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We report the first observation of sub-terahertz bulk-magnetization precession, using terahertz time-domain spectroscopy. The magnetization precession in gallium-substituted ε-iron oxide nano-ferromagnets under zero magnetic field is induced by the impulsive magnetic field of the THz wave through the gyromagnetic effect. Just at the resonance frequency, the linear to circular polarized wave conversion is realized. This is understood as the free induction decay signal radiated from a rotating magnetic dipole corresponding to the natural resonance. Furthermore, this demonstration reveals that the series of gallium-substituted ε-iron oxide nano-ferromagnets is very prospective for magneto-optic devices, which work at room temperature without external magnetic field, in next-generation wireless communication.
©2010 Optical Society of America
1. Introduction
High-frequency wireless communication using terahertz (THz) and sub-THz waves is a promising next-generation technology [1–13]. In addition to developing active devices (such as radiation sources, amplifiers, and modulators), creating passive devices (such as absorbers, isolators, and circulators) is required for separating and mixing of signals, and also for avoiding electromagnetic interference (EMI). Especially, isolators and circulators usable in the sub-THz frequency are desired for cutting-edge wireless communications [3,6,9–11], while advantages of ferromagnetic resonances in magnetic substances have been widely utilized for this purpose at lower frequencies (microwave region). Since magnetic permeability shows a large dispersion around ferromagnetic resonance through magnetic dipole transition, a large magneto-optic effect is expected. Up to now, there are some reports on the ferromagnetic resonance in THz range using by the conventional frequency domain measurement or the optical time domain measurement [14,15].
In common magnetic materials, a high external magnetic field is necessary to tune a ferromagnetic resonance to a high frequency region, which is inappropriate for practical device applications. Realization of ferromagnetism at room temperature is also an important factor. Although single molecule magnet Mn12Ac [14] and SrRuO3 [15] show ferromagnetic resonance at high frequencies (300 GHz and 220 GHz, respectively), they do not work at room temperature. An insulating ferromagnetic substance with a large magnetic coercive field (H c) having a high natural resonance (ferromagnetic resonance under a zero magnetic field) frequency is an optimum candidate. In particular, ε-Fe2O3 and ε-MxFe2- xO3 (M = metal) magnets (Fig. 2(a) ) are suitable systems for this target [12,13,16–19], because these materials exhibit a large H c value up to 23 kOe at room temperature, and moreover, possess a sharp absorption peak due to the magnetic dipole transition in the wave range up to 0.182 THz [12,13], which is the highest natural resonance frequency for magnetic materials.
Fig. 2 (a) Crystal structure of ε-Fe2O3 and ε-MxFe2-xO3. This orthorhombic crystal structure in the Pna21 space group has four non-equivalent Fe sites (FeA–FeD sites), that is, the coordination geometries of the FeA–FeC sites are octahedral {FeO6} units and those of the FeD sites are tetrahedral {FeO4} units. ε-GaxFe2-xO3 exhibits ferrimagnetic ordering such that the sublattice magnetizations at the FeA and FeD sites are ordered antiparallel relative to those at the FeB and FeC sites [12]. (b) Magnetization (M) vs. external magnetic field (H) for ε-Ga0.23Fe1.77O3 at 300 K. Inset is a photograph of the pellet sample used in the THz time-domain measurement.
The THz time domain spectroscopy is a powerful tool for investigating response of solids to electromagnetic (EM), because it enables us to directly observe temporal waveforms of the electric amplitude of the EM waves and to obtain information about the phase shift without an interferometer [20,21]. The high sensibility and broad spectrum range of this method will be ideal for the evaluation of the magneto-optic effect in the sub-THz and THz wave ranges. To date, there has been no report of magneto-optical effect based on the magnetic dipole transitions using THz time domain spectroscopy, although the external magnetic field-induced magneto-optic effect of the free carriers have been observed through electric dipole transition [22,23].
Very recently, the ultrafast studies on the spin precession motions in time domain using femtosecond laser pulses were reported [15,24–28]. In these reports, however, the spin precessions were induced mainly by inverse Faraday effect of the pump light and the detection was made utilizing Faraday or Kerr rotation in visible or near infrared frequency region. This means that both processes are indirect in the sense that they rely on the interaction of visible radiation with the spin system through spin-orbit and exchange interactions. In contrast, THz pulses can detect directly the response of the permeability through the magnetic dipole interaction between the spin and the magnetic field of the input THz waves.
The concept of our experiment is shown in Fig. 1(a) . Due to the gyromagnetic effect [29], the impulsive magnetic field associated with a short pulse of EM wave tilts the spontaneous magnetization along the direction perpendicular to the magnetic easy axis, leading to coherent precession motion around the easy axis. The rotating coherent bulk-magnetization radiates emission at a particular frequency at ferromagnetic resonance. This phenomenon is so-called free induction decay of the spin system in ferromagnet.
Fig. 1 (a) Schematic illustration of the natural resonance due to the gyromagnetic effect caused by the impulsive magnetic field of the THz wave. (b) Schematic experimental layout of the THz time domain spectroscopy.
Here, we report large magneto-optic effect due to coherent bulk-magnetization precession induced by the magnetic field of the THz wave around the natural resonance over 0.1 THz in ε-GaxFe2-xO3 nano-ferromagnet.
2. Experimental methods
To observe the magneto-optic effect based on the natural resonance using the THz time-domain system, ε-Ga0.23Fe1.77O3 (H c= 11.6 kOe) and ε-Ga0.40Fe1.60O3 (H c= 8.8 kOe) nanomagnet were used. A typical magnetization curve is shown in Fig. 2(b) for x = 0.23, where the hysteresis curve has a half width as large as 11.6 kOe [12].
Pellet samples with a diameter of 13 mm were prepared for the THz time-domain measurements by compressing a powder (their filling factors were 60%). The prepared pellets of ε-Ga0.23Fe1.77O3 and ε-Ga0.40Fe1.60O3, which have thicknesses (d) of 1.9 and 0.7 mm, respectively, were magnetized along the direction perpendicular to the surface by an 8 Tesla pulsed magnetic field with a 200 ms time width. After removing the pulse magnetic field, the remanent magnetization of the pellet was stable.
Transmission-type THz time-domain spectroscopy was performed at room temperature. Schematic experimental set up is described in Fig. 1(b). A mode-locked Ti:sapphire laser delivered ultrashort (20 fs) light pulses with a central photon energy of 1.55 eV at a repetition rate of 76 MHz. The emitter and detector of the THz waves were dipole-type and bowtie-type low-temperature-grown GaAs photoconductive antennas, respectively. The emitted THz wave was collimated and incident on the sample. The transmitted THz electric field was detected by the photoconductive antenna, which was triggered by optical probe pulses with a variable time delay. Three free standing wire-grid polarizers (P1-P3) were used for measuring the horizontal and vertical polarization components. The photoconductive antennas emits and detects only the horizontal polarization component of the electric field in the THz wave, whose direction is determined by the direction of the gap on the antenna. Polarizers P1 and P3 were placed after the emitter and before the detector, respectively, to precisely define the polarization of the THz wave as horizontal (0°). The vertical polarization components were obtained as the difference of the components at 45° and −45° measured by rotating polarizer P2, which was placed after the sample, whereas the horizontal components were obtained by their sum [23]. We confirmed actually that the waveform of the horizontal component obtained by the vector sum agrees with the waveform measured directly at horizontal component (0°).
3. Results and discussions
Figure 3(a) shows the observed waveforms of the electric field of the THz waves without a sample. The vertical component of the input THz pulse was negligible; that is, the input THz pulse was perfectly polarized in the horizontal direction. Figure 3(b) shows the transmitted signals in the horizontal and vertical polarization components through the ε-Ga0.23Fe1.77O3 magnet. The main peak appeared at 10 ps in the horizontal component, whereas the peak around 45 ps was ascribed to the multiple reflections of the main pulse. These oscillation signals in both the horizontal and vertical components originate from rotating bulk-magnetization excited by an impulsive THz magnetic field (along the vertical direction). As can be seen from the insets of Figs. 3(b) and (c), the horizontal component is composed of the oscillation and slowly decaying background components corresponding to the tail of the main pulse around 10 ps, while the vertical component is composed only of oscillation component.
Fig. 3 (a) Observed electric fields of the THz wave without a sample. Bold and thin curves denote the horizontal and vertical polarizations, respectively. (b) Observed electric fields of the THz wave in ε-Ga0.23Fe1.77O3. Bold and thin curves are the horizontal and vertical polarizations, respectively. (Magnetic pole is antiparallel to the THz light propagating direction.) (c) THz wave for a sample with inverted magnetic pole direction. Blue bold and thin curves are the horizontal and vertical polarizations in ε-Ga0.23Fe1.77O3, respectively. (Magnetic pole is parallel to the THz light propagating direction.)
As shown in Figs. 3(b) and 3(c), reversing the magnetization direction caused the polarity of the vertical components to switch, but did not affect the polarity of the horizontal components. It is seen from Fig. 3(b) that the phase shift for the vertical and horizontal components is close to π/2 and the amplitude is nearly the same, indicating that the propagating THz wave has a nearly circular polarization. Figure 4 shows the three-dimensional trajectory plots of the horizontal and vertical components for ε-Ga0.40Fe1.60O3, and clearly demonstrates circular polarization. This result directly reflects the magnetization precession at the natural resonance induced by the magnetic field of the THz input pulses (Fig. 1(a)). Because the rotating magnetization radiates circularly polarized THz light, the damping reflects the relaxation of the magnetization precession. The decay rate of the free induction decay signal determined from the vertical component was about 30 ps.
Fig. 4 (a) Three-dimensional trajectory plot (red) for the transmitted THz electric fields of ε-Ga0.40Fe1.60O3 with both horizontal and vertical components. (b) Trajectory for a sample with opposite magnetic pole direction.
The Fourier transformed spectra of the waveforms in Fig. 3 (b) are shown in Fig. 5(a) . A dip in horizontal component and a peak in vertical component appear around 0.102 THz and 0.083 THz for ε-Ga0.23Fe1.77O3 and ε-Ga0.4Fe1.6O3, respectively. These structures reflect the oscillating component in Fig. 3 and are ascribed to the magnetic dipole transition due to the natural resonance [12,19]. The origin of resonance modes in ε-GaxFe2-xO3 have been discussed in detail for x = 0.51, 0.56, 0.61 [19]. Based on the transmittance and reflection measurements, it has been confirmed that they are ascribed to the response by the magnetic permeability not by the dielectric function. Furthermore, as shown in Fig. 5(b), the linear dependence of the resonance frequency on H c for ε-MxFe2-xO3 (M = Ga, Al), which is a typical behavior of natural resonance in magnets with a uniaxial magnetic anisotropy [29], indicates that the origin of the observed dip and peak is the natural resonance. It is seen in Fig. 5(a) that the magnitudes of the dip and the peak of each spectrum are almost the same, indicating that linear polarization of the input wave is converted into nearly perfect circular polarization. ε-MxFe2-xO3 nano-ferromagnets, which have high natural resonance frequencies up to 0.182 THz for ε-Fe2O3, are very prospective for magneto-optic devices in sub-THz wave range, because they can cover most of the millimeter wave range without external magnetic field by controlling composition ratio.
Fig. 5 (a) Fourier-transformed spectra of the waveforms in ε-Ga0.23Fe1.77O3 obtained from the waveform between −20 and 40 ps in Fig. 3(b) to avoid the effect of the multiple reflections. (b) Natural resonance frequency vs. coercive field for ε-MxFe2-xO3 (M = Al or Ga). ε-Ga0.23Fe1.77O3 and ε-Ga0.40Fe1.60O3 (closed red circles), ε-GaxFe2-xO3 (open blue squares) [12], and ε-AlxFe2- xO3 (open blue triangles) [13].
The polarization rotation angle and ellipticity are obtained from the horizontal and vertical components (Ex(t), Ey(t)) of the transmitted electric fields. Those electric field components are given by
The rotation angle φ(ω) and ellipticity η(ω) spectra are given by [30] where δ(ω) = δ1(ω) -δ2(ω) is the difference of the phase. We can obtain directly φ(ω) and η(ω) from the Fourier transformed amplitude and phase of the temporal waveforms. Figure 6 shows the rotation angle and ellipticity spectra for the natural resonance of ε-Ga0.23Fe1.77O3. These spectra were obtained by the waveforms from −20 ps to 40 ps. The rotation angle has a dispersive pattern centered at 0.102 THz, while the ellipticity spectrum exhibits an absorptive pattern at the same frequency, which are characteristic to the magnetic resonance. In the rotation angle spectrum, the rotation at 0.104 THz was −44 degrees, which meets the specification for sub-THz wave isolators. The ellipticity at 0.102 THz showed a high value of 0.97, showing that the transmitted sub-THz wave is close to a circularly polarized wave. Although these values realized in the simple powder pellet are already sufficiently high, we can further improve the efficiency of Faraday rotation by using the highly oriented pellet and increase the transmission efficiency by using matching technique which will diminish the reflection loss.Fig. 6 Spectra of the (a) rotation angle and (b) ellipticity for ε-Ga0.23Fe1.77O3 with 1.9 mm thickness. Spectra are derived from the waveforms between −20 ps and 40 ps.
7. Conclusion
In this work, time-domain spectroscopy was successfully applied to observation of the gyromagnetic effect in a series of ε-GaxFe2- xO3 at the sub-THz region without an external magnetic field. Hence, this series has high potential for practical applications in sub-THz wave isolators and circulators. The observed magneto-optic effect by the sub-THz light through the magnetic dipole transition significantly differs from the conventional Faraday effect observed through electric dipole transition in the visible or near-infrared region.
Acknowledgements
We thank Dr. Kojima and Prof. Takeyama in ISSP, the University of Tokyo for their aid in magnetizing the pellets. We are grateful to T. Nuida, H. Tokoro, and Y. Tsunobuchi for preparing the figures. This work has been supported in part by a Grant-in-Aid for Young Scientists (B) (No. 2176004) and Young Scientists (S) (No. 20675001) from JSPS, the Asahi Glass Foundation, DOWA technofund, and the Center for Nano Lithography & Analysis, the University of Tokyo, supported by MEXT Japan. A. N. is grateful to JSPS Research Fellowships for Young Scientists.
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