Downloaded by guest on September 27, 2021 a Aronson C. M. and YFe Gannon in J. W. transition phase quantum Local www.pnas.org/cgi/doi/10.1073/pnas.1721493115 fluctua- QC and identifies a experimental of definitively of tions comparison phenomena the QC where So case phases. theoretical no (AF) is antiferromagnetic there nearby far, mag- in become peaks eventually (FL) will Bragg liquid that netic vectors Fermi wave conventional the of near behavior breakdown the con- and In tuations fluctuations. indicating quantum observed, BaFe on strong is experiments scattering lack (3–5) neutron parameter trast, behavior systems order field the these mean of that Only fluctuations to 2). corre- related (1, temporal are and to spatial that systems of lations growth certain the transitions in documents phase scattering extended for- classical moment be of to picture can correspond conventional that The those involving mation. and order, symmetry, magnetic to broken related a are that QCPs between tion order. magnetic to only lead that to those leading than character transitions Phase correspondingly at temperature. formation a moment nonzero tiny at a still order even magnetic but induce to low alterna- lead cannot or could they that that insulators moment weak in so possible correlations can moments tively, that magnitude large a may the with electrons approach moment localized mobile spatially the a among produce is correlations moment provided where a electrons, compensation whether Kondo determines at the that retained is electrons conduction it by electrons, be f can of metals, localized types in different suppress which by moments, Magnetic can produced magnetic QCPs. that requires these inter- also produce geometries order to competing certain phases of with ordered magnetically frustration lattices on the dimen- actions alternatively, low with or associated fluctuations sionality quantum strong where the variables is and It nonthermal at field, these only of occurs magnetic be order values or extremal can are composition, state there ground pressure, order ordered by magnetic magnetically to destabilized transition The phase approached. the is as distances longer over M magnetism creation the themselves. with moments originate the may of that transition phase Zero quantum correlations. of spatial YFe fluc- without in order the entirely temperature however, are temperatures; and moments energies tuating low at found diverge are moments to localized of a fluctuations mechanical to quantum YFe close conventional neu- in very this replaced present naturally be that we must showing Here, new the picture measurements lived. within a fluctuations scattering long of the tron become and regions system regions correlated the correlated span when 2017) 13, to December occurs grow review for phase transition (received 2018 phase 9, May approved A and MA, Cambridge, University, Harvard Sachdev, Subir by Edited and 37831; d TN Ridge, Oak Laboratory, eateto hsc n srnm,TxsAMUiest,CleeSain X77843-4242; TX Station, College University, A&M Texas Astronomy, and Physics of Department ainlIsiueo tnad n ehooyCne o eto eerh ainlIsiueo tnad n ehooy atesug D20899; MD Gaithersburg, Technology, and Standards of Institute National Research, Neutron for Center Technology and Standards of Institute National thspoe ifiutt aeaceneprmna distinc- experimental clean a make to difficult proven has It e eateto aeil cec n niern,Uiest fMrln,CleePr,M 20740 MD Park, College Maryland, of University Engineering, and Science Materials of Department 1.85 ain,wihbcm nraigyln ie n extend and corre- lived magnetic long of increasingly growth become the which from lations, arises order agnetic Co | T unu matter quantum T 0.15 0 = 0 = a,1 As .S Wu S. L. , re aaee faykn 9.Nonetheless, (9). kind any of parameter order otpyisgvrstemr eoaie d delocalized more the governs physics Mott . 2 7 )fidsrn unu rtcl(C fluc- (QC) critical quantum strong find 8) (7, a T T 0 = 0 = 2 Al T | b,2 h unu rtclPit(QCP). Point Critical Quantum the , eto scattering neutron 10 = r xetdt aeavr different very a have to expected are c .A Zaliznyak A. I. , odne atrPyisadMtrasSineDvso,Bokae ainlLbrtr,Utn Y11973; NY Upton, Laboratory, National Brookhaven Division, Science Materials and Physics Matter Condensed unu hs rniin Fully transition. phase quantum 0 sahee ya nieylcltype local entirely an by achieved is T 2 Al 0 = 10 opudta forms that compound a , ntblte.Frspatially For instabilities. CeCu T 0 = c 6−x .H Xu H. W. , hr neutron where , C Au x C 6 and (6) c .M Tsvelik M. A. , 1073/pnas.1721493115/-/DCSupplemental ulse nieJn 8 2018. 18, June online Published at online information supporting contains article This 2 1 the under Published Submission. Direct PNAS a is article This interest. of conflict paper. no the declare wrote authors M.C.A. The and J.A.R.-R., and Y.Q., A.M.T., data; W.H.X., analyzed I.A.Z., W.J.G. L.S.W., research; W.J.G., performed I.A.Z., M.C.A. L.S.W., W.J.G., and research; J.A.R.-R., Y.Q., designed A.M.T., W.H.X., M.C.A. and L.S.W., W.J.G., contributions: Author ieteprmna vdneo h ovrestain hr an where situation, lack magnetic converse we the to of however, evidence transitions; lead experimental direct localization to electronic phase via likely Magnetic mation systems. very of is at frustrated insta- most transitions physics, topological the a in Mott by except order, either by metal, or a in emergence bility moment the magnetic speaking, a delocalized Practically of to (18–20). magnetic orbitals and nonmagnetic more localized or and being one where from transition transition phase can a theoretical for general weaker. (17) a structure provides much orbital (OSMT) the be transition metals, Mott to electron-based selective otherwise presumed d moments would for are individual that appropriate correlations of Particularly interactions spatial intersite dynamics to the the In lead and is 16). QC, it (15, is correlations cases, that insta- electronic these topological strong of with a both metal of a consequence in the bility as one formation different and very localized moment A be not. will QC that does electron that by the sur- not containing Fermi two one accompanied between (12) faces, fluctuations is a QC QCP by It near rather, magnetic but 14). as transition, a (13, fluctuations, one at parameter to exactly order close occur of simply collapse may The or effect 11). (10, enough Kondo electron strong the moment-bearing are sce- a order localize breakdown magnetic to QC Kondo the with compounds, the associated fermion play heavy In fluctuations electron may f QCPs. for formation near proposed moment nario role that important evidence an mounting is there eateto hsc,SuhUiest fSineadTcnlg fCia Shenzhen, China, of Technology and China.y Science 518055, of University South Physics, of [email protected] Department Email: addressed. be should correspondence whom To ei oeti YFe mag- in each where moment local, is paradigm netic transition this phase where observed here transition Our Reported a fails. static. of become evidence increase and experimental regions system is ordered the small that span of transition they lifetime until phase and size of the type when a of at discovery occurs the report We Significance oet e ahmmn olw h aesetu of spectrum in same present transition the phase YFe The follows fluctuations. moment critical quantum each yet moment, oeiec o h raigo rnltoa ymtythat symmetry translational of order. magnetic with breaking accompanies moments, the for magnetic evidence of no formation the to corresponding 2 c Al .Qiu Y. , 10 saraiaino cnrool itda ytheory, by at hinted only scenario a of realization a is T = b eto cteigDvso,OkRdeNational Ridge Oak Division, Scattering Neutron T d .I otnospaetastos re occurs order transitions, phase continuous In 0. NSlicense. PNAS .A Rodriguez-Rivera A. J. , 0 = PNAS ontrqiesmlaeu oetfor- moment simultaneous require not do | 2 2 uy3 2018 3, July Al Al 10 . sidpneto vr other every of independent is T 10 0 = | o.115 vol. hs rniinenvisages transition phase www.pnas.org/lookup/suppl/doi:10. d,e T , 0 = | o 27 no. antcphase magnetic | 6995–6999

PHYSICS electronic localization transition leading to moment formation the structure factor S(q, E), which probes correlations among can exist independent of magnetic order. It is significant that the moments. The latter can be isolated (Fig. 1 C and D) by com- 2+ neutron scattering results reported here show that YFe2Al10 is paring I (qK , E) with both the isotropic Fe atomic form factor 2 an example of a metal on the verge of moment formation but (26) and the form factor Fxz,yz (qK ) of the Fe dxz,yz Wannier without any vestige of magnetic order (21, 22). orbitals obtained from a tight binding band structure calculation 2+ In materials that are magnetically ordered or nearly so, mag- (SI Appendix). I (qK ) falls off more quickly than the Fe atomic netic correlations depend strongly on wave vectors q that reflect form factor, implying a minimal degree of Fe moment delocaliza- the spatial periodicity of the magnetic structure. Our inelastic tion in YFe2Al10 that is well-captured by the calculations. Unlike 2+ neutron scattering measurements show (Fig. 1 A and B) that the the spherically symmetric Fe atomic form factor, I (0, qK , qL) magnetic fluctuations in YFe2Al10 are very different. Here, the is strikingly anisotropic, and the dominance near the Fermi level scattered intensity I (q) is dominated by a broad ridge of scatter- of dxz,yz orbitals provides a natural explanation (SI Appendix, ing along wave vectors q parallel to [0, 0, L], lying in the critical Fig. S3). After the computed form factor is removed from the 2 ac plane defined by the Fe layers (Fig. 1D, Inset and SI Appendix) measured intensity I (qK , E) = Fxz,yz (qK )S(E), there is no fur- (21, 23, 24). Consistent with the T /B 0.6 scaling observed in the ther wave vector dependence of the structure factor, which is magnetization and specific heat (25), the scattering is strongly solely a function of energy E, S(q, E) = S(E) (Fig. 1D). Since suppressed by magnetic fields B (Fig. 1A). The critical part of an atomic energy scale ∼1 eV controls the spatial distribution of I (q) can be exposed by using similar data obtained at 9 T (Fig. the moment density in the dxz orbital that is reflected in the form 1A, Right) as an improvised background for the B = 0 data (Fig. factor, the wave vector modulation of I (qK ) is correspondingly 1A, Left). Fig. 1B shows that the result is a weak and broad modu- unaffected by temperatures from 0.07 to 20 K, magnetic fields as lation of the field-dependent component of the scattering in the large as 9 T , and excitation energies from 0.35 − 1.5 meV (SI [0, K, 0] direction I (qK ) perpendicular to the Fe layers, with a Appendix, Fig. S6). Remarkably, the moments in YFe2Al10 are breadth that extends over more than the full Brillioun zone. highly localized in space and fluctuate independently, with no The neutron intensity I (q, E) is the product of the magnetic sign of the spatial correlations that are a foundational element form factor F 2(q), reflecting the spatial distribution of mag- of conventional phase transitions and their T = 0 analogs. netization clouds associated with the fluctuating moments, and Despite the absence of spatial correlations among the fluctu- ating moments in YFe2Al10, their dynamics are manifestly QC, with the strongest scattering associated with fluctuations hav- ing the lowest energies or longest lifetimes. Inelastic neutron AB scattering experiments (Fig. 2A) reveal a gapless spectrum of excitations, where the structure factor S(E), obtained from the data in Fig. 1 by integrating over qK (SI Appendix), is expressed in terms of the magnetization squared M 2. The critical behavior of the energy dependence is determined by plotting the inverse of M 2 − C , where C is a small and energy-independent con- tribution to the moment, as a function of E ∆, and within their accuracy, the neutron scattering data are consistent with ∆ = 1.4, which is the power law exponent that was previously reported for the temperature divergence of the magnetic susceptibility −1.4 χ(T ) ∝ T . The QC dynamics are a continuum that extends to the lowest energies probed in this experiment (Fig. 2B). Since CD 2 M must remain finite, the QC energy dependence S(E) ∼ E −1.4 cannot extend to E → 0. The local QC behavior reported here is likely a high-temperature phenomenon, and it will be cut off at lower temperatures either by residual interactions that lead to ordered states, like magnetic order or superconductiv- ity, or perhaps, by interactions within the ordered lattice of Fe moments that lead to a coherent ground state as in a Kondo lattice. By expressing M 2 in absolute units, we see that the fluctu- ating local moments responsible for the scattering in the energy window of our experiment from 0.35 to 1.5 meV have magnitudes of ∼ 0.3 − 0.4 µB /Fe, similar to the local moment magnitude deduced from fitting the Curie–Weiss law to the static suscep- Fig. 1. Spatially localized magnetic fluctuations in YFe2Al10.(A) The inten- sity of neutrons scattered with energy transfer 0.5 meV in the [0, K, L] plane tibility χ0(T ) in the temperature range 100 − 750 K (21). The at 0.07 K in fields of 0.025 T (Left) and 9 T (Right) and their difference energy-independent scattering C likely reflects the presence of a I(0 T) − I(9 T)(B). The tails of nuclear Bragg peaks are clearly observed in A broad and weakly correlated band of quasiparticle excitations as at integer values of K and L. A diffuse ridge of scattering is evident along [0, implied by the modest Pauli susceptibility and Sommerfeld coef- 0, L] at qK = 0 rlu. Data are monitor normalized. (C) Wave vector qK depen- ficient reported for YFe2Al10 (21). The breadth of this band is dence of the qL integrated intensity I(qK ) is better described by the YFe2Al10 estimated as ∼ 0.7 eV (Fig. 2A), which is the energy where the 2 magnetic form factor Fxz,yz(qK ) from electronic structure calculations (black integral of the fit to the experimental data reaches the square of line) ( ) than isotropic Fe2+ form factor (green line) (26). Both 2+ 2 2 SI Appendix the full spin S = 2 Fe moment M = 24 µB . form factors are scaled to the data. Strong anisotropy in the intensity indi- Conventionally, proximity to a phase transition results in cates that dxz,yz orbitals dominate. (D) The T = 0.07 K structure factor S(qK ) is 2 the transfer of spectral weight to lower energies. Something isolated for different fixed energies by dividing I(qK ) by F , (qK ). Solid lines xz yz very different occurs in YFe2Al10, where the qL integrated are obtained by fitting I(qK ) to a Lorentzian and dividing by the computed F2 (q ), showing that S(q ) is independent of wave vector q .(Inset) The scattering I (qK , E) (Fig. 3A) as well as the associated S(E) xz,yz K K K (Fig. 3B) are constant over almost three decades of tempera- correspondence between the scattering wave vectors qK and qL and the ac planes containing the nearly square Fe nets in YFe2Al10. The magnetic field ture from 0.07 to 20 K. This simple observation has remark- is oriented in the critical ac plane along the (100) direction. All data were able consequences. Namely, the principle of detailed balance 00 measured on MACS (46). Error bars in each figure represent 1 SD. gives S(E, T ) ∼ χ (E, T )/(1 − exp(−E/kB T )), where kB is

6996 | www.pnas.org/cgi/doi/10.1073/pnas.1721493115 Gannon et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 oefrdsre nteQ eairo YFe of behavior QC the temperature in and disorder for energy role strong the that of out fluctuations. divergences QC pointing same worth the is probe It measurements both that of measurements imply susceptibility dependencies exper- magnetic temperature and our scattering and in neutron the energy accessed matching energies the and and iments, temperatures in of energies data range scaled low the the with arbitrarily temper- compared and is energy to cutoff particular ature a extend for proposal a cannot and temperatures, it that implies .I diin the of addition, divergence strong In The finite. 2B). remain (Fig. must itself experiment integral scattering neutron the of of 1 = determinations ∆ independent two these where rmr–rngrlto gives relation Kramers–Kronig plotting expression by the by x curve well-reproduced that universal is show curve single to sal a possible onto also χ is collapse it data temperatures, these and energies of YFe in ments ueet n h rvosyrpre eprtr depen- temperature susceptibility reported mea- static scattering previously the of neutron the dence the and between surements connection needed the zone. to Brillouin amounting entire experiment, an this than in more accessed vectors wave of wave range con- of In range order. limited magnetic the a incipient trast, with over associated observed are only that is vectors it and order, netic the 3C Fig. and 27–32), (6–8, transitions hall- that phase the QC are itself of temperature than mark fluctuations other QC scale factor. energy balance no having detailed the of dependence ture h mgnr ato h yaia susceptibility of function dynamical a the be of also must part imaginary the otmn’ osat h ealdblnefactor balance detailed The exp constant. Boltzmann’s SD. 1 represent figures both of function a as to fit law power the fluctuations 0.034 h oi leln safi otedt where data the to fit a is line blue solid The 7Kand K 0.07 squared magnetization the anne al. et Gannon 2. Fig. AB

−∆ 2 2 00

χ M ( /meV•Fe) h nryadtmeauedpnece of dependencies temperature and energy The B T 0.2 0.1 (−E 0 E 0 χ 1.4 (T tanh(x µ au hti hlywti h xeietlbounds experimental the within wholly is that value a .4, /T 0 00 B 2 χ unu otnu nYFe in continuum quantum A /meV = ) = safnto of function a as /k 00 E E cln sawy soitdwt h olpeo mag- of collapse the with associated always is scaling χ B B aE /T Z 00 1.4 = with ), T · −1.4 (E e h ahdrdln steitga vrtemaue QC measured the over integral the is line red dashed The Fe. E 0.025 E dE )) 2 ∝ 1.4 cln of scaling (meV) χ Al /T hl h ahdbu ierpeet h nerlover integral the represents line blue dashed the while , tanh(x 0 smnfsl ucinof function a manifestly is 12 h leln niae h etlna t ro asin bars Error fit. linear best the indicates line blue The . M χ 10 and ) T 00 2 1 = ∆ (E eal ftenraiainaein are normalization the of Details . nYFe in (E r are u vrsc ra range broad a such over out carried are for ) χ , ) M T (E χ 00 npeiul netgtdsystems, investigated previously In .4 and 2 E 00 )/E r nossetwt nappreciable an with inconsistent are fteflcutn oet nYFe in moments fluctuating the of 2 > /k nYFe in Al E 0 0.5 k B x /k B 10 = T T

= 2 2 2 h nes of inverse The (B) . B M ( B /Fe) Al χ T ) swl.Bcueormeasure- our Because well. as E T 0 10 2 ,weeteuniver- the where 3D), (Fig. −∆ (T /k Al

h nrydpnec of dependence energy The (A) . 2 -1 2 -1 htcnestetempera- the cancels that (M -C) ( B /meV•Fe) 15 45 30 B 10 ) M Z 0 T ∼ 0 2 xed vrteentire the over extends (E dx gemn between Agreement . T ) χ 2 = −1.4 Al 0 E tanh(x (T C E /k 10 χ For Appendix. SI + 1.4 00 ) M B 2) ic the since (25), aE (meV (33–37). (E eursthat requires T 2 12 −1.4 − χ )/x n thus, and , IAppendix SI , 00 T C χ 1.4 with , 00 splotted is 1+∆ )T provide ) (E 2 χ shows Al 00 1.4 (1 , 10 (E , [1] C T − ∝ at = ) ) . ueeteeg evst u f h iegne h simplest mea- The divergence. or takes the Zeeman, 2B) off (Fig. thermal, cut case the to serves of energy largest surement the otherwise, zero; general- the in susceptibility divergence ized the Specifically, (6). dependence field par- of dependencies A CeCu temperature temperatures. system QC lowest benchmark of the the formulation at simple YFe heat ticularly specific in and observed tization dependencies field the and gr ersn SD. 1 represent figure function the when fits curve are of universal lines tion single solid a The circles). onto (red collapsed K energy 0.07 different expression at of the range meV to a 1.5 for to and 0.35 meV circles) from 0.35 (black transfers of meV transfers 0.7 energy for and K circles) 24 vectors. (blue to wave 0.07 same from temperatures these different over at integrated been also has S 3. Fig. fdtie balance, detailed of cir- (blue K factor 20 form and integrating computed vectors circles), by scaled (green the obtained is K is line 8 black circles), The (red cles). K 0.07 temperatures scattering grated eto eprtrsi h ag rm00 o2 o h xdenergies fixed the for K 24 to 0.07 from range E the in temperatures of dent yaia ucpiiiyhsa vctv eddpnec at dependence field 4A evocative Fig. an T susceptibility? has susceptibility dynamical dynamical the in YFe well in temperatures suscep- and static to the corresponds of T QCP analyses Scaling the magnetism. if tibility fluc- of fields the QC onset magnetic affect weakens the would these will temperature as Increasing composition to tuations order. or modifications to stress, therefore, tendency pressure, and via a occur, quantities which may under conditions transition the determine material CD AB (E

= 2

'' ( /B h tutr,smere,aditrcin rsn nagiven a in present interactions and symmetries, structure, The

/meV•Fe) I(q) (cnts./std. mon.) 0 = 0.3 0.2 , B 0.1 5mV(lecrls and circles) (blue meV 0.35 T 3 4 2 0 0.1 1 oteiaiaypr ftednmclsusceptibility dynamical the of part imaginary the to ) b 0.6 7K, .07 0 = q E E 2-1 -2 χ L /k /T otosteQ utain o ierneo fields of range wide a for fluctuations QC the controls 0 and B .19 ∼ cln ftemgei yaisi YFe in dynamics magnetic the of scaling T x 1 h oi re iecmae h clddata scaled the compares line green solid The . −∆ q T K T χ q −1.4 ihnteacrc formeasurements, our of accuracy the Within . E χ I tanh(x K 00 −0.6 (q /k (rlu) 00 0 ∼ 0100 10 K B χ ∝ χ T f o neeg rnfro .5mVi rsne at presented is meV 0.35 of transfer energy an for ) [ 00 (T meV A tanh(x ol nyocrif occur only would (E ,where ), B PNAS 12 + , /B T 0 = S 0.07 K 8 K 20 K ) bB (q, · ∼ ,where ), 0.6 Fe/µ E 2 | S 0.6 E Al = and (E ) x vreprmna auso h wave the of values experimental over ) uy3 2018 3, July = , e bakcrls.(C circles). (black meV 0.7 ] aesonta igevariable single a that shown have 10 T χ −1 B 2 E ) χ 00 T /k (1 6−x ugsigapsil ikto link possible a suggesting , x 2) Is (25). 00 ol esprtdfo the from separated be could = 1.4 2 1.4 with B − ''•T ( K /meV•Fe) 0 = T

B in proposed previously was 10 10 10 10 E Au 10

exp(−E S(E) (cnts./std. mon.) 10 and /k -3 -2 5 0 -1 hr h energy the where K, .07 0 0.1 1 x B χ | A T E hr h nryand energy the where , 00 ∆ h aain data The (D) . o.115 vol. 2 T 3 = 0.1 T , /k Al 1.4 ..Errbr neach in bars Error 1.4. = 0.7 meV 0.35 meV T /B 2 B 10 Al 5meV .65 1 and , T spotda func- a as plotted is sue orelate to used is , ) 10 0.6 χ hw htthe that shows F E ntemagne- the in The (A) . xz | T 2 00 /k 1 (K) ,yz (E χ S T B 0100 10 o 27 no. bevdas observed h principle The ) B (E 00 T , (q T χ (E sindepen- is ) 0 = K approach splotted is ) 00 , .(B). ). · T T C Fe/µ ,which ), 1.4 10 q | phase a be can L inte- with 6997 S (E B 2 ) ,

PHYSICS 20 imply that YFe2Al10 forms very close to an electronic local- AB0.35 meV 0.4 meV ization transition. As was shown in both Fe and Mn pnictides 0.28 0.5 meV -1 0.7 meV and chalcogenides (41–43), such moments result from Hunds 15 1.0 meV 1.25 meV and Coulomb interactions that provide electronic correlations 0.26 that are potentially strong enough to localize one or more Fe /meV/Fe)

/meV/Fe) 10 2

2 d orbitals in YFe2Al10. Since the localized moments emerge B B from a relatively flat band (SI Appendix, Fig. S3), it is likely '' ( 0.24 '' ( 5 that the form factor of the moments, which encodes the orbital 1/ content, will dominate the q dependence of the scattering, just 0.22 0 as we have observed. The stabilization of the Fe moments is 0369 0 123 4 0.6 0.6 envisaged as a continuous cross-over or transition between a B (T) B (T ) coherent metallic state where the localized moments are wholly Fig. 4. Magnetic fields and the Quantum Critical Scaling of the dynamics in quenched and a state where this compensation has failed, leading 00 YFe2Al10.(A) The field dependence of χ , measured at T = 0.07 K, with an to incoherent and localized magnetic moments (41). A Mott-like energy transfer E = 0.35 meV. The solid line is a fit to the expression χ00 ∼ transition could ensue at T = 0 for a critical interaction strength −0.6 2 −0.6 2 A + bB , with A = 3.62 meV · Fe/µB and b = 0.19 T meB · Fe/µB. accompanied by QC fluctuations between these two topologically (B) The inverse of χ00 plotted as a function of B0.6 for T = 0.07 K at different distinct states that are degenerate at the QCP. The comparison fixed energy transfers as indicated. Error bars represent 1 SD. of the measured and computed form factors suggests that it is the dxz,yz orbitals that are most localized in YFe2Al10, while the   dependence dominates and gives 1/ χ00 − C˜ =aE ˜ 1.4, with other orbitals are represented as delocalized and weakly corre- lated electronic states that result in the overall metallic character ˜ 2 C = 0.053 µB /meV · Fe providing a scale for the fine tuning of YFe2Al10, evident from the temperature dependence of the needed to drive YFe2Al10 exactly to the QCP. These neutron electrical resistivity as well as the modest Pauli susceptibility scattering experiments directly probe the response to the fluctu- and Sommerfeld constant. Consequently, it seems possible that ating fields associated with the QCP in YFe2Al10 for energies YFe2Al10 is very close to an OSMT (17–20) and that it is QC that are, for the most part, larger than the thermal energy kB T fluctuations between these phases at T = 0 that lead to the non- 00 and the Zeeman energy gµB B. The inverse of χ is plotted as a FL properties of YFe2Al10. Detailed investigations of the Fermi 0.6 function of B at different fixed energy transfers in Fig. 4B. The surface in YFe2Al10, ideally as pressure or another nonthermal 00 B = 0 intercept of 1/χ decreases with decreasing energy, con- parameter tunes the localized moments to extinction, will be sistent with an energy dependent cutoff. However, the slope of required to further evaluate this proposal. 0.6 the B dependence is also energy dependent, proving that the For now, the nature of the T = 0 phase transition that drives 00 energy and field dependencies of χ are significantly intertwined the quantum critical behavior that is so dominant in YFe2Al10 and cannot be readily separated, even when energy provides the remains unknown, although its consequences are transforma- largest scale. Still, it is reasonable to expect that the T /B 0.6 scal- 00 tive. Neutron scattering provides a powerful and direct means ing found in χ0(T ) is most likely to be observed in χ when to show that this phase transition is not of the conventional the excitation energy E is small compared with the thermal and Landau–Ginsburg–Wilson type. Unlike previously studied sys- magnetic field scales, a regime that is largely unaddressed in our tems, where similar measurements found that QC behavior was neutron scattering measurements. never wholly free of the magnetic correlations associated with The previously reported scaling analysis made it clear that proximate magnetic order, the complete absence of these cor- YFe2Al10 is naturally located by its composition to be very close relations in YFe2Al10 indicates that here the QCP stands alone to a T = 0 phase transition. The neutron scattering measure- and is definitively of a type that has never been observed before. ments reported here reveal that this phase transition is highly YFe2Al10 is almost unique in that no fine tuning is required unconventional. Specifically, the near divergence of S(E) as to access its QCP, which affects a remarkably broad range of E → 0 shows that QC magnetic fluctuations with a timescale ξτ temperatures and fields. In this sense, it might be considered dominate at the low energies probed in these experiments, while the d-electron analog of β − YbAlB4 (44, 45). Since no bulky spatial correlations ξr among these moments are absent. This pressure apparatus and no potentially disruptive disorder from violates the foundational property of conventional phase transi- compositional variation are necessary in YFe2Al10 to fine tune tions (38), where ξr and ξτ are related by the dynamic exponent z the QCP, our results open the door for further explorations z, ξr = ξτ . An intriguing alternative has recently been suggested, of the nature and properties of this quantum phase transition where a topological phase transition could produce anomalously using the most powerful spectroscopic and imaging tools at our weak spatial correlations as well as reproduce several of the disposal. experimental findings in YFe2Al10 (39, 40). Our major finding is that the excitations detected by our Materials and Methods neutron scattering measurements in YFe2Al10 are those of indi- Samples and Experimental Setup. To measure the excitation spectrum of vidual and highly localized magnetic moments, each fluctuating YFe2Al10, neutron scattering measurements were carried out in the 0, qK , qL independently with the same anomalous spectrum, without any scattering plane on the Multi Axis Crystal Spectrometer (MACS) instrument evidence for a nearby broken symmetry. The low-temperature at the Center for Neutron Research at the National Institute of Standards divergences of quantities, like the magnetic susceptibility, the and Technology (46). Apart from a small orthorhombic distortion in the ac specific heat, and the electrical resistivity, all attest to the break- basal plane, we would expect to find similar data in the (nearly) equiva- down of normal metallic behavior, which we now know occurs lent qH, qK , 0 scattering plane. The sample consisted of two coaligned single in the absence of magnetic order at temperatures as low as crystals of YFe2Al10 with a total mass of 2 g mounted in a dilution refrig- 0.07 K. The observation of E/T scaling in the neutron scattering erator equipped with a superconducting magnet with an 11-T vertical field measurements indicates that the magnetic excitations are fun- aligned with the (100) crystal direction. To reduce background scattering in the double-focusing mode, we used a 3.3 × 7.7-cm beam mask to focus damentally modified relative to the damped spin waves or the the neutron beam on the 1.5 × 2.5-cm sample. For all measurements, a continuum of single-particle excitations that are expected near a small bias field of about 0.025 T was used, suppressing superconductivity classical magnetic phase transition. of the aluminum sample holder at low temperatures and for consistency The small but localized moments identified by both the Curie– at temperatures above Tc of aluminum, 1.2 K. Undesired background scat- Weiss susceptibility and the neutron scattering measurements tering was eliminated by setting the dark angle of the magnet at 90°

6998 | www.pnas.org/cgi/doi/10.1073/pnas.1721493115 Gannon et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 0 oea ,P P, Coleman 10. 1 iQ ael ,IgretK mt L(01 oal rtclqatmpaetransitions phase quantum critical Locally (2001) JL Smith K, Ingersent S, Rabello Q, Si 11. 4 ekuA ta.(02 rsa tutr fytimio lmnu 121) YFe (1/2/10), aluminium iron yttrium of structure Crystal LnT (2012) al. aluminides et A, Ternary Kerkau (1998) 24. W Jeitschko T, Ebel YFe VMT, in dynamics Thiede spin 23. quantum-critical Anomalous (2018) al. et K, Huang 22. critical quantum heavy-fermion a across evolution Hall-effect (2004) al. et S, Paschen 12. 1 akK ta.(01 il-ue em iudi unu rtclYFe critical quantum in liquid Fermi Field-tuned (2011) out al. transition et Mott K, Kondo Orbital-selective Park (2009) and X 21. transition Dai M, Mott Capone (2005) SR, Hassan S L, Medici Biermann de’ G, Kotliar 20. A, Orbital-selective Georges (2002) L, M Medici Sigrist de’ TM, Rice 19. DE, Kondakov IA, Nakrasov VI, Anisimov beyond. and 18. metals. fermions Heavy liquid transitions: Mott non-Fermi Orbital-selective (2010) and M Vojta surfaces near Fermi 17. liquids Critical non-Fermi Ge-substituted (2008) and in magnetism T Weak phase Senthil (2004) liquid 16. S non-Fermi Sachdev M, a Vojta for T, Evidence Senthil (2010) 15. al. et point J, critical quantum Custers antiferromagnetic 14. the Detaching (2009) al. et S, Friedemann 13. yta ag of range that by the of along range areas summed) results numerically flux, The (i.e., masked. neutron integrated were reflections were incident Bragg from the tails by by contaminated space intensity measured temperatures, the transfers, the malizing energy in fixed fields different magnetic and at intensity neutron tered eerha h ainlIsiueo tnad n ehooy(6 (Fig. (46) Technology and Standards of Institute 1A National the at Research χ χ h qaeo h antcfr factor form magnetic the of square (47). the way straightforward a in q ity vector factor wave structure given a at measurements ing Analysis. Data (q as indexed are vectors lattice rocal E h eto oreadtesml,wieB (for Be while sample, the and source energy neutron neutron the final (λ using and meV direction 3.7 (010) the from away anne al. et Gannon .ScdvS(08 unu ants n criticality. and magnetism Quantum (2008) S quasi-two- Sachdev in function response 9. critical Quantum (2015) A Schroder L, temperature-dependent Zhu CM, and Varma dynamics 8. spin Normal-state metals. (2010) heavy-fermion al. in in et points antiferromagnetism DS, of critical Inosov Onset quantum 7. (2000) on al. temperature et nonzero A, a Schroeder of 6. Effect (1993) JA Millis 5. heavy-fermion (1985) the T phenomena. Moriya in critical Quantum 4. fluctuations (1976) JA quantum Hertz Field-induced 3. (2011) al. et DK, Singh 2. .KaoW amn ,LjyP lqe 20)Atfroantcciiaiya a at criticality Antiferromagnetic (2009) J Floquet P, Lejay S, Raymond W, Knafo 1. f K 00 00 = u esrmnso h ASisrmn tteCne o Neutron for Center the at instrument MACS the on measurements Our iesoa tnrn antiferromagnets. itinerant dimensional BaFe doped optimally 181. in energy spin-resonance Nature systems. fermion itinerant 56. Vol Berlin), (Springer, Sciences Solid-State CeCu superconductor die? transition. phase quantum heavy-fermion rsalg e rs Struct Cryst New Kristallogr Z series. iron-containing the of YbFe with T=Fe,Ru,Os) and Nd,Sm,Gd-Lu B Rev metals. correlated strongly in 84:094425. point. fbn degeneracy. band of metals. f-electron in screening Ca in transition Mott-insulator Phys Temp 78:035103. points. critical heavy-fermion YbRh YbRh in reconstruction surface - Fermi the from = χ (q, (q, a neapeo h aa cur the acquire data) the of example an has 00 e)fitr eeue ewe h apeaddtco.Alrecip- All detector. and sample the between used were filters meV) 3.7 b 2π/ E (q, L E hsCnesMatter Condens Phys J ) 2 ) 97:155110 ∼ 08 .]rcpoa atc nt ru n eete normalized then were and (rlu) units lattice reciprocal 1.8] [0.8, = Si Nature 407:351–355. srltdto related is E 2 S = . ) f ohrlt oormaue eto cteigintensity scattering neutron measured our to relate Both . hsRvLett Rev Phys ( = 161:203–232. q, 0.62 pnC iQ aaahiiR(01 o oFrilqisgthayand heavy get liquids Fermi do How (2001) R Ramazashvili Q, Si C, epin ´ 2ad4.70 and 5.22 h uniiso neetdtrie nornurnscatter- neutron our in determined interest of quantities The 432:881–885. E S ) pigrSre in Series Springer Magnetism, Electron Itinerant in Fluctuations Spin (q,  q A ˚ L 1 −1 , − E hsRvLett Rev Phys 2 ∆q Ge ) S and e n h mgnr ato h antcsusceptibil- magnetic the of part imaginary the and 104:186402. −E (q, 2 L . hsRvB Rev Phys hc oesoefl rloi oe hszone This Zone. Brillouin full one covers which , c Rep Sci 13:R723–R738. /k q q= E ae Chem Mater J hsRvB Rev Phys Nature 227:289–290. L B ) 2−x ,rsetvl) efitr eeue between used were filters Be respectively). A, hsRvLett Rev Phys ˚ T = ytepicpeo ealdblne where balance, detailed of principle the by  [0, S c 2π/ Sr o ie temperature given a for 102:126401. 1:117. (q, x K, 413:804–808. RuO 48:7183–7196. E 2 ln (the plane L] = ) 69:035111. hsRvB Rev Phys H Al 4 sdtrie ydividing by determined is a Phys Nat . 0.70 q 10 F 8:125–130. u hsJB J Phys Eur 95:066402. K 2 yesrcueadmgei properties magnetic and structure type q (q), hsRvB Rev Phys q 2 n energy and L Si A ˚ ,wt eirclltieunits lattice reciprocal with ), 2 1.85 −1 S 5:753–757. . 92:155150. q (q, a Phys Nat a Phys Nat . Co E eedneo h scat- the of dependence f q 25:191–201. E 0.15 14:1165. = K )∼ –q q e)o e (for BeO or meV) 3.0 L I L 5:465–469. As E 4:173–185. ( ieto vrthe over direction T ln) fe nor- After plane). q, r h magnetic the are 2 . . E 2 a Phys Nat )/F Al 2 Al E 10 f 10 2 . hsRvB Rev Phys 2 ,while (q), . and 3.0 = I hsRvB Rev Phys Al ( (Ln=Y,La- q, 10 I 6:178– 2 ( E . Low J Al q, Phys ) by 10 E q ) . 8 adnS,e l 19)Mgei utain nLa in fluctuations Magnetic (1991) al. et SM, state normal Hayden the of 28. Phenomenology (1989) S Schmitt-Rink PB, Littlewood CM, Varma 27. factors. form Magnetic fluctuations (2006) critical PJ Quantum Brown (2014) MC Aronson 26. AM, Tsvelik K, Park MS, Kim LS, Wu 25. 9 emrB ta.(91 cln eairo h eeaie ucpiiiyin susceptibility generalized the of behavior Scaling (1991) al. et B, Keimer 29. 3 cal E ta.(04 nteoii ftecag a nLaMnPO. in gap charge the of origin the On (2014) al. et magnetic DE, the McNally of nature 43. the and frustration Kinetic (2011) G Kotliar K, Haule ZP, Yin 42. critical quantum in fluctuations of local response versus magnetic Extended the (2003) al. of et scaling W, liquid Montfrooij Non-Fermi 31. (1995) al. et MC, Aronson 30. 4 asmt ,e l 21)Qatmciiaiywtottnn ntemxdvalence mixed the in tuning without criticality Quantum (2011) al. et Y, Matsumoto 44. iron of state two normal the in the crossover Coherence-incoherence (2009) of G Kotliar K, quantum-criticality dissipative Haule two-dimensional the and 41. in criticality Quantum diagram (2016) CM Varma Phase C, Hou L, (2016) Zhu 40. CM Varma C, phenomena. critical Hou dynamic of 39. Theory (1977) of Heisenberg BI behaviour Halperin itinerant liquid PC, Hohenberg non-Fermi in Disorder-driven 38. effects (2005) V Griffiths Dobrosavljevic Quantum E, Miranda (2005) alloys: 37. J Ce Schmalian and U T, in Vojta behavior 36. Non-Fermi-liquid (2000) BA Jones AH, glass. spin Neto Ising Castro quantum of 35. behavior Equilibrium quan- (1995) DA chains. antiferromagnetic Huse spin Ising M, putative field Thill transverse Random a 34. (1992) DS near Fisher dynamics 33. Spin (2015) al. et MG, Kim 32. 7 qie L(2012) GL at spectrometer neutron Squires cold intensity 47. high new MACS–A without (2008) metal al. Strange et (2015) JA, S Rodriguez Nakatsuji P, 46. Coleman Y, Uwatoko K, Kuga T, Tomita 45. a eetdt iiiepsil otmnto rmtedrc em This beam. direct the the yields from procedure contamination possible minimize to selected was S6 of Examples nttt fSadrsadTcnlg n h ainlSineFoundation Science Center National DMR-1508249. the the Agreement and under by Technology National and the provided Standards between Founda- was of partnership a Institute Science MACS Scattering, National the Neutron the Resolution by to High at for supported Access performed PHY-1066293. is was Grant which Strongly work tion Physics, this Functional Department for of US Center of Part Aspen under DE-FOA-0001276. Design sup- Grant Spectroscopy Computational Energy was Theoretical of for W.H.X. and DE-SC0012704. Center Materials Contract Correlated the Sciences Basic by Energy, Energy of of ported Department at Basic Office US of Energy, of conducted auspices of Office the was under Department supported have A.M.T. research separately US and been W.H.X., I.A.Z., this of DE-AC02-98CH1886. Contract auspices of Sciences Energy the sup- Part Aeppli, were under M.C.A G. Broholm. and ported L.S.W., Chakravarty, W.J.G., C. S. where Laboratory, Shu, National and Brookhaven L. MacLaughlin, Raymond, D. S. Abrahams, E. Varma, C. ACKNOWLEDGMENTS. in described is which factor, form S (q, . fC- ihtmeauesuperconductors. high-temperature Cu-O of 454–461. pp C, Vol NJ), Hoboken, (Wiley, E Prince YFe layered in La 66:821. n aaantcsae nio ncie n rnchalcogenides. iron and pnictides 935. iron in states paramagnetic and Ce(Ru UCu compound 90:180403R. coupling. rule Hund’s of importance and oxypnictides -II. model XY quantum model. XY quantum dissipative dimensional Phys electrons. correlated magnets. singularities. Griffiths-McCoy and dissipation, 62:14975–15011. disorder, Criticality, 214:321–355. BaFe Cu-substituted superconductivity. in point critical tum CmrdeUi rs,Cmrde UK). Cambridge, Press, Univ (Cambridge NIST. criticality. magnetic I E (E 2−x and ) a eotie ihasmlritgaino the of integration similar a with obtained be can ) 5−x 49:435. esSiTechnol Sci Meas 1−x Sr Pd x CuO S hsRvB Rev Phys Fe x (E β I (x=1,1.5). x (q –YbAlB r bandfo hs uniisatracutn o the for accounting after quantities these from obtained are ) ) 4+y 2 2 K Ge Al , E 10 . 2 I hsRvB Rev Phys n 4A and 3A, 1C, Figs. in given are ) hsRvLett Rev Phys (q . (x Science 4 nrdcint h hoyo hra eto Scattering Neutron Thermal of Theory the to Introduction 72:045438. rcNt cdSiUSA Sci Acad Natl Proc q e rgPhys Prog Rep . hsRvLett Rev Phys K = Science K 19:034023. , hsRvB Rev Phys E h uhr cnweg sfldsusoswith discussions useful acknowledge authors The x eedneo u esrdintensity, measured our of dependence c )= PNAS = 349:506–509. 0.76). Z 92:214404. 331:316–319. rlu 0.8 1. 67:1930. | rlu 8 94:235156. 75:725. hsRvLett Rev Phys 68:2337–2408. IAppendix SI uy3 2018 3, July I (q nentoa alsfrCrystallography for Tables International 2 As K 111:14088–14093. , hsRvLett Rev Phys hsRvB Rev Phys 2 q L n t eaint high-temperature to relation its and , E 91:087202. . )dq | 1.95 e Phys J New o.115 vol. L 94:201101. /∆q Ba 63:1996–1999. hsRvLett Rev Phys and 0.05 L . CuO IAppendix SI | 11:025021. q a Mater Nat K o 27 no. 4 dependence. . I hsRvLett Rev Phys (q hsRvB Rev Phys 69:534–537. hsRvB Rev Phys K hsc A Physica , e Mod Rev | E 10:932– ), Fig. , 6999 ed , [2]

PHYSICS