**1. Introduction**

Multiferroic materials [1–7], with the coupling of two or more ferroic orders, have been attracting much attention due to their intriguing physics and great application potential. The *Pbnm* structured orthoferrites *R*FeO3 (*R* = rare earth element) have great potential value for application as magnetoelectric (ME) devices based on the mutual control of magnetization (*M*) and electric polarization (*P*) [8–11]. For example, at lower temperatures, the application of a large critical magnetic field along the *c*-axis induces a multiferroic (weakly ferromagnetic of Fe3+-sublattice and ferroelectric) state in DyFeO3, and the magnetic field induced *P* results from the movement of the Dy3+ ions toward the Fe3+ ions and backward, corresponding to the exchange striction [12]. The ME coupling and *P* are decided by the spin configurations of both Fe3+ and Dy3+ ions. In DyFeO3, Fe3+ ions (*S* = 5/2) exhibit the G*x*A*y*F*<sup>z</sup>* (magnetic configuration in Bertaut's notation below its Néel temperature of the Fe3+-sublattice *T*N(Fe) = 650 K) [13–16], in which the main component of the magnetic moment of Fe3+ ions lies along the *a*-axis, and due to the Dzyaloshinskii–Moriya interaction (DMI), a small fraction of the moment is canted along the *c*-axis, causing weak ferromagnetism (wFM) in the material [17]. With decreasing temperature, the spin-reorientation (Morin) transition occurs at *TSR* (in the range of about 35~70 K [18–21]), where the magnetic configuration of Fe3+ ions changes from G*x*A*y*F*<sup>z</sup>* to A*x*G*y*C*z*, and then the wFM disappears. Below the antiferromagnetic (AFM) ordering temperature of the Dy3+-sublattice *T*N(Dy) = 4.2 K, the Dy3+ magnetic configuration is G*x*A*<sup>y</sup>* [22,23] with the Ising axis deviation of about 33◦ from the *b*-axis. When a magnetic field (higher than about 3 T) is applied

**Citation:** Zeng, Z.; He, X.; Song, Y.; Niu, H.; Jiang, D.; Zhang, X.; Wei, M.; Liang, Y.; Huang, H.; Ouyang, Z.; et al. High-Magnetic-Sensitivity Magnetoelectric Coupling Origins in a Combination of Anisotropy and Exchange Striction. *Nanomaterials* **2022**, *12*, 3092. https://doi.org/ 10.3390/nano12183092

Academic Editor: Sam Lofland

Received: 1 August 2022 Accepted: 2 September 2022 Published: 6 September 2022

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along the *c*-axis below *TSR*, the spin configuration of the Fe3+-sublattice is driven to G*x*A*y*F*<sup>z</sup>* again [4].

For spin-driven ferroelectricity, there are mainly three types of microscopic mechanism models, i.e., the inverse Dzyaloshinskii–Moriya (IDM) mechanism [24], spin-dependent *p*-*d* hybridization model [25], and exchange striction model [26,27], for explaining ME behaviors. According to these models, the emergence of ferroelectricity is hardly understood only by the local spin arrangement, since the symmetry of the crystal structure needs to be considered. In DyFeO3, below *T*N(Dy), the *Pc* (the direction of *P* is parallel to the *c*-axis) can be induced when the magnetic fields (higher than 2.4 T at 3.0 K [4]) are applied along the *c*-axis. However, the ME behaviors in DyFeO3, i.e., the *Pc* is induced with the magnetic fields along other crystal axes, remain to be further understood. Moreover, some abnormal behaviors have been observed. For example, a small *P* drop was observed on the *P*-*H* curve at *BC*(Fe) [4]. Abnormal heat transport was measured, and a FeIII state (a metastable phase) was speculated [18]. These abnormal behaviors indicate that there may be complex and delicate magnetic interactions in ME behaviors, such as the competition between the anisotropic energy of the Dy3+-sublattice, the coupling energy between the Dy3+ and Fe3+-sublattices, and Zeeman energy [28].

In DyFeO3, when the magnetic field is in the *ab* plane, ME coupling with smaller critical fields of 0.8 T (*a*-axis) and 0.5 T (*b*-axis) is triggered. Inspired by these lower critical magnetic fields, we revisited the structure of DyFeO3, in which two AFM sublattices (the Fe3+- and Dy3+-sublattices) are nesting with each other (see Figure 1a,b). The Fe3+-sublattice (blue balls) has strong AFM coupling (G*x*A*y*) and wFM (F*z*), and the Dy3+-sublattice (red balls) has weak AFM coupling and strong magnetic anisotropy (the AFM vector is localized in the *ab* plane). Under a lower magnetic field in the easy plane (*ab* plane), the direction of the magnetic anisotropy of the Dy3+-sublattice might be disturbed or changed, which leads to the change in exchange striction between the Fe3+- and Dy3+-sublattices and triggers *Pc.* Thus, we believe that single-phase materials with nested AFM lattices (as shown in Figure 1c,d) can be designed or found, where the A-sublattice (blue spheres) has strong AFM coupling in the plane and weak FM outside the plane, while the B-sublattice (red spheres) has weak AFM coupling, and the B-site ions have strong magnetic anisotropy. Such AFM systems are expected to achieve highly magnetically sensitive ME coupling induced by in-plane magnetic fields. Although the observed magnetoelectric effects mainly occurred at low temperatures (below *T*N(Dy)), which may be difficult to apply directly in the traditional industry, our work deepens the understanding of the ME coupling in DyFeO3. On the other hand, the ME systems controlled by a combination of multiple parameters (such as magnetic anisotropy and exchange striction) may have high sensitivity to the external magnetic field.

**Figure 1.** (**a**) The crystal structure and (**b**) magnetic configuration of DyFeO3 below the Dy3+ ordering temperature. Two AFM sublattices nesting with each other at (**c**) zero field and (**d**) applied magnetic field.
