Cite this Article
Luo Jun, Wang Chunguang, Wang Zhicheng, Guo Qi, Yang Ji, Zhou Rui, Matano K, Oguchi T, Ren Zhian, Cao Guanghan, Zheng Guo-Qing. NMR and NQR studies on transition-metal arsenide superconductors LaRu2As2, KCa2Fe4As4F2, and A2Cr3As3. Chinese Physics B, 2020, 29(6): 067402  
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NMR and NQR studies on transition-metal arsenide superconductors LaRu2As2, KCa2Fe4As4F2, and A2Cr3As3
Luo Jun1, ‡, Wang Chunguang1, 2, Wang Zhicheng3, Guo Qi1, Yang Ji1, Zhou Rui1, 4, Matano K5, Oguchi T6, Ren Zhian1, 2, Cao Guanghan3, Zheng Guo-Qing1, 2, 5, §
Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Department of Physics, Zhejiang University, Hangzhou 310027, China
Songshan Lake Materials Laboratory, Dongguan 523808, China
Department of Physics, Okayama University, Okayama 700-8530, Japan
Institute of Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan

 

† Corresponding author. E-mail: junluo@iphy.ac.cn gqzheng123@gmail.com

Project supported by the National Natural Science Foundation of China (Grant Nos. 11674377, 11634015, and 11974405), the National Key R&D Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300502), and J. Y. also acknowledges support by the Youth Innovation Promotion Association of Chinese Academy of Sciences.

Abstract

We report 75As-nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on transition-metal arsenides LaRu2As 2, KCa2Fe4As4F2, and A2Cr3As3. In the superconducting state of LaRu2As2, a Hebel–Slichter coherence peak is found in the temperature dependence of the spin-lattice relaxation rate 1/T1 just below Tc, which indicates that LaRu2As2 is a full-gap superperconducor. For KCa2Fe4As4F2, antiferromagnetic spin fluctuations are observed in the normal state. We further find that the anisotropy rate is small and temperature independent, implying that the low energy spin fluctuations are isotropic in spin space. Our results indicate that KCa2Fe4As4F2 is a moderately overdoped iron-arsenide high-temperature superconductor with a stoichiometric composition. For A2Cr3As3 (A = Na, K, Rb, Cs), we calculate the electric field gradient by first-principle method and assign the 75As-NQR peaks to two crystallographically different As sites, paving the way for further NMR investigation.

PACS: ;74.25.nj;;74.40.-n;;74.25.Dw;
Keyword:;transition-metal arsenides;;3d and 4d orbitals;;nuclear magnetic resonance;;iron-based superconductor;
1. Introduction

Transition metal arsenides (TMAs) belong to a big family. The binary TMAs, like TaAs, TaP, NbP, and XP2 (X = Mo, W),[1] are topological Weyl semimetals, whose low energy excitations in the bulk can be viewed as chiral massless Weyl Fermions. The ternary TMAs show rich novel properties, with examples including density wave[2] and superconductivity.[3] The discovery of superconductivity in transition metal arsenide LaFeAsO1–xFx opens a door to another high-temperature superconducting family besides cuprates.[4] More importantly, the physical properties of TMAs can be tuned by chemical substitution,[5,6] doping,[4] or pressure.[7] Therefore, transition-metal arsenides provide a rich material base for exploring exotic physical phenomena.

Among the TMA family, compounds with ThCr2Si2-type layered crystal structure have attracted much attention in condensed matter physics. High temperature superconductivity in AFe2As2 (A = Ca, Sr, Ba, etc.) was induced by doping[8] or pressure.[9] Iron and ruthenium are in the same group. Many Ru-based compounds show unconventional superconductivity.[10,11] Naturally, it is practical to look for unconventional superconductivity in ruthenium-based compounds with ThCr2Si2 structure. Recently, Guo et al. found that LaRu2As2 shows superconductivity with zero resistivity at 6.8 K.[12] LaRu2As2 and LaRu2P2 are isostructural and their physical properties have been studied by ab initio calculations,[13,14] which indicate that the conduction band electrons are mainly contributed from La-5d and Ru-4d orbitals.

KCa2Fe4As4F2 is a newly discovered superconductor with separated double Fe2As2 layers, whose Tc reaches as high as 33.5 K.[15] It can be regarded as the intergrowth of 1111-type CaFeAsF and 122-type KFe2As2.[15] The Fe valence in CaFeAsF and KFe2As2 is +2 and +2.5, respectively. Appointing the insulted compound CaFeAsF as the parent compound, KCa2Fe4As4F2 can be viewed as a self hole-doping system, which is consistent with the Hall effect measurements and electronic structures calculations.[15,16] In the superconducting state, the inverse square penetration depth () with a linear temperature dependence detected by muon spin rotation (μSR) suggests a line node in the gap function of KCa2Fe4As4F2 and CsCa2Fe4As4F2.[17,18] However, optical conductivity, thermal conductivity, and ARPES measurements suggest a nodeless gap.[19–21]

A2Cr3As3 (A = Na, K, Rb, Cs) is the first chromium-based superconducting family under ambient pressure, with Tc ranging from 8.0 K to 2.2 K.[22–25] In the crystal structure, [Cr3As3]∞ chains are separated by the alkaline metal. Owing to the asymmetric distribution of the alkaline metal, there exists two types of As sites. Density function theory (DFT) calculations show that the Fermi surface is formed by one three-dimensional (3D) band γ and two quasi-one-dimensional (1D) bands α and β.[26,27] Experimental results point to unconventional superconductivity in A2Cr3As3.[28–34] In the normal state, ferromagnetic fluctuation (FM) was revealed[29] and further found to be enhanced by small radius alkaline metal replacement.[35] Similar to iron-pnictide superconductors, A2Cr3As3 shows a close relationship between magnetic fluctuations and superconductivity. More recently, nontrivial topological aspects in A2Cr3As3 have been pointed out.[35,36]

In this work, we perform nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on LaRu2As2, KCa2Fe4As4F2, and A2Cr3As3. We investigate the properties of LaRu2As2 and KCa2Fe4As4F2. For A2Cr3As3, we assign the one to one correspondence between the two NQR transition lines and the two As crystallographic sites, by combining with the first-principle calculation.

2. Experiment

Polycrystalline LaRu2As2 and KCa2Fe4As4F2 samples were grown by conventional solid state reaction, as previously reported in Refs. [12,15]. The single crystals of A2Cr3As3 were synthesized by high-temperature solution method with A = Cs, Rb, K, Na0.75K0.25 or ion-exchanged reaction with A = Na, the details of synthesis can be found in Refs. [22–25]. The Tc of LaRu2As2 and KCa2Fe4As4F2 were determined by AC susceptibility using an in-situ NMR coil. The electric field gradient (EFG) of K2Cr3As3 was calculated by the all electron full-potential linear augmented plane wave (FLAPW) method implemented in Hiroshima Linear-Augmented-Plane-Wave (HiLAPW) code with generalized gradient approximation including spin–orbit coupling.[37] The NMR and NQR spectra were obtained by scanning RF frequency and integrating spin-echo intensity at a fixed magnetic field H0. The spin-lattice relaxation time T1 was measured by the saturation-recovery method. The T1 was obtained by fitting the nuclear magnetization M(t) to 1–M(t)/M0 = exp(–3t/T1) in NQR case and 1–M(t)/M0 = 0.1exp(–t/T1)+0.9exp(–6t/T1) in NMR case, where M(t) and M0 are the nuclear magnetization at time t after the single comb pulse and at thermal equilibrium, respectively.

3. Results and discussion
3.1. LaRu2As2

Figure 1 shows the temperature dependence of the resonance frequency of the NMR coil. The superconducting transition temperature Tc of the sample is found to be around 6.2 K, which is similar to an earlier report of Tc = 6.8 K determined by DC susceptibility measurement.[12] There are two primitive cells with 10 atoms in one unit cell of LaRu2As2 as shown in the inset of Fig. 1. The As–Ru–As blocks are intercalated by La atoms, and they are alternately arranged along the c axis. As a result, all As sites are equivalent in LaRu2As2.

Fig. 1. Temperature dependence of the NMR coil resonance frequency. Tc is determined by the cross point of the two straight lines shown in the figure. The inset shows the crystal structure of LaRu2As2.

Figure 2(a) shows the 75As NMR spectrum measured at T = 5 K under a magnetic field of μ0H0 = 12.951 T, which is a typical powder pattern for nucleus with spin I = 3/2. Considering the tetragonal lattice of LaRu2As2, the total Hamiltonian for I = 3/2 nucleus can be expressed as[38]

where K is the Knight shift, eq = VZZ = ∂V2/∂ Z2 is the EFG along principle axis Z, Q is the nuclear quadrupole moment, and θ is the angle between the magnetic field and the principle axis of the EFG. The nuclear quadrupole resonance frequency νQ is defined as . The two peaks (marked by two black arrows) observed at 89.2 MHz and 97.8 MHz correspond to the transitions (3/2 ↔ 1/2) and (–1/2↔ –3/2). The central transition frequency νres for I = 3/2 to the second order is given by[38]

The observed spectrum is in agreement with the theoretically expected characteristic powder pattern with two peaks at θ = 42° and 90°. For a randomly oriented powder sample, the peak at θ = 42° would have a larger intensity than that at θ = 90°. Thus our observation suggests that the powder is partially oriented. Figure 2(b) shows the NQR spectrum, in which only one transition (±1/2 ↔ ±3/2) is observed, owing to that there is only one As site in this compound. We fitted the 75As NQR spectrum by a Gaussian function, and deduced νQ = 9.65 MHz.

Fig. 2. (a) 75As NMR spectrum of LaRu2As2 at T = 5 K and H0 = 12.951 T. There are two satellite peaks. The central transition frequency νres has two peaks with θ = 42° and θ = 90° due to the second order perturbation. The dashed line corresponds to K = 0. (b) 75As NQR spectrum of LaRu2As2 at T = 8 K. The curve is Gaussian fitting of the spectrum.

Figure 3 shows the temperature dependence of 1/T1 measured via 75As NQR. The blue dashed line is a guide to the eyes showing the relation of T1T = constant. We note that 1/T1 shows a clear Hebel–Slichter peak just below Tc = 6.2 K and decreases exponentially at low temperatures, which are characteristics of an isotropic superconducting gap. The relaxation rate below Tc is expressed as[39]

where Δ is the magnitude of the energy gap, is the DOS in the superconducting state, (1 + Δ2/E2) is the coherence factor, and f(E) is the Fermi distribution function. We convolute Ns(E) to a rectangular broadening function with a width 2δ and a height 1/2δ.[40] The solid curve in Fig. 3 is the simulation with the parameters 2Δ/kBTc = 3.2 and r = Δ/δ = 12, which is in good agreement with the experimental data. The value of 2Δ/kBTc is close to the BCS value of 3.5.

Fig. 3. The temperature dependence of 75As NQR spin-lattice relaxation rate 1/T1. 1/T1 shows a coherence peak just below Tc. The dashed line shows a T1T = constant relation. The solid curve is the fitting result assuming an s-wave gap.
3.2. KCa2Fe4As4F2

Figure 4(b) shows a typical NMR spectrum of KCa2Fe4As4F2. There are two types of As sites, as shown in Fig. 4(a), namely, As1 site close to K site and As2 close to Ca site.[15] As mentioned above, there will be two center peaks for each 75As site, with low frequency peak and high frequency peak corresponding to θ = 42° and θ = 90°, respectively. So the four peaks around the central transition of KCa2Fe4As4F2 are observed, which can be seen more clearly in the inset of Fig. 4(b). We assign the inner two peaks to the As1 site and outer two peaks to the As2 site, as will be elaborated below.

Fig. 4. (a) Crystal structure of KCa2Fe4As4F2. There are two types of As sites marked by dark red and pink, respectively. (b) Nuclear magnetic resonance spectrum of KCa2Fe4As4F2 at H0 = 11.999 T and T = 33 K. The dark red arrow and pink arrow correspond to the satellite peaks of As1 site and As2 site, respectively. Insets: central peaks after zooming in. Temperature dependence of NQR spectrums of (c) As2 site and (d) As1 site.

Figure 4(c) shows the waterfall plot of NQR spectrums of As2 site at different temperatures. No splitting or broadening is seen in the NQR spectrums, indicating that magnetic order is absent in the studied compound. By using a Lorentz function to fit the spectrums, we deduced the temperature dependence of νQ, as summarized in Fig. 5(a). The νQ of the As2 site increases from T = 275 K to 50 K but saturates below 50 K, as also seen in the As2 site of CaKFe4As4.[41] The νQ(100 K) of the As1 site is 10.9 MHz and νQ(130 K) of the As2 site is 20.1 MHz, close to νQ(100 K) = 12.4 MHz of KFe2As2[42] and νQ(130 K) = 19.2 MHz of CaFeAsF.[43] We therefore assign the inner two peaks of the central peaks to the As1 site and the outer two peaks of the central peaks to the As2 site.

Fig. 5. (a) Temperature dependence of νQ of the As2 site. (b) Temperature dependence of Knight shift for the two As sites. (c) Temperature dependence of 1/T1T measured at the two NMR peaks corresponding to θ = 90° at H = 11.999 T and As2 site at H = 0 T. The olive dashed curve is a fitting by the 2D antiferromagnetic fluctuations model. The black dashed-dotted line characterizes Tc.

After subtracting the second order perturbation effect according to Eq. (2), the Knight shift for As1 site and As2 site, is obtained as shown in Fig. 5(b). The Knight shift decreases from T = 100 K to Tc, which is similar to most of iron based superconductors.[44–48] The spin-lattice relaxation rate 1/T1 was measured at two central peaks corresponding to θ = 90° which has a stronger intensity, and also at NQR peak of As2 sites. The results are presented in Fig. 5(c). The magnitude of both K and 1/T1T for As1 site is bigger than that of As2 site. This is likely due to different hyperfine coupling constants at the two sites. In iron-based superconductors, hyperfine coupling is determined by the overlap of the electron cloud between Fe and As, namely, by the distance between Fe and As. From the original data in Ref. [15], we obtain the distances between As and Fe planes h(As-Fe) to be 1.405 Å and 1.436 Å for As1 site and As2 site, respectively. A smaller h(As1-Fe) leads to a bigger hyperfine coupling constant, which can explain the larger K and 1/T1T for As1 site. The difference in the magnitude between 1/T1T obtained by NMR and NQR will be explained later. The 1/T1T shows a monotonic increase as the temperature decreases from T = 275 K to 40 K, indicating the existence of antiferromagnetic spin fluctuations in KCa2Fe4As4F2. We use a phenomenological 2D antiferromagnetic fluctuations model[49,50] 1/T1T ∝ a+C/(T + Θ) to fit our data, where C/(T + Θ) is related to the low energy spin fluctuations and a is due to other contributions. The fitting result is shown by the olive dashed curve in Fig. 5(c). We obtain a = 0.015 s−1⋅K−1 and Θ = 149 K. Figure 6 shows the comparison of 1/T1T between KCa2Fe4As4F2 and Ba0.45K0.55Fe2As2. After shifting the starting point of the right axis upward by 0.32 s−1⋅K−1, we see that the 1/T1T of these two compounds are scaled very well. Thus it seems that the low energy spin fluctuations are quite similar for these two compounds. {As seen in Fig. 6, the dynamic susceptibility starts to decrease at T ≈ 40 K (above Tc), which is qualitatively similar to the features observed in cuperates.[51] This ‘pseudogap’ behavior was also observed in Ba0.45K0.55Fe2As2[52] and over-doped La1111.[53,54] The valence of Fe in KCa2Fe4As4F2 is +2.25, meaning that the equivalent doping level is 0.25 hole/Fe. This is close to the value in Ba0.45K0.55Fe2As2, where the doping level is 0.275 hole/Fe.

Fig. 6. Comparison of 1/T1T for KCa2Fe4As4F2 and Ba0.45K0.55Fe2As2. For clarity, the starting point of the right axis is 0.32 s−1⋅K−1 higher than that of the left axis. The scale of the two axes is the same.

To further study the nature of the AFM spin fluctuations, we compare the 1/T1 for H0 parallel to c direction and perpendicular to c direction. In this compound, the principle axis of EFG is along c direction. Therefore, T1 measured in the NMR central peaks with θ = 90° corresponds to , while T1 measured in the NQR peaks corresponds to , as the principle axis of EFG is along the c direction. Then we can obtain the anisotropy ratio of 1/T1T, . We find that it is only around 1.5 and nearly temperature-independent as shown in Fig. 7. For the stripe order where the wave vectors of the spin fluctuations are [π, 0] and [0, π],[45,55] and can be expressed as

where A is the hyperfine coupling constant and is the imaginary part of the dynamic susceptibility along i (i = a, b, c) direction at the measured angular frequency ω0. Therefore, one obtains

If , the ratio RAF will be equal to 1.5. Thus our observation suggests that the low energy spin fluctuations are isotropic in spin space. This is in sharp contrast with the spin fluctuations of the optimally-doped Ba0.68K0.32Fe2As2, which are anisotropic.[45] This result again indicates that the origin of the low energy spin fluctuations in KCa2Fe4As4F2 is different from that in the optimally-doped Ba0.68K0.32Fe2As2. {The anisotropic spin fluctuations in Ba0.68K0.32Fe2As2 were ascribed to a spin–orbit coupling (SOC) which was estimated to be 10–20 meV. Our result therefore suggests that the SOC is smaller in KCa2Fe4As4F2. Rather, the stoichiometric compound KCa2Fe4As4F2 provides a unique platform for studying the overdoped region of iron-based superconductors. {Equations (4) and (5) also explain why 1/T1T obtained by NQR is smaller than that by NMR, as in the former case the quantized axis is along the c-axis.

Fig. 7. Temperature dependence of the ratio for As2 sites.

Finally, we discuss the property in the superconducting state. Figure 8 shows the temperature dependence of 1/T1. Below Tc, no coherence peak appears and T1 decreases more rapidly than T3. Below T = 15 K, 1/T1 starts to be proportional to T, indicating the existence of strong impurity scattering in this sample.[56,57] We further simulate our results by assuming different gap symmetries as shown in Fig. 8. In the past decade of researches on iron-pnictides, multiple gaps have been found.[58,60] In fact, the s+− wave gap symmetry in which the gap sign reverses between hole Fermi pocket and electron Fermi pocket can account for the hump behavior of 1/T1 in various compounds.[44,45,53] Due to strong impurity scattering, however, the hump feature in 1/T1 is not visible in the present case. We tried to fit our data with various models. A simple d-wave model with Δd = 2.5kBTc or a two-band (two gap) s+− wave with Δs1 = 2kBTc, Δs2 = 3.75kBTc and equal weight for the two bands deviates from our data severely at low temperatures. Following the T1 calculation method of d-wave with impurity in literature,[57] we found that the parameter Δd = 2.5kBTc, η = 0.064Δd can fit our data well. On the other hand, two-gap s+−-wave with impurity scattering can also account for our data. In the s+−-wave model,[61] 1/T1 is expressed as

where Na is DOS in hole or electron Fermi surface. We define . If there exists impurity scattering, ω will be replaced by ω + iη. Using this model, we found that the parameters , , α = 0.5, reproduce our data well. In order to distinguish d-wave and s+−-wave, more measurements on a single crystal are required.

Fig. 8. Temperature dependence of 1/T1 in KCa2Fe4As4F2. The black dashed line is a guide to the eyes, indicating a T3 variation of 1/T1. The green dotted, purple short-dashed, blue dashed-dotted, and orange dashed curves show the fitting results of d wave, two-gap s+− wave, d wave with impurity scattering, and two-gap s+− wave with impurity scattering, respectively.
3.3. A2Cr3As3

Next, we turn to A2Cr3As3 (A = Na, Na0.75K0.25, K, Rb, Cs). Figure 9(a) shows the NQR spectra for A2Cr3As3 at T = 150 K, the five samples commonly show two peaks originating from two inequivalent As sites. In the previous reports, the site assignment was not performed. We assign the left peak to As2 site and the other peak to As1 site based on the following two facts. Firstly, neutron diffraction measurements found a displacement of the K2 sites towards CrAs tube with decreasing temperature in K2Cr3As3.[62] As shown in Fig. 9(b), the As1 site has four nearest A1 neighbors, while the As2 has two nearest A1 neighbors and two nearest A2 neighbors. Therefore, the displacement of the A2 sites makes a stronger variation of the EFG for the As2 sites, leading to a stronger temperature variation of νQ for As2 site than As1 site. Indeed, the change of νQ defined as δνQ = δνQ(T = 4.2 K) − δνQ(T = 300 K) is bigger for the left peak than that for the right peak.[28,29,63] It can be seen more clearly in Fig. 9(c), where we normalize the original νQ data by νQ(T = 4.2 K). Secondly, we calculate the EFG of two As sites for K2Cr3As3. The calculation is based on HiLAPW which is an extension of FLAPW.[37] We use generalized-gradient approximation (GGA) as the exchange correlation function, and include SOC. The nuclear quadrupole moment Q = 3.141 × 10−29 m2 was used for nucleus 75As.[64] The inputting lattice constant is from Ref. [22] at T = 300 K. The calculational result is shown in Table 1. The EFG tensors are defined as Vαα = ∂V2/∂α2 (α = X, Y, Z), where V is the electric potential. In case of , the νQ is defined as , where EFG eq = VZZ and VZZ is the principle-axis value. As shown in Fig. 10, the principle axis of A2Cr3As3 is in the ab plane. The resulting νQ = 41.64 MHz of As1 site is bigger than νQ = 39.94 MHz of As2 site, which supports the above mentioned site assignment. The site assignment will help further study the physical properties of two As sites by NMR, which is vitally important to identify the pairing symmetry.

Fig. 9. (a) 75As NQR spectra of A2Cr3As3 (A = Na, Na0.75K0.25, K, Rb, Cs) measured at T = 150 K. The two peaks correspond to two As sites, namely, As1 site and As2 site. The data for the right peak of K2Cr3As3 was referred from Ref. [28]. (b) Surrounding environments of As1 site and As2 site, respectively. (c) Temperature dependence of νQ normalized by its value at 4.2 K. The original data of K2Cr3As3 and Cs2Cr3As3 were referred from Refs. [28,63].
Fig. 10. EFG principle axes (VZZ) for K2Cr3As3, which are shown by the blue and red sticks for As1 site and As2 site, respectively.
Table 1.

Comparison of experimental and theoretical results of νQ for K2Cr3As3. The experimental data were obtained at 300 K. In the EFG calculation, the lattice constant at 300 K which was referred from Ref. [22] was used. The units of Vαα = ∂V2/∂α2 (α = X, Y, Z) and νQ are 1019 V/m2 and MHz, respectively.

.

Before closing, we note that the three transition-metal arsenides reported here show quite different normal-state properties and the superconducting gap symmetry in these compounds is also different. LaRu2As2 shows superconductivity with a full gap, whose origin maybe electron–phonon coupling.[13,14] On the other hand, unconventional superconductivity is caused by AFM spin fluctuations in KCa2Fe4As4F2 and FM spin fluctuation in A2Cr3As3.[29,35] Future issues include clarifying whether spin triplet pairing is realized by the FM spin fluctuation in A2Cr3As3.

4. Conclusion

We have performed NMR and NQR measurements on three types of transition metal arsenides, LaRu2As2, KCa2Fe4As4F2, and A2Cr3As3. In LaRu2As2, different from Fe-based superconductors with the same crystal structure, a coherence peak in the temperature dependence of 1/T1 appears just below Tc, indicating that the superconducting gap is fully open. In double Fe2As2 layers compound KCa2Fe4As4F2, the strength of antiferromagnetic spin fluctuations is found to be similar to that in Ba0.45K0.55Fe2As2, indicating that the stoichiometric compound KCa2Fe4As4F2 is in the moderately hole-overdoped region. In fact, the anisotropy of 1/T1, is only 1.5, implying that the spin fluctuations are isotropic, which is in sharp contrast to the nearly optimally-doped Ba0.68K0.32Fe2As2. For A2Cr3As3, we identified the one-to-one correspondence between NQR peaks and As sites. Our research revealed a wide variety of the physical properties of transition metal arsenides.

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