Breakdown of single spin-fluid model in heavily hole-doped superconductor CsFe2As2

TL;DR

This study reveals the breakdown of the single spin-fluid model in heavily hole-doped CsFe2As2 using site-selective NMR, highlighting coexistence of localized and itinerant spins and the emergence of a coherent state at low temperatures.

Contribution

First observation of the breakdown of the single spin-fluid model in CsFe2As2, demonstrating coexistence of localized and itinerant spins and proposing a Kondo liquid scenario.

Findings

Distinct temperature-dependent behavior of Knight shift and relaxation rates at 133Cs and 75As.

Breakdown of single spin-fluid model due to coexistence of localized and itinerant spins.

Recovery of single spin-fluid behavior at low temperatures with a coherent state.

Abstract

Although Fe-based superconductors are multiorbital correlated electronic systems, previous nuclei magnetic resonance (NMR) measurement suggests that a single spin-fluid model is sufficient to describe its spin behavior. Here, we firstly observed the breakdown of single spin-fluid model in a heavily hole-doped Fe-based superconductor CsFe2As2 by site-selective NMR measurement. At high temperature regime, both of Knight shift and nuclei spin-lattice relaxation at 133Cs and 75As nuclei exhibit distinct temperature-dependent behavior, suggesting the breakdown of single spin-fluid model in CsFe2As2. This is ascribed to the coexistence of both localized and itinerant spin degree of freedom at 3d orbits, which is consistent with orbital-selective Mott phase. However, single spin-fluid behavior is gradually recovered by developing a coherent state among 3d orbits with decreasing temperature. A Kondo liquid scenario is proposed for the low-temperature coherent state. The present work sets strong constraint on the theoretical model for Fe-based superconductors.

Equations

$$K_s(T)=\sum _{\sigma }{A}_{\sigma }{\chi }_{\sigma }(T),(\sigma =xz,yz,xy,z^2,x^2+y^2)$$

Full text

In high-Tc cuprate superconductors, single spin-fluid model has been widely adopted as a theoretical starting point although at least one 3d and two 2p orbits from copper and oxygen sites should be considered together in theoretical model in principleLee . The basis of such hypothesis is mostly based on the celebrated concept of Zhang-Rice singletZhang , which successfully converts the complex reality into single band t-J model. Such single spin-fluid model has been validated by early site-selective nuclei magnetic resonance (NMR) measurement on 89Y, 63Cu and 17O nuclei in YBa2Cu3O6+xAlloul ; Takigawa .

In Fe-based superconductors, the multiorbital nature is a key factor to understand its basic propertiesYi . Considering correlation effect due to Hund′s coupling, single spin-fluid model should be insufficient in this caseYin2 . However, previous site-selective NMR measurement on F-doped LaOFeAs found that Knight shift and nuclei spin-lattice relaxation on different nuclei are nearly identicalGrafe , including 75As, 57Fe, 19F and 139La nuclei. This result suggests a single spin-fluid model, which is consistent with weak coupling theory based on itinerant nature of Fe 3d electronsHirchfeld ; Chubukov . Similar behavior was also observed in many other Fe-based superconductorsMa1 ; Kitagawa ; Ma2 . On the other hand, strong coupling theory based on local nature of Fe 3d electrons has also been proposed for Fe-based superconductorsYu , in which the coexistence of itinerant and localized electrons at different 3d orbits would appear in a so-called orbital-selective Mott phaseAnisimov ; Medici1 ; Georges . Recently, orbital-selective Mott phase has been widely observed in FeSe-derived superconductors by angle-resolved photoemission spectroscopy (ARPES)Yi1 ; Yi2 . However, site-selective NMR experiment has not yet observed any breakdown of single spin-fluid model in FeSe-derived superconductorsMa1 .

Very recently, a similar orbital-selective Mott phase has also been proposed in heavily hole-doped Fe-based superconductors AFe2As2 (A = K, Rb, Cs)Hardy ; Medici2 . Furthermore, a so-called “Knight shift anomaly” phenomenon has been observed by 75As NMR in AFe2As2 (A = K, Rb, Cs)Wu , which hints a possible deviation from single spin-fluid model. In order to further examine the single spin-fluid model in heavily hole-doped Fe-based superconductors AFe2As2 (A = K, Rb, Cs), we conducted a site-selective NMR experiment on CsFe2As2 single crystal by measuring 133Cs and 75As nuclei.

As shown in Fig.1a, considering the spatial distribution of 3d orbits, the 3d orbits at Fe sites could be divided into two categories. The first category includes 3$d_{xy}$ and 3$d_{x^{2}+y^{2}}$ and the second one includes 3$d_{xz}$, 3$d_{yz}$ and 3$d_{z^{2}}$. It’s very obvious that the orbits in second category have much larger spatial distribution along c-axis than that in the first one. In Fe-based superconductors, the dominated hyperfine interaction between 3d electrons at Fe site and 75As nuclei is verified to be transferred hyperfine interaction mediated by 4s orbit of 75AsKitagawa2 . In this case, the overlap between 3d and 4s orbits would largely determine the strength of the transferred hyperfine interaction. Therefore, in principle, the electrons on different 3d orbits have different transferred hyperfine interaction with 75As nuclei as shown in Fig.1a. We could express the spin part of Knight shift from different 3d orbits as the following equation:

[TABLE]

$A_{\sigma}$ is the hyperfine coupling tensor from different 3d orbits. $\chi_{\sigma}(T)$ is the orbital-dependent local spin susceptibility. Considering similar transferred hyperfine interaction, the 133Cs nuclei in spacer layer with distinct out-of-plane distance to Fe site would only have significant overlap with the 3d orbits in above second category, suggesting an orbital-selective NMR probe. Based on this fact, the site-selective NMR by measuring both 75As and 133Cs nuclei would have the ability to examine single spin-fluid model in our case. Our following results unambiguously confirm the breakdown of single spin-fluid model in CsFe2As2.

High-quality CsFe2As2 single crystals are grown by the self-flux techniqueWang . All NMR measurement on 75As and 133Cs nuclei are conducted from 2 K to 300 K under an external magnetic field of 14 Tesla parallel to c axis. The nuclei spin number $I_{nuclei}$ for 75As and 133Cs nuclei are 3/2 and 7/2 respectively. The standard full spectrum of 75As and 133Cs nuclei are shown in Fig.1b. There are three transition lines for 75As nuclei and seven transition lines for 133Cs nuclei. For 133Cs nuclei, all NMR peaks have a similar linewidth of $\sim$20 KHz at 2 K, suggesting a magnetic broadening origin. This is also consistent with small quadrupole frequency below. For 75As nuclei, the linewidth for satellite peaks and central peak are $\sim$300 KHz and $\sim$30 KHz at 2 K, indicating that the linewidth of satellite peaks is dominated by quadrupole broadening. Similar behavior has already been seen in previous studyLi . By measuring the separation between each transition lines, the quadrupole frequency $\upsilon$Q for 75As and 133Cs nuclei are determined to be $\sim$13.6 MHz and $\sim$0.058 MHz respectively. Both of Knight shifts for 75As and 133Cs nuclei are determined by measuring the frequency position of the central transition line. Nuclei spin-lattice relaxations rate 1/T1 are also measured on the central transition line for both 75As and 133Cs nuclei.

The main results in this letter are shown in Fig.2. As shown in Fig.2a, the temperature-dependent Knight shift of 75As (75**K) nuclei exhibits a characteristic crossover behavior. At high temperature regime, 75**K is gradually increasing as temperature decreasing. This is also consistent with high-temperature bulk magnetic susceptibility, which suggests a localized spin behaviorWu . As temperature further decreasing, 75**K shows a maximum and then starts to decrease with lowering temperature. Below 20 K, 75**K becomes saturated and shows a temperature-independent behavior. Above temperature-dependent behavior has been ascribed to an incoherent-to-coherent electronic crossover, which is also observed in KFe2As2 and RbFe2As2 with different crossover temperatureWu . In sharp contrast, the remarkable crossover behavior in temperature-dependent Knight shift of 75As nuclei is completely absent in that of 133Cs nuclei. As shown in Fig.2a, the temperature dependent Knight shift of 133Cs (133**K) nuclei shows a monotonous decreasing in the whole temperature range. The localized spin behavior as shown in high-temperature bulk susceptibility and 75**K does not show up in 133**K. This result indicates that the localized spin behavior probably comes from 3$d_{xy}$ or 3$d_{x^{2}+y^{2}}$ orbits. As we mentioned before, the hyperfine interaction between 3d electrons and 133Cs nuclei is dominated by the transferred hyperfine interaction which is dependent on the overlap between 3d orbits at Fe site and 6s orbits at Cs site. Since both of 3$d_{xy}$ or 3$d_{x^{2}+y^{2}}$ orbits at Fe site has less overlap with 6s orbits at Cs site due to limited spatial distribution along c axis, the transferred hyperfine interaction would be not sensitive to 3$d_{xy}$ or 3$d_{x^{2}+y^{2}}$ orbits. In this case, we could ascribe the origin of electronic crossover behavior observed by 75As nuclei to the 3$d_{xy}$ or 3$d_{x^{2}+y^{2}}$ orbits. Based on previous theoretical calculationHardy ; Backes , the 3$d_{x^{2}+y^{2}}$ orbit has much less mass renormalization effect than other 3d orbits. Considering this point, the high-temperature localized spin behavior could only be ascribed to 3$d_{xy}$ orbit, which is also consistent with that the 3$d_{xy}$ orbit has the maximum mass renormalization effect among all 3d orbitsHardy ; Backes . Therefore, we believe that the temperature dependence of 133**K is dominated by itinerant 3d orbits but the temperature dependence of 75**K, especially for the incoherent-to-coherent crossover, is mainly dominated by localized 3$d_{xy}$ orbit. This result strongly proves the breakdown of single spin-fluid model in CsFe2As2. By scaling both temperature-dependent 75**K and 133**K, we found an identical temperature dependent behavior below T∗ $\sim$ 75 K. As shown in the inset of Fig.2a, single spin-fluid behavior is recovered below T∗. This result indicates that, although single spin-fluid model is broken above T∗ due to coexistence of localized and itinerant 3d electrons, a coherent state involving both localized and itinerant 3d electrons appears below T∗ which still follows single spin-fluid model. Similar crossover behavior was also observed in FeSe-derived superconductors by ARPES, in which the high-temperature incoherent state is ascribed to orbital-selective Mott phaseYi1 ; Yi2 . Here, we also believe that a similar orbital-selective Mott phase might appear above T∗ in CsFe2As2. Low-temperature ARPES and STM experiments have already observed a coherent peak from 3d**xy orbit close to Fermi level below 20 K in KFe2As2Fang . Further ARPES experiment with whole temperature range is needed to verify the exact nature of the high-temperature incoherent state in CsFe2As2.

In Fig.2b, we also measured the temperature dependent 1/T1 for both 75As and 133Cs nuclei. Similar to Knight shift result, the temperature-dependent 1/T1 also shows a distinct temperature-dependent behavior for both 75As and 133Cs nuclei above T∗. For 133Cs nuclei, the temperature-dependent 1/T1 follows an approximate power-law behavior with 1/T1 $\sim$ T1.36, which looks like a strange metallic behavior. For 75As nuclei, the temperature-dependent 1/T1 is almost temperature independent, which is consistent with a localized moment behaviorWu . This result further confirms the above conclusion on the breakdown of single spin-fluid model above T∗. Below T∗, an identical temperature dependent behavior for both 75As and 133Cs nuclei with 1/T1 $\sim$ T0.75 appears as shown in the inset of Fig.2b. This result is consistent with the formation of a coherent state below T∗. A deviation from T0.75 power-law behavior is also observed at very low temperature. This is due to the appearance of two-component behavior in spin-lattice relaxation decay. The details has been discussed in our previous work and we found that such two-component behavior is dependent on external magnetic fieldWu ; Li . When we measure nuclei spin-lattice relaxation under zero field, a perfect spin-lattice relaxation decay with single component is observed and the T0.75 power-law behavior is extended to the lowest temperatureWu . Based on this observation, we ascribe the low-temperature T0.75 power-law behavior to the characteristic property of the low-temperature coherent state. The field-induced deviation from T0.75 power-law behavior due to two-component behavior in spin-lattice relaxation decay might be other novel effect but this is not the focus in this letter.

Based on above results on Knight shift and nuclei spin-lattice relaxation, we found that the high-temperature incoherent state above T∗ looks like a so-called orbital-selective Mott phaseAnisimov ; Medici1 ; Georges , in which 3dxy orbit is probably localized and other 3d orbits remain itinerant. As shown in Fig.3a, orbital-selective Mott phase has already been proposed in phase diagram based on strong coupling theoryYu ; Medici1 . Previous theoretical study suggests that the 3dxy orbit would firstly occurs orbital-selective Mott localization among all 3d orbits in AFe2As2 (A = K, Rb, Cs)Hardy ; Backes . This is consistent with our present site-selective NMR results. In detail, the contrasting temperature dependence of 133**K and 75**K suggests that the orbital-selective Mott localization or at least the strongest correlation effect happens on 3dxy orbit, which leads to a localized spin behavior above T∗. Further ARPES experiment would be expected to verify the exact nature of 3dxy orbit above T∗.

Below T∗, a coherent state between localized and itinerant 3d orbits is developed, which is also verified by low-temperature ARPES and STM results on KFe2As2Fang . How to understand the underlying mechanism of such incoherent-to-coherent crossover? In fact, incoherent-to-coherent crossover has already been proposed in early dynamical mean field theory (DMFT) by K. Haule and G. KotliarHaule , in which each 3d orbit would have a different crossover temperature and the lowest one determines the crossover temperature for whole systemYin . Recently, this scenario has been further developed by using numerical renormalization group as a viable multi-band impurity solver for DMFT, suggesting that strong Kondo-type screening correlation exists during the incoherent-to-coherent crossoverStadler . On the other hand, our previous NMR study also observed “Knight shift anomaly” and relevant scaling behavior in AFe2As2 (A = K, Rb, Cs), which are ascribed to emergent Kondo lattice behavior of 3d electron systemWu . Based on all these facts, as shown in Fig.3b, we proposed that the emergent coherent state below T∗ might be treated as a Kondo liquid state similar as that in heavy fermion system with f-electronYang1 ; Yang2 .

In f-electron heavy fermion system, Kondo liquid state is an emergent state due to collective Kondo coupling between localized and itinerant electrons. In Kondo liquid state, the localized spin degree of freedom would be screened out by itinerant electrons, which leads to the decomfinement of localized moments. In our case, we also believe that a similar decomfinement of localized 3d electrons happens due to certain Kondo-type coupling between localized and itinerant 3d electrons, such as off-site Kondo couplingAnisimov2 . If this scenario is finally validated, the Kondo-type coupling between localized and itinerant spin degree of freedom for 3d electrons should be an important ingredient in effective theoretical model for Fe-based superconductorsWeng . This would stimulate further theoretical investigation in AFe2As2 (A = K, Rb, Cs) system and bring new understanding on the mechanism of superconducting pairing in Fe-based superconductors.

Finally, we would like to address that the strong coupling feature observed in AFe2As2 (A = K, Rb, Cs) is probably due to the Mott insulating phase at 3d5 configurationYu ; Medici2 . Based on DMFT calculation, the realization of Mott insulating phase would be much easier at half filling than other integer fillingsGeorges . For example, the critical mutual Coulomb replusion (Uc) for Mott transition has a minimum at half filling. For 3d electron system, the half filling is 3d5 configuration. In Fe-based superconductors, the parent compound with 3d6 configuration is indeed a bad metal but not Mott insulator. However, we could expect a real Mott insulating phase appears at 3d5 configuration and this has already been proposed in previous theoryMedici2 . In this case, when we doped considerable holes from parent compound with 3d6 configuration, the system is actually approaching to Mott insulating phase at 3d5 configuration. Therefore, the emergence of orbital-selective Mott phase between 3d5 configuration and 3d6 configuration is not a surprising in strong coupling scenario. In sharp contrast, when we doped electrons from parent compound with 3d6 configuration, the correlation effect would becomes weaker during the evolution from 3d6 configuration towards 3d7 configurationYu ; Georges . This is consistent with experimental results on Co-doped BaFe2As2Medici2 . In cuprate superconductors, the most novel strongly correlated physics (such as pesudogap, stripe, nematicity, charge order, etc.) always emerges in the underdoped regime with hole dopingKeimer . Here, in Fe-based superconductors, considering above Mott physics at 3d5, the most novel strongly correlated physics would happen in the overdoped regime with hole doping from parent compound at 3d6. It needs further experimental and theoretical survey to figure out the exact nature of strongly correlated physics in this regime.

This work is supported by the National Key R$\&$D Program of the MOST of China (Grant No. 2016YFA0300201 2017YFA0303000), the National Natural Science Foundation of China (Grants No. 11522434, 11374281, U1532145), Science Challenge Project (Grants No. TZ2016004), the Fundamental Research Funds for the Central Universities and the Chinese Academy of Sciences. T. W. acknowledges the Recruitment Program of Global Experts and the CAS Hundred Talent Program.