npsm 새물리 New Physics : Sae Mulli

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Research Paper

New Phys.: Sae Mulli 2023; 73: 1041-1045

Published online December 31, 2023

Copyright © New Physics: Sae Mulli.

The Magnetic Structural Analysis of Two-dimensional Triangular Heisenberg Antiferromagnetic Yb0.42Sc0.58FeO3

Shin-ichiro Yano1*, Chin-Wei Wang1, Junjie Yang2

1National Synchrotron Radiation Research Center, Hsinchu 30077, Taiwan
2Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA

Correspondence to:*

Received: August 31, 2023; Revised: October 16, 2023; Accepted: October 16, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

We report the magnetic structure of Yb0.42Sc0.58FeO3 determined by powder neutron diffraction. The symmetry of the crystal structure is P63cm. The magnetic structure was described by the linear combination of irreducible representations Γ1 and Γ2. Two irreducible representations are necessary to describe the magnetic structures of two-dimensional Heisenberg antiferromagnets such as hexagonal-RMnO3 and hexagonal-RFeO3. The result is important in discussing the exchange parameters and the origin of the multiferroicity. We discuss possible ways to uniquely determine the magnetic structure and the origin of the multiferroicity of these systems.

Keywords: Magnetic structural analysis, Powder neutron diffraction, Multiferroics, Antiferromagnets

Multiferroics, materials that exhibit ferroelectric and magnetic ordering, have been the focus of great attention over the last two decades. Cross-coupling of the electric and magnetic degree of freedom is quite interesting not only for applications but also for basic science[1-3].

Among multiferroic materials, hexagonal manganites R MnO3 (R = rare earth) were found as research of multiferroic materials in the early stages and were classified as type I multiferroics. The symmetry of the crystal structure is reported as non-centrosymmetric P63cm. Under this symmetry, there are six irreducible representations of the magnetic structures. These are Γ1 (P63cm), Γ2 (P63cm), Γ3 (P63cm), Γ4 (P63cm), Γ5 (P63) and Γ6 (P63). Among them, Γ14 are one-dimensional irreducible representations and Γ56 are two-dimensional irreducible representations. Γ1 (P63cm), Γ2 (P63cm), Γ3 (P63cm), Γ4 (P63cm) have been used to describe the magnetic structures of hexagonal RMnO3 with some exceptions.

A key parameter of this system is the atomic position of Mn. It is because the magnetic atoms Mn occupy (xMn,0,0), xMn 13 and equivalent sites, that is, they form a triangular lattice and interactions between Mn and Mn in the plane are antiferromagnetic, so magnetic frustration in this system is expected. If the position was exactly xMn=13, the intralayer exchange interactions are J1=J2 and the interlayer interactions J1c and J2c cancel out. If xMn,Fe>13, there are 4 J1 and 2J2 in the intralayer interactions while 2 J1c and 4 J2c in the interlayer interactions. On the other hand, if xMn,Fe<13, there are 2 J1 and 4 J2 in the intralayer interactions, while 4 J1c and 2 J2c in the interlayer interactions[4].

Interesting physics appears for this delicate parameter xMn. One is the so-called trimerization[5, 6]. The atomic position xMn 13 shows a large shift that can induce the coupling with the electric dipole moment at TN in RMnO3. Lee et al.[5] discussed that magneto-elastic coupling is the source of magnetoelectric coupling. The other is spin reorientation. HoMnO3 and ScMnO3 show spin reorientation at low temperature, whereas YbMnO3 does not. The phenomenon occur at the crossover of xMn=13. xMn increases below TN in HoMnO3, while it decreases in ScMnO3. The temperature of crossing xMn=13 matches the spin reorientation temperature. YbMnO3 shows no spin reorientation and xMn remains lower than 13 over the whole temperature down to 1.5 K.

In this paper we focus on the hexagonal RFeO3 (R = Lu, Sc, and Yb) which are also multiferroic materials and exhibit the same 2D-triangular lattice Heisenberg antiferromagnetic system (2D-THA) with P63cm. Hexagonal RFeO3 compounds are rare, with only a few examples reported, such as Lu0.5Sc0.5FeO3[7-9] and Yb0.42Sc0.58FeO3[10]. The magnetic moment of Fe corresponds to S=52 while that of Mn is S=2, and comparing these helps to better understand the 2D-THA. Yb0.42Sc0.58FeO3 shows successive magnetic phase transitions at TN 165 K, the spin reorientation temperature TSR 40 K, and the Yb3+ ordering temperature TYb 15 K[10]. The magnetic structure of Yb0.42Sc0.58FeO3 was reported as Γ1 + Γ2 below T = 25 K. The weighting coefficients of the two irreducible representations were not reported but they are necessary. It is essential to accurately determine the magnetic structure of this system in order to accurately model inelastic neutron scattering data and capture magnetoelastic excitations, magnon-phonon interactions, and other related phenomena[11] Here, we report the magnetic structural analyses of Yb0.42Sc0.58FeO3 and discuss the multiferroics of these two 2D-THAs, RMnO3 and RFeO3.

The Yb0.42Sc0.58FeO3 polycrystalline samples were synthesized using the solid-state reaction method. High-purity Yb2O3, Sc2O3, and Fe2O3 powders were stoichiometrically mixed and ground. The mixed powders were pelletized and sintered at 1200 °C for 24 h and then at 1400 °C for 24 h in air with two intermediate grindings. The neutron powder diffraction patterns were collected on the high resolution powder diffractometer Echidna[12] installed on the Opal Research Reactor at ANSTO, Australia. The incident neutron wavelength of 2.4395 Å was selected by Ge (331) reflection at the take-off angle of 140 degrees. The sample was loaded in a 9 mm diameter vanadium can. The sample temperatures were at T = 3.5, 10, 25, 50, 100, 125, 150, 250, and 300 K achieved by using a closed cycle refrigerator with top loading.

We have performed a series of neutron scattering studies of Lu1-yYyMnO3, Lu1-yScyFeO3, and Yb1-yScyFeO3 including inelastic neutron scattering experiments by using large single crystal samples of Lu0.3Y0.7MnO3 and Lu0.47Sc0.53FeO3. The magnetic structures of Lu1-yYyMnO3 have been reported[13] and inelastic neutron scattering data of Lu0.3Y0.7MnO3 and Lu0.47Sc0.53FeO3 will be reported elsewhere.

This paper presents the powder neutron diffraction data and the magnetic structural analysis of Yb0.42Sc0.58FeO3. The determined crystal structural parameters at 300 K are summarized in Table 1. The lattice parameters determined were a = 5.85912(2) Å and c = 11.69126(7) Å with the space group P63cm at T = 300 K. Yb and Sc are not distinguishable in neutron powder diffraction, so the composition was fixed. We assume that Yb and Sc are uniformly distributed. The sample contains 1.78(11)% ScFeO3.

Table 1 . Refined structural parameters of Yb0.42Sc0.58FeO3 at 300 K. The lattice parameters are a = 5.85912(2) Å and c = 11.69126(7) Å.

Atom (Wyck.)xyzocc.B-iso

Figure 1 shows four representative powder neutron diffraction patterns of Yb0.42Sc0.58FeO3. There are three magnetic phases. Magnetic R factors and χ2 values are shown in these figures.

Figure 1. (Color online) Four representative neutron powder diffraction patterns (a) T = 3.5 K (b) 50 K (c) 125 K (b) 300 K. Experimental data are shown as filled red circles, the fitted profile as a black line, and the difference between these two as a blue line. The peak positions are shown as tick marks.

Figure 2 shows the temperature dependence of the magnetic moment and the atomic position of Fe. The temperature dependence of the magnetic peak showed up below 200 K and reached the 3.7 μB / Fe atom at base temperature. The atomic position remains xFe=13 at most temperatures. Below T = 25 K, there is a slight change from xFe=13 but it changes again to xFe=13 by further decreasing the temperature. The weak trimerization appears at TYb= 25 K, which implies that interactions between R3+ and Fe3+ could be the cause of the trimerization in the Yb0.42Sc0.58FeO3.

Figure 2. (a) Temperature dependence of magnetic moment of Fe (b) Temperature dependence of Fe atomic position (xFe,0,0).

The magnetic structures are fitted using the model below and shown in Fig. 3,

Figure 3. (Color online) Temperature dependence of coefficients of the magnetic structure of Yb0.42Sc0.58FeO3.


Here, Γ1 is P63cm, Γ2 is P63cm in the plane, and Γ2z has the magnetic moment along the c-axis. The irreducible representation Γ2 accounts for all the magnetic peaks in the magnetically ordered phase below TN = 150 K. In hexagonal RFeO3 (R = Lu, Sc, Yb), a weak ferromagnetic moment is reported. The compatible irreducible representation is Γ2. The magnetic (100) Bragg peak developed at T = 50 K, and another irreducible representation Γ1 was introduced to solve the magnetic structure. Either Γ1 or Γ3 could contribute to the (100) peak, but only Γ1 fits the pattern well. We observed rotations of magnetic moment in the plane by changing the ratio of Γ1 and Γ2. Spin reorientation is not as drastic as reported in the literature[4]. Interestingly, the magnetic moment of Fe with Γ2z is stable below TN = 150 K to the base temperature. The magnetic moment of Yb orders below T = 25 K. The best fit showed that the magnetic moments of both Yb(2a) and Yb(4b) are along the c-axis but they are in opposite directions. The results are qualitatively consistent with[10].

In the hexagonal RFeO3 (R = Lu, Sc, Yb), a weak ferromagnetic moment is reported[7, 8, 10]. So, the only compatible irreducible representation So, the only is Γ2. In addition to Γ2, Γ1 is necessary to describe for powder neutron diffraction below T = 100 K. C1Γ1 + C2Γ2 is the correct magnetic structure of RFeO3. Lu1-yYyMnO3 adopts the Γ4 because there is no ferromagnetic moment observed by the magnetization measurement. If we used Γ4, the magnetic structure fit to the neutron powder diffraction data should be C3Γ3 + C4Γ4. In fact, the neutron diffraction and polarimetric study by Brown and Chatterji[14] reported the magnetic structure of YMnO3 with Γ6 (P6'3) with angle deviation from the axial directions being Ψ = 11 degrees from Γ3 (P6'3cm'). Neutron scattering data show Lu1-yYyMnO3 is C3Γ3 + C4Γ4[13] and Yb0.42Sc0.58FeO3 is C1Γ1 + C2Γ2.

To uniquely determine the magnetic structure, there are several difficulities. As Katsufuji[6] notes, if there is no trimerization distortion, the nuclear (100) Bragg peak is forbidden. On the contrary, if there is trimerization distortion, both nuclear and magnetic scattering could contribute to the Bragg (100) peak. That makes it difficult to determine the crystal and magnetic structure precisely by neutron diffraction alone. A simple polarized neutron diffraction should show whether the Bragg (100) peak is a magnetic peak or not. By investigating the (h0l) plane with polarized neutrons, one can observe that the magnetic moment out of the plane to demonstrate that the Γ2 phase exists. Magnetization measurement also supports the existence of weak ferromagnetism. However, to uniquely determine magnetic structures, even neutron polarimetry with cryopad[14] is inconclusive, since Γ5 and Γ6 are compatible with the results[14]. We would require a combination of measurements such as magnetization, second harmonic generation,[17] and polarized neutron scattering to be conclusive.

Determining the magnetic structure is an important issue because only Γ1 and Γ2 allow magnetoelectric coupling, while Γ3 and Γ4 do not[18]. In the case of Lu1-yYyMnO3, neither Γ3 nor Γ4 should have magnetoelectric coupling, so multiferroicity should be through magnetoelastic coupling. On the other hand, Γ1 or Γ2 can have a magnetoelectric coupling that is consistent with[19,20]. Therefore, even though the crystal structure is similar in RFeO3 and RMnO3, there could be different mechanisms for multiferroicity. If the ferromagnetic component Γ2z is the source of multiferroicity of RFeO3, the magnetic field might be able to control it by stabilizing the domain in the material. For example, the ferromagnetic moment of Lu0.5Sc0.5FeO3 decreases while the sample is cooled, which means that the component or domain of Γ2 is decreasing[7-9]. Further investigation of the weak ferromagnetic component and multiferroic properties is needed.

In another point, Fabréges[4] discussed the interlayer interactions that cause spin reorientation in the RMnO3 system by showing the curvature of spin wave dispersion along (1,0,Ql) where the value of J1cJ2c is critical. However, the spin dynamics of (Lu,Sc)FeO3[21] do not show a clear dispersion along the (1,0,Ql) even though a clear spin reorientation is observed in the RFeO3. The spin reorientation of the RFeO3 system could have a different origin than the the interlayer interaction of J1c and J2c. This could be because the Fe magnetic moment is larger than the Mn magnetic moment, so intralayer interactions J1 and J2 are 2.5 meV in RMnO3 while J1 and J2 are 4.0 meV in RFeO3. In addition, the ratio of the lattice parameters ca of RFeO3 is typically larger compared to those of RMnO3[9]. Interlayer interactions are less important to have spin reorientation in RFeO3.

We show the coefficients of the magnetic structure differnet orderd sites of using two irreducible representations in this paper. The optimized magnetic structures of 2D-THA are necessary to understand magnetic excitations and multiferroic properties. They should be discussed based on the correct magnetic structures to extract precise parameters such as exchange parameters, magnetoelastic coupling, or magnetoelectric coupling in these RMnO3 and RFeO3 systems[19-21].

We used powder neutron diffraction to analyze Yb0.42Sc0.58FeO3 and identified three magnetic phases. The structure requires two irreducible representations, Γ1 and Γ2, for explanation. These representations also apply to hexagonal-RMnO3 and hexagonal-RFeO3, but differences in magnetic symmetries suggest distinct origins for spin reorientation and multiferroicity. The weak ferromagnetic moment of Fe may be pivotal for ferroelectricity.

S.Y. is financially supported by the National Science and Technology Council, Taiwan, with Grants No.110-2112-M-213-013, 111-2112-M-213-023, and 112-2112-M-213-019. The work at NJIT was supported by the US Department of Energy under Grant No. DOE: DE- SC0021188. The experiments were carried out under the ANSTO user program (MI17467:Echidna).

  1. T. Kimura, et al., Nature 426, 55 (2003).
    Pubmed CrossRef
  2. R. Ramesh, Nature 461, 1218 (2009).
    Pubmed CrossRef
  3. N. A. Spaldin, S.-W. Cheong and R. Ramesh, Phys. Today 63, 38 (2010).
  4. X. Fabrèges, et al., Phys. Rev. Lett. 103, 067204 (2009).
  5. S. Lee, et al., Nature 451, 805 (2008).
    Pubmed CrossRef
  6. T. Katsufuji, et al., Phys. Rev. B 66, 134434 (2002).
  7. A. Masuno, et al., Inorg. Chem. 52, 11889 (2013).
    Pubmed CrossRef
  8. L. Lin, et al., Phys. Rev. B 93, 075146 (2016).
  9. S. M. Disseler, et al., Phys. Rev. B 92, 054435 (2015).
  10. Y. S. Tang, et al., Phys. Rev. B 103, 174102 (2021).
  11. S. L. Holm, et al., Phys. Rev. B 97, 134304 (2018).
  12. M. Avdeev and J. R. Hester, J. Appl. Crystallogr. 51, 1597 (2018).
  13. S. Yano, et al., Phys. Rev. B 107, 214407 (2023).
  14. P. J. Brown and T. Chatterji, J. Phys.: Condens. Matter 18, 10085 (2006).
  15. F. Tasset, P. J. Brown and J. B. Forsyth, J. Appl. Phys. 63, 3606 (1988).
  16. F. Tasset, Physica B 156-157, 627 (1989).
  17. M. Fiebig, et al., Phys. Rev. Lett. 84, 5620 (2000).
    Pubmed CrossRef
  18. C. J. Howard, et al., Acta Cryst. B69, 534 (2013).
    Pubmed CrossRef
  19. J. Oh, et al., Phys. Rev. Lett. 111, 257202 (2013).
  20. J. Oh, et al., Nat. Commun. 7, 13146 (2016).
  21. J. C. Leiner, et al., Phys. Rev. B 98, 134412 (2018).

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