Gigantic terahertz magnetochromism via electromagnons in the hexaferrite magnet Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$

Effects of temperature (6–225 K) and magnetic field (0–7 T) on the low-energy (1.2–5 meV) electrodynamics of the electromagnon, the magnetic resonance driven by the light electric field, have been investigated for a hexaferrite magnet Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$ by using terahertz time-domain spectroscopy. We find the gigantic terahertz magnetochromism via electromagnons; the magnetochromic change, as defined by the difference of the absorption intensity with and without magnetic field, exceeds $500$% even at 0.6 T. The results arise from the fact that the spectral intensity of the electromagnon critically depends on the magnetic structure. With changing the conical spin structures in terms of the conical angle $\theta$ from the proper screw ($\theta =0^{°}$) to the ferrimagnetic ($\theta ={90}^{°}$) through the conical spin-ordered phases ($0^{°}<\theta <{90}^{°}$) by external magnetic fields, we identify the maximal magnetochromism around $\theta \approx {45}^{°}$. On the contrary, there is no remarkable signature of the electromagnon in the proper screw and spin-collinear (ferrimagnetic) phases, clearly indicating the important role of the conical spin order to produce the magnetically controllable electromagnons. The possible origin of this electromagnon is argued in terms of the exchange-striction mechanism.

Figure 1

Crystal and spin structures of Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$ in zero magnetic field. Schematic illustrations of (a) hexagonal structure and spin structures in (b) ferrimagnetic, (c) proper screw, and (d) longitudinal conical spin ordered phases. The conical angle $\theta$ is defined in (d). The unit cell can be conveniently divided by two sublattice blocks: spinel $S$ and hexagonal $L$ sublattice blocks along [001]. In the conical spin ordered phase shown in (d), electromagnon becomes active when the light $E$ vector is set parallel to [001].

Figure 2

Schematic illustration of experimental setup for terahertz time-domain spectroscopy combined with split-type superconducting magnet. We employed the photoconducting sampling technique with low-temperature-grown GaAs (LT-GaAs) as terahertz emitter and detector. The magnetic field was applied up to 7 T in Voigt geometry to prevent the conventional magneto-optical effect.

Figure 3

Gigantic magnetochromism via electromagnons in the paraelectric phases of Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$. Imaginary part of the dielectric constant spectra $({\epsilon }_2)$ in magnetic fields up to 7 T, measured at (a) 6 K originally in the longitudinal conical spin ordered phase, at (b) 64 K near the conical to proper screw transition temperature, at (c) 90 K and at (d) 164 K originally in the proper screw phase. Respective ${\epsilon }_2$ spectra are arbitrarily offset for clarity; the offset revel is indicated by the horizontal solid line. The light $E$ vector was set parallel to [001] and the magnetic field $H$ was applied along [001] in Voigt geometry.

Figure 4

Magnetic phase diagram of Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$, as determined by the signature of the electromagnon. The magnetic field $H$ was applied along [001] to finely control the conical angle $\theta$ of the longitudinal conical structure, as schematically shown in the inset of (a). (a) Magnetization along [001] $M_{[001]}$ and estimate $\theta$ as a function of magnetic field, measured at 6 K. (b) Contour map of the spectral weight (SW) of the electromagnon in terms of temperature and magnetic field. The measured points are indicated by open circles. The magnitude of SW (see text for the definition) is shown with the scale color bar. The unit of SW is arbitrary.

Figure 5

Gigantic magnetochromism via electromagnons in the ferroelectric phase of Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$. Imaginary part of the dielectric constant spectra $({\epsilon }_2)$ in magnetic fields up to 7 T measured at (a) 5.5 K originally in the conical spin ordered phase, at (b) 60.3 K near the conical to proper screw transition temperature, at (c) 91 K and at (d) 164 K originally in the proper screw phase. Respective ${\epsilon }_2$ spectra are arbitrarily offset for clarity; the offset revel is indicated by the horizontal solid line. The light $E$ vector was set parallel to [001] and the magnetic field $H$ was applied along [100] in Voigt geometry.

Figure 6

Magnetoelectric phase diagram of Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$, as determined by the signature of the electromagnon. The magnetic field $H$ was applied along [100] to induce the transverse conical spin phase, as schematically shown in the inset of (a). In this phase, the ferroelectricity emerges along [120], perpendicular to both [100] and [001] (see also Fig. 1). (a) Magnetization along [100] $M_{[100]}$ and spontaneous polarization along [120] as a function of magnetic field, measured at 5 K. (b) Contour map of the spectral weight (SW) of the electromagnon in terms of temperature and magnetic field. The measured points are indicated by open circles. The magnitude of SW (see text for the definition) is shown with the scale color bar. The unit of SW is arbitrary. The solid line represents the region where the transverse conical spin structure was identified by the neutron-scattering experiments (Ref. 25). In this region, the spontaneous polarization emerges, as shown in (a).

Figure 7

Schematic illustrations of the spin arrangement in Ba${}_2$Mg${}_2$Fe${}_{12}$O${}_{22}$. (a) According to the previous neutron-scattering experiments (Ref. 19), $L$ and $S$ sublattice blocks were composed of Fe ions, which are labeled by 1, 4, 5, 8, 11, 12, 11${}^{\prime }$, 8${}^{\prime }$, 5${}^{\prime }$, 4${}^{\prime }$, and 1${}^{\prime }$. (b) In the ferrimagnetic phase at 2947nbsp;K, the spins at respective sites are collinear with a turn angle of 0${}^{ˆ}$; the reported data were taken from Ref. 19. (c) In the proper screw phase at 77 K, the spins are noncollinear with a turn angle of 59.6${}^{ˆ}$ (Ref. 19). (d) Possible source of the electromagnons we observed here in the conical spin ordered phase. Within the framework of the symmetric-exchange induced striction, electromagnon becomes active when $\Delta S_i$ is not perpendicular to $S_j$. We focus on the Fe 4, 5, and 8 sites. In the conical phase, the components of the spins projected on to (120) plane can give rise to the electromagnon activity, as schematically shown in (d). In this case, the electromagnon intensity depends on the conical angle $\theta$ and shows the maximum at $\theta$ of ${45}^{°}$. This can be experimentally realized in magnetic fields. Furthermore, there is no chance to produce the electromagnon activity with $\theta$ of $0^{°}$ or 90${}^{ˆ}$. These are all consistent with present experiments.