Unexpected Enhancement of Three-Dimensional Low-Energy Spin Correlations in Quasi-Two-Dimensional Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ System at High Temperature

TL;DR

This study reveals an unexpected increase in three-dimensional low-energy spin correlations in Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ at high temperatures, challenging existing models based solely on spin degrees of freedom.

Contribution

It demonstrates a temperature-induced transition from 2D to 3D spin correlations linked to orbital effects, providing new insights into the magnetic behavior of the system.

Findings

Spin correlations are 2D at low temperatures in superconducting samples.

Spin correlations become more 3D at temperatures above $T_c$, with increased correlation length perpendicular to Fe planes.

The transition from 2D to 3D correlations cannot be explained by spin degrees alone, indicating orbital contributions.

Abstract

We report inelastic neutron scattering measurements of low energy ($\hbar \omega < 10$ meV) magnetic excitations in the "11" system Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. The spin correlations are two-dimensional (2D) in the superconducting samples at low temperature, but appear much more three-dimensional when the temperature rises well above $T_c \sim 15$ K, with a clear increase of the (dynamic) spin correlation length perpendicular to the Fe planes. The spontaneous change of dynamic spin correlations from 2D to 3D on warming is unexpected and cannot be naturally explained when only the spin degree of freedom is considered. Our results suggest that the low temperature physics in the "11" system, in particular the evolution of low energy spin excitations towards %better satisfying the nesting condition for mediating superconducting pairing, is driven by changes in orbital correlations.

Full text

Fe-based superconductors Mazin (2010); Paglione and Greene (2010); Tranquada et al. (2014); Johnson et al. (FBS) share many similarities with the high-$T_{c}$ cuprate family, one of which being that in general both systems have parent compounds with long-range antiferromagnetic (AFM) order. When the AFM order is gradually suppressed by doping, superconductivity emerges. The surviving magnetic excitations are widely believed to play vital roles in mediating electron pairing required for superconductivity Scalapino (2012); Dai (2015). While the magnetic order in the parent compounds of both FBS and high-$T_{c}$ cuprates are always three-dimensional (3D), magnetic excitations in their superconducting derivatives are, however, in general more two-dimensional (2D) in character Hayden et al. (1991, 1996); Lumsden et al. (2009); Ramazanoglu et al. (2013). The spin excitations depend only weakly on momentum transfer perpendicular to the Fe/Cu planes. The interplanar spin correlations are significantly weaker than the in-plane correlations, suggesting the importance of reduced dimensionality for the pairing mechanism in these unconventional superconductors.

On the other hand, unlike high-$T_{c}$ cuprates where only the Cu $d_{x^{2}-y^{2}}$ orbital contributes to bands near the Fermi energy; in FBS, Fe $d_{xz},d_{yz}$ and $d_{xy}$ orbitals all have significant contributions. The multi-orbital nature of the FBS leads to a plethora of new physics. Most notably, electronic nematicity has first been found to develop in the BaFe2As2 (122) system Chu et al. (2010); Yi et al. (2011); Chu et al. (2012); Kuo et al. (2013); Shapiro et al. (2015); Lu et al. (2014), and then in other FBS as well Rosenthal et al. (2014); Baek et al. (2015); Johnson et al. (2015). It is commonly accompanied by (i) splitting of the $d_{xz}$ and $d_{yz}$ orbitals; (ii) magnetic order that breaks the $C_{4}$ rotational symmetry; and (iii) lowering of lattice symmetry from $C_{4}$ to $C_{2}$. Yet there are situations when not all these features are present. For instance, recent work on the Fe-chalcogenide superconductor (“11” compound) FeSe shows that both lattice and orbital symmetry breaking occur at low temperature without static magnetic order Baek et al. (2015). A competition between stripe-type (0.5,0.5) and Néel-type (1,0) (notations based on the two-Fe unit cell) low-energy magnetic excitations is observed instead Wang et al. (2016). Close to optimal doping in the superconducting 11 compound FeTe1-xSex, there is no structural transition or magnetic ordering that breaks the $C_{4}$ symmetry. Nevertheless, lifting of the degeneracy of the $d_{xz}$- and $d_{yz}$-derived electronic bands due to spin-orbit coupling has been observed Johnson et al. (2015), which is consistent with the lowering of $C_{4}$ symmetry of the local hybridization pattern down to $C_{2}$ in the presence of stripe-type (0.5,0.5) dynamic short-range magnetic correlations detected by neutron scattering Zaliznyak et al. (2015); Xu et al. (2016). The nematic susceptibility is also found to diverge at low temperature Kuo et al. (2016). It appears, therefore, that changes in the orbital and spin correlations may be behind various features observed in the FBS at low temperature, including nematicity. Understanding which one is the fundamental driving force is central to the debate over the superconducting (SC) mechanism Fernandes et al. (2014).

In this letter, we report inelastic neutron scattering measurements of low-energy ($\lesssim 10$ meV) magnetic excitations from a series of FeTe1-xSex samples. Since they appear to be relevant to both SC and nematicity, the behavior of low-energy spin fluctuations in FBS is of considerable interest. We show that in the SC samples, upon heating, in addition to the change of in-plane spin correlations from stripe AFM ${\bf Q}_{\rm SAF}=(0.5,0.5)$ to bi-collinear double-stripe AFM ${\bf Q}_{\rm DSAF}=(0.5,0)$ as reported before Xu et al. (2016), the development of the interplanar spin correlations for low energy spin fluctuations also becomes apparent. Specifically, the low temperature state with stripe AFM in-plane correlations is virtually 2D, with very weak correlations perpendicular to the Fe planes. The high temperature state, however, shows clear correlations between the Fe planes for slowly fluctuating spins, with the interplanar dynamic correlation length approaching the intraplanar one. Similar effects can also be achieved by changing the chemical composition toward non-superconducting (NSC) phases. Our results suggest a highly unusual cross-over from a 2D-type spin-liquid state at low $T$ to a 3D-type spin-liquid upon heating. This unexpected enhancement of 3D dynamic spin correlations with increasing temperature cannot be explained with effective spin-only models; it is likely due to the change of hybridizations between the Fe $d_{xz}$, $d_{yz}$ and $d_{xy}$ orbitals, which implies that the low temperature physics in the “11” material is orbitally driven.

The single crystal Fe1-z(Ni)zTe1-xSex samples used in this experiment were grown by a unidirectional solidification method Wen et al. (2011) at Brookhaven National Laboratory. Two SC samples were used, one with optimal doping, FeTe0.6Se0.4 (SC40) with $T_{c}\sim$ 14 K, and another with 2% Ni doping, Fe0.98(Ni)0.02Te0.55Se0.45 (Ni02) with T${}_{C}=8$ K. The two NSC samples used in these measurements are Fe1.1Te0.3Se0.7 (NSC70) and Fe0.9(Ni)0.1Te0.55Se0.45 (Ni10). The neutron scattering experiments 111We use the unit cell that contains two iron atoms. The lattice constants are $a=b\approx 3.8$ Å, and $c\approx 6$ Å. The data are described in reciprocal lattice units (r.l.u.) of $(a^{*},b^{*},c^{*})=(2\pi/a,2\pi/b,2\pi/c)$. The measurements in the $(HK0)$ plane were taken on SEQUOIA with the incident neutron beam along the sample [001], $E_{i}=50$ meV, and a chopper frequency of 360 Hz. For the measurements in the $(HHL)$ and $(H0L)$ planes taken on HYSPEC, the samples were mounted with [1$\bar{1}$0] and [010] vertically, respectively, perpendicular to the horizontal scattering plane. During the HYSPEC measurements, the in-plane orientation of the sample was rotated to cover a range of 180o with 2o step. The data were measured with $E_{i}=20$ meV and a chopper frequency of 180 Hz. The area detectors of HYSPEC covered neutrons with scattering angles from 5o to 65o. From the combined data, the constant $\hbar\omega$ slices and linear scans have been symmetrized. Measurements on BT7 were performed with final energy of 14.7 meV, collimations of open-$80^{\prime}$-$80^{\prime}$-$120^{\prime}$ and a PG filter after the sample. were performed on the time-of-flight instruments SEQUOIA (BL-17) Granroth et al. (2010) and HYSPEC (BL-14B) Winn, Barry et al. (2015) at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL); and the BT7 triple-axis-spectrometer at the NIST Center for Neutron Research.

Low-energy magnetic excitations ($\hbar\omega=7$ meV) in the $(HK0)$ plane from the SC40 and Ni10 samples are shown in Fig. 1. Here the data are integrated along the out-of-plane direction. One can see that in the SC40 sample, the low energy magnetic excitations appear around $(0.5,0.5)$ in-plane wave-vector for $T\sim T_{c}$, and there is a clear enhancement of the intensity due to the spin resonance for $T<T_{c}$. As discussed in previous work Xu et al. (2014, 2016), the low energy spectral weight from SC “11” samples shifts from ${\bf Q}_{\rm SAF}$ to ${\bf Q}_{\rm DSAF}$ in-plane wave-vector upon heating, reflecting a change of in-plane low energy spin correlations from the “stripe” type to the “double stripe/bicollinear” type. This behavior is observed in SC40 as well when the temperature is raised significantly above $T_{c}$ [Fig. 1 (c)]. The same measurements from NSC samples show that the low energy spin excitations are always around ${\bf Q}_{\rm DSAF}=(0.5,0)$ Liu et al. (2010) with little variation with $T$ [Fig. 1 (d)].

In order to probe the out-of-plane spin correlations we measured the $L$-dependence of the magnetic scattering intensities. We first performed measurements in the $(HHL)$ plane, mainly for low energies along [110] from the low temperature stripe-type correlations, marked as the solid arrow in Fig. 1 (a). In Fig. 2 we show the intensities at $\hbar\omega=6.5$ meV. This is the energy where the spin-resonance occurs in optimally-doped “11” SC samples, and also where the change of spectral weight with temperature or doping is most pronounced. In panel (a) we see that the magnetic scattering intensity forms a narrow vertical stripe along the $L$ direction around $(H,H)=(0.5,0.5)$. The breadth of the intensity along the $L$-direction indicates that the real-space correlations along the $c$-axis are weak. When the sample is heated slightly above $T_{c}$ to $T=20$ K, the extra intensity from the spin-resonance disappears but the shape of the low energy spectral weight is still defined by the vertical stripe along $L$ [panel (c)]. Linear cuts along $(0.5,0.5,L)$ are plotted in panel (b) and (d); here we see that the $L$-dependence of the intensities near ${\bf Q}_{\rm SAF}$ at low temperatures is well described by the Fe2+ magnetic form factor, suggesting strongly 2D behavior, consistent with previous reports on “11” SC samples Qiu et al. (2009). It has been observed in other FBS that the spin-resonance could have 3D dispersions Chi et al. (2009). In our case, note that the 2D spin correlation is present not only for the “spin-resonance” intensity, but also for the low energy spin excitations in the normal state for $T$ not far above $T_{c}$. When heated further to 100 K and 300 K, the stripe-type correlations are destroyed and the intensity near ${\bf Q}_{\rm SAF}$ is entirely suppressed [Fig. 2 (e)-(h)]. Similarly, no magnetic scattering is observed along $(0.5,0.5,L)$ from NSC samples (not shown) for all temperatures measured.

In the NSC samples, or in SC samples but at temperatures significantly higher than $T_{c}$, the low energy magnetic spectral weight shifts to ${\bf Q}_{\rm DSAF}$ corresponding to the bicollinear-type in-plane spin correlations. Measurements along [100] in the $(H0L)$ plane [marked as the dashed arrow in Fig. 1 (a)] are plotted in Fig. 3. Here, we show 2D slices and linear cuts at $\hbar\omega=4$ meV. The reason for this choice of energy transfer is to avoid possible contamination from an anomalous phonon mode Fobes et al. (2016) that comes in around $(0.5,0,0)$ for energies around 7 to 8 meV. Measurements from the NSC70 sample are plotted in panels (e)-(h), at $T=5$ K and 300 K. The $L$-dependence for the low energy magnetic scattering from the NSC sample is best described by two peaks around $L=\pm 0.5$ (r.l.u.), suggesting an AFM type correlation between two adjacent Fe planes 222Note that a modified magnetic form factor, with a faster fall off, is necessary to explain the absence of intensity at $L=\pm 1.5$; see Zaliznyak et al. (2015).. The intensity from the NSC sample does not change much from 5 K to 300 K, confirming that any contamination from the anomalous phonon mode (which should increase significantly with temperature due to the Bose factor) is negligible at this energy transfer.

For the SC40 sample, at base temperature (T=5 K), there is no magnetic scattering intensity near ${\bf Q}_{\rm DSAF}$ [see panels (a) and (b)], as expected. The development of spectral weight near ${\bf Q}_{\rm DSAF}$ in SC40 only becomes apparent when the temperature is well above $T_{c}$. Data measured at 300 K are shown in panels (c) and (d). In contrast to the stripe shape intensity distributed broadly along the $L$-direction in the $(HHL)$ plane at low temperature, at high temperature the magnetic scattering in the $(H0L)$ plane has a much narrower span along $L$ [panel (c)], similar to the data from the NSC sample. The linear cut along $(0.5,0,L)$ in panel (d) indicates that the intensity profile decreases much faster with $L$ than what would be expected from the magnetic form factor alone. Compared to the results from the NSC sample, one can still fit the SC40 data with two symmetric peaks [the red line in panel (d)] but there appears to be more intensity near $L=0$ from the SC sample instead, suggesting some possible FM component of spin correlations between Fe planes. If we fit the data with Lorentzian functions along $L$ and $H$ directions, we can obtain the dynamic correlation lengths for slowly fluctuating spins along different directions. For the Ni10 sample, $\xi_{c}\sim 1.6(4)$ Å and $\xi_{ab}\sim 2.2(4)$ Å; for the SC40 sample, $\xi_{c}\sim 1.4(3)$ Å (with fits to two symmetric peaks at $L=\pm 0.5$), and $\xi_{ab}\sim~{}1.7(4)$ Å. Compared to the situation at low temperature, there is a dramatic enhancement of the interplanar spin correlation in the SC sample, with the interplanar correlation length close to the in-plane one. These results demonstrate that the low energy magnetic excitations near ${\bf Q}_{\rm DSAF}$, either from the high temperature phase in the SC sample, or from the NSC sample at all temperatures, appear three-dimensional in nature.

Measurements on “11” samples with other compositions not too close to either end (FeTe or FeSe) of the phase diagram [Fig. 4 (a) and (b)] confirm this trend for slowly fluctuating spins with energy scales of a few meV — 3D-like correlations appear in NSC samples at all temperatures, or in SC samples at high temperature, while 2D correlations appear in SC samples at low temperature (temperatures lower than or comparable to $T_{c}$). The strength of the 3D spin correlations gradually diminishes with cooling in the SC sample [Fig. 4 (c)], yet in the NSC sample the spin correlations remain 3D for the entire temperature range (5 K to 300 K) measured.

The 3D spin correlations in the NSC samples are not entirely unexpected, since many, if not all of these NSC “11” samples already exhibit 3D short-range magnetic order characterized by ${\bf Q}\approx(0.5,0,0.5)$ at low temperature Wen et al. (2009). It is much more of a puzzle for the 3D spin correlation to become established at high temperature in SC “11” samples and then change to 2D upon cooling. The temperature scale for the 3D to 2D transformation is significantly higher than $T_{c}$, suggesting that it is at least not directly tied to the SC phase transition. Also, no explicit magnetic phase transition occurs in this temperature range, nor does the change of the lattice structure favor such an enhancement of the interplanar correlations — the $a/c$ ratio actually decreases at higher temperature in SC “11” samples Xu et al. (2016). Since thermal fluctuations apparently work against such a trend, it is difficult if not impossible to interpret such a spontaneous transformation as driven by spin interactions that can be modeled with a spin-only model. With orbital correlations being the other important degree of freedom in Fe-based superconductor systems, we look for possible explanations from the change of the different Fe $3d$ orbitals. ARPES measurements Yi et al. (2015) on a SC “11” sample show that in addition to the lifting of degeneracy between $d_{xz}$ and $d_{yz}$ orbitals at low temperatures due to the spin-orbit coupling, a strong renormalization of the $d_{xy}$ orbital is observed, where the $d_{xy}$ orbital spectral weight decreases at higher temperature, indicative of an orbital selective Mott transition (OSMT) de’ Medici et al. (2009); Lee et al. (2010); Yu and Si (2013). When the $d_{xy}$ orbital delocalizes upon cooling, it can hybridize and interact strongly with the $d_{xz}$ and $d_{yz}$ orbitals. These interactions can create a tendency for an instability that may break the C4 symmetry at low temperature Stanev and Littlewood (2013), thus explaining the reported growth in nematic susceptibility Kuo et al. (2016). Our results confirm that spin correlations are also significantly affected by this OSMT — when the $d_{xy}$ electrons become less itinerant and carry more local moment at high temperatures, an enhancement of the interplanar spin correlations is observed in the low-energy spin channel. This behavior is reminiscent of the orbital selective electronic localization at high temperature that was first observed in the “11” parent material FeTe Zaliznyak et al. (2015); Fobes et al. (2014). In other words, while changes in both orbital and spin channels occur in the same temperature range, the change of spin correlations is likely a result of changing orbital correlations.

Although no electronic nematic order is present in our samples at low temperature, the 2D low-energy spin excitations around (0.5,0.5) are directly related to nematicity observed in both FeSe Wang et al. (2016) and other FBS systems Lu et al. (2014). It is also noteworthy that in the “11” system, as well as in many other Fe-based superconductors, the Fermi surface at low temperature typically forms 2D cylinders at $\Gamma$ and $X$ points Sunagawa et al. (2014); Subedi et al. (2008). In the “11” system we found that the low energy magnetic excitations at high temperatures appear highly three-dimensional and are located around in-plane wave-vector ${\bf Q}_{\rm DSAF}=(0.5,0)$. If they are indeed the bosons that mediate SC pairing at low temperature, these excitations apparently need to become quasi-2D and appear near in-plane wave-vector ${\bf Q}_{\rm SAF}=(0.5,0.5)$ to satisfy the nesting conditions. With the scenario discussed above, a change in the orbital hybridization is therefore essential for this evolution to quasi-2D spin correlations to occur before superconductivity can set in. Such doping and temperature dependent changes of the orbital hybridization pattern have been recently proposed in the context of the evolution of the in-plane correlations Zaliznyak et al. (2015). Our results thus strongly support the idea that both nematicity and superconductivity in the “11” system appear to be fundamentally orbital-driven.

The work at Brookhaven National Laboratory was supported by the Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DE-SC0012704. Z.J.X. and R.J.B. are also supported by the Office of Science, Basic Energy Sciences, U.S. Department of Energy through Contract No. DE-AC02-05CH11231. The work at ORNL was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC05-00OR22725. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.The work at Nanjing University was supported by NSFC No. 11374143 and 11674157.