NMR Determination of an Incommensurate Helical Antiferromagnetic Structure in EuCoAs
We report Eu, As and Co nuclear magnetic resonance (NMR) results on EuCoAs single crystal. Observations of Eu and As NMR spectra in zero magnetic field at 4.3 K below an antiferromagnetic (AFM) ordering temperature = 45 K and its external magnetic field dependence clearly evidence an incommensurate helical AFM structure in EuCoAs. Furthermore, based on Co NMR data in both the paramagnetic and the incommensurate AFM states, we have determined the model-independent value of the AFM propagation vector k = (0, 0, 0.73 0.07)2/ where is the lattice parameter. Thus the incommensurate helical AFM state was characterized by only NMR data with model-independent analyses, showing NMR to be a unique tool for determination of the spin structure in incommensurate helical AFMs.
pacs:75.25.-j, 75.50.Ee, 76.60.-k
I I. Introduction
Understanding the magnetism in FeAs ( = Ca, Ba, Sr, Eu) known as 122 compounds with a ThCrSi-type structure at room temperature became one of the important issues after the discovery of iron-pnictide superconductors Kamihara2008 (); Johnston2010 (); Canfield2010 (); Stewart2011 (). These systems undergo coupled structural and magnetic phase transitions at a system-dependent Néel temperature , below which long-range stripe-type antiferromagnetic (AFM) order emerges originating from Fe electron spins. Superconductivity (SC) in these compounds emerges upon suppression of the stripe-type AFM phase by application of pressure and/or carrier doping. Because of the proximity between the AFM and the SC phases, it is believed that stripe-type AFM spin fluctuations play an important role in driving the SC in the iron-based superconductors, although orbital fluctuations are also pointed out to be important Kim2013 (). Recently ferromagnetic (FM) correlations were revealed to also play an important role in the iron-based superconductors Johnston2010 (); Nakai2008 (); PaulPRB (); PaulPRL (); JeanPRB ().
EuFeAs, which exhibits SC under the application of 2–3 GPa of pressure and/or carrier doping Tereshima2009 (); Jin2016 (), is a special member in the “122” class of compounds, as Eu has a large magnetic moment ( 7/2, = 0), where , , and are the total, spin and orbital angular momenta, respectively. EuFeAs exhibits the stripe-type AFM order at 186 K due to the Fe spins, while the Eu moments order antiferromagnetically below 19 K with an A-type AFM structure where the Eu ordered moments are FM aligned in the plane but the moments in adjacent layers along the axis are antiferrmagnetically aligned Jeevan2008 (). With substitution of Co atoms for the Fe atoms in Eu(FeCo)As, the ground-state magnetic structure of the Eu spins is found to develop from the A-type AFM order in the parent compound, via the A-type canted AFM structure with some net FM moment component along the crystallographic direction at intermediate Co doping levels around 0.1, and then to the pure FM order along the axis at 0.18 (Ref. Jin2016, ). With further substitution up to = 1, EuCoAs is reported to again exhibit A-type AFM order of the Eu ordered moments below 40 K Raffius1993 (); Ballinger2012 (), similar to the parent compound. On the other hand, recent neutron diffraction (ND) measurement reported a planar helical AFM structure below 47 K where the Eu ordered moments are aligned in the plane with the helical axis along the axis Tan2016 (). Therefore, it is important to elucidate the magnetic state of Eu in EuCoAs by using different experimental techniques.
Nuclear magnetic resonance (NMR) is a powerful technique to investigate magnetic properties of materials from a microscopic point of view. In particular, one can obtain direct and local information of magnetic state at nuclear sites. Although Eu, Co and As are NMR active nuclei in EuCoAs, there have been no NMR studies of this compound up to now to our knowledge.
In this paper, we have carried out NMR measurements to investigate the magnetic and electronic states of each ion in EuCoAs, where we succeeded in observing NMR signals from all three Eu, Co and As nuclei. From the external field dependence of Eu and As NMR spectra at 4.3 K, below = 45 K an incommensurate helical AFM state shown in Fig. 1(a) was clearly evidenced in EuCoAs. Furthermore, the AFM propagation vector characterizing the helical AFM state is determined to be k = (0, 0, 0.73 0.07)2/ from the internal magnetic induction at the Co site obtained by Co NMR under zero magnetic field. Co NMR revealed that no magnetic ordering of the Co electron spins occurs in the helical AFM state, evidencing that the magnetism in EuCoAs originates from only the Eu spins. These results are consistent with the recent neutron diffraction measurements Tan2016 ().
Ii II. Experiment
A single crystal ( mm) of EuCoAs for the NMR measurements was grown using Sn flux Sangeetha2017 (). NMR measurements of Eu ( = , = 4.632 MHz/T, 2.49 barns), Co ( = , = 10.03 MHz/T, 0.4 barns), and As ( = , = 7.2919 MHz/T, 0.29 barns) nuclei were conducted using a homemade phase-coherent spin-echo pulse spectrometer. In the AFM state, Eu, As and Co NMR spectra in zero and nonzero magnetic fields were measured in steps of frequency by measuring the intensity of the Hahn spin echo. In the paramagnetic (PM) state, Co NMR spectra were obtained by sweeping the magnetic field at = 51.1 MHz. The As nuclear spin-lattice relaxation rate 1/ was measured with a saturation recovery method T1 ().
Iii III. Results and discussion
At the bottom panel of Fig. 1(b) the Eu NMR spectrum in the AFM state for EuCoAs is shown, measured in zero magnetic field at a temperature = 4.3 K. The observed spectrum is well reproduced by the following nuclear spin Hamiltonian which produces a spectrum with a central transition line flanked by two satellite peaks on both sides for = 5/2, , where is the internal magnetic induction at the Eu site, is Planck’s constant, and is nuclear quadrupole frequency defined by for = 5/2) where is the electric quadrupole moment of the Eu nucleus, is the electric field gradient (EFG) at the Eu site, and is the asymmetry parameter of the EFG Slichter_book (). Since the Eu site in EuCoAs has a tetragonal local symmetry (4), is zero. The blue lines shown at the bottom panel of Fig. 1(b) are the calculated positions for Eu zero-field NMR (ZFNMR) lines using the parameters = 27.5(1) T, = 30.6(1) MHz and . Here represents the angle between and the principle axis of the EFG tensor at the Eu sites. As shown by the red curve in the figure, the observed Eu ZFNMR spectrum was well reproduced with a broadening of 1.1 T of the calculated lines originated from a distribution of probably due to Eu ordered moment distributions.
Since is perpendicular to the axis as will be shown below, the principle axis of the EFG is found to be the axis, which is similar to the case of the Eu nucleus in EuGa with the same ThCrSi-type crystal structure in which the similar values of = 27.08 T and = 30.5 MHz for Eu have been reported Yogi2013 (). is proportional to where is the hyperfine coupling constant and is the ordered Eu magnetic moment. The hyperfine field at the Eu sites mainly originates from core polarization from 4 electrons and is oriented in a direction opposite to that of the Eu moment Freeman1965 (). For = 27.5(1) T and the reported AFM ordered moment = 7.26(8) /Eu from ND Tan2016 (), is estimated to be 3.78 T/ where the sign is reasonably assumed to be negative due to the core-polarization mechanism. The estimated is not far from the core-polarization hyperfine coupling constant 4.5 T/ estimated for Eu ions Freeman1965 (). The small difference could be explained by a positive hyperfine coupling contribution due to conduction electrons which cancel part of the negative core polarization field.
In order to determine the direction of with respect to the crystal axes, we measured Eu NMR in the single crystal in nonzero . When is applied along the axis, almost no change of the Eu NMR spectrum is observed [see the top panel in Fig. 1(b) where the simulated spectra shown by blue and red lines are the same as the case of = 0]. This indicates that is perpendicular to the ordered Eu moments and thus to . Since the effective field at the Eu site is given by the vector sum of and , i.e., = + , the resonance frequency is expressed for as = . For our applied field range where , any shift in the resonance frequency due to would be small, as observed.
In the case of applied perpendicular to the axis, on the other hand, each line broadens as shown in the middle panel of Fig. 1(b). The broadening of each line cannot be explained by the A-type AFM state. In this case, one expects a splitting of each line into two lines corresponding to two Eu planes where the Eu ordered moments are parallel or antiparallel to . In order to explain the observed spectrum, we consider a planar helical structure which produces a two dimensional powder pattern. The blue solid line is a calculated spectrum for an incommensurate helical AFM state. With the inhomogeneous magnetic broadening due to the same distribution of as in the = 0 T spectrum, the observed spectrum at = 1 T is reasonably reproduced as shown by the red solid curve. Thus these NMR results reveal an incommensurate helical spin structure with the ordered moments aligned in the plane, consistent with recent ND measurements Tan2016 (). The observed -plane alignment of the ordered moments is also consistent with the prediction of the moment alignment from magnetic dipole interactions between the Eu spins Johnston2016 (). A similar incommensurate helical spin structure has been reported in EuCoP Reehuis1992 (); Sangeetha2016 ().
The incommensurate planar helical structure is also revealed by As NMR measurements. The bottom panel in Fig. 2 shows the As ZFNMR spectrum at 4.3 K in the AFM state, where the blue lines are the expected positions for the three lines (for = 3/2) calculated with the parameter = 5.86 T, = 17.0 MHz and . As in the case of the Eu ZFNMR spectrum, the observed As ZFNMR spectrum is well reproduced with an inhomogeneous magnetic broadening of 4 kOe, as shown by the red curve. The distribution of originates from the distributions of the Eu ordered moments and its directions. When is applied along the axis, almost no change of the spectrum is observed as typically shown in the top panel of Fig. 2 where = 0.5 T. This indicates that is perpendicular to at the As site. On the other hand, when is applied parallel to the plane, similar to the case of Eu ZFNMR spectrum, each line broadens and exhibits a characteristic shape, again expected for the incommensurate planer helical AFM state.
According to Yogi et al., the direction of is parallel to the Eu ordered moments in the case where the Eu ordered moments are ferromagnetically aligned in the Eu plane Yogi2013 (). Therefore, one can expect almost no change of the As ZFNMR spectrum when is perpendicular to the Eu ordered moment, as observed in the As ZFNMR spectrum for axis. On the other hand, if one applies plane, a splitting of the As ZFNMR spectrum is expected similar to the case of the Eu ZFNMR spectrum. The blue lines in the two middle panels of Fig. 2 are calculated spectra of As NMR for the planar helical AFM structure under = 0.5 T and 1 T. With the same inhomogeneous magnetic broadening ( 4 kOe) due to a distribution of , both spectra are well reproduced as shown by the red curves.
The dependence of the As ZFNMR spectrum is shown in Fig. 3(a). With increasing , the spectra shift to lower frequency due to reduction of the internal magnetic induction which decreases from 5.86 T at 4.3 K to 3 T at 40 K. No obvious change in = 17.0 MHz is observed. The dependence of shown in Fig. 3(b), which is the dependence of the order parameter of the planar helical AFM state, is well reproduced by a Brillouin function which was calculated based on the Weiss molecular field model with = = 7/2, = 45 K and = 5.86 T. This indicates that the magnetic state of the Eu ions is well explained by the local moment picture although the system is metallic as determined from electrical resistivity measurements Sangeetha2017 (). The metallic ground state was confirmed by the dependence of measured at the central line of the As-ZFNMR spectrum. As shown in Fig. 3(c), is proportional to , thus obeying a Korringa law = 190 (sK). This confirms a metallic state from a microscopic point of view.
Now we discuss our Co NMR data for both the PM and AFM ordered states. Figure 4(a) shows the field-swept Co NMR spectra in the PM state at = 60 K for and . For = 7/2 nuclei, one expects a central transition line with three satellite lines on both sides. The observed spectra, however, do not show the seven distinct lines but rather exhibit a single broad line due to inhomogeneous magnetic broadening. The dependence of the NMR shift for () and () is shown in Fig. 4(b), where we fit the data with the Curie-Weiss law . The solid curves are fits with = 553 (440) and = 24.0 (24.0) K for (). The values = 24.0 K for both field directions indicate predominant FM exchange interactions between Eu spins. This is consistent with the in-plane FM exchange interactions responsible for the planar helical AFM structure.
The hyperfine coupling constants and for Co surrounded by four Eu ions can be estimated from the slopes of - plots with the relation = , where is Avogadro’s number and is the number of nearest-neighbor Eu ions around a Co atom. As shown in the inset of Fig. 4(b), both and vary linearly with the corresponding . From the respective slopes, we estimate = (0.875 0.09) kOe//Eu and = (1.09 0.17) kOe//Eu, respectively. These values are much smaller than a typical value = 105 kOe/ for Co electron core polarization Freeman1965 (). This indicates that the hyperfine field at the Co site originates from the transferred hyperfine field produced by the Eu spins and that no spins on the Co sites contribute to the magnetism of EuCoAs.
We now consider the influence of the planar helical AFM state on the Co NMR data. We have succeeded in observing the Co ZFNMR spectrum at 4.3 K as shown in Fig. 4(d), where the internal magnetic induction at the Co site is estimated to be = 10.3 kOe. Based on the analysis for by Yogi for EuGa (Ref. Yogi2013, ), we extended their calculation of to an incommensurate helical AFM state and found that at the Co site appears in only the plane when the Eu ordered moments lie in the plane and is expressed by
where is the turn angle along the the axis between the Eu ordered moments in adjacent Eu planes, which characterizes the helical structure. In the case of = corresponding to an A-type collinear AFM state, is zero due to a cancellation of the internal magnetic induction from the four nearest-neighbor Eu ordered moments. On the other hand, if deviates from corresponding to a helical state, one can expect a finite . Thus the observation of the finite is direct evidence of the planar incommensurate helical AFM state in EuCoAs. Furthermore, using Eq. (1), we can determine the AFM propagation vector k = (0, 0, )2/, where is the -axis lattice parameter of the body-centered tetragonal Eu sublattice. Since the distance along the axis between adjacent layers of FM-aligned Eu moments is = /2, the turn angle between the ordered moments in adjacent Eu layers is = , as shown in Fig. 4(c). Using = 7.26(8) Tan2016 (), = 0.875 kOe//Eu and = 10.3 kOe, the turn angle is estimated to be 132 corresponding to a helical wave vector k = (0, 0, 0.73 0.07)2/. This value of k is in very good agreement with = (0, 0, 0.79)2/ obtained from ND data Tan2016 ().
Iv IV. Summary
In summary, we have shown that by analyzing the NMR spectrum in zero field and its external-field dependence, one can determine directly an incommensurate helical AFM structure in EuCoAs. The AFM propagation vector characterizing the incommensurate helical AFM state was determined model-independently to be k = (0, 0, 0.73 0.07)2/ from the internal magnetic field at the Co site obtained by Co NMR under zero magnetic field. Thus NMR can be a unique tool for a model-independent determination of the spin structure in incommensurate helical antiferromagnets. This should prove valuable for the future investigation of local spin configurations in other europium compounds such as in EuCoP which is also reported to exhibit an incommensurate helical AFM structure below 66 K Reehuis1992 (); Sangeetha2016 (). Our NMR approach can also be used to study in detail the magnetism originating from the Eu spins in Eu(FeCo)As SCs where the magnetic structure of the Eu spins changes from the A-type AFM state to a canted AFM state, and then to the ferromagnetic state with increasing Co substitution Jin2016 (). Such a detailed study would provide clues about the origin of the coexistence of SC and magnetism in the Eu(FeCo)As system.
V V. Acknowledgments
The authors thank Mamoru Yogi at University of the Ryukyus for helpful discussions. The research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358. N. H. thanks the Japan Society for the Promotion of Science KAKENHI : J-physics (Grant Nos. JP5K21732, JP15H05885, and JP16H01078) for financial support to be a visiting scholar at the Ames Laboratory.
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