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Magnetic properties of the helimagnet Cr NbS observed by µSR 1/3 2 D. Braam,1 C. Gomez,1 S. Tezok,1 E.V.L. de Mello,2 L. Li,3 D. Mandrus,3,4 Hae-Young Kee,5,6 and J.E. Sonier,1,6 1Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada 2Instituto de F´ısica, Universidade Federal Fluminense, Niterói, RJ 24210-340, Brazil 3Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA 4Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5Department of Physics, University of Toronto, Ontario M5S 1A7, Canada 5 6Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada 1 (Dated: March 3, 2015) 0 We haveperformed muon spin rotation/relaxation (µSR) measurements on single crystals of the 2 chiral helimagnet Cr1/3NbS2 at zero to low magnetic field. The transition from the paramagnetic r to helical magnetically ordered phase at zero field is marked by the onset of a coherent oscillation a of the zero-field muon spin polarization below a critical temperature T . An enhancement of the M c muon spin precession frequency is observed below T ∼50 K, where anomalous behavior has been observed in bulk transport measurements. The enhanced precession frequency indicates a low- 2 temperaturemodification ofthehelicalmagneticstructure. ALandaufreeenergyanalysissuggests thatthelow-temperaturechangeinthemagneticstructureiscausedbyastructuralchange. Wealso ] i suggest a longer periodicity of helicity below T∼50K, which can beverified byneutron scattering c experiments. s - l PACSnumbers: 75.30.-m,75.10.-b,76.75.+i r t m . Cr1/3NbS2 is an itinerant chiral helimagnet near Tc, indicative of changes to the electronic structure t a (CHM) with an hexagonal non-centrosymmetric and/or the effects of the magnetism on the mobility of m crystal structure.1 In crystals belonging to a non- the charge carriers. Likewise, anomalous behavior has centrosymmetric space group, CHM order is generally been observed in magnetoresistance, thermopower and - d understoodtobe aconsequenceofcompeting symmetric Hall resistivity data below T∼50 K.5 At these low tem- n Heisenberg exchange and Dzyaloshinsky-Moriya (DM) peratures the magnetoresistance at high fields becomes o interactions. TheCHMorderinCr NbS continuously anisotropic,thereisarapiddecreaseoftheSeebeckcoef- c 1/3 2 [ evolves into an incommensurate chiral magnetic solition ficientwithdecreasingtemperature,andthe fielddepen- lattice (CSL) upon application of a magnetic field dence of the Hall resistivity drastically changes. To gain 2 perpendicular to the helical c-axis (H⊥cˆ).2,3 The CSL futher insight into the sources of the transport anoma- v consistsofperiodicdomainsofferromagneticallyordered lies, we have used the µSR technique to investigate the 4 ◦ spins in the ab plane separated by 360 spin domain nature of the accompanying magnetism. 9 0 walls. The period of the CSL increases monotonically Our µSR measurements were performed at TRIUMF 3 with the magnitude of the applied field, resulting on a ∼50 mm2 mosaic consisting of seven ∼0.25 mm 0 in a continuous phase transition to a commensurate thick plate-like Cr NbS single crystals, which were 1/3 2 1. ferromagnetic (FM) state. The ability to easily tune grown as described in Ref. 6. The positive muon (µ+) 0 the size of the magnetic domains of the CSL, and hence beam was directed at the large face of the mosaic, with 5 the magnetic potential experienced by the spins of the the linear momentum of the beam parallel to the c-axis 1 intinerant electrons, makes Cr1/3NbS2 an appealing of the crystals (z-direction). The initial muon spin po- v: candidate for spintronics applications. larization P(t=0) for all measurements was rotated to i At elevated temperatures there is a transition to a be perpendicular to the c-axis (x-direction). Data was X paramagnetic (PM) state. Reported values of the PM- collected with zero applied magnetic field (ZF), and for ar to-CHM phase transition temperature Tc vary between a transverse field (TF) [i.e. perpendicular to P(t=0)] 118 K (Ref. 4) and 133.5 K (Ref. 5). While the long- applied perpendicular to the c-axis (y-direction). Note range magnetically ordered phases of Cr NbS have that for the desired H⊥côrientation the field must be 1/3 2 been established, the details of the transition from the appliedperpendiculartothe beam,sincethecrystalsare PM phase to the CHM or CSL phases are unresolved. toothintoorientwiththebeamshiningonthea-corb-c Anomalies in the magnetic field dependence of the resis- planefaces. Theensuingbeamdeflectionbythemagnetic tivity, and the temperature dependences of the Seebeck forceexertedontheincomingµ+ limitedtheappliedfield and Hall coefficients near T have been reported.6,7 In strength to H≤600 Oe. c particular, at T a signficant negative magnetoresistance Figure 1(a) shows representative ZF-µSR asymmetry c (withH⊥cˆ)hasbeenobserved,withnosaturationofthe spectra. The data for 135≤T≤170 K were best fit to resistivity at fields where both the resistivity and mag- 2 netization saturate at lowertemperatures.6 The Seebeck A(t)=XAiGKT(∆i,t)e−λt+Ab, (1) and Hall coefficients also show a pronounced minimum i=1 2 1.0 0.25 0.25 S site (a) 0.20 0.8 Nb site 0.15 Total 0.20 0.10 (t) 0.6 0.05 As A(t)0.15 H =1 03 5O Ke 0.000.0 0.2 0.4 0.6 0.4 129 K 0.2 0.10 5 K 0.0 0.05 -0.2 0.0 0.1 0.2 0.3 0.4 0.5 t ( s) 0.00 FIG.2: (Coloronline)Simulationsofthesample(s)contribu- 0 2 4 6 8 tiontotheZF-µSRsignalforCr1/3NbS2 intheCHMground state. The dashed curves show the contribution from muons 0.3 H = 600 Oe 160 K 130 K (b) stopping near Nb at (0.77, 0.32, 0.96) and near S at (0.37, 135 K 3 K 0.78, 0.6), where the coordinate values are multiples of the 0.2 respectivelattice constantsa=b=5.7˚A,and c=12.1 ˚A.The Cr magnetic moment is assumed to be 4.4 µ . The occupa- B 0.1 tion probability of the muon site near S is taken to be twice ) (t that of thesite near Nb. A 0.0 where G (∆ ,t) is a static Gaussian Kubo-Toyabe re- -0.1 KT i laxation function, and A is a small time-independent b background signal. The fits yield A /A ≈ 2, ∆ = -0.2 1 2 1 0.091(4)µs−1, ∆ =0.414(5) µs−1, and a relaxation rate 2 0.0 0.1 0.2 0.3 0.4 0.5 λthatexhibitsadivergentincreaseasthetemperatureis lowered. Based on these results and nuclear dipole field t ( s) calculations,we attribute the two sample components to a muon stopping site near a S atom and a site near Nb. 0.25 (c) The amplitude ratio A /A implies that the probability 0 Oe 1 2 ofthemuonstoppingattheSsiteisapproximatelytwice 100 Oe 0.20 600 Oe that of the Nb site. A0 For T ≤130 K the relaxation rate is sufficiently fast 0.15 thatsomeofthe measuredZF-µSRsignalis dampedout intheinitialdeadtimeoftheµSRspectromter,resulting inareductionofthe initialamplitude A =A +A +A 0.10 0 1 2 b [see Fig. 1(c)]. The asymmetry spectra at these temperatures were fit to 0.05 0 20 40 60 80 100 120 140 160 A(t)=A e−Λ1tcos(2πft)+A e−Λ2t+A . (2) 1 2 b T (K) The oscillating term is indicative of magnetic order,and FIG.1: (Coloronline)(a)RepresentativeZF-µSRasymmetry the spin precession frequency f is related to the magni- spectraofCr1/3NbS2recordedatdifferenttemperatures. The tude of the mean field B sensedby the muonensemble, inset shows the asymmetry spectra at early times, with the µ datapackedintosmaller timebins. Thesolid curvesthrough where f=(γµ/2π)Bµ and γµ/2π=135.54 MHz/T is the the data points are fits to Eqs. (1) or (2). (b) Representa- muongyromagneticratio. Despitetherebeingtwomuon tive TF-µSR asymmetry spectra of Cr1/3NbS2 recorded at stoppingsites, we couldnotresolvetwodistinct frequen- different temperatures with H =600 Oe. The solid curves cies. Thisisunderstandablefromsimulationsofthe con- through the data points are fits to Eq. (3). (c) Temperature tribution ofeachof these sites to the ZF-µSRsignal(see dependenceof the total initial asymmetry A0. Fig. 2), where the signal from muons stopping near Nb is smaller and rapidly damped. The temperature depen- denceoff indicatesamagnetictransitionatT =129.6K c (see Fig. 3), which is close to previous estimates of the Curie temperature of Cr NbS .1 1/3 2 Figure 1(b) shows representative TF-µSR spectra for 3 H⊥cândH=600Oe. Theexternalfieldaddsvectorially to the local field generated by the spin structure. At all temperatures the TF-µSR spectrum is well described by the sum of sample and background contribution of the 20 following form (a) A(t)=Ase−Λtcos(2πft)+Abe−σ2t2cos(2πfbt), (3) 15 100 Oe 600 Oe where A0=As+Ab is the total signal amplitude. There z) H is a rapid signal depolarization below Tc, which mani- M10 fests itself in a reduction of A0 that is more severe than f ( 0 Oe with H = 0 [see Fig. 1(c)]. Bulk magnetization mea- surementssuggestthatthe CSL stateis notfully formed 5 untilH≈850Oe.6 AdistortionoftheCHMorderintoan imhomogeneous helicoid is consistent with the enhanced 0 depolarization observed here at weaker fields. As shown inFig.3(a),thetemperaturedependenceofthespinpre- 0 20 40 60 80 100 120 140 160 cessionfrequencyf issimilartothatobservedwithH=0, but shifted in value by the applied field. There is some 10 (b) enhancement of f at low temperatures, which is indica- ] 0 Oe z tive of a structural change and/or modification of the H 100 Oe bspeilnowstTru≈ctu50re.KA, wthHer=e0asOmeeanntdioHne=d1e0a0rliOere,tahniosmocaclouurss K) [M 1 0.3 1356 K00 Oe behavior has been observed in transport measurements. 0 140 K 7 0.1 150 K Figure 3(b) shows the temperature dependence of the 1 0.2 160 K ( frequency difference f(T)−f(T =170 K). With H >0, - f the spin precession frequency increases as the zero-field f 0.1 0.01 magnetic transition temperature T is approached from c 0.0 0 200 400 600 above. As shown in the inset of Fig. 3(b), f(T)−f(T= H (Oe) 170 K) ∝ H at temperatures Tc < T < 170 K, where 1E-3 the proportionality constant is roughly proportional to 0 20 40 60 80 100 120 140 160 1/(T −Tc). Hence the observedfrequency shift aboveTc T (K) isconsistentwiththelow-fieldresponseofaparamagnet, whereby the induced magnetiztion is linearly dependent FIG. 3: (Color online) Temperature dependence of (a) the onH. Afullandtemperature-independentamplitudeA muon spin precession frequency f observed for different ap- 0 is observed above T [see Fig. 1(b)], indicating that the plied magnetic field strengths, and of (b) the frequency shift c f(T)−f(T=170K)plottedwith alogarithmic verticalscale. paramagnetism occurs throughout the sample volume. The black solid curves through the data points in both pan- To provide a possible explanation for the enhanced els are guides to the eye. The red curve in (b), which ex- mean magnetic field sensed by the muon ensemble (∼f) tends off the logarithmic scale, comes from a fit of the high- at low temperatures, we adopt a Landau free energy temperature data for H=0 Oe to f(T)=f(0)(1−T/T )n, c analysis. In the absence of the H ⊥ cˆ magnetic field, yielding T =129.58(4) K and n=0.366(6). The inset shows c the helimagnetic phase occurs via FM and DM interac- themagneticfielddependenceoff(T)−f(T=170K)attem- tions due to a lack of inversion symmetry. As shown in peratures aboveT . c Fig. 4, the Cr atoms form layered triangular lattices in Cr NbS ,withanhexagonalspacegroupofP6 22. For 1/3 2 3 eachCratominalayer,therearethreenearest-neighbor where Q=Q0zˆ, S=Sxxˆ+iSyyˆ, andby sysmmetry|Sx|= Ctrryaextoismtssaibnoaunt aandjaaxciesnltoclaatyeedr.haClf2waroytbateitowneaelnstywmomCer- |tShye|≡exSch.aSnigneceotfhQe f→ree−eQneragnydshSou→ld−bSe∗i,nvitariisangtivuenndteor atoms in the different layers, with inversion symmetry fourth order by8,9 about this point brokenby the S atoms. The DM vector F =α S·S∗+DQ S2+α Q2S2+βS4, (5) linking the two Cr atoms (D ) then lies in a plane per- 0 0 1 0 1 pendicular to the C2 axis, as shown in Fig. 4. Since the whereDrepresentsthestrengthoftheDMinteraction,10 threeCratomswithinalayerarerelatedbyC3rotational andtheparameterβ isassumedtobepositive,suchthat symmetry (about an axis parallel to the z-axis), there the free energy is bound. Minimizing F with respect to arethree DMvectorsrelatedbysymmetry(D1, D2, and Q0,wefindQ0=−D/2α1,resultinginthesimplifiedfree D3), which when summed together give a resultant DM energy equation vector D pointing along the z-axis. Consequently, the spin density of the helical order can be described by8,9 F =αQS2+βS4, (6) S(r)=Sexp(iQ·r)+S∗exp(−iQ·r), (4) where α =α −D2/4α . Subsequent minimization of Q 0 1 4 S, which implies an increase in the negative value of α Q and/or a decrease in the positive value of β. Since β originates from the spin-spin interaction, smaller β implies a stronger FM interaction between the Cr spins — although this effect would be quite small. On the other hand, a larger negative value of α corresponds to a Q weaker DM interaction D. This will occur if there is a change in the ratio between the a (and b) and c-axis latticeconstants,suchthatthereisarotationofthevec- tors D , D , and D towards the xy plane. Thus we 1 2 3 propose a change in the length of one or more of the lattice constants below T∼50 K. In conclusion, our µSR measurements reveal a possi- blechangeinthemagneticstructureofCr NbS below 1/3 2 T ∼50 K, which is the same temperature region where anomalousbehaviorhas beenobservedinbulk transport measurements. The low-temperaturemodificationof the magnetic structure can be explained by a change in latticeconstants,whichcanbe confirmedbyprecisionmea- FIG. 4: (Color online) Illustration of the DM interaction in surements of the crystalstructure. Moreover,to confirm Cr1/3NbS2. EachCratom(bluespheres)islinkedtothreeCr thatthe changeinlattice constantsissuchthatitcauses atomsinoneoftheadjacentplanes(indicatedbythebluear- rows). TheSandNbatomsaretheyellowandgreenspheres, a reduction of the DM interaction, we suggest a neutron respectivley. The cylindrical red arrow represents a C2 ro- scattering measurement to look for a change of the or- tational symmetry axis located halfway between the two Cr deringwavevectorQ —sinceaconsequenceofasmaller 0 atoms. The DM vector D1 linking these two Cr atoms (flat DM interaction is a longer spin-helix period. Lastly, we red arrow) lies in the red-shaded plane perpendicular to the do not find anything unusual about the magnetism near C2 axis. NotethepreciseorientationofD1 inthered-shaded thePMtransitionatlowfield(suchasphaseseparation) plane is unknown. The related DM vectors D2 and D3 link- thatwouldcontributetotheanomaliesobervedintrans- ing the lower Cr atom with the other two Cr atoms in the port measurements near T . upper layer are not shown. The gray arrow represents a C3 c rotational symmetry axis relating the three Cr atoms in the upperlayer. Theshort bluearrow abovethis istheresultant DM vectorD=D1+D2+D3. Acknowledgments F with respect to S, yields S= −α /2β. 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