamagneticmoment J of up to 0.22 µB per Fe atom. As a function of doping and of temperature a crossover from short 6 rangetolongrangemagneticorderisobserved,characterized byabroadlydistributedspontaneous internalfield. However,they=0.14 and y=0.17 remain in the short range ordered state down to ] thelowestinvestigatedtemperature. Thetransitionfromshortrangetolongrangeorderappearsto l e beaccompaniedbyachangeofthecharacterofthespinfluctuations,whichexhibitspinwaveexcita- - tionssignatureintheLROpartofthephasediagram. M¨ossbauerspectroscopyfory=0.27and0.32 r t indicates that the internal field lies in the plane perpendicular to the crystallographic c axis. The s fielddistribution anditsevolution with dopingsuggest that thedetails oftheFemagnetic moment . t formation and theconsequent magnetic stateare determinednot only bythedopant concentration a m butalso by theway thereplacement of theGa atoms surroundingthe Feis accomplished. - PACSnumbers: 76.75.+i76.80.+y71.10.Hf d n o I. INTRODUCTION that leads to metallic-like transportandCurie-Weiss be- c [ havior already at low Co concentrations24. Large Co doping induces substantial disorder as reflected by the 1 Tuning a material’s physical properties by chemical line broadening of the 69,71Ga Nuclear Quadrupole Res- v dopingorbyapplicationofsomeexternalcontrolparam- onance(NQR)spectraandbythedeviationofthelattice 8 etersuchashighpressureormagneticfieldoftenchanges 1 itsbehaviorandinducesnewandexoticstatesofmatter1. parameters from Vegard’s law17. Fe1 xCoxGa3 remains 6 paramagnetic for all Co concentrati−ons investigated11, Arecentexampleistheelectrondopingoftheintermetal- 1 while showing a complex magnetic behavior including lic FeGa that leads to enhanced thermoelectric figures 0 3 itinerantand localized momentcharacterand strong an- . of merit2–10 and to emergent magnetic behavior accom- 1 tiferromagnetic(AFM)spinfluctuationsforCosubstitu- panied by the possible observation of a Ferromagnetic 0 tion close to 0.518. Quantum Critical Point (FMQCP)11–21. 7 1 FeGa3 is a semiconductor with tetragonal structure In contrast, electron doping by substituting Ga with v: (space groupP42/mnm)2 and a narrowband gap of ap- Ge in FeGa3 has more dramatic effects on the magnetic i proximately 0.5 eV caused by the hybridization of the properties. It first suppresses the semiconducting and X 3d Fe and 4p Ga bands2–4,16,24,25. It is diamagnetic over diamagnetic properties, and induces metallic and para- r a broad temperature range and has a small Sommerfeld magnetic behavior at a Ge doping as low as y =0.00611. a coefficient (γ =0.03 mJ )3,11,16. The Fe atoms occur in Already at a low critical concentration y = 0.13 0.15 molK c dimer pairsorientedalongthe a andbdirections. Aunit a weak ferromagnetic (FM) state appears11,15 di−splay- cell contains 4 formula units where each Fe has eight Ga ing features of non-Fermi liquid behavior12. 71Ga NQR neighbors at two distinct sites Ga1 (0.236 nm, 2 atoms) measurements, while not evidencing intrinsic structural and Ga2 (0.239 nm, 2 atoms and 0.246 nm, 4 atoms, disorder related to the Ge doping, point to an evolution above the plane containing Fe)2. Whereas hole doping from a correlated local moment metal at low Ge dop- by Zn at the Ga site or Mn at the Fe site14 does not ing to a weakly itinerant 3D-ferromagnetism and indi- induce an insulating-metal transition and introduces in- cateacrossoverfromshortrangetolongrangemagnetic gap states16, electron doping either at the Fe or the Ga order15. For y = 0.15 the divergence in 1 at T = 0 site destroys the semiconducting behavior, and remark- K indicates very pronouncedand pure 3DTq1uTantum crit- ably influences other physical properties11–21,24–26. ical fluctuations whereas the y = 0.2 data can be well Electron doping via Co substitution of Fe induces a fitted within the self-consistent renormalization (SCR) shift of the Fermi level towards the conduction band, theory15,27. The FM quantum critical behavior is man- 2 ifested also by a temperature dependence of the specific II. EXPERIMENTAL DETAILS heat and of M/H as that predicted by the SCR theory for FM spin fluctuations in three-dimensionalsystems11. Single crystalline specimens of FeGa Ge (y = 3 y y 0.11,0.14,0.17,0.22,0.27,0.29,0.32) have b−een grown at In spite of several investigations, experimental as well UFABC using the Ga selfflux route22,23. High purityel- as theoretical, the nature and evolution of the magnetic ements were sealed in an evacuated quartz ampoule and order in FeGa3 yGey is far from being well understood. heated in a box furnance to 1100 ◦C and then slowly Magnetism in F−eGa3 yGey has been discussed in terms cooledto 550◦C over150h. Moredetailsonsinglecrys- of itinerant magnetis−m, of local magnetic moments or tal growth of these materials are provided elsewhere14. of a combination of both. The itinerant view is sup- TheeffectiveGeconcentrationyofthesampleswereesti- ported by the small saturated moment and correspond- matedusingenergydispersiveX-rayspectroscopy(EDS) ing large Rhodes-Wohlfarth ratio11,12. DFT calculations measurements in a JEOL model JSM-6010LA scanning in a weakly correlated picture find that itinerant mag- electron microscope with a Vantage EDS system. The netism in FeGa3 can be obtained by modest electron estimated y gives effective moment and transition tem- (butalsohole)doping,withoutthepresenceofpreformed perature compatible with reported results11. moments. The density of states increasing very rapidly Magnetizationmeasurementsin the 2 - 300K temper- withnarrowbandsnearthebandedgessuggeststhepos- ature range were performed for each sample in a MPMS sibility of a Stoner mechanism of ferromagnetism when QuantumDesignMagnetometer(SQUID-VSM)underan doped13. Botana et. al. compared results from weakly applied field H = 1 T (Fig. 1). For all Ge concentra- and strongly correlated pictures and found that in both tions, zero field (ZF) and weak transverse field (wTF) cases magnetism including itinerant phases appears eas- muonspinrotationspectrawereobtainedattheGPSand ily with doping20. Dolly,atthe SwissMuonSourceofthe PaulScherrerIn- stitut, Switzerland. For y = 0.14 we performed selected RecentDFT calculationssupportedbysome magnetic pressure dependent µSR measurements at the GPD in- susceptilibity measurements have suggested a complex strument. Temperaturedependent57FeMo¨ssbauerspec- development of the magnetism of Ge doped FeGa with tra(MS)forFeGa Ge andFeGa Ge wereob- 3 2.73 0.27 2.68 0.32 a gradual evolution from localized moments to a more tained at the Brazilian Center for Research in Physics delocalized character state and a combination of local- (CBPF),Brazil,byrecordingtheenergydependentγ-ray ized and itinerant moments accompanied by interplay of transmission on powdered specimens of the above men- ferromagnetism and antiferromagnetism until itinerant tioned single crystals. A 14.4keV γ-rayradiationsource magnetism is established at high doping level of about of57CoinRhmatrixdeliveringabout50mCi,keptatthe y = 0.4. This behavior appears to depend not only on sametemperatureoftheabsorber,andastandardtrans- the dopant concentration but also on the local Ge con- missionspectrometerwithsinusoidalvelocitysweepwere figuration with respect to Fe19. used. Thetemperature rangesforthe µSRandMSmea- surements were from 0.25 K to 300 K and from 4.2 K to The rich and complex behavior including magnetism 300 K, respectively. and quantum critical behavior observed by partial sub- stitution in FeGa calls for investigations that are sensi- 3 tive to the local Fe environment. We present here muon III. RESULTS spinrotation/relaxation(µSR)and57FeMo¨ssbauerspec- troscopymeasurementsonFeGa Ge asfunctionofGe A. Magnetization Results 3 y y doping. These techniques are ab−le to give unique infor- mation about the localmagnetic fields, field distribution The magnetic response M/H as a function of tem- andfluctuationsatthemuonandtheFesite,respectively. perature (Fig. 1) clearly reflects the FM nature of In particularµSR is sensitive to static and dynamic spin FeGa Ge . The ferromagnetic moment ranges from 3 y y correlations in systems with critical behavior29–31 and 0.09 µ− per Fe atom for the y = 0.17 sample, to 0.22 B can determine the degree of homogeneity of the mag- µ per Fe atom for y = 0.32, significantly smaller B netic phase and how it develops with temperature. 57Fe than that of pure Fe (2.22 µ ). The inset of Fig. B Mo¨ssbauerspectroscopygivesinformationabouttheelec- µeff 1 shows the Rhodes-Wohlfarth ratio (RWR= ) for tricandmagneticsurroundingofFe atalattice position. µ sat different Ge concentrations, clearly above the expected Our results indicate an evolution from short range to value (RWR=1) for localized ferromagnetism11,12,19,28. long range order magnetism, displaying near y a large c degree of inhomogeneity with peculiarities that can be related to the magnetic moment distribution of the Fe B. µSR Results atoms. The spin fluctuations appear to have different character close to the QCP when compared to that of Selected ZF-µSR spectra from FeGa Ge single 3 y y the well established FM phase. crystals are shown in Fig. 2. The evolution−of the mag- 3 1 0.12 10 P (t)=(1 f)Ppm(t)+f exp( λ t)+ WR) 8 Z − Z (cid:20)3 − l Oe) 0.10 / (Reffsat 46 +23(cid:0)1−λt−σT2t2(cid:1)exp(cid:18)−σT22t2(cid:19)exp(−λt)(cid:21), ol 0.08 2 (2) m emu/ 0.06 00 10 20 TC3 (0K) 40 50 60 σ w=heγre√λ∆isBt2hiestLhoerGenatuzsiasinanmmuounonspreinlaxrealtaioxnatriaotne,raanted, T µ M/H 0.04 00..1117 00..1242 lλalriazcactoiounn,tscoforrretshpeonsdminalgl dtoamslpoiwngdoyfntahmeictafliluoctfutahteiopnos-. 0.27 0.29 This accounts for the strong muon spin depolarization 0.02 0.32 observed in Fig. 2, as being caused by two different sources of magnetism: a dense distribution of magnetic 0.00 moments producing a Gaussian field distribution with 0 50 100 150 σ2 T (K) variance γTµ2 (γµ =2π×135.5MHz/T)inanenvironment ofdilutedmagneticmomentsproducingaLorentziandis- FIG.1. TemperaturedependentZFCmagnetizationmeasure- tributionwithHWHM λ . Bothdistributionsprobedby mentsforFeGa3 yGey. singlecrystalsina1Texternalfield. γµ In the inset the−Rhodes-Wohlfarth ratios obtained for each the muonsarecenteredarounda localfieldBµ withzero sample are shown. x, y, and z components. The value 1 of the tail reflects 3 the isotropic distribution of the local fields. For larger doping y > 0.17 the magnetic contribution netismasafunctionofdopingandacrossthecriticalcon- to the data cannot be simply described by an isotropic centration yc is already evidenced in Fig. 2(a). Whereas distribution around Bµ = 0, instead a spontaneous field the y = 0.11 sample shows only weak temperature in- Bµ = 0 at the muon site has to be taken into account. 6 dependent muon spin depolarization (see also Fig. 3(b)) ThecaseofanisotropicGaussiandistributionaroundan with characteristic Gaussian Kubo-Toyabe behavior due isotropic static field of constant magnitude is known as to the static nuclear magnetic moments of Ga and Fe, the Koptev-Tarasov model32,33, from which for Bµ = 0 the fast relaxation which sets in at early times on low- theKubo-Toyabeformulaiseasilyrecovered. Fornottoo ering the temperature for y 0.14 reflects the onset of small Bµ the polarization function can be described by electronic magnetism. The fl≥at behavior of the polariza- Eq.3, which is used to fit the low temperature data: tion at late times for y & 0.2 reflects static magnetism. The weak decay of this tail for 0.14 y 0.17 (see Fig. 2(c)-(d)) indicates the persistence of≤som≤e slow (∼MHz) PZm(t)=aexp(−λlt)+ spin fluctuations in the low doping range. The (quasi) σ2t2 +(1 a)exp T cos(γ B t), (3) static nature of the magnetism is confirmed by longitu- µ µ − (cid:18)− 2 (cid:19) dinalfield datafor y =0.17(Fig. 2(e)), whichshowsthe completedecouplingofthemuonspinfromthelocalfield together with a temperature dependent contribution in a longitudinal field of 0.1 T. describingtheparamagneticfractiongivenbyEq. 1. We At high temperatures all the spectra display the typi- have therefore for P (t) Z cal muon spin relaxation behavior due to the very small static nuclear magnetic moments of Ga and Fe. The muon polarization in this non-magnetic regime can be P (t)=(1 f)Ppm+fPm(t), (4) Z − Z Z modeled as wherePpm(t)andPm(t)arethepolarizationfunctions Z Z in the paramagnetic and the magnetic state. B is the µ Ppm(t)= 1 + 2 1 σ2t2 exp σnt2 , (1) internalfieldsensedatthe muonsite,andthe parameter Z 3 3 − n (cid:18)− 2 (cid:19) a is related to the fraction of muons with initial spin (cid:0) (cid:1) parallel to an internal field component. Note that a= 1 3 where σ is the Gaussian muon spin relaxation rate corresponds to an isotropic distribution of fields. Since n caused by nuclear moments. The model that best de- oursampleconsistsofasetofsinglecrystals,adeviation scribes the spectra at y = 0.14 and y = 0.17 is the from a = 1 indicates a preferred orientation of the local 3 sum of two sample volume contributions: a paramag- field with respect to the crystal axes. netic fraction 1 f described by Eq.1 and a magnetic The temperature dependence of B and of √∆B2 are µ − one f describedby the so-calledcombinedKubo-Toyabe plotted in Fig. 3(a) and (b). For the y = 0.14 and function: y = 0.17 samples, where B = 0, we have plotted µ 4 ZF @ base temperature ZF y=0.11 ZF y=0.14 y = 0.32 2 K 0.85 K 1.0 y = 0.29 1.0 90 K 1.0 2.01 K y = 0.27 2.7 K 0.8 a) 0.8 0.8 y = 0.22 5.5 K (t)Z0.6 yy == 00..1174 0.6 0.6 P 0.4 y = 0.11 0.4 0.4 0.2 0.2 0.2 b) c) 0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 ZF y=0.17 LF y=0.17 - T=1.57 K ZF y=0.22 1.57 K 0 T 1.0 5.18 K 1.0 25 mT 1.0 5.74 K 50 mT 0.8 0.8 0.8 f) 6.30 K 100 mT (t)Z0.6 67..8461 KK 0.6 0.6 13.05.97 9K K P 0.4 7.97 K 0.4 0.4 57.1 K 8.52 K 0.2 9.62 K 0.2 0.2 e) 0.0 d) 0.0 0.0 0 1 2 3 4 5 6 7 8 9 0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8 1.0 ZF y=0.27 ZF y=0.29 ZF y=0.32 4.4 K 1.0 1.0 1.0 34.23 K g) 44.23 K 0.8 0.8 0.8 54.17 K (t)Z0.6 14.25.45 3K K 0.6 44.84. 2K2 K 0.6 5568..2246 KK P 0.4 58.5 K 0.4 54.25 K 0.4 64.25 K 0.2 0.2 0.2 h) i) 0.0 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 t (µs) t (µs) t (µs) FIG. 2. (a) Lowest temperature measurements of the muon spin polarization in ZF for all investigated Ge concentrations y. (b)-(d),(f)-(i)TemperatureevolutionoftheZFµSRspectraforFeGa3yGey atvariousy. (e)showstheLFspectrafory =0.17 at fields upto 100 mT. the width of the Lorentzian distribution λ as a mea- value 1 for the isotropic case indicates that the field has γµ 3 sure of the local field strength. Both B (T 0) and a preferred orientation with respect to the crystal axis, µ √∆B2(T 0) as well as T increase as the→Ge con- as also suggested by the Mo¨ssbauer spectra discussed in C → the following section. centration increases, in agreement with the observed in- We also determined the magnetic volume fraction crease of the spontaenous magnetic moment saturation per formula unit11. However, the doping dependent low Vm(T) as a function of temperature from the precess- ing asymmetry measured in weak transverse field exper- temperature values of the internal field and field width iments of 5 mT. The results are shown in Fig. 3(d). reflect a change of the magnetic regime at y 0.2 with ∼ For Ge doping y & 0.22 the magnetic volume fraction a step like increase of both parameters. For y > 0.2 the temperature dependence of B and √∆B2 are similar is nearly 100 %, shows a sharp transition at TC at the µ highest doping and a small rounding below. This to- and represent the build-up of the local order parameter gether with the gradual increase of the local order pa- of a magnetic transition of second order. rameter mentioned above is an additional signature of Interestingly, the ratio √∆B2 (Fig. 3(c)), which is ef- second order transition. By contrast, at y = 0.14 and Bµ 0.17, which are just above the critical Ge concentration, fectively infinite for y = 0.14 and 0.17 where B = 0 µ magneticorderdevelopsgraduallywithtemperatureand and where also γµ√∆B2 is large, remain quite large for reaches only about 70 % of the sample volume even at λ y > 0.17 reflecting a broad field distribution at all in- the lowest temperature. The magnetic volume fraction vestigated Ge concentrations. The relatively low values of y = 0.14 under external pressure of 2 GPa shows a of B (0) andits evolutionwith Ge doping are consistent further decrease down to 40 %, indicating the suppres- µ withaweakFMstateevolvingfromshortrangeorderfor sionofthe magneticgroundstatebypressure,whichhas y . 0.17 to more long range order with increasing con- been previously shown to induce a decrease in T 11. C centration. The parameter a of Eq.3 ranges from 0.12 ByplottingB (0),√∆B2(0)andV (0)versusGecon- µ m to 0.27 for 0.22 y 0.32. The deviation from the centration, the effect of doping in the magnetic proper- ≤ ≤ 5 a) 0.040 b) c) y=0.32 0.035 0.020 101 y=0.29 y=0.27 0.030 y=0.22 y=0.17 0.025 T)0.015 Bµ y=0.14 (T)Bµ0.020 2 (∆B0.010 2/∆B y=0.14 2 GPa 0.015 (cid:1) (cid:1)100 0.010 0.005 0.005 0.000 0.000 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 T (K) T (K) T (K) d) 100 e) 0.040 Bµ(0) 100f) 0.14 M/H 80 T) 00..003305 (cid:0)λγ(µ0∆)Bµ2(0) 80 Oe)00..1102 Normalized M/H (%)V(T)m 4600 2, (B(0)(0)∆Bµ(cid:1)0000....000011220505 VVmm((00),P) 4600mV(T)(0) (%) M/H(0) (emu/mol 000...000468 20 20 0.005 0.02 0 0.000 0 0.00 0 10 20 30 40 50 60 70 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 T (K) y (Ge concentration) y (Ge concentration) FIG. 3. Doping dependence of various parameters obtained from the µSR measurements of FeGa3 yGey single crystals. Temperature dependence of (a) spontaneous internal field Bµ(T). For y = 0.14 and 0.17, where Bµ =−0, γλµ is plotted. (b) Field width √∆B2(T), (c) ratio √∆B2, (d) magnetic volume fraction as obtained from the analysis of the weak transverse Bµ field µSR spectra. The corresponding points for the magnetic volume fraction under pressure is represented by hollow circles. (e) Doping dependence of the low temperature limit of the spontaneous internal field Bµ(0), of the field width √∆B2(0) and of the magnetic volume fraction Vm(0). (f) Doping dependent saturation magnetization M(0)/H obtained from Fig. 1, and normalized to themagnetic volume fraction. ties (Fig. 3(e)) is clearly seen. A continuous decrease (see Fig. 4). These spectra have low resolution due to of Bµ(0) and √∆B2(0) down to Ge y = 0.22 is ob- the small values of Bhf, therefore their analysis depends served,andV (0) remainsnearlyconstantinthis range. to some degree on the chosen procedure. Obviously the m Lower Ge concentrations induce a dramatic decrease in strengths of nuclear electric quadrupole interaction and B (0), √∆B2(0), and V (0) starts to decrease, and fi- magnetic hyperfine interaction are comparable necessi- µ m nallyaty =0.11nomagneticorderisdetected. Fig. 3(f) tatingthesolutionofafullHamiltoniancomprisingboth showsthesaturationmagnetizationM(0)/H foreachGe interactions for the determination of line positions and concentration, and the corresponding quantity normal- their proper intensities. We have employed the codes of ized M(0)/H by V (0) (Fig. 3(e)), which indicates a MOSSWIN34 and private ones35 allowing also for trans- m smoother development of the average effective magnetic mission integral corrections of spectral line shape. moment with doping. For the spectra of the absorber with y =0.27 taken in applied magnetic fields at 4.2 K (not shown) we had to assumearandomorientationofanaxialelectricfieldten- C. 57Fe M¨ossbauer Spectroscopy Results sor versus the direction of applied field. For the sample with y =0.32 we could achieve an alignment of crystal- 57Fe Mo¨ssbauer absorption spectra on samples of lites along the applied field as could be traced from the missingnucleartransitionswith∆I =0(I beingthenu- FeGa Ge (y =0.27 and 0.32) are shown in Fig. 4. z z 3 y y A clea−r doublet profile is observed in the paramagnetic clearspinprojection)connectingthe nuclearexcitedand ground states with spin I = 3 and I = 1, respectively. state,whichwasfittedwithanuclearelectricquadrupole z 2 z 2 interaction between the iron nucleus and its surround- Above the magnetic ordering temperatures the values ings. When the temperature is lowered and the mag- of quadrupole splittings eV Q/2 (e is the elementary ZZ netically ordered regime is entered, the resonance lines charge, V is the electric field gradient major compo- ZZ broaden and the absorption profiles become asymmetric nent, Q the nuclear quadrupole moment for 57Fe in its reflecting the effect of the magnetic hyperfine field B excited state) are practically equal with 0.25(3) mm/s hf 6 internal fields and field widths √∆B2 in Fig 3. The sat- FeGa2.73G e0.27 FeGa2.68G e0.32 uration values of Bhf measured at lowest temperatures -2 0 2 -2 0 2 are consistent with those derived from spectra obtained n (a.u.) 11% 60 K n (a.u.) 11% 80 K in applied magnetic fields. o o ssi 45 ssi 60 mi mi ns 40 ns 55 IV. DISCUSSION a a e Tr 35 e Tr 50 elativ 20 elativ 40 The results obtained in the present investigation by R R local probe techniques show the development of weak 10% 4.35 10% 4.35 FMuponelectrondopingofFeGa Ge ,withanevolu- 3 y y -2 0 2 -2 0 2 tion of the characterof the magnet−ic order on increasing v (mm/s) v (mm /s) y. The presence of Fe atoms and their dimer arrange- mentwithrelativedistanceof0.277nm(tobe compared 2 y=0.27 1.00 y=0.27 withanearestFe-Fedistanceof0.248nminthebcc iron y=0.32 y=0.32 0.75 metal)hasraisedthe questionaboutthe pre-existenceof B (T)HF1 (T)0.50 mthaegunnedtiocpmedomcoemnptsouannddFtheGeiar m,waghnicehticshboewhsadviiaomr eavgennetiinc 3 0.25 properties. LDA calculationsincluding a realisticonsite 0 0.00 repulsion have suggested an antiferromagnetic arrange- ment of Fe equivalent to a Fe spin singlet state with a 0 20 40 60 80 100 0 20 40 60 80 100 2 T (K) T (K) Fe magnetic moment of 0.6 µB and suggested that the doped induced magnetism would be linked to the break- FIG.4. 57FeM¨ossbauerspectrafory=0.27and0.32crystals ing of the singlets into free spins10. On the other hand, at different temperatures. In the bottom part of the figure calculationsbySinghwithintheGGAapproximationex- the temperature dpendence of the Fe hyperfine field and its plainedthemagnetismofdopedFeGa withoutresorting distribution width are shown. 3 to the coupling of pre-existing spins.13 At the lowest doping investigated in this work (y = 0.11), below the concentration where a FMQCP is ex- forbothy =0.27and0.32. Also,isomershifts areequal, pected,averysensitivelocalmagneticprobesuchasµSR withδIS =0.28(1)mm/s(vs. Fe metalatroomtempera- does not find indication of a magnetic state. The weak ture). When entering the magnetically orderedstate the exponential relaxation, which appears on increasing the derived values for the quadrupole interactions are only temperature in the ZF µSR spectra (see Fig. 2(b) may about half of those above TC, if it is assumed that the indicateaparamagneticcontributionrelatedtothepres- electric field gradient main component VZZ is oriented ence of some free magnetic moments. This appears diffi- along Bhf. From the spectra in applied field on the ori- cult to reconcile with the antiferromagnetic order as the ented sample y =0.32, however, it becomes clear that onelowestinenergycalculatedbyYinandPickett10 and the latter assumption is erroneous and instead the ax- with results of recent neutron powder diffraction mea- ial field gradient tensor is oriented perpendicular to Bhf surements that found magnetic Braggpeaks aboveroom with a negative value VZZ. This means that the nu- temperaturealsointheundopedFeGa3indicatingacom- clearelectricquadrupoleinteractionintheparamagnetic plex magnetic structure16. and the ferromagnetic state is the same. Assuming the The µSR spectra show an evolution from short range main axis of the electric field gradient to be tetragonal order(inthey =0.14andy =0.17samples)tomorelong c axis, we have to conclude that Bhf lies within the ab range order magnetism above y 0.20. This is reflected plane. This is in agreement with the µSR results which in the field distribution and ma∼gnetic volume fraction pointtoapreferredorientationoftheinternalfields. For probed by the polarized muons. The SRO is character- further analysis of the Mo¨ssbauer spectra in the mag- ized by a broadfield distribution centered arounda zero netically ordered regime this was taken into account for internalfield. Moreover,magnetismdevelopsonly apar- both samples. Whereas line widths in the paramagnetic tialvolumefraction. Bycontrastabovey 0.20thefield regimedonotrevealanoticeablebroadeningcausedbya distribution, while remaining broad, is ch∼aracterized by distribution of isomer shift and quadrupole interactions, the presence of a non-zerointernalfield B , with the ZF µ we haveto introducea wide distributionofmagnetic hy- spectrashowingaheavilydampedspontaneousspinpre- perfine splittings in the magnetic state. Best fits were cession. This indicates LRO of a magnetic ground state achieved with a Gaussian distribution width σ around a which,asshownbytheweakTFmeasurements,develops mean value Bhf. in the full volume fraction. Mean magnetic hyperfine fields B and Gaussian The evolution of the character of the magnetic order hf widths σ obtained from the fits described above are with doping is also apparent in the temperature depen- shown in Fig. 4, following a similar behavior as the µSR dence of the local magnetization expressed by the inter- b) 7 which deviates from the SCR prediction. This doping M/H region closer to the putative FMQCP displays other un- 60 Bhf Mag. Vol. Frac. usual behavior. The evolution of the magnetic fraction 50 pBµ∆B2 SRO FM indicates an inhomogeneous disappearance of the mag- netic order in its vicinity, as indicated by the reduction ofV (0)neary . TheµSRresultsaroundy =0.14 0.17 m c − 40 1.5 evidencethecoexistenceofshort-rangeorderedspinclus- ters coexisting with a non-magnetic environment. The T (K)30 , αβ 1.0 βα combined Lorentz-Gauss field distribution indicate that 0.5 the spin structure of these clusters consists of a diluted 0.0 distribution of larger magnetic moments embedded in a 20 0.11 0.22 0.33 densematrixofrandomlydistributedmomentsofsmaller y (Ge concentration) value. This corresponds to the situation where a few Fe 10 PM LRO FM atomspossessalargemomentinaseaoflowermomenta Fe. The ratio σT 1, can be taken as a rough measure λ ≃ 2 of the relative magnitudes of the two types of moments. 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 This finding is in agreementwith recent first-principle y (Ge concentration) DFT calculations19 which have indicated that the mag- netic moments are not uniformly distributed throughout all Fe atoms as we would expect in a simple itinerant FIG. 5. Phase diagram of FeGa3 yGey. The transition tem- − picture and that, depending on the doping concentra- peraturesasobtainedfrommagnetization,µSRandMSanal- ysis are shown. The blue region corresponds to short range tionandthelatticedistributionoftheGedopants,differ- magneticorder,theredregioncorrespondtolongrangemag- entgroupingsofmagneticmoments onthe Fe atomswill neticorderinteractions. Intheinset theα andβ parameters form. Qualitatively,theinhomogeneoussituationaround obtained from the fits of the temperature dependence of the y = 1 0.17maybeseenalsoasaconsequenceoftheFe internal field and field width are shown. coord6in≃ation. Since each Fe has 6 Ga neighbors, around this concentration, on average,one Ge atom will occupy a neighbor Ga site, inducing the small moment states nal field measured by µSR and Mo¨ssbauer spectroscopy andonlyinafewcasestwoGeimpuritiesclosetoFewill B (T) and B (T), which were fitted with the generic µ hf induce a higher spin density. Specifically, in the DFT expression calculationsdifferentvaluesofmagnetic momentsonthe Featomsarepredictednotonlydependingontheirposi- α β tion with respect to the Ge impurity but also depending T B (T)=B 1 . (5) whether the impurity occupies a Ga1 or the more likely (µ,hf) 0(cid:18) −(cid:18)TC(cid:19) (cid:19) Ga2 position. For small dopant concentrations, some Fe sites are predicted to carry no moments. Our µSR mea- The curves with the best sets of parameters are plotted surements find a sizable non-magnetic volume fraction in Fig. 3(a)-(b) and Fig. 4 and the evolution of α and even at y =0.17. The local probe character of µSR puts β with y is plotted in the insert of Fig. 5. Because of a lower limit to the size of the non-magnetic regions to thescarcityofpointsclosetoT wefixedorrestrainedin C at least a few lattice constants. This finding also sup- somecasesβ. Itturnsoutthatthechoiceofβ = 1,which 3 ports the picture of a complex nature of the magnetism reproducethe evolutionofthe magnetizationclosetoT C of FeGa Ge with the exact lattice position and dis- inmost3Dmagneticsystemsapproximatelywell36,gives tribution3−oyf eaych Ge dopant directly influencing the ap- the best agreement with the experimental data in the pearance and site of the Fe spin. regionwithLRO.Thisvalueissupportedbythefactthat α is then found to be very close to 3 as expected in the TheLROorderandthefullmagneticfractionfoundon 2 increasingthedopantdistributionreflecttheevolutionto caseoflowtemperaturecontributionstospinfluctuations amoreuniformmagnetismwithallFeatomshavingsimi- arising from spin wave excitations. On lowering the Ge larmoments,whichappearstobeaccompaniedbyamore concentration there is a trend toward a reduction of β itinerant character as indicated by nuclear quadrupolar andanincreaseofα. Fory =0.22,thelocalfieldplotted resonance measurements15. Interestingly, in most of the inFig. 3(a)iswelldescribedbyβ =0.5andα=1.29(8), distributions leading to these fully ferromagnetic states, in agreement with the prediction from the SCR theory for spin fluctuations (β =0.5 and α= 4)27. the induced magnetic moments are predicted to be ori- 3 entedinthesamedirection19. Thisisconsistentwiththe At lower doping where SRO is observed and B = 0, µ presentµSRandMSresults,suggestingalocalhyperfine we fitted λ(T) and σ(T), since both quantities are also field lying perpendicular to the crystallographicc axis. a measure of the local magnetization. The temperature β Fig. 5 shows the phase diagram as obtained from the dependence is of the form 1 T with α = 1 and (cid:16) − TC(cid:17) presentµSR,MSandmagnetizationmeasurements. The β =0.74(30) for y =0.17 and β =0.77(23) for y =0.14, temperatures defining the phase boundaries have been 8 derived from the inflection point of the magnetization damped spontaneous precession showing up for y =0.22 (Fig. 1), from the 50 % value of the magnetic volume and above. For the low dopant concentration y = 0.14 fraction and from the onset temperature value where an and 0.17 part of the sample remains in a non-magnetic internal field and broadening are detected by µSR and state even at the lowest temperatures. Mo¨ssbauerspectroscopy(Fig. 3and4). Nointernalfield B has been detected at low doping. This together with The ZF data indicate that the magnetic moment for- µ the previously discussed field distribution is a strong in- mation,itssizeandtheconsequentcharacterofthemag- dication of FM with SRO in this part of the phase dia- netic order, depends not only on the dopant concentra- gram. SRO develops into LRO with increasing y. How- tion but also on details of the Ge dopant distribution as ever,evenat dopings where the low temperature state is suggested by recent DFT calculations19. The suppres- long range ordered, magnetism appears at the thermal sionof magnetism in a fraction of the sample volume for phaseboundaryfirstasSRObeforegraduallydeveloping dopings close to the y = 0.13 where a critical point is into the LRO state. This is also reflected by the onset expected calls for more detailed study of the critical be- temperature of the field broadening being higher than havior by a local probe. The pressure induced decrease the one of the internal field and is also reflected by a of the magnetic volume fraction for y = 0.14 and of TC monotonic increase of √∆B2 on approaching the Curie in high doping samples11 suggest also that the critical Bµ behavior could be tuned by pressure. temperature from below (see Fig. 3(c)). Acknowledgement: The research leading to these results has received funding from the Euro- V. CONCLUSIONS pean Community’s Seventh Framework Programme (FP7/2007-2013)under grant agreement n.290605 (PSI- Inconclusion,magnetization,ZF,TFandLFµSRand FELLOW/COFUND), and from the Brazilian funding Mo¨ssbauer spectroscopy measurements have been per- agencies CNPq, FAPESP (grant n. 2011/19924-2) and formed on FeGa Ge singlecrystalline samples with y CAPES. The authors thank H. Luetkens, J. C. Orain, 3y y rangingfrom0.11to0.32. TheµSRandMSspectrapro- A. Amato, R. Khasanov and Z. Shermadini for the sup- videevidenceformagnetismdevelopingfromshortrange port during the muon spin rotation experiments, and H. orderneartheFMQCPtolongrangeorderwithaheavily Micklitz for the discussions held. ∗ E-mail: [email protected] 13 D. J. Singh, Phys.Rev.B 88, 064422 (2013). 1 Elbio Dagotto, Science 309, 257-262 (2005). 14 M. Cabrera-Baez, E. T. Magnavita, R. A. Ribeiro, M. 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