Probing the quantum phase transition in Mott insulator BaCoS_2 tuned by pressure and Ni-substitution
Z. Guguchia, B.A. Frandsen, D. Santos-Cottin, S.C. Cheung, Z. Gong, Q. Sheng, K. Yamakawa, A.M. Hallas, M.N. Wilson, Y. Cai, J. Beare, R. Khasanov, R. De Renzi, G.M. Luke, S. Shamoto, A. Gauzzi, Y. Klein, Y.J. Uemura
ppreprint(January 24, 2019)
Probing the quantum phase transition in Mott insulator BaCoS tuned by pressureand Ni-substitution Z. Guguchia,
1, 2
B.A. Frandsen, D. Santos-Cottin, S.C. Cheung, Z. Gong, Q. Sheng, K. Yamakawa, A.M. Hallas, M.N. Wilson, Y. Cai, J. Beare, R. Khasanov, R. DeRenzi, G.M. Luke,
5, 7, 8
S. Shamoto, A. Gauzzi, Y. Klein, and Y.J. Uemura ∗ Department of Physics, Columbia University, New York, NY 10027, USA Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA IMPMC, Sorbonne Universit`es-UPMC, CNRS, IRD, MNHN, 4, place Jussieu, 75005 Paris, France Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1 Canada Department of Mathematical, Physical and Computer Sciences, Parco delle Scienze 7A, I-43124 Parma, Italy Canadian Institute for Advanced Research, Toronto, ON Canada M5G 1Z7 TRIUMF, Vancouver, BC, Canada V6T 2A3 Advanced Science Research Center, Japan Atomic Energy Agency (JAEA), Tokai, Naka, Ibaraki 319-1195, Japan IMPMC UMR7590, Sorbonne Universit`e, CNRS,IRD, MNHN, 4, place Jussieu, 75005 Paris, France
We present a muon spin relaxation study of the Mott transition in BaCoS using two independentcontrol parameters: (i) pressure p to tune the electronic bandwidth and (ii) Ni-substitution x onthe Co site to tune the band filling. For both tuning parameters, the antiferromagnetic insulatingstate first transitions to an antiferromagnetic metal and finally to a paramagnetic metal withoutundergoing any structural phase transition. BaCoS under pressure displays minimal change inthe ordered magnetic moment S ord until it collapses abruptly upon entering the antiferromagneticmetallic state at p cr ∼ S ord in the Ni-doped system Ba(Co − x Ni x )S steadilydecreases with increasing x until the antiferromagnetic metallic region is reached at x cr ∼ .
22. Inboth cases, significant phase separation between magnetic and nonmagnetic regions develops whenapproaching p cr or x cr , and the antiferromagnetic metallic state is characterized by weak, random,static magnetism in a small volume fraction. No dynamical critical behavior is observed near thetransition for either tuning parameter. These results demonstrate that the quantum evolution ofboth the bandwidth- and filling-controlled metal-insulator transition at zero temperature proceedsas a first-order transition. This behavior is common to magnetic Mott transitions in RE NiO andV O , which are accompanied by structural transitions without the formation of an antiferromag-netic metal phase. PACS numbers:
INTRODUCTION
The Mott metal-insulator transition (MIT), known toprovide a platform for emergent phenomena such as high-temperature superconductivity and colossal magnetore-sistance, remains one of the most intensely studied top-ics in condensed matter physics [1–6]. This transitioncan occur as a thermal phase transition or as a quantumphase transition (QPT) near zero temperature. In thelatter case, the transition is typically controlled by vary-ing the electronic bandwidth using hydrostatic or chem-ical pressure or by varying the band filling via chemicalsubstitution. The Mott transition usually occurs froman antiferromagnetic insulator (AFI) phase to a param-agnetic metal (PMM) phase and is often accompaniedby a structural phase transition. In some Mott systems,a direct one-step transition from AFI to PMM phase isobserved, while in others the transition occurs in twosteps involving an intermediate antiferromagnetic metalphase (AFM). In order to understand fully the physics ofthe Mott transition, the following challenges need to bemet: (i) Disentangling the different contributions of the charge, magnetic, and structural interactions; (ii) estab-lishing whether the transition is first-order or continuous;(iii) clarifying the similarities and differences between theone-step and two-step transitions; and (iv) comparing theeffects of bandwidth control versus filling control.Here, we attempt to address these challenges by eluci-dating the mechanism of the quantum MIT in the quasitwo-dimensional system Ba(Co − x Ni x )S [7–11], wherethe MIT can be controlled either by pressure or by thepartial substitution of Co for Ni [9]. The crystal struc-ture, shown in Fig. 1(a), consists of alternately stackedside-sharing (Co,Ni)S pyramids, where the Co and Niions form a square lattice. Previous studies have shownthat the unsubstituted ( x = 0) BaCoS compound isan antiferromagnetic insulator with a N´eel temperature T N = 300 K at ambient pressure. Neutron scatteringstudies [9] indicate that Co is in the high spin statewith an ordered moment of ∼ µ B , which is progressivelyreduced upon Ni substitution. As shown in the phase dia-grams in Figs. 1(b) and (c), the Mott transition from AFIto PMM occurs at a critical pressure of p cr ∼ . x cr ∼ .
22 [7, 14]. Con- a r X i v : . [ c ond - m a t . s t r- e l ] J a n trary to the commonly studied systems RE NiO ( RE =Rare Earth) and V O , the Mott transition of BaCoS does not involve any structural distortions and it occursin two steps with the formation of an intermediate AFMphase. Because only electronic degrees of freedom comeinto play, BaCoS is a model system to investigate theMott MIT. A study of the evolution of the magnetic prop-erties across the MIT would enable a comparison withthe previously studied RE NiO and V O systems, pos-sibly clarifying the role of structural transitions and ofthe intermediate AFM phase in the Mott transition.To achieve this, we have carried out a systematic muonspin relaxation ( µ SR) study of the MIT in BaCoS us-ing p and x as control parameters for the bandwidth-tuned and filling-tuned transitions, respectively. µ SR isan ideal probe for our purpose, since it can independentlydetermine the magnitude of the local ordered momentand the volume fraction of the magnetically ordered re-gions, as well as detect dynamic magnetic critical behav-ior via measurements of the 1/ T relaxation rate. Since µ SR is a point-like real-space magnetic probe which de-tects magnetic transitions in time space, we use the term”magnetic order” in this paper as implying static spinfreezing while not referring to specific spatial spin cor-relation length. Taking advantage of these features, sig-nificant progress was made by recent µ SR studies of theaforementioned prototypical Mott systems RE NiO andV O [15], where the substitution of RE ions of dif-ferent size and the application of hydrostatic pressurein V O enable a bandwidth-controlled Mott transition,accompanied by a first-order structural transition. Inboth systems, the QPT from the AFI phase to the PMMphase occurs through a gradual reduction of the mag-netically ordered volume fraction near the QPT until itreaches zero at the transition, while the magnitude ofthe ordered moment in the ordered regions of the sam-ple remains unchanged until dropping abruptly to zeroin the PMM state. No dynamical critical behavior oc-curs. These are typical features expected in the case ofa first-order phase transition, as illustrated in Fig. 2.Such behavior was previously observed in weak itinerantmagnets like MnSi and (Sr,Ca)RuO , where the mag-netic transition is tuned by hydrostatic pressure [16] orthe Ca/Sr substitution [16]. In MnSi, Fe substitution onthe Mn site turns this transition to a continuous tran-sition, as shown by a recent µ SR experiment [17] and atheoretical study [18].In this paper, we show that the Mott QPT in BaCoS is also first order for both pressure and Ni substitution.For both tuning parameters, the magnetically orderedvolume fraction steady decreases near the AFI to AFMtransition and reaches zero at the AFM to PMM tran-sition, revealing a broad region of phase separation be-tween magnetically ordered and disordered regions. Inthe case of pressure, the ordered moment retains its max-imal value until an abrupt reduction occurs upon enter- ing the AFM state, whereas the Ni substitution shows amore gradual decrease of the ordered moment with in-creasing Ni concentration. In both cases, the quantumevolution to the PMM state occurs without dynamicalcritical behavior. These observations lead to the conclu-sion that both the bandwidth- and filling-controlled Motttransitions in BaCoS are first order. We also confirmedabsence of static magnetism in the x = 1 end-membercompound BaNiS . EXPERIMENTAL DETAILS
Polycrystalline samples of Ba(Co − x Ni x )S were syn-thesized using a conventional solid state reaction method,as described in detail elsewhere [14, 19]. µ SR experi-ments under pressure were performed at the GPD in-strument ( µ E1 beamline) of the Paul Scherrer Institute(Villigen, Switzerland) [20]. Time differential and ambi-ent pressure µ SR measurements were performed usingthe General Purpose Surface-Muon Instrument (GPS)[21] with a standard low-background veto setup at the π M3 beam line of the Paul Scherrer Institute in Villigen,Switzerland and using the Los Alamos Meson PhysicsFacility (LAMPF) spectrometer with a helium gas-flowcryostat at the M20 surface muon beamline (500 MeV)of TRIUMF in Vancouver, Canada. In a µ SR experi-ment, positive muons µ + with nearly 100 % spin polar-ization are implanted into the sample one at a time. Themuons thermalize at interstitial lattice sites, where theyact as magnetic microprobes [22, 23]. In a magneticallyordered material, the muon spin precesses in the localfield B µ at the muon site with the Larmor frequency ν µ = γ µ /(2 π ) B µ (muon gyromagnetic ratio γ µ /(2 π ) = 135.5MHz T − ).Pressures up to 2.0 GPa were generated in a double-walled, piston-cylinder type of cell made of MP35N mate-rial, specially designed for µ SR experiments [20, 24–26].Daphne oil was used as a pressure transmitting medi-umd. The pressure was measured by tracking the su-perconducting transition of a small indium plate usingAC magnetic susceptibility. The sample filling factor ofthe pressure cell was maximized, resulting in ∼
40% ofthe muons stopping in the sample and the rest in thepressure cell. Therefore, the µ SR data in the whole tem-perature range were analyzed by decomposing the signalinto a contribution of the sample and a contribution ofthe pressure cell according to A ( t ) = A S P S ( t ) + A P C P P C ( t ) , (1)where A S and A P C are the initial asymmetries and P S (t)and P P C (t) are the muon-spin polarizations belongingto the sample and the pressure cell, respectively. Thepressure cell signal was modeled with a damped Kubo-Toyabe function [27]. The response of the sample consists T ( K ) Metalic
AFI
PMI A F M BaCoS p (GPa) PMM
Insulating
AFMPMMPMIAFI
Ni-content ( x ) BaCo Ni x S (c)(b) MetalicInsulating (b) (c)(a)
FIG. 1: (Color online) (a) Crystal structure of BaCoS . Schematic Temperature-Pressure (b) and Temperature-Doping(c) phase diagrams of BaCoS and BaCo − x Ni x S , respectively (adapted from Refs. [12,13]). PMI stands for paramagneticinsulator, AFI for antiferromagnetic insulator, PMM for paramagnetic metal, and AFM for antiferromagnetic metal. Theconductive metal-insulator transition occurs at the broken vertical lines. Continuous transition First-order transitionThermal or Quantum phase transitions
FIG. 2: (Color online) Schematic illustration of the thermalor quantum evolution of the ordered moment, magneticallyordered volume fraction, and relaxation rate in the case ofcontinuous (left) and first-order (right) transitions. Phaseseparation seen in the gradual change of the ordered volumefraction is a sufficient but not necessary condition for a first-order transition. of a magnetic and a nonmagnetic contribution: P S ( t ) = N (cid:88) i =1 V m (cid:34) α i e − λ iT t cos( γ µ B iµ t ) + β i e − λ iL t (cid:35) +(1 − V m ) e − λ nm t . (2)Here, N = 2 for x = 0 and N = 1 for x ≥ α i and β i = 1 - α i , are the fractions of the oscillating andnon-oscillating µ SR signal. V m denotes the volume frac-tion of the magnetically ordered part of the sample, and B iµ is the average internal magnetic field at the muonsite. λ T i and λ Li are the depolarization rates repre-senting the transverse and longitudinal relaxing compo-nents of the magnetic parts of the sample. The trans-verse relaxation rate λ T i is a measure of the width ofthe static magnetic field distribution at the muon siteand is also affected by dynamical effects (spin fluctua-tions) [28]. The longitudinal relaxation rate λ L = 1/ T is determined solely by dynamic magnetic fluctuations. λ nm is the relaxation rate of the nonmagnetic part ofthe sample. The total initial asymmetry A tot = A S (0) + A PC (0) (cid:39) A S (0)/ A tot (cid:39) A S (0)/ A tot (cid:39) µ SRtime spectra were analyzed using the open-source soft-ware package musrfit [29].
RESULTS
We first present the data for pressure-tuned BaCoS .Fig. 3(a) displays representative zero-field (ZF) µ SR time ( a )
B a C o S
0 G P a 1 . 3 3 1 1 . 5 G P a 1 . 2 8 PS ( t ) + P PC( t ) t ( m s ) P r e s s u r e C e l l C o n t r i b u t i o n
05 01 0 01 5 02 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00 . 00 . 20 . 40 . 60 . 81 . 0 T N T N
0 G P a 1 1 . 2 8 1 . 3 3 1 . 5 G P a
Static Field Size D ( m s-1) B a C o S ( b )( c ) B a C o S
0 G P a 0 . 5 1 1 . 2 8 1 . 3 3 1 . 3 9 1 . 5 G P a
Magnetic Volume Fraction V m T ( K ) FIG. 3: (Color online) (a) Muon spin polarisation in zerofield for BaCoS recorded at T = 2 K under various appliedpressures. The solid curves represent fits to the data by meansof Eq. (2). (b) The temperature dependence of the static in-ternal field size ∆( T )=[(2 πν ) + λ T )] / under various ap-plied hydrostatic pressures. The arrows mark the magneticordering temperature T N . (c) Same as (b), but displaying themagnetically ordered volume fraction. spectra taken at 2 K for various pressures, revealing clearoscillations for pressures up to p = 1.28 GPa. This in-dicates the existence of a well-defined internal field, asexpected in the case of long-range magnetic order. Notethat two distinct precession frequencies occur in the µ SR spectra, which indicates that two magnetically inequiva-lent muon stopping sites are present in BaCoS . Below,we will show and discuss the pressure evolution of themagnetic quantities for one component, since the sec-ond component behaves similarly. The ZF oscillation x = 0 0 . 2 50 . 1 5 0 . 30 . 2 0 . 3 5 0 . 2 2 P S ( t ) t ( m s ) B a C o
N i x S ( a )
05 01 0 01 5 02 0 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 00 . 00 . 20 . 40 . 60 . 81 . 0 T N ( b ) x = 0 0 . 1 5 0 . 2 0 . 2 2 0 . 2 5 0 . 3 Static Field Size D ( m s-1) B a C o
N i x S T N B a C o
N i x S x = 0 0 . 1 5 0 . 2 0 . 2 2 0 . 2 5 0 . 3 0 . 3 5 Magnetic Volume Fraction V m T ( K )( c ) FIG. 4: (Color online) (a) Muon spin polarisation in zerofield for Ba(Co − x Ni x )S recorded at T = 2 K for variousvalues of x . The solid curves represent fits to the data bymeans of Eq. (2). (b) The temperature dependence of thestatic internal field size ∆( T )=[(2 πν ) + λ T )] / for variousvalues of x . The arrows mark the magnetic ordering temper-ature T N . (c) Same as (b), but displaying the magneticallyordered volume fraction. T N / T N ( 0 ) D / D ( 0 ) T N/ T N(0), D / D (0), V M p ( G P a ) B a C o S ( a ) P M MA F MA F I V M I n s u l a t i n g M e t a l i c
05 01 0 01 5 02 0 02 5 03 0 03 5 0 T N T N (K) T N / T N ( 0 ) D ( T ) / D ( 0 ) T N/ T N(0), D / D (0), V M N i - c o n t e n t ( x ) I n s u l a t i n g M e t a l i cA F M V M A F I
B a C o x N i x S ( b )P M M
05 01 0 01 5 02 0 02 5 03 0 03 5 0 T N T N (K)
FIG. 5: (Color online) The pressure (a) and doping (b)dependence of the normalized magnetic ordering tempera-ture T N / T N ( x = 0 , p = 0), the normalized zero-temperaturestatic field size ∆/∆( x = 0 , p = 0), and the zero-temperaturemagnetically ordered volume fraction V M for BaCoS underpressure and BaCo − x Ni x S , respectively. The broken verti-cal lines denote the phase boundary between insulating andmetallic phases. The shaded area in panel (a) refers to theAF metallic region. frequency and amplitude are directly proportional to thesize of the ordered moment and the magnetically orderedvolume fraction, respectively. Slight damping of the os-cillations is visible over the time window displayed. Ingeneral, damping may be caused by the finite width ofthe static internal field distribution or by dynamic spinfluctuations. In the present case, the damping is predom-inantly due to the former effect, as the latter possibilitywas excluded by applying a longitudinal external field(data not shown). When the system enters the AFMstate for p = 1.33-1.5 GPa, we observe relaxation oc-curring only in a small fraction of the signal with nowell-defined oscillations, indicating the existence of dis-ordered static magnetism in a small volume fraction ofthe sample. / T ( μ s - ) , Δ ( μ s - ) N BaCoS p = 1.5 GPa(a) / T ( μ s - ) , Δ ( μ s - ) Ni S (b)T N FIG. 6: (Color online) The static field size ∆ =[(2 πν ) + λ T )] / and the dynamic relaxation rate 1 /T for BaCoS atthe applied pressure of p = 1.5 GPa (a) and for the Ni-dopedsample of BaCo − x Ni x S with x = 0.2 (b). Using the data analysis procedure described above, weobtained quantitative information about the oscillationfrequency ν , the relaxation rates λ T and λ L , the mag-netic volume fraction V M , and the magnitude of the staticinternal field at the muon site. The latter is calculatedas B int = ∆ /γ µ , where ∆=[(2 πν ) + λ T )] / . We notethat ∆ is proportional to the size of the local orderedmoment. Fig. 3(b) displays this quantity for BaCoS atvarious pressures ranging from ambient to 1.5 GPa. Hereand elsewhere, we display the fields and the relaxationrates for only one component in the model, since the sec-ond component behaves similarly. Up to p = 1 .
28 GPa,∆ increases continuously from zero as the temperature isdecreased below T N (marked by black arrows), indicativeof a continuous phase transition as a function of temper-ature for these pressures. The value of ∆ at the lowestmeasured temperature ( ∼ p = 1 .
35 GPa, at whichpoint the system is in the AFM state. For p = 1 . p ≤ . p = 1 .
28 GPa, close tothe AFI - AFM transition at 1.33 GPa, indicating thatthe ground state of BaCoS is characterized by intrin-sic phase separation between magnetically ordered anddisordered phases at this pressure. The ground-statemagnetic volume fraction is further reduced to 30% for p = 1 .
35 GPa in the AFM phase, and 10% or less forhigher pressures in the AFM phase.The corresponding results for the Ni-doped system areillustrated in Fig. 4. As seen in Fig. 4(a), long-lived oscil-lations are observed only in the ZF spectrum for x = 0,while the spectra for x ≥ .
15 display fast relaxationwithout any oscillations. This ZF relaxation, which canbe decoupled in a longitudinal field, points to fairly dis-ordered static magnetism for these high values of x . TheZF relaxation rate decreases with increasing x , indicat-ing a steady reduction of the internal field at the muonsite. This is demonstrated in Fig. 4(b), which displaysthe temperature dependence of ∆ for x between 0 and0.3. The low-temperature value of ∆ decreases steadilyas x increases, reaching zero around the expected dopinglevel of ∼ under pressure, which showedno change in ∆ until an abrupt drop in the AFM state.On the other hand, the behavior of the magnetically or-dered volume fraction for Ni substitution seen in Fig. 4(c)is similar to that of the pressure case, showing a steadyreduction of the ground-state ordered volume fraction tozero at the AFM - PMM transition. We also confirmedthat the end-member compound BaNiS exhibits no re-laxation or oscillations, indicating an absence of staticmagnetism.These results can be summarized in Fig. 5, which dis-plays T N , V M , and ∆ extrapolated to zero temperatureand normalized by its value for pure BaCoS at ambi-ent pressure, each as a function of p [Fig. 5(a)] and x [Fig. 5(b)]. With pressure tuning, ∆ (and therefore theordered moment) displays little change until an abruptreduction upon entering the AFM state, whereas Ni dop-ing causes a smooth reduction to zero upon entering thePMM state. This behavior, reminiscent of the restorationof a continuous QPT observed in Fe-doped (Mn,Fe)Situned by pressure [17], may be related to effects of dis-order [30] introduced by (Co,Ni) substitution. On theother hand, both pressure and Ni doping show a signif-icant reduction of V M in the vicinity of the QPT, indi-cating phase separation between antiferromagnetic andparamagnetic regions. Such behavior is consistent witha first-order quantum phase transition, not a continuoustransition. For both tuning methods, the AFM state is characterized by a small magnetic volume fraction, weakinternal field, and lack of clear oscillations in the ZF spec-tra, indicative of weak, random, static magnetism in thisstate.The first-order versus continuous nature of the QPTcan be further clarified by investigating any associ-ated dynamical critical behavior. We performed de-tailed measurements of BaCoS with p = 1 . − x Ni x )S with x = 0 . p and x place the system near the QPT, so any quantum criticaldynamics from a continuous QPT would be observableby µ SR. The temperature dependence of the dynamicrelaxation rate 1 /T under these conditions is shown asblue diamonds in Figs. 6(a) and (b) for the pressure-and Ni-tuned samples, respectively, along with the staticrelaxation parameter ∆ in red squares for comparison.For both samples, the magnitude of 1 /T is less than1 % of the static relaxation rate ∆( T =0) and no clearpeak is observed at T N . This differs from the case ofcontinuous transitions in (Mn,Fe)Si [17] and dilute spinglasses CuMn and AuFe [31], in which the temperaturedependence of 1 /T exhibits a clear peak at the order-ing/freezing temperature with a peak value close to 10 %of the static field parameter [17, 31]. The absence of dy-namical critical behavior in the present data gives furtherevidence for first-order quantum evolution in BaCoS forboth pressure and doping control. DISCUSSION
The µ SR results presented here provide unambiguousevidence for a first-order Mott QPT in BaCoS accessedby pressure (bandwidth control) and Ni doping (fillingcontrol). This finding is consistent with the recent ob-servation of first-order quantum evolution in the canon-ical bandwidth-controlled Mott insulators RE NiO andV O , despite the fact that no structural transition ac-companies the MIT in BaCoS . The similarity amongdisparate Mott systems suggests that first-order quan-tum phase transitions are ubiquitous in strongly corre-lated Mott systems, in agreement with previous theoret-ical predictions [15, 32–36].First-order Mott QPTs such as the one observed inBaCoS are reminiscent of the magnetic phase transi-tion observed at the antiferromagnetic/superconductingphase boundary in unconventional superconductors, in-cluding high- T c cuprates, FeAs systems, A C , andheavy fermion systems. Similar behavior is also foundin He at the boundary between the solid hexagonalclose packed (HCP) phase and the superfluid phase[37]. In these systems, the superconducting/superfluidphase is accompanied by inelastic excitations associ-ated with short-range correlations having a periodic-ity characteristic of the competing order (i.e. mag-netic or solid HCP). These excitations are referred toas the magnetic resonance mode in unconventional su-perconductors and rotons in superfluid He [37], as dis-cussed elsewhere [37, 38]. Given the similarities withnon-superconducting Mott systems, the universality ofinelastic magnetic excitations may extend to BaCoS , RE NiO , V O , and other materials. Therefore, thepresent results call for further investigations of the role ofinelastic soft modes in non-superconducting Mott transi-tion systems.Another new aspect of the MIT that emerges from thepresent work is that the AFM region between the AFIand PMM states is characterized by weak, random, staticmagnetism in a very small volume fraction of the sample.It seems plausible that the magnetic volume is confinedto islands embedded in the surrounding PMM phase, sug-gesting a scenario of metallic conduction through percola-tion. One open question is the distinction, if any, betweenthe above scenario of separation between AFI and PMMphases and the magnetic phase separation observed inV O and RE NiO coexisting with insulating bulk con-ductivity. One possibility is that conductive percolationis achieved in BaCoS but not in V O and RE NiO .The length scale and texture of this phase-separated statecannot be probed by µ SR, so suitable techniques such asscanning tunneling or magnetic force microscopes and/orspatially-resolved optical probes [39] should be used toobtain complementary information in future studies.
CONCLUSIONS
The present µ SR results unambiguously demonstratethat the QPT from AFI to PMM in BaCoS inducedby pressure (bandwidth control) and by Ni-doping (fill-ing control) proceeds as a first-order transition withoutdynamic critical behavior. Upon approaching the QPTfrom the AFI phase, the magnetically ordered volumefraction decreases steadily until it reaches zero at thePMM phase, resulting in a broad region of electronicphase separation. Sudden destruction of the orderedmagnetic moment at the QPT in BaCoS under pres-sure and the absence of any dynamical critical behav-ior in BaCo − x Ni x S further supports the notion of afirst-order transition in these materials. Similar behav-ior is observed in RE NiO and V O , indicating thatthe basic first-order nature of the Mott transition per-sists whether or not the MIT is associated with struc-tural phase transition ( RE NiO and V O ) or the de-velopment of an intermediate AFM state (BaCoS ). Weexpect the present findings to provide further guidancein the quest to understand the complex process of phasetransitions in strongly correlated Mott systems. ACKNOWLEDGMENTS
The µ SR experiments were carried out at the SwissMuon Source (S µ S) Paul Scherrer Insitute, Villigen,Switzerland and the TriUniversity Meson Facility (TRI-UMF) in Vancouver, Canada. The authors sincerelythank the TRIUMF Center for Material and Molecu-lar Science staff and the PSI Bulk µ SR Group for in-valuable technical support with µ SR experiments. Workat the Department of Physics of Columbia University issupported by US NSF DMR-1436095 (DMREF), NSFDMR-1610633 and the JAEA Reimei project and a grantfrom the friends of U Tokyo Inc. Z. Guguchia grate-fully acknowledges the financial support by the SwissNational Science Foundation (SNF fellowship P300P2-177832). DSC acknowledges financial support of a PHDgrant of the ”Emergence program” from Sorbonne Uni-versit´e. ∗ Electronic address: [email protected][1] M. Imada, A. Fujimori, and Y. Tokura, Metal-insulatortransitions. Rev. Mod. Phys. , 1039 (1998).[2] B. Keimer, S.A. Kivelson, M.R. Norman, S. Uchida, andJ. Zaanen, From quantum matter to high-temperaturesuperconductivity in copper oxides. Nature , 179-186(2015).[3] M. Vojta, Quantum phase transitions. Rep. Prog. Phys. , 2069-2110 (2003).[4] J.B. Torrance, P. Lacorre, A.I. Nazzal, E.J. Ansaldo,and C. Niedermayer, Systematic study of insulator-metaltransitions in perovskites RNiO (R = Pr, Nd, Sm, Eu)due to closing of charge-transfer gap. Phys. Rev. B ,8209-8212 (1992).[5] D.B. McWhan, T.M. Rice, and J.P. Remeika, Mott tran-sition in Cr-doped V O . Phys. Rev. Lett. , 1384-1387(1969).[6] Y. J. Uemura, T. Yamazaki, Y. Kitaoka, M. Takigawa,and H. Yasuoka, Positive muon spin precession in mag-netic oxides MnO and V O : local fields and phase tran-sition. Hyperfine Interact. , 339 (1984).[7] L.S. Martinson, J.W. Schweitzer, N.C. Baenziger, Metal-insulator transitions in BaCo − x Ni x S − y . Phys. Rev.Lett. , 125 (1993).[8] S. A. M. Mentink, T. E. Mason, B. Fisher, J. Genos-sar, L. Patlagan, A. Kanigel, M. D. Lumsden, and B. D.Gaulin. Antiferromagnetism, structural properties, andelectronic transport of BaCo . Ni . S . . Phys. Rev. B , 12375 (1997).[9] K. Kodama, Shin-ichi Shamoto, H. Harashina, J.Takeda, M. Sato, K. Kakurai, and M. Nishi. ElectronicStructure of the Quasi Two-Dimensional Mott SystemBaCo − x Ni x S . J. Phys. Soc. Japan , 1782 (1996).[10] Shin-ichi Shamoto, K. Kodama, H. Harashina, M.Sato, and K. Kakurai. Neutron Scattering Study ofBaCo . Ni . S . J. Phys. Soc. Japan , 1138 (1997).[11] Yukio Yasui, Hisashi Sasaki, Shin-ichi Shamoto, andMasatoshi Sato. Phase Diagram and Pressure Effects onTransport Properties of BaCo − x Ni x S . J. Phys. Soc. Japan , 3194 (1997).[12] Y. Yasui, H. Sasaki, M. Sato, M. Ohashi, Y. Sekine, C.Murayama, and N. Mori, Studies of Pressure-InducedMott Metal-Insulator Transition of BaCoS . J. Phys.Soc. Japan , 1313 (1999).[13] M. Sato, H. Sasaki, H. Harashina, Y. Yasui, J. Takeda, K.Kodama, S. Shamoto, K. Kakurai, and M. Nishi, Metal-Insulator Transition of BaCo − x Ni x S Induced by Pres-sure and Carrier Number Control. Rev. High PressureSci. Technol., , 447-452 (1998).[14] D. Santos-Cottin, A. Gauzzi, M. Verseils, B. Bap-tiste, G. Feve, V. Freulon, B. Placais, M. Casula,and Y. Klein. Anomalous metallic state in quasi-two-dimensional BaNiS . Phys. Rev. B , 125120 (2016).[15] B.A. Frandsen, L. Liu, S.C. Cheung, Z. Guguchia, R.Khasanov, E. Morenzoni, T.J.S. Munsie, A.M. Hallas,M.N. Wilson, Y. Cai, G.M. Luke, B. Chen, W. Li, C.Jin, C. Ding, S. Guo, F. Ning, T.U. Ito, W. Higemoto,S.J.L. Billinge, S. Sakamoto, A. Fujimori, T. Murakami,H. Kageyama, J.A. Alonso, G. Kotliar, M. Imada andY.J. Uemura. Volume-wise destruction of the antiferro-magnetic Mott insulating state through quantum tuning.Nature Communications , 12519 (2016).[16] Y.J. Uemura, T. Goko, I. M. Gat-Malureanu, J. P. Carlo,P. L. Russo, A. T. Savici, A. Aczel, G. J. MacDougall,J. A. Rodriguez, G. M. Luke, S. R. Dunsiger, A. McCol-lam, J. Arai, Ch. Pfleiderer, P. Boni, K. Yoshimura, E.Baggio-Saitovitch, M. B. Fontes, J. Larrea, Y. V. Sushko,and J. Sereni, Phase separation and suppression of criti-cal dynamics at quantum phase transitions of MnSi and(Sr − x Ca x )RuO . Nature Physics , 29-35 (2007)[17] Tatsuo Goko, Carlos J. Arguello, Andreas Hamann,Thomas Wolf, Minhyea Lee, Dmitry Reznik, AlexanderMaisuradze, Rustem Khasanov, Elvezio Morenzoni, andYasutomo J. Uemura, Restoration of quantum criticalbehavior by disorder in pressure-tuned (Mn,Fe)Si. npjQuantum Materials , 44 (2017).[18] Y. Sang, D. Belitz, T.R. Kirkpatrick, Disorder Depen-dence of the Ferromagnetic Quantum Phase Transition.Phys. Rev. Lett. , 207201 (2014).[19] S. Shamoto, S. Tanaka, E. Ueda, and M. Sato, Singlecrystal growth of BaCo − x Ni x S . J. Cryst. Growth ,197 (1995)[20] R. Khasanov, Z. Guguchia, A. Maisuradze, D. Andre-ica, M. Elender, A. Raselli, Z. Shermadini, T. Goko, F.Knecht, E. Morenzoni, and A. Amato, High pressure re-search using muons at the Paul Scherrer Institute. HighPressure Research , 140-166 (2016).[21] A. Amato, H. Luetkens, K. Sedlak, A. Stoykov, R.Scheuermann, M. Elender, A. Raselli, and D. Graf. Thenew versatile general purpose surface-muon instrument(GPS) based on silicon photomultipliers for µ SR mea-surements on a continuous-wave beam. Review of Scien-tific Instruments , 093301 (2017).[22] R. Kubo, and T. Toyabe, Magnetic Resonance and Re-laxation (North Holland, Amsterdam, 1967).[23] R.S. Hayano, Y.J. Uemura, J. Imazato, N. Nishida, T.Yamazaki, and R. Kubo, Zero-and low-field spin relax-ation studied by positive muons. Phys. Rev. B , 850(1979).[24] D. Andreica 2001 P h.D. thesis
IPP/ETH-Z¨urich.[25] Z. Guguchia, A. Amato, J. Kang, H. Luetkens, P.K.Biswas, G. Prando, F. von Rohr, Z. Bukowski, A. Shen-gelaya, H. Keller, E. Morenzoni, R.M. Fernandes, and R. Khasanov. Direct evidence for the emergence of apressure induced nodal superconducting gap in the iron-based superconductor Ba . Rb . Fe As . Nature Com-munications , 8863 (2015).[26] Z. Guguchia, A. Maisuradze, G. Ghambashidze, R.Khasanov, A. Shengelaya, and H. Keller, Tuningthe static spin-stripe phase and superconductivity inLa − x Ba x CuO ( x = 1/8) by hydrostatic pressure.New Journal of Physics , 093005 (2013).[27] A. Maisuradze, B. Graneli, Z. Guguchia, A. Shen-gelaya, E. Pomjakushina, K. Conder and H. Keller,Effect of pressure on the Cu and Pr magnetism inNd − x Pr x Ba Cu O − δ investigated by muon spin rota-tion Phys. Rev. B , 054401 (2013).[28] Z. Guguchia, A. Shengelaya, A. Maisuradze, L. Howald,Z. Bukowski, M. Chikovani, H. Luetkens, S. Katrych, J.Karpinski, and H. Keller. Muon-spin rotation and mag-netization studies of chemical and hydrostatic pressureeffects in EuFe (As − x P x ) . J. Supercond. Nov. Magn. , 285 (2013).[29] A. Suter, and B.M. Wojek, Musrfit: A Free Platform-Independent Framework for µ SR Data Analysis. PhysicsProcedia , 69-73 (2012).[30] In the pressure method, the pressure is quite homoge-neous, so the whole volume feels the same effect andtherefore sees the same environment. In the dopingmethod, the doping is random, so there will be Co andNi rich local regions, so this would naturally give a rangeof local dopings and therefore a disorder.[31] Y.J. Uemura, T. Yamazaki, D.R. Harshman, M. Senba,and E.J. Ansaldo, Muon-spin relaxation in AuFe andCuMn spin glasses. Phys. Rev. B , 546 (1985).[32] S. Watanabe, and M. Imada, Precise determination ofphase diagram for two-dimensional hubbard model withfilling- and bandwidth-control mott transitions: grand-canonical path-integral renormalization group approach.J. Phys. Soc. Jpn , 1251-1266 (2004).[33] T. Misawa, and M. Imada, Quantum criticality aroundmetal-insulator transitions of strongly correlated electronsystems. Phys. Rev. B , 115121 (2007).[34] M. Imada, Universality classes of metal-insulator transi-tions in strongly correlated electron systems and mecha-nism of high-temperature superconductivity. Phys. Rev.B , 075113 (2005).[35] R. Chitra, and G. Kotliar, Dynamical mean field theoryof the antiferromagnetic metal to antiferromagnetic insu-lator transition. Phys. Rev. Lett. , 2386-2389 (1999).[36] H.Park, A.J. Millis, and C.A. Marianetti, Total energycalculations using DFT+DMFT: computing the pressurephase diagram of the rare earth nickelates. Phys. Rev. B , 245133 (2014).[37] Y.J. Uemura. Superconductivity: Commonalities inphase and mode. Nature Materials , 253 (2009).[38] Y.J. Uemura, Condensation, excitation, pairing, and su-perfluid density in high- T c superconductors: magneticresonance mode as a roton analogue and a possible spin-mediated pairing. J. Phys.: Condens. Matter , S4515-S4540 (2004).[39] A. S. McLeod, E. van Heumen, J. G. Ramirez, S. Wang,T. Saerbeck, S. Guenon, M. Goldflam, L. Anderegg, P.Kelly, A. Mueller, M. K. Liu, Ivan K. Schuller, and D. N.Basov. Nanotextured phase coexistence in the correlatedinsulator V O . Nature Physics13