Dynamics of Collective Modes in an unconventional Charge Density Wave system BaNi_{2}As_{2}
Vladimir Grigorev, Amrit Raj Pokharel, Arjan Mejas, Tao Dong, Amir A. Haghighirad, Rolf Heid, Yi Yao, Michael Merz, Matthieu Le Tacon, Jure Demsar
CCollective modes in BaNi As probed by time-resolved spectroscopy Vladimir Grigorev, Arjan Mejas, Amrit Raj Pokharel, Tao Dong, Amir A.Haghighirad, Rolf Heid, Yi Yao, Michael Merz, Matthieu Le Tacon, and Jure Demsar Institute of Physics, Johannes Gutenberg-University Mainz, 51099 Mainz, Germany Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria and Institute for Quantum Materials and Technologies,Karlsruhe Institute of Technology, 76344 Karlsruhe, Germany
BaNi As is a non-magnetic analogue of BaFe As , the parent compound of a prototype ferro-pnictide high-temperature superconductor. Recent diffraction studies on BaNi As demonstrate theexistence of two types of periodic lattice distortions above and below the tetragonal to triclinic phasetransition, suggesting charge-density-wave (CDW) order to compete with superconductivity. Weapply time-resolved optical spectroscopy and demonstrate the existence of collective CDW amplitudemodes. The smooth evolution of these modes through the structural phase transition implies theCDW order in the triclinic phase smoothly evolves from the unidirectional CDW in the tetragonalphase and suggests that the CDW order drives the structural phase transition. As in cuprate superconductors, high-temperature su-perconductivity in Fe-based superconductors [1–5] isfound in the proximity to the magnetically ordered state,with the interplay between the magnetic order and super-conductivity long being at the forefront of the research.Detailed studies soon revealed the presence of anothertype of ordering, the electronic nematicity, where the de-generacy between the two equivalent orthogonal direc-tions in the square Fe planes is lifted, inducing a sym-metry reduction from tetragonal to orthorhombic [6, 7].This so-called nematic phase transition, which is in mostcases preceding the magnetic one, i.e. T S > T M , hasbeen considered to be driven by magnetic fluctuations.Indeed, in the parent compound of the prototypical sys-tem, BaFe As (Fe-122), a stripe-type spin-density-waveground state is realized below T M ≈
134 K, the tran-sition being slightly preceded by the nematic one at T S [8]. Upon doping (or application of pressure) high-temperature superconductivity is realized in this system.BaNi As (Ni-122) is a non-magnetic analogue of Fe-122. It shares the same tetragonal high-temperaturestructure while below T S = 137 K (upon warming) thestructure is triclinic. It displays superconductivity al-ready in the undoped case ( T c ≈ . T ) [9].Instead, recent X-ray diffraction studies suggest two dis-tinct charge-density-wave (CDW) orders above and be-low T S [10]. What is particularly striking, is the observedsix-fold enhancement of the superconducting T c and a gi-ant phonon softening observed when doping Ni-122 to alevel where the structural transition is completely sup-pressed [11]. Similar T c enhancement at the quantumcritical point between the triclinic and tetragonal phaseswas recently obtained also on strontium substituted Ni-122 [12]. There, electronic nematic fluctuations weredemonstrated and showed a dramatic increase near thequantum critical point [12]. The observed correlationbetween the enhancement of superconductivity and theincrease in nematic fluctuations, with the same B g sym- metry breaking of both the nematic fluctuations and theCDW order, may suggest a charge-driven electronic ne-maticity in Ni-122 [12]. The interplay between electronicnematicity, CDW order and superconductivity in Ni-122system thus currently presents one of the key topics in thepnictide research, especially given the parallels to cupratesuperconductors [13] that can be drawn.The existence of the periodic lattice distortion (PLD)in Ni-122 system has been demonstrated by X-ray diffrac-tion studies [10, 12, 14]. In the tetragonal phase the ap-pearence of superstructure reflections at ( h ± . , k, l )were attributed to a weak unidirectional I-CDW (theindexing throughout of the paper refers to the high- T tetragonal phase) [15]. In undoped Ni-122, the T -rangeof the I-CDW is limited to a range of about 10 K above T S = 137 K [10], but diffuse peaks can be resolved upto room temperature [14]. In the triclinic phase, a newperiodicity of PLD is observed, attributed to I-CDW with ( h ± / δ , k, l ∓ / δ ) superstructure reflec-tions. The discommensuration vanishes, i.e. δ →
0, atthe lock-in transition temperature T l ≈
128 K [10], re-sulting in a commensurate C-CDW [10, 14] with a wave-vector (1 /
3, 0 , / T l there are no abrupt changes inthe displacement amplitude [10]. In the electronic chan-nel, however, optical studies [16, 17] show no signatures ofthe CDW-induced optical gap. To get further evidencefor the CDW origin of the observed PLD [10, 12, 14]and to gain insights into the relation between CDWs andnematicity the information on CDW collective modes isrequired. To this end, we apply time-resolved opticalspectroscopy which has been demonstrated to be partic-ularly sensitive to study low-energy q ≈ . − [19], access to modes at frequen-cies down to the 100 GHz (3 cm − ) [20], and is suitablealso for investigation of disordered/inhomogeneous sam-ples [23]. The information on the temperature [18–21] a r X i v : . [ c ond - m a t . s up r- c on ] F e b and excitation fluence ( F ) dependent [24] dynamics pro-vide further insights into the nature of collective groundstates.In this Letter, we report systematic T - and F -dependent study of transient reflectivity in BaNi As . Atlow- T , starting at ≈
10 K above T S , we observe severaloscillating q = 0 modes. Their frequencies do not matchthe calculated q = 0 phonon frequencies of the tetragonalphase - see Supplementary Information (SI) [25]. Basedon that and their T - and F -dependence, matching thebehavior seen in prototype CDW systems [19], we at-tribute these modes to collective amplitude modes of theCDW [19, 26, 27]. From their T -dependence we concludethat the I-CDW transforms into the I-CDW by gainingadditional periodicity along the c-axis. This suggests aCDW driven nematicity in BaNi As .Single crystals of BaNi As with typical dimensions2 × × were grown by self-flux method similarto reported literature [11, 28]. Crystals were mechani-cally freed from the flux and characterized using X-raydiffraction and energy-dispersive x-ray spectroscopy [25].The samples were cleaved along the a − b plane beforemounting into an optical cryostat and were kept in vac-uum during the measurements. We studied the T - and F -dependence of the photoinduced reflectivity dynamicsusing optical pump-probe technique. A commercial 300kHz Ti:Sapphire amplifier producing 50 fs laser pulses at λ = 800 nm (photon energy of 1.55 eV) was used as asource of both pump and probe pulse trains. The beamswere at near normal incidence, with polarizations at 90degrees with respect to each other to reduce noise (nopronounced dependence on pump or probe polarizationwas observed). The induced changes of an in-plane re-flectivity (R) were recorded upon warming from 10 K,utilizing a fast-scan technique enabling high signal-to-noise level [19]. The fluence was varied between 0.1 - 4mJ/cm while the probe fluence was about 30 µ J/cm .Figure 1(a) presents the T -dependence of photoin-duced reflectivity transients, ∆ R/R ( t ), recorded uponwarming from 10 K, with F = 0.4 mJ/cm [29]. Clearoscillatory response is observed up to ≈
146 K, withthe magnitude showing a strong decrease near and above T S - see Figure 2(e). Similarly to the oscillatory signal,the overdamped signal is also strongly T -dependent. Toanalyze the dependence of the oscillatory and the over-damped components on T , we decompose the signal asshown in panel (b). We fit the overdamped componentsby∆ RR = H ( σ, t ) (cid:104) A e − t/τ + B + A (cid:16) − e − t/τ (cid:17)(cid:105) , (1)where H ( σ, t ) presents the Heaviside step function withan effective rise time σ . The terms in brackets representthe fast decaying process with A , τ , a themomodulationoffset B , and the slower process taking place on a 10 pstimescale ( A , τ ) - see inset to Fig. 1(b). − ∆ R / R ( - ) T e m pe r a t u r e ( K ) time (ps) − ∆ R / R ( - ) time (ps) − ∆ R / R ( - ) time (ps) τ τ (a) (b) FIG. 1. (color online) (a) Photo-induced in-plane reflectiv-ity traces on undoped BaNi As single crystal between 10and 146 K, measured upon warming with F = 0 . .(b) Decomposition of the transient at 10 K into overdampedand oscillatory components. Insert shows the individual over-damped components (dotted blue and dash-dotted green line)together with the sum of the two (dotted red line). Figure 2 presents the analysis of the T - dependenceof the oscillatory response. Panel (a) shows the T - dependence of the Fast Fourier Transformation (FFT)of the residual signal, left after subtracting best fits withEq.(1) from the original transients, as shown in Fig. 1(b).The broad background in the FFT extending up to ≈ T , all of themvanishing above ≈
146 K - see Figure 2. Generally, thepump-probe technique is mostly sensitive to A g sym-metry modes, which couple directly to carrier density[22, 31]. The stronger the coupling to the electronic sys-tem, the larger the spectral weight of the mode.We start by analyzing the two dominant modes at 1.57THz (52 cm − ) and 2.05 THz (68 cm − ). Calculationsof the phonon dispersion in the tetragonal phase do notshow q = 0 modes in this frequency range [25]. There-fore, and based on their T - and F -dependence discussedbelow, we attribute the modes to collective amplitudemodes of the CDW order. I.e. these modes at q = 0 area result of linear coupling of the electron density modula-tion and phonons at the CDW wave-vector in the high- T phase [19, 21, 26, 27, 32], as elaborated in the SI - see alsoFig. S2 [25]. The FFT spectra in the range of the dom-inant two modes are shown in Figure 2(b) for selectedtemperatures. The modes can be reasonably well fitted T (K) n ( T H z ) - 2 - 1 F F T ( a ) w ( c m - 1 ) FFT (arb.units) n ( T H z ) ( b ) n (THz) T ( K )( c ) G i (ps-1) T ( K )( d ) x 0 . 5 T l T S T l T S Si (arb. units)
T ( K )( e ) T l T S FIG. 2. (color online) (a) The temperature dependence of theFast Fourier Transform (FFT), demonstrating the presenceof several modes at low temperatures (denoted by verticaldotted white lines). The solid line present the FFT spectraof the 10 K data starting from 1.2 ps delay (see text). (b)The FFT spectra at selected temperatures focusing on themodes at 1.57 and 2.05 THz. (c)-(e) The temperature de-pendence of the modes’ parameters, obtained by Lorentzianfit to the FFT spectra: (c) central frequency, (d) linewidth,(e) spectral weight. T l and T S are denoted by vertical dottedand dashed lines, respectively. The dashed blue line in (d)presents the expected T -dependence of the linewidth of 1.57THz mode for the case, when damping is governed by theanharmonic phonon decay into two acoustic modes, given by[35] Γ( ω, T ) = Γ + Γ (1 + 2 / ( e (cid:126) ω/ k B T − by the sum of two Lorentzians, with T- dependencies oftheir central frequencies ( ν i ), linewidths (Γ i ), and spec-tral weights ( S i ) shown in panels (c)-(e), respectively.Here T S and T l are denoted by the vertical dashed anddotted lines, respectively.At low- T , the 1.57 THz mode parameters evolve simi-larly as the main amplitude mode in the prototype quasi-1D CDW system K . MoO well below its second orderCDW phase transition temperature [19, 21, 33]. Thisincludes the pronounced mode softening, the particu-lar T -dependence of Γ, which cannot be attributed toan anharmonic decay (see Fig. 2(d)), as well as the T -dependence of its spectral weight [19]. Within the model,where amplitude modes are a result of linear coupling be-tween the electronic order and the normal modes at theCDW wavevector [19, 21, 27], the T -dependence of themode frequency and damping reflect the T -dependenceof the strength of the electronic order. Indeed, the T -dependence of PLD [10] as well as of the charge/orbitalorder [14] suggest a pronounced T-dependence within the C-CDW phase.The 2.05 THz mode also shows substantial softeningand loss of spectral weight upon warming as in pro-totypical CDWs [19, 21]. Interesting is, however, theanomalous broadening of the 2.05 THz linewidth uponcooling within the C-CDW phase. Such broadening, al-beit less pronounced, was observed for selected modes inFe y Te − x Se x [36, 37] and NaFe − x Co x As [38] aboveand/or below the respective structural phase transitions.While several interpretations have been put forward [36–38], the origin is still unclear.Noteworthy, the two main modes are seen well in theI-CDW phase up to ≈
146 K, with the mode frequenciesand linewidths remaining nearly constant through T S .Several weaker modes, which display weak softeningare also observed. There is a weak mode at ≈ − ). Such low frequency mode could origi-nate from the acoustic shock wave, propagating with thesound velocity from the sample surface along the c-axis[39]. In such a scenario, the mode frequency is given by ν a = nv s λ , with n being the refractive index at λ = 800nm and v s the sound velocity along the c-axis. Using v s from the calculated phonon dispersions [25], and with n ≈ . ν a ≈
30 GHz. Thus, this mode is alsolikely a result of coupling to the underlying electronic in-stability. Note that in case of broken inversion symmetry,even infrared active modes can be observed [34]. In thiscase, this mode could be attributed to the pinned phasemode. However, up to now no evidence of inversion sym-metry breaking in Ni-122 has been reported. There arefurther weak modes at 3.5 THz ( ≈
117 cm − ), 6 THz(200 cm − ) and 6.4 THz (215 cm − ). In principle, themode at 6 THz could be attributed to an A g mode thatmodulates the distance between Ni and As planes. Thismode is commonly observed in time-resolved studies ofFe-122, albeit at ≈ . − ) inBaNi As [25], suggesting the 6 THz mode is not a reg-ular q = 0 phonon either. The modes at 3.5 and 6.4 THzdo roughly match the calculated q = 0 phonon frequen-cies [25]. However, the disappearance of all these modesat high- T suggests they may also be a result of couplingof normal modes at the CDW wavevector to the elec-tronic instability [19, 25, 41]. Apart from the 150 GHzmode, for all of the observed modes we can find phononsat similar frequencies in the calculated phonon spectra atboth q I − CDW and q I − CDW ( q C − CDW ) wavevectors [25].Further support for the CDW orders in BaNi As [10,14] is provided by the T -dependence of the overdampedcomponents. Figure 3(a) presents the T -dependence ofamplitudes A , A and B extracted by fitting the tran-sient reflectivity data using Eq.(1). In CDW systemsthe fast decay process ( A , τ ) has been attributed toan overdamped collective response of the CDW conden-sate [19, 21], while the slower process ( A , τ ) has beenattributed to incoherently excited collective modes [21]. A B Amplitude (10-4)
T ( K ) T l T S T S T l ( a ) ( b ) t t t , t ( ps ) T ( K )
FIG. 3. (color online) The temperature dependence of ampli-tudes (a) and relaxation times (b) of the electronic response,obtained by fitting the reflectivity transients using Eq. 1.Note that τ is multiplied by 100 for presentation purpose.The dotted and dashed vertical lines signify T l and T S , re-spectively. As both are related to the CDW order, their amplitudesshould reflect this. Indeed, all components are stronglyreduced upon increasing the temperature, with slightanomalies near T l and T S - see Fig. 3(a). Above ≈
150 Kthe reflectivity transient shows a characteristic metallicresponse, with fast decay on the 100 fs timescale.The evolution of timescales τ and τ is shown in Fig.3(b). In the C-CDW phase up to ≈
110 K the twotimescales show qualitatively similar dependence as inprototype 1D CDWs [19–21], with τ increasing while τ decreasing with T [19–21]. As τ was shown to be in-versely proportional to the CDW strength [19, 21], its T -dependence is consistent with the observed softeningof the oscillatory modes. Naturally, the T -dependenceis not as pronounced as in CDW systems with continu-ous phase transition, where timescales can change by anorder of magnitude [18–21]. Near T l , τ is reduced andremains nearly constant up to ≈
146 K, similarly to fre-quencies and linewidths of the oscillatory modes. On theother hand, τ displays an increase for T (cid:38) T l , thoughthe uncertainties of the extracted parameters start to di-verge as signals start to faint. Noteworthy, all of theobservables seem to continuously evolve through T S , de-spite the pronounced changes that can be seen e.g. in thec-axis transport [28] and optical conductivity [16, 17].Finally, we performed a F -dependence study at 10 K,the results of which are summarized in Figure 4. First,it follows from Fig. 4(a) that no significant saturation ofthe overdamped response is observed up to the highest F . Such saturation is commonly observed in fully gapedCDW systems, usually at substantially lower F [24]. Infully gaped CDW systems, such a saturation can be at-tributed to the photoinduced collapse of the CDW gapwhen the excess electronic energy exceeds the condensa- D R/R (normalised to F, arb. units) t i m e ( p s ) ( a ) n i (THz) F ( m J / c m ) ( b ) t F ( m J / c m ) ( c ) FIG. 4. (color online) Excitation density dependence of dy-namics recorded at 10 K. (a) Reflectivity transients normal-ized to excitation fluence in mJ/cm . (b) The extracted re-laxation timescale τ vs F . F = 1 mJ/cm corresponds to theabsorbed energy density of about 50 J/cm . (c) Excitationdensity dependence of the frequencies of 1.57 and 2.05 THzmodes. tion energy [24]. The absence of spectroscopic signatureof the CDW induced gap [17] suggests that such an elec-tronic gap may be limited to distinct points at the Fermilevel, while most of the Fermi surface remains unaffectedby the CDW order. In such a case, no carrier relaxationbottleneck exists and the photoexcited carriers can effec-tively transfer their energy to the lattice [42] just as inthe high- T metallic phase. Nevertheless, the fact thatsignal amplitudes do show a strong T -dependence, whichis correlated with the intensity of superlattice reflections[10], provides a strong evidence for the existence of thecoupled electronic order. Moreover, we note that the re-laxation timescale τ , as well as the collective modes areaffected by the increasing excitation density in a similarfashion as in prototype CDW systems [24]. From thedata in Fig. 4(a) it is clear that spectral weights of os-cillatory modes show a sub-linear F -dependence. Themost prominent are however the strong F -dependence of τ and softening of the 1.57 THz mode, shown in pan-els (b) and (c). Both display similar behavior as seen inK . MoO [24]. Especially τ ( F ) implies a continuoussuppression of the underlying electronic order with in-creasing F , providing further support to the assignmentof the fast decaying component to an overdamped mode,describing the recovery of the electronic part of the orderparameter [19, 21].Our results clearly demonstrate the existence of CDWcollective modes in BaNi As . Their T-dependence pro-vides further insights to the relation of CDWs and thestructural phase transition. While the XRD data [10, 14]clearly show two distinct modulations in the tetragonaland triclinic phases, the collective modes show no dis-continuities at T S . This suggests that I-CDW evolvesfrom the I-CDW by gaining additional periodicity alongthe c-axis. The sequence of phase transitions thus sug-gests a CDW driven nematicity in BaNi As which maybe linked also to the structural phase transition. The T - and F -dependence of the overdamped response implythe existence of an associated charge gap, which mustbe strongly directional. As far as the microscopic ori-gin of the charge instability driving the CDW order inBaNi As is concerned, recent photoemission data [43]suggest the band reconstruction to be consistent with theproposed orbital-selective Peierls instability [44]. Such ascenario is supported also by the finding of Ni-Ni dimers[14]. In this view, systematic doping and pressure depen-dent studies may provide valuable additional clues to theunderlying microscopic interactions.This work was funded by the Deutsche Forschungsge-meinschaft (DFG, German Research Foundation) - TRR288 - 422213477 (projects B03 and B08). The contribu-tion from M.M. was supported by the Karlsruhe NanoMicro Facility (KNMF). R.H. acknowledges support bythe state of Baden-W¨urttemberg through bwHPC. [1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,J. Am. Chem. Soc. , 3296 (2008).[2] F.C. 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