NMR study of the new magnetic superconductor CaK ( Fe 0.951 Ni 0.049 ) 4 As 4 : Microscopic coexistence of the hedgehog spin-vortex crystal and superconductivity

The coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by an 75 As nuclear magnetic resonance study on singlecrystalline CaK ( Fe 0.951 Ni 0.049 ) 4 As 4 . The hedgehog SVC order is clearly demonstrated by the direct observation of internal magnetic induction along the c axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature T N ∼ 52 K. The nuclear spin-lattice relaxation rate 1 / T 1 shows a distinct decrease below T c ∼ 10 K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the 1 / T 1 data, the hedgehog SVC-type spin correlations are found to be enhanced below T ∼ 150 K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor. Disciplines Condensed Matter Physics | Fluid Dynamics Authors Qing-Ping Ding, William R. Meier, A. E. Böhmer, S. L. Bud’ko, Paul C. Canfield, and Yuji Furukawa This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/ameslab_manuscripts/80 RAPID COMMUNICATIONS PHYSICAL REVIEW B 96, 220510(R) (2017) NMR study of the new magnetic superconductor CaK(Fe0.951Ni0.049)4As4: Microscopic coexistence of the hedgehog spin-vortex crystal and superconductivity Q.-P. Ding, W. R. Meier, A. E. Böhmer, S. L. Bud’ko, P. C. Canfield, and Y. Furukawa Ames Laboratory, U.S. DOE, and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Received 26 October 2017; revised manuscript received 11 December 2017; published 29 December 2017) The coexistence of a new-type antiferromagnetic (AFM) state, the so-called hedgehog spin-vortex crystal (SVC), and superconductivity (SC) is evidenced by an As nuclear magnetic resonance study on single-crystalline CaK(Fe0.951Ni0.049)4As4. The hedgehog SVC order is clearly demonstrated by the direct observation of internal magnetic induction along the c axis at the As1 site (close to K) and a zero net internal magnetic induction at the As2 site (close to Ca) below an AFM ordering temperature TN ∼ 52 K. The nuclear spin-lattice relaxation rate 1/T1 shows a distinct decrease below Tc ∼ 10 K, providing also unambiguous evidence for the microscopic coexistence. Furthermore, based on the analysis of the 1/T1 data, the hedgehog SVC-type spin correlations are found to be enhanced below T ∼ 150 K in the paramagnetic state. These results indicate the hedgehog SVC-type spin correlations play an important role for the appearance of SC in the new magnetic superconductor. DOI: 10.1103/PhysRevB.96.220510 The relationship between antiferromagnetism (AFM) and superconductivity (SC) has received wide interest in the study of high-temperature SC in iron-based superconductors. Among the iron-based superconducting compounds, those of the 122-type family AFe2As2 (A = Ca, Ba, Sr, Eu) with a ThCr2Si2-type structure at room temperature attracted the most attention [1–3]. In these systems, by lowering the temperature, the crystal structure changes from high-temperature tetragonal (C4 symmetry) to low-temperature orthorhombic (C2 symmetry) at, or just above, a system-dependent Néel temperature TN, below which long-range stripe-type AFM order emerges. SC in these compounds emerges upon suppression of both the structural and magnetic transitions by application of carrier doping and/or pressure. The stripe-type AFM order with C2 symmetry coexists with the SC phase in various doped “122” compounds such as Ba1−xKxFe2As2, BaFe2(As1−xPx)2, Ba(Fe1−xCox)2As2, and Ba(Fe1−xRux)2As2 [4–12], but not in Ca(Fe1−xCox)2As2 [13]. Recently, new magnetic states with C4 symmetry have attracted much attention [14]. These states are characterized by the wave vectors Q1 = (π,0) and Q2 = (0,π ) as in the stripeordered state, and can be understood as the superposition of two spin density waves (SDWs) S(r) = M1eiQ1·r + M2eiQ2·r [14–16]. Here, M1 and M2 are the magnetic order parameters associated with the two wave vectors Q1 and Q2, respectively. When M1 and M2 are either parallel or antiparallel, a nonuniform magnetization is produced where the average moment at one lattice site vanishes and a staggeredlike order appears at the other lattice sites [15]. This so-called charge-spin density wave (CSDW) has been demonstrated to be realized in Sr1−xNaxFe2As2 [17], and likely occurs in Ba(Fe1−xMnx)2As2, Ba1−xNaxFe2As2, and Ba1−xKxFe2As2 as well [18–24]. A possible coexistence of CSDW and SC is reported in Ba1−xNaxFe2As2 [19], and Ba1−xKxFe2As2 [20,22,24]. Very recently, a new magnetic state called the “hedgehog” spin-vortex crystal (SVC) with C4 symmetry has been identified in the electron-doped 1144-type iron pnictide SC CaK(Fe1−xMx)4As4 (M = Co or Ni) [25] (Fig. 1). The hedgehog SVC state is another double-Q SDW state in the iron-based systems, in which M1 and M2 are orthogonal. Importantly, CaK(Fe1−xMx)4As4 (M = Co or Ni) crystallizes through alternate stacking of the Ca and K layers across the Fe2As2 layer as a result of the large ionic radius difference [25–27]. The ordering of the Ca and K layers changes the space group from I4/mmm in AFe2As2 to P4/mmm in CaKFe4As4 (CaK1144). Consequently, as shown in the inset of Fig. 1, there are two inequivalent As sites: As1 and As2 sites close to the K and Ca layers, respectively. The multiband nature and two nodeless isotropic superconducting gaps have been revealed in the parent compound by various techniques [28–33]. Whereas an overlap between the hedgehog SVC and the SC regions appears in the phase diagram compiled in Ref. [25] and shown in Fig. 1, it remains an important question whether or not this new AFM state coexists with SC at a microscopic scale. Furthermore, the spin fluctuations in the materials with hedgehog SVC order have never been investigated. Here, we have carried out an As NMR study on CaK(Fe0.951Ni0.049)4As4 (4.9%Ni-CaK1144) single crystals (TN ∼ 52 K, Tc ∼ 10.5 K) in order to investigate the magnetic and electronic properties from a microscopic point of view. The well-defined NMR signals from the As1 and As2 sites allow us to determine the temperature dependence of hyperfine fields and magnetic fluctuations at each site separately, providing clear evidence of the coexistence of the hedgehog SVC and SC. Single crystals of 4.9%Ni-CaK1144 for the NMR measurements were grown out of a high-temperature solution rich in transition metals and arsenic [25,27,34]. NMR measurements of As (I = 2 , γN 2π = 7.2919 MHz/T, Q = 0.29 barns) nuclei were conducted using a laboratory-built phase-coherent spinecho pulse spectrometer. In situ ac magnetic susceptibility (χac) was measured by monitoring the resonance frequency f of the NMR coil tank circuit as a function of temperature (T ) using a network analyzer. The As-NMR spectra were obtained by sweeping the magnetic fieldH at a fixed frequency f = 43.2 MHz. The As nuclear spin-lattice relaxation rate 1/T1 was measured with a saturation recovery method [35]. Preliminary results of As NMR spectrum measurements have been reported in a previous paper [25]. 2469-9950/2017/96(22)/220510(6) 220510-1 ©2017 American Physical Society RAPID COMMUNICATIONS Q.-P. DING et al. PHYSICAL REVIEW B 96, 220510(R) (2017) FIG. 1. Phase diagram of CaK(Fe1−xNix)4As4. TN and Tc determined from resistivity and magnetization are from Ref. [25]. The inset shows the crystal structure of CaKFe4As4 where the two crystallographically inequivalent As sites exist: As1 and As2 sites close to the K and Ca layers, respectively. Figures 2(a) and 2(b) show the T dependence of field-swept As-NMR spectra of 4.9%Ni-CaK1144 at f = 43.2 MHz for two magnetic field directions, the H ‖ c axis and H ‖ ab plane, respectively. The typical spectrum for a nucleus with spin I = 3/2 with Zeeman and quadrupolar interactions can be described by a nuclear spin Hamiltonian H = −γ h̄(1 + K)HIz + hνQ 6 (3I 2 z − I 2), where H is the external field, h is Planck’s constant, h̄ = h/2π , K is the Knight shift, and νQ is the nuclear quadrupole frequency. The nuclear quadrupole frequency for I = 3/2 nuclei is given by νQ = eQVZZ/2h, where Q is the nuclear quadrupole moment and VZZ is the FIG. 2. T dependence of the field-swept As-NMR spectra of 4.9%Ni-CaK1144 measured at f = 43.2 MHz, for (a) the H ‖ c axis and (b) the H ‖ ab plane. The inset in (a) enlarges the central transition around 5.9 T. The inset in (b) shows the sketch of the hedgehog SVC spin structure on an Fe-As layer. The burgundycolored arrows represent the magnetic moments at the Fe sites and the red arrows represent the magnetic induction Bint at the As1 sites. electric field gradient at the As site. When the Zeeman interaction is greater than the quadrupolar interaction, this Hamiltonian produces a spectrum with a sharp central transition line flanked by one satellite peak on either side. The two inequivalent As sites of this 1144 structure result in two sets of I = 3/2 quadrupole split lines which are actually observed for both H directions in the paramagnetic state, as seen in Fig. 2. The observed spectra are very similar to those in the pure CaK1144 where the lower-field central peak with a greater Knight shift K (and also larger νQ) has been assigned to the As2 site and the higher-field central peak with a smaller K (and also smaller νQ) has been attributed to the As1 site [32]. Figure 3 shows the T dependence of νQ, Kab (H ‖ ab), and Kc (H ‖ c axis) for the two As sites. Due to the poor signal intensity at high T , νQ and Kab can only be determined precisely up to 150 K. For both the As sites, K’s are nearly independent of T . A similar weak T dependence of K has been observed in the nonmagnetic CaK1144 [32], indicating that static magnetic susceptibility is almost insensitive to the electron doping and also to the magnetic or nonmagnetic ground states. The T dependences of νQ of As1 and As2 of 4.9%NiCaK1144 are similar to those of νQ of the As sites in pure CaK1144 [32], as shown in Fig. 3(a). For the As1 site, with increasing T , νQ increases from 12.2 MHz at 4.3 K to 12.75 MHz at 150 K, while the As2 site shows an opposite trend where νQ decreases from 15.0 MHz at 4.3 K to 14.2 MHz at 150 K. The first-principles analysis shows the different T dependences of νQ’s for the two As sites can be explained by hedgehog SVC magnetic fluctuations [32]. The full width at half maximum (FWHM) of the central line for the H ‖ c axis is nearly independent of T with ∼114 and ∼142 Oe for the As1 and As2 sites, respectively, in the paramagnetic state. The FWHMs of each satellite line are estimated to be 1.60 and 1.65 kOe for the As1 and As2 sites at 55 K and the H ‖ c axis, respectively. The linewidths of both the central and satellite lines are much greater than those in the pure CaK1144, which could be due to the disorder in the FeAs layer introduced by the substitution of Ni for Fe. When T is lowered below TN = 52 K, for the H ‖ c axis, each line of 4.9%Ni-CaK1144 starts to broaden and the observed spectra become more complex, as typically shown in the middle panel of Fig. 2(a). As reported in Ref. [25], the observed spectra in the magnetic state are well explained by the superposition of the NMR spectrum from two As sites: six peaks from the As1 site (doubling the number of resonance lines due to internal magnetic induction Bint) and three peaks from the As2 site. Here, it is noted that the different νQ value for each As site makes unambiguous peak assignments of the complicated spectrum in the AFM state possible. When H is applied parallel to the ab plane, in contrast, no splitting for the As1 NMR line is observed, as shown in Fig. 2(b). The effective magnetic induction Beff is given by the vector sum of Bint at the nucleus site and H, i.e., |Beff| = |Bint + H|. Therefore, when Bint is parallel or antiparallel to H, Beff = H ± Bint and a splitting of each line is expected. On the other hand, when H ⊥ Bint, no splitting of the line is expected since Beff is expressed by Beff = √ H 2 + B2 int. Thus, doubling the resonance lines at the As1 site only forH ‖ c clearly shows that Bint at the As1 site is oriented along the c axis. The absence of a