Magnetoelectricity in multiferroic hexaferrites as understood by crystal symmetry analyses

Abstract

Magnetoelectric (ME) properties under rotating magnetic field H are comparatively investigated in two representative hexaferrites Y-type Ba 0.5 Sr 1.5 Zn 2 (Fe 0.92 Al 0.08 ) 12 O 22 and Z-type Ba 0.52 Sr 2.48 Co 2 Fe 24 O 41 , both of which have exhibited a similar transverse conical spin structure and giant ME coupling near room temperature. When the external H is rotated clockwise by 2π, in-plane P vector is rotated clockwise by 2π in the Y-type hexaferrite and counterclockwise by 4π in the Z-type hexaferrite. A symmetry-based analysis reveals that the faster and opposite rotation of P vector in the Z-type hexaferrite is associated with the existence of a mirror plane perpendicular to c-axis. Moreover, such a peculiar crystal symmetry also results in contrasting microscopic origins for the spin-driven ferroelectricity; only the inverse DM interaction is responsible for the Y-type hexaferrite while additional p-d hybridization becomes more important in the Z-type hexaferrite. This work demonstrates the importance of the crystal symmetry in the determination of ME properties in the hexaferrites and provides a fundamental framework for understanding and applying the giant ME coupling in various ferrites with hexagonal crystal structure.

Magnetization switching using topological surface states

“…Note that there exists a magnetoelectric effect in BaFe 12 O 19 , but this effect is not responsible for the observed magnetization switching for two reasons. First, in contrast to the Y-type and Z-type hexagonal ferrites that show strong multiferroic effects, the magnetoelectric effect in BaFe 12 O 19 , an M-type hexagonal ferrite, is weak ( 36 – 38 ). Second, during the switching experiments, there is no apparent electric field across the BaFe 12 O 19 film, since the bottom sapphire substrate is electrically insulating and the electric current flows only in the top Bi 2 Se 3 layer.…”

Low-temperature crystal and magnetic structures of the magnetoelectric material Fe4Nb2O9

“…In type-II multiferroic, the ME coupling below the magnetic-ordering temperature has been explained in terms of three well-known models, i.e., the spin-current mechanism for noncollinear magnetic structure [26], the magnetostriction model for collinear spin arrangements [27], and d-p hybridization mechanism between spin and its ligand atoms with spin-orbital interaction [28], in some low-symmetry crystals with noncollinear magnetic orders. In order to extract more information about the microscopic origin of ME coupling, we introduce a symmetry-based local ME tensor technique [29], which has successfully resolved the microscopic origin of polarization in multiferroic hexaferrites [30]. Let us consider that a spin pair S 1 and S 2 can produce a local dipole p as the quadratic functions in Einstein convention: p = p(S 1 , S 2 ) + p(S 1 ) + p(S 1 )…”

“…where vector e i = (e ix , e iy , e iz ) connects the transition metal i and its neighbor ligand atom. By introducing the crystal symmetry, the forms of the local ME tensors can be greatly simplified due to its polar tensor property [30]. For simplicity, we assume: (i) there are only three kinds of two-spin interactions that can generate local dipole, Fe1-Fe1, Fe2-Fe2, and Fe1-Fe2.…”

Magnetoelectric Coupling Triggered by Noncollinear Magnetic Structure in M‐Type Hexaferrite

“…While as shown by Equation ( 1), spin current model only allows P ⊥ H but forbids P ‖ H since ΣS i × S j is parallel or antiparallel to H. Therefore, the comparative value of P and similar P-H curves under P ⊥ H and P ‖ H indicate that the ME coupling of Indoped BaFe 12 O 19 ceramics mainly stems from the d-p hybridization mechanism, where P ‖ H is allowed in ab-plane of the lattice based on P6 3 /mmc symmetry and has been confirmed in Z-type hexaferrite with the same space group. [10,12] P is originally positive due to the +E and +H poling, and then the tilting angle of the spin conical axis decreases with the decrease of H and becomes zero at −H c , where M and P also reduce to zero. Here, the peaks of P under H ‖ E deviate obviously from H c (Figure 6j-l) due to the larger geometric demagnetizing factor during the measurement.…”

“…For the spin-dependent metal-ligand orbital hybridization, so-called d-p hybridization mechanism, P is given by [6] P ∝ ∑ e il ( e il ⋅ S i ) 2 (2) where e il denotes the unit vector from magnetic ionic site i to a neighboring ligand site l. No matter which mechanism the ME coupling is generated by, the macroscopic P demands the broken spatial inversion symmetry by spiral magnetic order. Direct ME coupling has been validated in Y-type (Ba,Sr) 2 (Mg,Zn) 2 (Fe,Al) 12 O 22 [8][9][10] and Z-type (Ba,Sr) 3 Co 2 Fe 24 O 41 [10][11][12] hexaferrites. Their strong ME coupling from spiral magnetic structures and high operating temperatures make hexaferrites promising room-temperature ME materials.…”