Avoided quantum criticality and magnetoelastic coupling in BaFe{}_{2-x}Ni{}_{x}As{}_{2}

Avoided quantum criticality and magnetoelastic coupling in BaFeNiAs

Xingye Lu Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    H. Gretarsson Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada    Rui Zhang Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    Xuerong Liu Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA    Huiqian Luo Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    Wei Tian Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    Mark Laver Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen, Switzerland Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark    Z. Yamani Canadian Neutron Beam Centre, National Research Council, Chalk River, Ontario, K0J 1P0 Canada    Young-June Kim Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada    A. H. Nevidomskyy Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA    Qimiao Si Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA    Pengcheng Dai pdai@utk.edu Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
July 26, 2019
Abstract

We study the structural and magnetic orders in electron-doped BaFeNiAs by high-resolution synchrotron X-ray and neutron scatterings. Upon Ni-doping , the nearly simultaneous tetragonal-to-orthorhombic structural () and antiferromagnetic () phase transitions in BaFeAs are gradually suppressed and separated, resulting in with increasing as was previously observed. However, the temperature separation between and decreases with increasing for , tending towards a quantum bi-critical point near optimal superconductivity at . The zero-temperature transition is preempted by the formation of a secondary incommensurate magnetic phase in the region , resulting in a finite value of  K above the superconducting dome around . Our results imply an avoided quantum critical point, which is expected to strongly influence the properties of both the normal and superconducting states.

pacs:
74.70.Xa, 75.30.Gw, 78.70.Nx

A determination of the structural and magnetic phase diagram in correlated electron materials is important for understanding their underlying electronic excitations. In the iron pnictides, superconductivity arises at the border of both antiferromagnetic (AF) and structural orders kamihara (); cruz (); qhuang (); mgkim11 (); dai (). This motivates the exploration of quantum critical points, where the transition temepratures for such orders are continuously suppressed to zero by a non-thermal control parameter. For the iron pnictide superconductors derived from electron or hole doping of their parent compounds, the most heavily studied materials are probably the electron-doped BaFeAs (where Co, Ni) because of the availability of high-quality single crystals sefat (); ljli (); nni08 (); jhchu09 (); prozorov (); clester (); dkpratt (); christianson09 (); mywang11 (); dkpratt11 (); hqluo (); mgkim12 (); nandi (). In the undoped state, BaFeAs exhibits a tetragonal-to-orthorhombic structural transition at temperature and an AF phase transitions below nearly the same temperature K qhuang (); mgkim11 (). Upon electron-doping of BaFeAs via partially replacing Fe by Co or Ni, various experiments, including transport nni08 (); jhchu09 (), neutron clester (); dkpratt (); christianson09 (); mywang11 (); dkpratt11 (); hqluo (), and high-resolution X-ray scattering mgkim11 (); nandi () reveal that the structural () and magnetic () phase transition temperatures in BaFeAs gradually decrease and separate with increasing , and have for all doping levels. In the initial X-ray prozorov () and neutron clester () scattering work on BaFeCoAs, it was suggested that the separated and smoothly extend into the superconducting dome, resulting in distinct structural and magnetic quantum critical points at different . Subsequent X-ray nandi () and neutron dkpratt (); christianson09 (); mywang11 () scattering experiments on superconducting BaFeAs samples with coexisting AF order revealed that superconductivity actually competes with the static AF order and lattice orthorhombicity. As a consequence, the smoothly decreasing and are reported to bend back below , and the orthorhombic structure above for optimally doped sample evolves back to a tetragonal structure well below (termed the “re-entrant” tetragonal phase) nandi ().

Figure 1: (a)Electronic phase diagram of BaFeNiAs as a function of Ni doping as determined from our neutron and X-ray scattering experiments. The PM Tet, PM Ort, AF Ort, IC Ort are paramagnetic tetragonal, paramagnetic orthorhombic, commensurate AF orthorhombic, incommensurate AF orthorhombic phases, respectively. The AF Ort, IC Ort, and PM Tet structures in the superconducting (SC) phase are clearly marked. The inset shows the expanded view of , , , and temperature dependence of the orthorhombic lattice distortion order parameter . The dashed region in the inset indicates the presence of a single Gaussian structural peak. (b) Schematic theoretical phase diagram for an avoided quantum bi-critical point.

Although previous neutron clester (); dkpratt (); christianson09 () and X-ray diffraction nandi () experiments have established the magnetic and structural phase transitions in BaFeCoAs, similar measurements have not been carried out on BaFeNiAs. In this Letter, we describe neutron and X-ray scattering studies of structural and magnetic phase transitions in BaFeNiAs, focusing on materials near optimal superconductivity [Fig. 1(a)]. While neutron scattering experiments on BaFeAs revealed a commensurate-to-incommensurate AF phase transition near optimal superconductivity dkpratt11 (); hqluo (); mgkim12 (), much remains unknown about the temperature and doping evolution of the orthorhombic lattice distortion for samples with an incommensurate AF order. Here, we find that for samples with commensurate AF order (), similar to the earlier results on BaFeCoAs clester (); dkpratt (); christianson09 (); nandi (). However, and tend to re-converge for larger values of : decreases for . This implicates a quantum bi-critical point at , which is interrupted by a secondary short-range incommensurate AF order with very small ordered moment hqluo (). The resulting overall phase diagram is illustrated schematically in Fig. 1(b). Our results are important to clarifying the nature of the purported quantum critical point in the carrier-doped iron pnictides, as inferred from the NMR Ning (); Ning10 (), thermoelectric Gooch09 (), and ultrasonic yoshizawa () measurements, as well as its connection with the quantum critical point of the iso-electronically tuned iron pnictides that was predicted by theory  Si-PNAS () and observed by extensive experiments delaCruz10 (); kasahara ().

Figure 2: (a) Transverse scans along the direction at different temperatures for BaFeNiAs with . The magnetic scattering each temperature was obtained by subtracting the K data as background. The change of the peak width between 18 K and 28 K indicates the emergence of the short range incommensurate AF order. Temperature dependence of the AF peak normalized to the weak nuclear Bragg peak intensity for (b) , (c) , and (d) and 0.108. The ’s and ’s are marked by vertical arrows. Although there are two-orders of magnitude magnetic scattering intensity reduction from to 0.0104, the ’s of the materials only decrease from K to K. The data at 7 K for was obtained by subtracting 50 K data as background.

We have carried out neutron scattering experiments on BaFeNiAs with and 0.108 using RITA-II cold neutron triple-axis spectrometer in Paul-Scherrer Institute, HB-1A thermal triple axis spectrometer at High-Flux Isotope Reactor (HFIR), Oak Ridge National Laboratory, and C5 triple-axis spectrometer at the Canadian Neutron Beam Centre, Chalk River Laboratories hqluoprb (). We have also performed high-resolution synchrotron X-ray diffraction (XRD) experiments on identical BaFeNiAs samples using beam line X22C at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory. The details of the experimental procedure are given in the Supplementary Material note (). Although neutron scattering probes the bulk sample whereas the length scale for XRD is typically about 5 micron rutt (), both techniques are measuring the intrinsic properties of these materials.

Figure 3: Temperature evolution of the orthorhombic and Bragg peaks for BaFeNiAs. Data in (a) is for , (b) down to 10 K, (c) down to 2 K, and (d) where one can only see peak broadening due to orthorhombic lattice distortion. These measurements were performed with keV synchrotron X-ray. The data were collected while warming system from base temperature to a temperature well above .

We first describe the determination of the Nel temperatures for BaFeNiAs using neutron scattering. Figure 2(a) shows transverse scans along the direction at different temperatures for sample. Consistent with earlier results hqluo (), a well-defined commensurate AF order appears below 44 K. Figure 2(b) shows temperature dependence of the magnetic order parameter. Again, consistent with earlier results dkpratt11 (); hqluo (); mgkim12 (), the AF order appears approximately below K and is suppressed from the onset of . Figure 2(c) plots similar data for and , showing and K, respectively hqluo (). In the previous work on optimally electron-doped BaFeNiAs schi (), it was suggested, based on cold neutron data on mosaic crystals (0.6 g) counting 1 min/point, that there is no measurable static AF order. Our new measurements on the sample (0.34 g) with much longer counting time (30 mins/piont on HB-1A) reveal a weak static AF order with magnetic scattering 5 times smaller than that of [Figs. 2(c) and (d)]. Similar measurements on also show the presence of a weak static AF order, which is 50% smaller than that of the sample. In spite of their small moments, the temperature dependence of the magnetic order parameters for both samples indicate that their Nel temperatures are essentially unchanged at K [Fig. 2(d)]. Finally, we find no evidence of static AF order for a sample (0.5 g) by counting 40 mins/point on C5 [Fig. 2(d)].

Figure 4: (a) Orthorhombic lattice distortion as a function of temperature for BaFeNiAs. The data denoted by the filled symbols are derived from fitting and Bragg peaks by two peaks, while the open symbols are data obtained from deconvolving the instrumental resolution-limited peak at a temperature above . The magnitude of for was multiplied by a factor of 4 for clarity. The vertical arrows indicate positions of and . Comparison of the temperature dependence of the magnetic order parameter and orthorhombic lattice distortion for (b) and (c) . (d) Ni-doping dependence of the magnetic Bragg peak intensity at 11 K and . The vertical dashed line indicates the boundary between commensurate and incommensurate AF order. (e) Comparison of Co nandi () and Ni doping dependence of . In both cases we see structural quantum critical point near optimal superconductivity at . (f) Electron doping dependence of .

In order to compare the onset of orthorhombicity with antiferromagnetism, high-resolution X-ray scattering measurements were performed on the samples identical to those used for neutron scattering. In all cases, we carried out longitudinal scans along the direction. Figure 3(a) shows the outcome for which has a superconducting K. At K, a temperature well above , we see a single instrumentation resolution-limited peak, consistent with a tetragonal lattice. On cooling to  K, 30 K and 17 K, the single peak splits into two peaks with increasing peak separations as temperature decreases down to . Upon further cooling below , the peak separations become smaller, as if the system turns back toward the tetragonal structure nandi (). Figure 3(b) shows similar temperature dependent scans for . Although the split peaks appear to become a single peak at K, its width is still larger than that in the tetragonal phase ( K), suggesting that the nearly optimal superconductor has an orthorhombic lattice distortion at K. To see how such orthorhombic lattice distortion evolves at lower temperatures, we carried out additional measurements using a cryostat capable of going down to 2 K. The longitudinal scans in Fig. 3(c) show broad peaks at temperatures below 10 K, suggesting the presence of an orthorhombic lattice structure even at 2 K.

To quantitatively analyze the temperature dependence of the orthorhombic lattice distortion, we define lattice orthorhombicity , where and are lattice parameters of the orthorhombic unit cell nandi (). Figure 4(a) shows the temperature dependence of for BaFeNiAs with , and 0.1. Figures 4(b) and 4(c) compare the ordered moment squared, , with the lattice orthorhombicity , and their similar temperature dependence suggests a strong magnetoelastic coupling.

The optimally doped sample ( K) deserves special attention. Its temperature dependent scans are shown in Figure 3(d). Although we can no longer see the double peaks, we observe a peak broadening that does not disappear at low temperatures. We therefore used the full width at half maximum (FWHM) of the peak in order to determine the lattice orthorhombicity , similar to the analysis of BaFeCoAs by Nandi et al. nandi (). The deduced temperature dependence of is shown in Fig. 4(a) with red squares and appears to have a sharp cusp near the superconducting . We conjecture that this cusp occurs because the electron-lattice coupling results in a lattice response to the superconducting fluctuations near . At the lowest temperature measured,  K, the value of is too small () in order to unambiguosly claim the orthorhombicity. However, taken together with magnetization squared for incommensurate AF order, see Fig. 4(c), which has a similar temperature dependence, we conclude that a weak static AF order likely coexists with orthorhombic lattice distortion in the optimally superconducting BaFeNiAs, different from the re-entrant tetragonal transition seen in BaFeCoAs nandi ().

Figure 4(d) shows the Ni-doping dependence of and the ordered moment squared , while Figure 4(e) compares the doping dependence of in BaFeNiAs and in the previously reported BaFeCoAs nandi (). The essentially continuous suppresion of both and near provides further evidence for an extrapolated quantum critical point. For the magnetic ordering, this represents a new understanding. On the other hand, for the orthorhombic distortion, the continuos suppression of with doping was already anticipated by ultrasound spectroscopy measurements fernandes (); yoshizawa ().

Theoretically, this can be considered through a Landau–Ginzburg action for such a criticality, ; the three terms, describing the magnetic and lattice parts, respectively, and their coupling, are given in the Supplementary Material note (). This model resembles the previously studied O(3)Z model Si-PNAS (), except that here the lattice quantum field is endowed with its own dynamics and undergoes Landau damping , making it inherently quantum critical with the dynamic exponent . In two spatial dimensions, for the field and for the fields. Because they are above/at the upper critical dimension, a quantum bi-critical point for both orders is expected in the presence of the magneto-elastic coupling . This is similar to the result of the O(3)Z model Si-PNAS (), and is indicated schematically in Fig. 1(b). Indeed, as noted above, our measurements find that and get closer to each other as the quantum critical point is approached [see Figs. 1(a) and 4(f)] and the two order parameters disappear at the same point [Fig. 4(d)]. However, the appearance of an emergent incommensurate magnetism at severely reduces the scattering rate and (in addition to modifying other parameters of the effective theory), thereby eliminating the quantum critical point. A quantum critical point preempted by an emergent order is often referred to as “avoided” quantum criticality coleman (); haule (); harrison ().

From direct measurements of the order parameters for both the AF and structural transitions, our results provide a solid basis for quantum criticality in carrier-doped iron pnictides, which has so far been indirectly deduced from the temperature dependences of magnetic, transport, or acoustic properties Ning (); Ning10 (); Gooch09 (); yoshizawa (). In addition, because the primary AF order in the electron-doped iron pnictides discussed here is commensurate, our results suggest that the quantum critical point arising under the carrier doping is surprisingly similar to that induced by iso-electronic doping  Si-PNAS (); delaCruz10 (); kasahara (); the main distinction of the carrier doping is to introduce a secondary incommensurate order. This reveals an important universality of the underlying physics for the iron pnictides under carrier and iso-electronic dopings.

Summarizing the results presented in Figs. 2-4, we show in Fig. 1(a) the refined phase diagram of BaFeNiAs, in agreement with the theoretically expected one [Fig. 1(b)]. While the phase diagram is mostly consistent with the earlier work on BaFeCoAs at low electron doping levels nandi (), our key new finding is that when approaches optimal doping, the magnetic and structural transition temperatures converge to the purported quantum bi-critical point, with both order parameters disappearing near [Fig. 4(d)] as a result of magneto-elastic coupling. However, the emergent short-range incommensurate magnetism helps the system avoid the quantum critical fate, resulting in an apparent saturation of  K above the superconducting near optimal doping , as shown in Fig. 1(a). These results elucidate the quantum criticality in the carrier-doped iron pnictides and its connection with that of the iso-electronically doped counterparts, and reveal a rich theoretical picture that should be further explored in future work.

The work at IOP, CAS, is supported by MOST (973 project: 2012CB821400 and 2011CBA00110) and NSFC (No.11004233). The work at UTK is supported by the U.S. NSF-DMR-1063866. The work at Rice University is supported by the U.S. NSF-DMR-1006985 and the Robert A. Welch Foundation Grants Nos. C-1411 and C-1818. Research at the University of Toronto was supported by the NSERC and CFI. Use of the NSLS was supported by the U.S. DOE,BES, under Contract No. DE-AC02-98CH10886. The work at the HFIR, ORNL, was sponsored by the Scientific User Facilities Division, BES, U.S. DOE.

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Supplementary material: Avoided quantum criticality and magnetoelastic coupling in BaFeNiAs

Section A: Details of the neutron and X-ray scattering experiments

Neutron scattering experiments: The RITA-II uses a pyrolytic graphite (PG) filter before the sample and a cold Be filter after the sample with the final neutron energy fixed at meV hqluo (). HB-1A spectrometer operates with a fixed incident neutron energy of meV using a double PG monochromator. The second-order contamination in the beam was removed by placing two PG filters located before and after the second monochromator. A collimation of --sample-- from reactor to detector was used throughout the measurements. C5 uses PG as monochromator and analyzer with fixed meV hqluoprb (). The sample orientation and setup are similar to those described previously hqluo (). Figure S1 shows the Ni-doping dependence of the incommensurate AF order. For BaFeNiAs samples with , we see clear incommensurate static AF order below .

X-ray diffraction experiments: The monochromator was Si(111) and incident beam energy was set at keV with spot size of mm on the samples. In all cases, the data were collected on warming from base temperature to a temperature well above .

Section B: The proposed theoretical model:
The proposed Landau–Ginzburg action is . The magnetic part (here refers to sublattice magnetization) is specified by

Here, describes the quadratic contribution of magnetic fluctuations, which includes a Landau damping  Hertz-Millis (). The quartic term describes mode-mode interaction between magnetic fluctuations on the same and on different magnetic sublattices; the last term has a negative coefficient (), favoring the collinear alignment of spins on the two sublattices  CCL (). There are also lattice parts:

The last term describes magneto-elastic coupling, leading to an Ising magnetic order when the lattice orthorhombicity develops.

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Figure 5: Ni-doping evolution of incommensurate magnetic peaks for (a) and (b) in BaFeNiAs. The data are obtained carrying out scans along the direction at different temperatuers. We obtain the net magnetic scattering at low temperatures by subtracting the high-temperature () background.
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