Abstract
To tune the magnetic properties of hexagonal ferrites, a family of magnetoelectric multiferroic materials, by atomic-scale structural engineering, we studied the effect of structural distortion on the magnetic ordering temperature (TN) in these materials. Using the symmetry analysis, we show that unlike most antiferromagnetic rare-earth transition-metal perovskites, a larger structural distortion leads to a higher TN in hexagonal ferrites and manganites, because the K3 structural distortion induces the three-dimensional magnetic ordering, which is forbidden in the undistorted structure by symmetry. We also revealed a near-linear relation between TN and the tolerance factor and a power-law relation between TN and the K3 distortion amplitude. Following the analysis, a record-high TN (185 K) among hexagonal ferrites was predicted in hexagonal ScFeO3 and experimentally verified in epitaxially stabilized films. These results add to the paradigm of spin-lattice coupling in antiferromagnetic oxides and suggests further tunability of hexagonal ferrites if more lattice distortion can be achieved.
| Original language | English |
|---|---|
| Article number | 237203 |
| Journal | Physical Review Letters |
| Volume | 121 |
| Issue number | 23 |
| DOIs | |
| State | Published - Dec 7 2018 |
Bibliographical note
Publisher Copyright:© 2018 American Physical Society.
Funding
Sinha Kishan 1 Wang Haohan 1 Wang Xiao 2 Zhou Liying 3,4 Yin Yuewei 1 Wang Wenbin 5 Cheng Xuemei 2 Keavney David J. 6 Cao Huibo 7 Liu Yaohua 7 Wu Xifan 3 Xu Xiaoshan 1,8 Department of Physics and Astronomy, 1 University of Nebraska , Lincoln, Nebraska 68588, USA Department of Physics, 2 Bryn Mawr College , Bryn Mawr, Pennsylvania 19010, USA Department of Physics, 3 Temple University , Philadelphia, Pennsylvania 19122, USA International Center for Quantum Materials, School of Physics, 4 Peking University , Beijing 100871, Peoples Republic of China Department of Physics, 5 Fudan University , Shanghai 200433, Peoples Republic of China Advanced Photon Source, 6 Argonne National Laboratory , Argonne, Illinois 60439, USA Neutron Scattering Division, 7 Oak Ridge National Lab , Oak Ridge, Tennessee 37831, USA Nebraska Center for Materials and Nanoscience, 8 University of Nebraska , Lincoln, Nebraska 68588, USA 7 December 2018 7 December 2018 121 23 237203 8 October 2018 9 July 2018 © 2018 American Physical Society 2018 American Physical Society To tune the magnetic properties of hexagonal ferrites, a family of magnetoelectric multiferroic materials, by atomic-scale structural engineering, we studied the effect of structural distortion on the magnetic ordering temperature ( T N ) in these materials. Using the symmetry analysis, we show that unlike most antiferromagnetic rare-earth transition-metal perovskites, a larger structural distortion leads to a higher T N in hexagonal ferrites and manganites, because the K 3 structural distortion induces the three-dimensional magnetic ordering, which is forbidden in the undistorted structure by symmetry. We also revealed a near-linear relation between T N and the tolerance factor and a power-law relation between T N and the K 3 distortion amplitude. Following the analysis, a record-high T N (185 K) among hexagonal ferrites was predicted in hexagonal ScFeO 3 and experimentally verified in epitaxially stabilized films. These results add to the paradigm of spin-lattice coupling in antiferromagnetic oxides and suggests further tunability of hexagonal ferrites if more lattice distortion can be achieved. National Science Foundation 10.13039/100000001 DMR-1552287 Division of Materials Research 10.13039/100000078 DMR-1454618 National Science Foundation 10.13039/100000001 DMR-1708790 DMR-1053854 ECCS-1542182 U.S. Department of Energy 10.13039/100000015 Oak Ridge National Laboratory 10.13039/100006228 Office of Science 10.13039/100006132 Argonne National Laboratory 10.13039/100006224 DE-AC02-06CH11357 Spin-lattice couplings have a significant impact on magnetic properties. In antiferromagnetic (AFM) orthorhombic R T M O 3 ( o - R T M O 3 ) for example, where R stands for rare earth, Y, or Sc, and T M stands for transition metal, a larger orthorhombic distortion from the cubic perovskite structure correlates with a lower Néel temperature ( T N ), which may be understood as the reduction of the AFM superexchange interactions caused by the smaller T M -O- T M bond angles due to the orthorhombic distortions [1,2] . The effect of spin-lattice couplings may be employed to tune the magnetic properties. Here we focus on increasing the T N of hexagonal R FeO 3 , a family of multiferroics materials that are promising candidates for applications because of their spontaneous electric and magnetic polarizations, and potential magnetoelectric effects due to the coupling between the ferroelectric and the magnetic orders [3,4] . For widespread applications, it is important to increase the T N of h - R FeO 3 [5] , by, e.g., atomic-scale structural engineering based on the spin-lattice couplings. On the other hand, in h - R FeO 3 , T N increases with the lattice distortion, which is a puzzling trend opposite to that in the AFM o - R T M O 3 [see Fig. S1] [6] . Previously, Disseler et al. discovered a correlation between T N and lattice constants in h - R MnO 3 and h - R FeO 3 [26] . The higher T N for smaller R has been attributed to closer Fe-Fe (or Mn-Mn) distances [26,27] . This understanding is worth revisiting, since it cannot explain that in AFM o - R T M O 3 , the smaller lattice constants do bring the T M atoms closer, but the reduced T M -O- T M bond angles actually decrease the AFM exchange interactions and T N . Hence, there should be a distinct mechanism of magnetic ordering and spin-lattice coupling in h - R MnO 3 and h - R FeO 3 . Elucidating this mechanism will not only provide guidance in increasing T N of h - R FeO 3 , but also add to the paradigms of spin-lattice coupling in AFM oxides. In this work, we examine the role of the structural distortion in the magnetic ordering in h - R MnO 3 and h - R FeO 3 . A symmetry analysis shows that the three-dimensional magnetic ordering is forbidden in the undistorted structure by symmetry, but can be induced by the K 3 distortion with a power-law relation between T N and K 3 magnitude. Based on these revelations, we have predicted a record-high T N in h - R FeO 3 when R = Sc and experimentally confirmed it in epitaxially stabilized films. Hexagonal ScFeO 3 (001) and YbFeO 3 (001) films ( 5 × 5 mm 2 and 10 × 10 mm 2 surface area, 70–200 nm thick) have been grown on Al 2 O 3 (001) and yttrium stabilized zirconia (YSZ) (111) respectively using pulsed laser (248 nm) deposition in a 5 mTorr oxygen environment, at 750 ° C with a laser fluence of about 1.5 J / cm 2 and a repetition rate of 2 Hz [28] . The film growth was monitored using the reflection high-energy electron diffraction (RHEED). The structural and magnetic properties have been studied using x-ray diffraction and spectroscopy, magnetometry, and neutron diffraction. X-ray diffraction experiments, including θ / 2 θ scan, ϕ scan, and reciprocal space mapping were carried out using a Rigaku D/Max-B diffractometer with Co- K α radiation (1.793 Å wavelength) and a Rigaku SmartLab diffractometer with Cu- K radiation (1.5406 Å). X-ray absorption spectroscopy (including x-ray linear dichroism) with a 20° incident angle was studied at beam line 4-ID-C at the Advanced Photon Source at Argonne National Laboratory. Neutron diffraction experiments were carried out at beam line CORELLI at the Spallation Neutron Source (SNS) and HB3A four-circle diffractometer (FCD) at the High Flux Reactor (HFIR) with a thermal neutron wavelength of 1.546 Å, in the Oak Ridge National Laboratory. Temperature and magnetic-field dependence of the magnetization was measured using a superconducting quantum interference device (SQUID) magnetometer with the field along the film normal direction. The crystal structure of isomorphic hexagonal R MnO 3 and R FeO 3 ( h - R MnO 3 and h - R FeO 3 ) has a P 6 3 cm symmetry, consisting of alternating FeO (or MnO) and R O 2 layers [Fig. 1(a) ]. AFM orders occur in h - R MnO 3 and h - R FeO 3 below about 70–140 K with spins in the FeO (or MnO) layers forming 120° structures [26,29–32] . Below about 1000 K, ferroelectricity in h - R MnO 3 and h - R FeO 3 is induced by a lattice distortion ( K 3 ) [Fig. 1(a) ] which tilts the FeO 5 (or MnO 5 ) local environment, shifts the R atoms along the c axis, and trimerizes the unit cell, with a sizable electric polarization ( P ≈ 10 μ C / cm 2 ) [33–36] . In addition, hexagonal R FeO 3 exhibits a weak ferromagnetism [26,30,34,35,37,38] [Fig. 1(a) ] due to the canting Fe spins. 1 10.1103/PhysRevLett.121.237203.f1 FIG. 1. (a) Atomic structure of h - R FeO 3 depicted by a hexagonal unit cell. The arrows through the Fe atoms indicate the spins. The arrows from the atoms indicate the atomic displacements of the K 3 lattice distortion. The table indicates the hexagonal stacking. (b) The geometric arrangement of Fe atoms in the z = 0 and z = c / 2 layers. The arrows through the Fe atoms indicate the spins. The atom Fe 0 is highlighted by its FeO 5 trigonal bipyramid to depict the local symmetry. (c) log { T N / [ S ( S + 1 ) ] / K } as a function of log ( Q K 3 ) . Inset: T N / [ S ( S + 1 ) ] as a function of the tolerance factor. The dashed line is a linear fit to the data. The data are from the literature (see text). Magnetic ordering relies on the underlying exchange interactions. In h - R FeO 3 and h - R MnO 3 , although the exchange interactions within the FeO (or MnO) layers are strong, the interlayer exchange interactions are weakened by the layered structure and hexagonal stacking. Using h - R FeO 3 as an example, Fig. 1(b) shows the arrangement of the Fe atoms and their spins in two neighboring FeO layers. The Fe atoms are on the hexagonal A and C sites in the two layers, respectively. One Fe atom ( Fe 0 ) in the z = c / 2 layer is highlighted by its tilted FeO 5 trigonal bipyramid. The interlayer nearest-neighbor exchange energy for Fe 0 is E inter = ∑ i = 1 3 J 0 i S → 0 · S → i , where S i is the spin on Fe i , and J 0 i is the exchange interaction coefficient between Fe 0 and Fe i . When there is no lattice distortion, the local symmetry of Fe 0 is C 3 v , leading to J 01 = J 02 = J 03 and E inter = 0 because ∑ i = 1 3 S → i = 0 . In other words, the interlayer exchange interactions are canceled; the spin alignment between the two layers is lost. Therefore, the three-dimensional magnetic ordering is forbidden in the undistorted P 6 3 / mmc structure by symmetry. On the other hand, the K 3 lattice distortion [Fig. 1(a) ] reduces the symmetry to C S , making J 03 ≠ J 02 = J 01 . Consequently, nonzero lattice distortion leads to the three-dimensional magnetic ordering because E inter = ( J 01 – J 03 ) S ( S + 1 ) ≠ 0 [39] . Since the interlayer exchange interaction is the bottleneck of the three-dimensional magnetic ordering, one has T N ∝ E inter = ( J 01 – J 03 ) S ( S + 1 ) . The dependence of T N on the K 3 distortion then hinges on the relation between J 01 – J 03 and the magnitude of K 3 ( Q K 3 ). Previously, Das et al. analyzed the relation between J 01 – J 03 and Q K 3 [3] . Expanding J 01 and J 03 with respect to Q K 3 around Q K 3 = 0 , the odd terms are expected to be zero due to the symmetry at Q K 3 = 0 , leaving J 01 – J 03 ∝ a 2 Q K 3 2 + a 4 Q K 3 4 , where a 2 and a 4 are coefficients. In Fig. 1(c) , we plot the log { T N / [ S ( S + 1 ) ] } as a function of log ( Q K 3 ) of h - R MnO 3 measured using the neutron diffraction from the literature [40,41] [see Fig. S2] [6] , where spin S is 2 for Mn. The data appear to fall on a straight line, indicating a power-law relation T N / [ S ( S + 1 ) ] ∝ Q K 3 n ; a fit shows n = 2.7 ± 0.05 . Given that the tilt of FeO 5 and MnO 5 caused by the K 3 distortion is on the order of several degrees which is not so small [29,40,41] , both the a 2 Q K 3 2 and the a 4 Q K 3 4 terms could play a role, resulting 2 < n < 4 . It is challenging to predict the T N using the direct dependence of T N on the K 3 distortion, however, because the K 3 distortion, which involves the displacement of oxygen atoms, is difficult to measure precisely. The tolerance factor t = ( r R + r O ) / [ ( r T M + r O ) 2 ] where r R , r T M , and r O are atomic radius of R , T M and oxygen, is a good measure of lattice distortion from the cubic perovskite structure in o - R T M O 3 . It could also be used to gauge the structural distortion in h - R FeO 3 and h - R MnO 3 , because a smaller R atom is expected to reduce the in-plane lattice constant, which needs to be accommodated by a larger K 3 distortion to reduce the distances between Fe (or Mn) atoms within the FeO (or MnO) layers. In other words, smaller t is expected to lead to larger T N , which is consistent with the data from the literature [Fig. 1(c) inset and Fig. S2] [6,31,40,41] , where a linear correlation between T N / [ S ( S + 1 ) ] and t in h - R FeO 3 and h - R MnO 3 is observed ( S is 2 and 2.5 for Mn and Fe, respectively). Following the trend in Fig. 1(c) , a smaller R , corresponding to a smaller t , will lead to a higher T N in h - R FeO 3 and h - R MnO 3 . Since Sc has a much smaller atomic radius than that of the rare earth and Y [42] , T N in h - ScFeO 3 is expected to be higher than that of other h - R FeO 3 . To verify the prediction, we studied the magnetic ordering temperature in h - ScFeO 3 . ScFeO 3 naturally crystallizes in bixbyite structure in bulk; high pressure growth of ScFeO 3 results in a corundum structure [43] . Previous studies show that partially substituting Lu with Sc in LuFeO 3 may stabilize the hexagonal structure [26,27,44] . However, the stabilization of pure ScFeO 3 in the P 6 3 cm structure has never been reported. In this study, we have successfully grown h - ScFeO 3 epitaxial films on Al 2 O 3 (001) substrates. The crystal structure and epitaxial relations of the h - ScFeO 3 films were characterized using x-ray diffraction. As shown in Fig. 2(a) , the θ / 2 θ scan shows a typical pattern of the P 6 3 cm structure with the epitaxial relation: h - ScFeO 3 (001) ∥ Al 2 O 3 (001). The ϕ scan [see Fig. S3] [6] demonstrates the sixfold rotation symmetry and the in-plane epitaxial relation: h - ScFeO 3 (100) ∥ Al 2 O 3 (100). The RHEED patterns [Figs. 2(b) and 2(c) ], which are signatures of the h - R FeO 3 structure, indicate a flat surface. The FeO 5 trigonal bipyramid configuration is confirmed by the similarity between the x-ray linear dichroism spectroscopy of h - ScFeO 3 [Fig. 2(d) ] and those of h - LuFe O 3 and h - YbFe O 3 observed previously [28,45–47] . From the x-ray reciprocal space mapping [see Fig. S3] [6] , the lattice constants of h - ScFeO 3 were determined: a = 5.742 Å and c = 11.690 Å , smaller than the values of other h - R FeO 3 [48–50] , suggesting a larger lattice distortion [51] . 2 10.1103/PhysRevLett.121.237203.f2 FIG. 2. Structural and magnetic characterizations of h - ScFeO 3 ( 001 ) / Al 2 O 3 films. (a) θ / 2 θ x-ray (1.789 Å) diffraction. (b) and (c) are the RHEED diffraction patterns measured when the electron beam are along the (1-10) and (100) directions respectively. (d) X-ray absorption spectra measured at the Fe L edges using s (in plane) and p (out of plane) linearly polarized x-ray beams. (e) A slice of the reciprocal space of h - ScFeO 3 at L = 1 measured using neutron diffraction at CORELLI (see text). (f) Temperature dependence of the neutron diffraction intensities of the (101) and (114) peaks measured at CORELLI and HB3A. (g) Temperature dependence of the magnetization per formula unit (f.u.) measured during warming after field cool (10 kOe) and zero field cool using 100 Oe and 500 Oe. (h) Magnetization-field hysteresis loop measured at 100 K. The magnetic field is along the film normal direction. T N of h - ScFeO 3 was measured by the neutron diffraction experiments at CORELLI in addition to that of h - YbFeO 3 . Using a wide wave-length-band neutron beam and a two-dimensional detector at CORELLI, a three-dimensional portion of the reciprocal space [using the Miller indices ( H , K , L ) as the coordinates] can be measured without rotating the sample [see Figs. S4–S7] [6] . The (101) and (114) diffraction peaks, were mapped out in the three-dimensional reciprocal space. As shown in Fig. 2(e) , the two magnetic Bragg diffraction peaks (101) and (1-11), which are equivalent because of the sixfold rotational symmetry along the c axis, were observed. The (101) Bragg peak is forbidden for the nuclear diffraction due to the crystal structure symmetry of h - R FeO 3 (space group P 6 3 cm ), but it is allowed for magnetic diffraction [29] . The observation of the (101) peak confirms the magnetic ordering in h - R FeO 3 , as previously shown in h - LuFeO 3 and h - R MnO 3 [26,29,32] . The temperature dependence of the (101) peak intensity suggests a transition at about 200 K, which is corroborated by the measurements at HB3A [Fig. 2(f) ]. In contrast, the intensity of the (114) peak, which mainly comes from the nuclear scattering, shows an insignificant temperature dependence. As shown in Fig. 2(g) , a similar transition temperature is observed in the temperature dependence of the magnetization measured using a SQUID magnetometer on warming, after cooling the sample in a 10 kOe magnetic field (field cool or FC) and after cooling in a zero magnetic field (zero-field cool or ZFC). The FC and ZFC curves diverge at around 185 K, giving a more precise determination of T N . As predicted, h - ScFeO 3 shows a high T N among all h - R MnO 3 and h - R FeO 3 , as shown in Fig. 3(a) , where our measurement on h - YbFeO 3 and data in the literature are also included [See Figs. S3 and S4] [6,26,29,31–35,37,41] ; the measured T N of h - ScFeO 3 is slightly lower than the value predicted by extrapolating the linear relation between T N and t , which is also true for h - ScMnO 3 [29] . The reduction of magnetization at low temperature in Fig. 2(g) hints at a possible spin reorientation at about 100 K in h - ScFeO 3 . However, the temperature dependence of the (101) peak intensity in Fig. 2(f) indicates that spin reorientation in h - ScFeO 3 may not be significant enough to change the spin structure from A 2 to A 1 [26] . 3 10.1103/PhysRevLett.121.237203.f3 FIG. 3. (a) The dependence of T N and T N / S ( S + 1 ) on the tolerance factor. The dashed line is a guide to the eye. (b) The magnetization from the canting of Fe spins ( M Fe ) as a function of the in-plane lattice constant. Except for h - YbFeO 3 and h - ScFeO 3 in (a) and h - ScFeO 3 in (b), the data are from the literature (see text). Finally, we discuss the effect of lattice distortion on the canting of Fe moments, which is responsible for the net magnetization M Fe along the c axis. The M Fe in h - ScFeO 3 can be inferred from the magnetometry data. As shown in Fig. 2(h) , the M – H curve shows a soft and a hard component, corresponding to two steps at H ≈ 0 and H ≈ 30 kOe , respectively. This two-component feature has been observed in both h - LuFeO 3 and h - YbFeO 3 films [38,45] . The jump of magnetization at the higher field corresponds to the intrinsic coercivity of the h - R FeO 3 , while the jump at the low field corresponds to the unavoidable structural boundaries in film samples of h - R FeO 3 that create uncompensated spins. From the 30-kOe jump, we found that M Fe = 0.015 ± 0.002 μ B / Fe in h - ScFeO 3 , which is smaller than that of h - LuFeO 3 and h - YbFeO 3 [38,45] , as shown in Fig. 3(b) . This result is counterintuitive, because a large K 3 distortion, corresponding to a larger tilt angle of the FeO 5 would seemingly generate a larger canting angle of the Fe moments ( θ cant ). However, θ cant results from a competition between the exchange interaction and the Dzyaloshinskii-Moriya (DM) interaction [52–54] . Relation between the canting angle ( θ cant ) of the Fe moments, tilt angle of the FeO 5 ( γ tilt ), lattice constant in the basal plane ( a ), and the intralayer exchange interaction coefficient J can be derived as θ cant ∝ a 2 γ tilt / J [See Fig. S8] [6] . Although h - ScFeO 3 is expected to have a larger γ tilt and smaller J , a is also smaller. Hence, the size of θ cant cannot be simply linked to the amplitude of γ tilt . If the effect of a dominates, M Fe would decrease for smaller R , which is what we found in our previous first-principle calculations [51] . In conclusion, using symmetry analysis, we showed that the three-dimensional magnetic ordering in h - R MnO 3 and h - R FeO 3 are forbidden in undistorted structures by symmetry, but can be induced by the structural distortions. We also showed that the dependence of T N on structural distortions manifests as a near-linear relation with the tolerance factor and a possible power law with Q K 3 , suggesting a higher T N in h - ScFeO 3 with respect to other hexagonal ferrites studied so far, which was realized in this work in epitaxially stabilized films. In addition to indicating that the multiferroic ordering in h - R FeO 3 and h - R MnO 3 may be further enhanced with larger lattice distortions, these results also establish a paradigm of structural origin of magnetic ordering and spin-lattice coupling in AFM oxides. This work was primarily supported by the National Science Foundation (NSF), Division of Materials Research (DMR) under Grant No. DMR-1454618. X. 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This research used resources at the Spallation Neutron Source and the High Flux Isotope Reactor, DOE Office of Science User Facilities operated by the Oak Ridge National Laboratory, and resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The research was performed in part in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, which are supported by the National Science Foundation under Grant No. ECCS-1542182, and the Nebraska Research Initiative.
| Funders | Funder number |
|---|---|
| Advanced Photon Source | |
| DMR-1454618 National Science Foundation | 10.13039/100000001 DMR-1708790 DMR-1053854 ECCS-1542182 |
| DOE Office of Science User Facilities | |
| NSF DMR-1708790 | DMR-1053854, DMR-1708790 |
| National Nanotechnology Coordinated Infrastructure | |
| Office of Science User Facility operated | |
| National Science Foundation | 10.13039/100000001 DMR-1552287 |
| U.S. Department of Energy | |
| Division of Materials Research | 10.13039/100000078 DMR-1454618, DMR |
| National Sleep Foundation | |
| Argonne National Laboratory | DE-AC02-06CH11357 |
| Oak Ridge National Laboratory | |
| Norsk Sykepleierforbund | |
| National Science Foundation | ECCS-1542182 |