key: cord-0670770-nwh7lcoq authors: Liu, Panpan; Klemm, Mason L.; Tian, Long; Lu, Xingye; Song, Yu; Tam, David W.; Schmalzl, Karin; Park, J. T.; Li, Yu; Tan, Guotai; Su, Yixi; Bourdarot, Frederic; Zhao, Yang; Lynn, Jeffery W.; Birgeneau, Robert J.; Dai, Pengcheng title: In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe$_2$As$_2$ date: 2020-09-09 journal: nan DOI: nan sha: 0c2407e1594b4b6eaf9f9d9ce0a5008e6dd66064 doc_id: 670770 cord_uid: nwh7lcoq A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe$_2$As$_2$, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature $T_s$. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature $T_N$ ($ T N by ∼0.75 K) [7] . The spins within each FeAs layer are collinear and arranged antiferromagnetically along the a-axis and ferromagnetically along the b-axis of orthorhombic structure with lattice parameters of a and b, respectively (a > b). Along the outof-plane direction, spins are arranged antiferromagnetically within one chemical unit cell (lattice parameter c), but have no net magnetic moment along the c-axis [ Fig. 1(a) ] [6, 7] . For a collinear Ising antiferromagnet with second order (or weakly first order) magnetic phase transition, magnetic critical scattering with moments polarized along the longitudinal (parallel to the ordered moment or a-axis) direction should diverge at T N , while spin fluctuations with moments polarized transverse to the ordered moment (b-and c-axis) direction should not diverge [28] [29] [30] [31] [32] . Unpolarized [33] and polarized [34] neutron scattering experiments on strain-free BaFe 2 As 2 confirm this expectation. While the longitudinal component (M a ) of the magnetic critical scattering, defined as low-energy spin fluctuations polarized Effect of uniaxial pressure on lattice parameters of BaFe 2 As 2 . The in-plane uniaxial pressure-induced tetragonal symmetry-breaking lattice distortion [δ(P = 0) − δ(P = 0), where δ = (a − b)/(a + b)] has a Curie-Weiss temperature dependence in the paramagnetic state and peaks near T N /T s , but is greatly suppressed below T N /T s when the intrinsic orthorhombic lattice of BaFe 2 As 2 sets in [ Fig. 1 (g)] [27] . In the paramagnetic state, NMR experiments on BaFe 2 As 2 suggest that an in-plane uniaxial strain can induce a diverging c-axis polarized spin susceptibility χ c , which equals to M c in the zero energy limit, on approaching T N /T s [26] . Since c-axis polarized low-energy spin fluctuations do not diverge around T N /T s in the strain-free BaFe 2 As 2 [34] , it is important to confirm the NMR results and determine if the diverging χ c is a precursor of a new magnetic order with a component along the c-axis [ Fig. 1 (f)] [28] . Neutron polarization analysis of spin excitations in detwinned BaFe 2 As 2 . Our polarized neutron scattering experiments were carried out on the CEA CRG-IN22 triple-axis spectrometer equipped with Cryopad capability at the Institut Laue Langevin and the BT-7 triple-axis spectrometer at the NIST Center for Neutron Research. The experimental setup for IN22 has been described in detail before [34] [35] [36] [37] [38] [39] , while polarized neutrons were controlled and analyzed using a polarized 3 He filter on BT-7 [40, 41] . We have also carried out unpolarized neutron diffraction experiments on BT-7 using an in-situ uniaxial pressure device [25] . The wave vector transfer Q in reciprocal space inÅ −1 is defined as Q = Ha * + Kb * + Lc * , with a * = (2π/a)â, b * = (2π/b)b, and c * = (2π/c)ĉ, where a ≈ b ≈ 5.6 A, c = 12.96Å, and H, K, L are Miller indices. In this notation, the collinear AF structure of BaFe 2 As 2 in Fig. 1 to Q but in the scattering plane (y), and perpendicular to both Q and the scattering plane (z) [ Fig. 1(c) ]. In this geometry, the neutron spin-flip (SF) scattering cross sections σ SF x , σ SF y , and σ SF z are related to the components M a , , B is the background scattering, M y = sin 2 αM a + cos 2 αM c with α being the angle between [H, 0, 0] and Q, and [34] [35] [36] [37] [38] [39] . Figure 1 (b) compares the temperature dependencies of the (1, 0, 3) magnetic Bragg peak for strain-free and strained BaFe 2 As 2 . At zero external pressure (P = 0 and strain-free), the magnetic scattering shows an order parameter like increase below T N = 136 K [34] . When an uniaxial pressure of P ≈ 20 MPa is applied along the b-axis of BaFe 2 As 2 , the Néel temperature of the sample increases to T N = 143 K [25] . The vanishingly small magnetic scattering intensity at Q = (0, 1, 3) suggests that the sample is essentially ∼100% detwinned [ Fig. 1 [26] . To further clarify the energy dependence of M a , M b , and M c , we estimate these components from measurements at the (1, 0, 1) and (1, 0, 3) positions as described in Ref. [34] . By comparing the energy dependence of M a , M b , and M c in strain-free [ Fig. 2(g) ] and strained [ Fig. 2 (h)] BaFe 2 As 2 , we again see that the effect of uniaxial strain is to enhance M c below about 4 meV, consistent with the NMR measurements which probe M c or χ c in the zero energy limit [26] . To demonstrate further the effect of uniaxial strain on the magnetic critical scattering of BaFe 2 As 2 , we show in Fig. 3 (1, 0, 3) position, which is more sensitive to M a , show diverging magnetic scattering at T N with and without uniaxial pressure consistent with the NMR results [ Fig. 3(f) ] [26] . Figures 3(g) and 3(h) show the temperature dependencies of the estimated M a , M b , and M c for strain-free and strained BaFe 2 As 2 , respectively, using the data in Figs. 3(a-d) . Comparing with the normal behavior of the strain-free BaFe 2 As 2 [ Fig. 3(g) ], the M c in strained BaFe 2 As 2 clearly diverges around T N /T s [ Fig. 3(h) ], although the error bars of the data became worst after the data manipulation [42] . Effect of uniaxial pressure on static AF order of BaFe 2 As 2 . In principle, a diverging dynamic spin susceptibility in the paramagnetic state of a system is an indication of the eventual magnetic order below T N [28] [29] [30] [31] [32] . For strain-free BaFe 2 As 2 , the magnetic ordered moment is along the a-axis with no net moment along the b-axis and c-axis directions [6, 7] . Therefore, only the M a component of the spin susceptibility diverges at T N [ Figs. 3(e,f,g) ] [34] . The observation of a diverging M c in strained BaFe 2 As 2 , in addition to the usual diverging M a [Figs. 3(e,f,h) ], suggests that the applied strain may induce static magnetic ordered moment along the c-axis. To test this hypothesis, we carried out polarized neutron diffraction measurements on BaFe 2 As 2 as a function of uniaxial pressure, focusing on the temperature and neutron polarization dependence of the scattering at Q = (1, 0, L) with L = 0, 1, 2, 3, and 5. At wave vectors (1, 0, 0) and (1, 0, 2), there is no evidence of magnetic scattering, consistent with uniaxial pressure-free BaFe 2 As 2 [42] . To further determine the effect of uniaxial pressure on c-axis ordered moment and its pressure dependence, we carried out unpolarized neutron diffraction measurements focusing on the magnetic scattering intensity ratio between (1, 0, 1) (I 101 ) and (1, 0, 3) (I 103 ) using an in-situ uniaxial pressure device. Since our polarized neutron diffraction measurements revealed no ordered moment M b , we used unpolarized neutron diffraction on BT-7 to improve the statistics of the data across T N . Figure 4 (e) compares the measured I 101 /I 103 from 130 K to 150 K at P ≈ 0 and 45 MPa uniaxial pressure. Consistent with earlier work [6, 7] , I 101 /I 103 is approximately temperature independent across T N at P ≈ 0, thus indicating that the internal strain of the system does not induce a c-axis ordered moment. Upon applying an uniaxial pressure of P ≈ 45 MPa, the identical measurement shows a dramatic peak at T N , thus confirming the results of Figs. 4(a-d) . [42] . In the low temperature AF ordered state, the strain-free and strained BaFe 2 As 2 have the standard collinear AF structure with no evidence of M c [right panel in Fig. 1 (e) and Fig. 4 (e)] [6, 7] . On warming to 143 K just below T N , the easy-axis tilts from the a-axis towards the c-axis with an angle of ∼28 • [middle panel in Fig. 1(e) ]. Finally, on warming to temperatures well above T N , there is no static AF order [left panel in Fig. 1(e) ]. Figure 1(g) shows the temperature dependence of M c at ∼20 (blue solid line) and ∼45 (pink solid line) MPa uniaxial pressure, compared with the uniaxial strain-induced lattice distortion δ(P ≈ 20 MPa) − δ(P = 0) (green solid circles and lines) obtained from neutron Larmor diffraction experiments [27] . The similarity of the data suggests that the c-axis aligned magnetic moment arises from the uniaxial pressure-induced lattice distortion. Theoretically, the in-plane electronic anisotropy of the iron pnictides is expected to couple linearly to the lattice orthorhombicity by the Ginzburg-Landau free-energy formalism if one ignores the effect of spin-orbit coupling induced magnetic anisotropy [9, 27] . From this perspective, in-plane uniaxial strain should only induce in-plane electronic anisotropy. The discovery of a c-axis ordered magnetic moment coupled exclusively with uniaxial pressure-induced lattice distortion suggests that such an effect cannot be only associated with the lattice orthorhombicity of the system, as M c becomes vanishingly small in the low-temperature orthorhombic phase with large in-plane lattice distortion. This is also different from the c-axis moment AF structure in Ba 1−x K x Fe 2 As 2 in the sense that the c-axis order appears exclusively in the tetragonal phase [43, 44] , while the c-axis moment appears in BaFe 2 As 2 only near the peak of the nematic susceptibility around T N /T s . Although there is currently no theoretical understanding of this observation, it must arise from spin-orbit coupling induced magnetic anisotropy [45] . Our discovery opens a new avenue to control magnetic order in nematic materials using mechanical strain instead of magnetic fields. The strong coupling of the c-axis aligned magnetic order with an in-plane pressure-induced lattice distortion offers the potential for the next generation of mechanical-strain-controlled magnetic switches. One must consider the presence of the magnetically ordered moment along the c-axis in mechanically detwinned iron pnictides in order to understand their intrinsic electronic, magnetic, and nematic properties. Alternatively, our observations are also consistent with strain inducing a proximate XY spin anisotropy near T N /T s . In this scenario, while a-axis is energetically favorable in terms of spin anisotropy, c-axis is very close. This allows for a distribution of large (resolution-limited but not long-ranged ordered) and long-lived (quasi-static) collinear magnetic domains, with their collinear spin direction in the ac-plane. The ratio between I 101 /I 103 [Figs. 4(d,e) ] is then a measure of the distribution, reflective of the difference in spin anisotropy energies along the a-and c-axis. Similar to when the easy axis tilts from a-axis towards c-axis under strain [ Fig. 1(e) ], the change to a proximate XY spin anisotropy under strain also indicates of a large and highly unusual effect of strain on the spin anisotropy. In conclusion, we have used polarized and unpolarized neutron scattering to study the magnetic structure and critical scattering in uniaxial strained BaFe 2 As 2 . We find that the uniaxial pressure necessary to make single domain samples of BaFe 2 As 2 also induces c-axis polarized critical magnetic scattering and static magnetic order around T N /T s . The size of the c-axis ordered moment is associated with the uniaxial pressure-induced lattice distortion, instead of the lattice orthorhombicity. These results indicate that in addition to detwinning BaFe 2 As 2 , uniaxial pressure applied on the sample actually modifies the magnetic structure of the system. Therefore, infrared [46] , angle resolved photoemission [16] , and Raman spectroscopy [47, 48] experiments on mechanically detwinned BaFe 2 As 2 near the magnetic and nematic phases should be re-examined to take into account the effect of strain-induced change to the spin anisotropy on the in-plane electronic and magnetic properties. Sample preparation and experimental details. BaFe 2 As 2 single crystals were grown by the self-flux method using the same growth procedure as described before [19] . Our polarized inelastic neutron scattering experiments were carried out using the IN22 CEA-CRG triple-axis spectrometer at the Institut Laue-Langevin, Grenoble, France [49] . Polarized neutrons were produced using a focusing Heusler monochromator and analyzed with a focusing Heusler analyzer with a final wave vector of k f = 2.662Å −1 . The experimental setups for uniaxial pressured and pressure freed experiments are identical. However, it is difficult to directly compare the scattering intensity of these two experiments since the sample masses, their relative positions in the beam, and background scattering of these two experiments are different. Nevertheless, one can safely compare the relative intensity changes of these two experiments. The polarized elastic neutron scattering experiments were carried out on BT-7 utilizing 3 He polarizers immediately before and after the sample at NIST center for neutron research, Gaithersburg, Maryland, USA [40, 41] . The unpolarized neutron diffraction experiments in Fig. 4 (e) were carried out using a pyrolytic graphite monochromator and analyzer with pyrolytic graphite filter in the beam. Experiments on twinned BaFe 2 As 2 without external uniaxial pressure were performed on ∼12-g aligned single crystals as described before [34] . The polarized inelastic neutron scattering experiments on uniaxial pressured detwinned BaFe 2 As 2 were performed using 12 pieces cut single crystals (∼3-g, Fig. S1 ) [21] . The BT-7 measurements were carried out on a single piece of BaFe 2 As 2 mounted on a newly built in-situ uniaxial pressure device and the neutron wave vectors are set at k i = k f = 2.662Å −1 . Determination of M a , M b and M c . In our previous polarized neutron scattering studies of iron pnictides, we have established the method for determining the spin-fluctuation components M β (β = a, b, c) along the lattice axes via comparing the spin-flip scattering σ SF γ (γ = x, y, z) at two equivalent magnetic wave vectors (such as Q 1 = (1, 0, 1) and Q 2 = (1, 0, 3) as shown in Fig. 1 of the main text) . The definition of the directions x, y and z are described in Fig. 1 . σ SF γ is directly related to the spin-fluctuation components by: where α is the angle between (1, 0, 0) and Q (Fig. 1) , F (Q) is magnetic form factor of Fe 2+ , R is the flipping ratio (R = σ N SF Bragg /σ SF Bragg ≈ 13), and B is the polarization-independent background scattering. From Eq. (1), we can get four equations for our results on Q 1 and Q 2 : in which r is the intensity ratio factor between Q 1 and Q 2 to account for the differences in sample illumination volume and the convolution with instrumental resolution. The third and fourth equations in Eq. (2) can be used to determine the ratio r and M b , and the first two equations for M a and M c . More details concerning the determination of the spin-fluctuation components M a , M b and M c can be find elsewhere [39] . Although this method can determine the values of M a , M b and M c , it also results in large error bars of their values. To more accurately determine the effect of uniaxial pressure on M a and M c , we consider the differences between σ SF z (Q) − σ SF y (Q) at Q 1 and Q 2 . As M b does not diverge in uniaxial pressured and pressure-free cases [26] , a comparison of σ SF z (Q 1 ) − σ SF y (Q 1 ) raw data should be most sensitive to changes in M c , while σ SF z (Q 2 ) − σ SF y (Q 2 ) should be sensitive to changes in both M a and M c . The outcome of this analysis is shown in Figs. 2(e,f), 3(e,f). In our polarized neutron diffraction experiment at BT-7, we have only measured σ SF x and σ SF z . In elastic channel, M β is proportional to the square of the ordered moment (m β ). The determination of M β follows the same method as described in Eqs. (1) and (2) . But we need to apply the Lorentz factor (L = 1 sin 2θ ) as we use the integrated intensity of θ − 2θ scan to calculate M β [50] , where 2θ is the scattering angle for Q. Moreover, since no divergence of critical spin fluctuations were observed along the b axis, we can assume the absence of static ordered moment (M b = 0) (even if we consider that quasi-elastic spin fluctuations along b axis within the energy resolution of the elastic scattering could be included in σ SF x and σ SF z , it can be neglected at least in σ SF z because of the small pre-factor 1 R+1 ≈ 0.07 before M b ). Then Eq. (2) can be written as: Given the magnetic moment is polarized along a axis at 40K<< T N with m a ≈ 0.87 µ B , we can get r, solve M a and M c from both σ SF x and σ SF z , and determine the magnitude of the c-axis moment induced by uniaxial strain. Taking m a = 0.87µ B at 40 K, we can get m a and m c at other temperatures using the data points shown in Fig. 1(f) . From σ SF z , we get m a ≈ 0.23 ± 0.05 µ B and m c ≈ 0.12 ± 0.03 µ B at 143K, resulting in a canting angle of ∼ 28 • at this critical temperature. The calculated canting angles are estimated to be about 14 • at 140 K and 149 K, and gradually decreases to zero below 135K. σ SF x,y,z and M a,b,c below and well above T N at the AF ordering wave vectors. Fig. S2 shows the results of σ SF γ (γ = x, y, z) below and well above T N under zero and P ∼ 20 MPa. At T = 135 K (< T N ), σ SF γ 's for uniaxial pressure-free and pressured cases are shown in Figs. S2(a-d) . A comparison of σ SF z (Q 1 ) − σ SF y (Q 1 ) scattering at P = 0 and ∼20 MPa in Fig. S2 (e) suggests that the applied uniaxial pressure may enhance M c around ∼8 meV. Similar data at Q 2 in Fig. S2 (f) suggest that the effect of uniaxial pressure is limited on M a at this temperature. Figs. S2(g,h) shows as the converted M a , M b and M c at T = 135 K. At T < T N , the data with P ∼ 20 MPa is qualitatively consistent with that measured on the P = 0 sample, except that both the M a and M b are gapped below E > 10 meV and ∼ 6 meV, respectively, while only M a is gapped below 6 meV for the P = 0 sample. Note T N is ∼ 136K for P = 0 and ∼ 143 K for P ∼ 20 MPa. In relative temperature T /T N , 135K is much lower in the P ∼ 20 MPa sample (0.94T N ) than that in free-standing sample (0.99T N ), thus the spin fluctuations are further gapped. For temperatures well above T N [Figs. S2(i-p)], spin-flip scattering becomes very weak and no qualitative difference were observed for P = 0 and P ∼ 20 MPa. Comparison of M β at Q=(1, 0) and (0, 1). To determine if the uniaxial pressure induced M c at the AF wave vector Q = (1, 0) is compensated by magnetic scattering reduction at (0, 1), we compare σ SF γ between Q = (1, 0, L) and (0, 1, L) (L = 1, 3) at T = 145 K [ Fig. S3(a-d) ]. Figures S3(e) and (f) show the energy dependence of σ SF z (Q)−σ SF y (Q) at Q = (1, 0, 1)/(0, 1, 1) and Q = (1, 0, 3)/(0, 1, 3), respectively. Compared with clear magnetic intensity gains below ∼6 meV at the AF wave vectors Q 1 = (1, 0, 1) and Q 2 = (1, 0, 3), paramagnetic scattering at Q = (0, 1, 1) and (0, 1, 3) is isotropic in spin space as illustrated by the zero values of σ SF z (Q) − σ SF y (Q) at these wave vectors. Figures S3(g) and (h) show the energy dependence of M a , M b , and M c extracted from Figs. S3(a-d) at the wave vectors (1, 0) and (0, 1), respectively. Therefore, the applied uniaxial pressure clearly has an impact on magnetic excitations at (1, 0) but has no observable effect at (0, 1), which has weak and featureless energy dependence of isotropic M a , M b and M c [ Fig. S3(h) ]. Consistent with the weak scattering at (0, 1, L) observed at 145K, temperature dependence of M a , M b and M c at Q = (0, 1) is much weaker than that at (1, 0, L) and decreases in intensity at T N (Fig. S4) , consistent with the temperature dependence of (0, 1, 1) in detwinned BaFe 2 As 2 measured with unpolarized neutron scattering [21] . Uniaxial pressure dependence of the magnetic order and correlations. Fig. S5 summarizes the elastic θ − 2θ scans of σ SF x across Q = (1, 0, L) (L = 1, 2, 3). Similar to the θ − 2θ scans of σ SF z as described in Fig. 4 of the main text, the scans for σ SF x [ Fig. S5 (a) and S5(b)] exhibits temperature-independent full-width-at-half-maximum (FWHM) from 40 to 143K [ Fig. S5(c) ], indicating that the spin-spin correlation length are resolution limited even in the temperature range above T N ∼ 136 K of unstrained sample. Fig. S5(d) plots the ratio between the scattering intensity at (1, 0, 1) and (1, 0, 3) (I 101 /I 103 ), which is greatly enhanced close to T N . Since σ SF x = 0.16M a + 0.84M c at Q = (1, 0, 1) and 0.37M a + 0.37M c at (1, 0, 3), the enhancement of I 101 /I 103 is consistent with the emergence of a c-axis magnetic moment induced by uniaxial strain. At temperature where M c is not induced, the ratio I 101 /I 103 = 0.16M a /0.63M a × sin 2 2θ2 sin 2 2θ1 ≈ 0.5 (black dashed line in Fig. S5(d) , where sin 2 2θ2 sin 2 2θ1 accounts for the Lorentz factor. The data points of I 101 /I 103 in Fig. S5(d) show that M c is absent at 149K and below 135K but reaches a maximum at 143K close to T N . The unpolarized data in Fig. 4(f) shows similar behavior. In addition to the emergence of M c , it is also important to understand whether M c forms a new periodicity along c-axis. The magnetic structure factor of the three-dimensional antiferromagnetic order of BaFe 2 As 2 (k = (1, 0, 1)) results in magnetic peaks at (1, 0, L) with L = 1, 3, 5... and the absence of magnetic scattering at (1, 0, L) with L = 0, 2, 4.... If the induced M c forms a larger magnetic unit cell along c axis that ensures the presence of (1,0,1) and (1,0,3), one can expect detectable magnetic scattering at L=0, 2. However, the three-point θ − 2θ across (1, 0, 2) in Fig. S5 shows that the intensity for (1, 0, 2) is smaller than 1/3000 of (1, 0, 3), which rules out this possibility and further confirm our conclusion about the canting-moment picture as shown in Fig. 1 of the main text. Data availability. The data that support the findings of this study are available from the corresponding authors on request, and will be available at [49] . npj Quantum Materials npj Quantum Materials Magnetic Critical Scattering See supplementary information for additional data and analysis All raw data from ILL will be Neutron Scattering with a Triple-Axis Spectrometer