Growth , Faraday and inverse Faraday characteristics of Tb 2 Ti 2 O 7 crystal

Tb2Ti2O7 (TTO) single crystal with dimensions of 20 × 20 × 16 mm was grown by the Czochralski method. Rietveld structure refinement of X-ray diffraction (XRD) data confirms that the compound crystallizes in the cubic system with pyrochlore structure. Transmission spectra, Magnetic circular dichroism (MCD) spectra, Faraday and inverse Faraday characteristics of TTO crystal have been measured and analyzed in detail. The results demonstrate that TTO crystal has high transmittance at 7001400 nm waveband and a larger Verdat constant than that of TGG reported. Magnetic circular dichroism (MCD) spectra showed that the 4f→4f transitions of Tb have significant contributions to the magneto-optical activity (MOA). In the time-resolved pump-probe spectroscopy, the rotation signals of the probe beam based on the inverse Faraday effect in magnetooptical crystal were observed at zero time delay, the full width at half maximum of the rotation and ellipticity signals can be as fast as ~500 fs, which indicates that TTO crystal can be a promising material for ultrafast all-optical magnetic switching. © 2016 Optical Society of America OCIS codes: (160.3820) Magneto-optical materials; (230.2240) Faraday effect; (320.7080)


Introduction
Faraday isolators are the important parts of currently used for high-power-laser machinery and advanced optical communications, guarantying an unidirectional light propagation in the laser systems [1,2].Due to recent progress in laser applications such as precise measurements and advanced display systems, the demand for optical Faraday devices is increasing at wavelengths of 400-1100 nm, where conventional yttrium iron garnets (YIG) and doped YIG are inapplicable because of their poor transparency.On the other hand, laser-induced switching and manipulation of the spins in magnetic materials is of great interest for the further development of magnetic storage, spin electronics and quantum computing [3,4].A lot of pump-probe experiments have shown a fast decay of the magneto-optical signal occurring on the subpicosecond time scale in magnetic material using the time-resolved magneto-optical Kerr and Faraday effect [5,6].In order to achieve all-optical magnetic switching, the candidate material should have low absorption in visible and infrared spectral region and exhibits large Faraday magneto-optical effects.
Rare earth titanates Ln 2 Ti 2 O 7 (Ln = Y, Sm-Lu) belongs to the family of compounds with the general chemical formula A 2 B 2 O 7 , having the cubic pyrochlore structure with a space group of 3 Fd m , where both the A and B atoms individually form a three-dimensional network of corner sharing tetrahedra [7].During the past decade, pyrochlore-type rare earth titanates have attracted much attention due to the geometrical frustrations and various low temperature magnetic behaviors [8][9][10][11][12][13][14][15][16].In addition, the titanates pyrochlores have many potential applications, including high-temperature gas sensors or fast ion conductors, catalysts, phosphors and materials for resisting to radiation damage [17][18][19][20].
Tb 3+ ion exhibits a strong Faraday effect due to the numbers of unpaired electrons and the transitions between 4f 8 -4f 7 5d [21,22].The compounds containing Tb 3+ ions show good magneto-optical performance in the visible and near-infrared regions, such as TGG and TAG [23][24][25].Tb 2 Ti 2 O 7 (TTO) has relatively high Tb 3+ concentrations (1.54 × 10 22 /cm 3 ) and large refractive index, no intrinsic absorption at the visible-near IR region.These features are advantages for a magneto-optical material candidate [26].Besides, TTO is congruent compound, could be grown by the Czochralski method.Recently, some pyrochlore-type rare earth titanates have drawn attentions in our research group because of their large Faraday rotations [27,28].In this work, we reported the Czochralski growth, Faraday and Inverse Faraday Characteristics of TTO single crystal.As a paramagnetic material, the reasons of its large Faraday and inverse Faraday effect were also discussed.

Experimental
Polycrystalline materials for crystal growth were prepared by solid-state reaction technique in air.Stoichiometric amounts of Tb 4 O 7 (4N) and TiO 2 (4N) were weighted accurately, then the mixture was sintered at three different temperatures (1250, 1350 and 1450 °C) for 30h each with intermediate grinding and pressing into tablets.TTO crystals were grown by the Czochralski method, in a Ф60 mm × 35 mm iridium crucible with radio frequency (RF) induction heating in N 2 or Ar protective atmosphere.When the polycrystalline materials melt completely, the furnace was evacuated to near 0.1 Pa pressure to driving away the bubbles produced in the melting process.The furnace was then filled with the protective gases to 0.04-0.06MPa pressure for crystal growth.One of as-grown TTO crystals is shown in Fig. 1.As can be seen, TTO crystal displayed relatively strong growth habits during CZ growth.Under the suitable transverse temperature gradients, TTO crystal grown along the [111] orientation had six fully exposed planes which were identified by X-ray diffraction to be {111} facets.The angles between these facets were approximately 70.5 degrees, which is close to the dihedral angle of a perfect octahedron.The growth morphology of TTO crystal is consistent with its ideal morphology simulated by Materials Studio software.Powder XRD measurement was carried out by Rigaku D/max-3c diffractometer.The measured diffraction data of TTO was refined through internal standard method with standard Si powder.As-grown TTO single crystals were cut along (111) plane, which were oriented by X-ray diffraction, and then grounded and polished carefully to different thickness for transmission and MCD spectra and all-optical magnetic switching measurement.The transmission spectra were measured over the wavelength range 400-1600 nm (Perkin-Elmer Lambda 900).Photothermal common-path interferometer (PCI) was applied to determine the weak absorption at 1064 nm.Faraday rotation of crystal sample in the [111] direction was measured at room temperature by the extinction method [29].In this measurement, lasers of 532, 633 and 1064 nm wavelengths were used as the probe light sources.The magnetic field was varied continuously from 0 to 1.2 T. MCD spectra of crystal samples were measured by using a circular dichroism spectrometer (Bio-Logic, MOS-450) equipped with a adjustable magnetic field equipment (the magnetic field paralleled to the propagation direction of probe light and had three intensities of 2000, 2500 and 3000 Oe, respectively).The photoinduced magnetization and all-optical magnetic switching in TTO crystal was measured using a pumpprobe technique, both pump and probe beams were delivered from a Ti:sapphire laser (Spectra-physics, Spitfire Pro.) with a pulse width of 120 fs and a repetition rate of 1 kHz at a photon energy of 1.55 eV (the center wavelength is 800 nm) [30].The two beams illuminated the sample from the same sides with a small deviation from the normal incidence, which is the only difference with the experimental setup as shown in the paper by R.V. Mikhaylovskiy et al [31].The pump beam could be varied from linearly to arbitrary elliptically and circularly polarized states by changing the angle Φ between the linearly polarized plane of pump beam and the fast axis of quarter-wave plate, while the signal beam remained linearly polarized.All measurements were performed at room temperature.

Results and Discussion
The observed, calculated and their difference X-ray diffraction profiles of the as-grown TTO crystal is displayed in Fig. 2. Rietveld structural refinements were carried out using commercial Jade 7.0 software package (Materials Data, Inc.).The results show the structure of TTO crystal belong to cubic system, space group is 3  Fd m .Refinement parameters is R wp = 5.91%.Cell parameters is a = 1.0158(4) nm, almost identical with the ICSD data [32].The transmission spectra of a magneto-optical material is an important parameter to characterize the magneto-optical performance.Figure 3 shows the transmission spectra of TTO samples with different thicknesses at 400-1500 nm waveband.Tb 3+ ion has no absorption bands at 500-1500 nm waveband according to its energy levels.At 700-1400 nm waveband, TTO samples with different thicknesses have almost same transmittance, up to 73%, while at 400-700 nm and 1400-1500 nm wavebands, the transmittance decreases with the increase of thickness.The transmission coefficient T could be calculated by the McLean's Equation: where d is the specimen thickness, α is the absorption coefficient, R stands for the reflection coefficient.The R value is related to the refractive index, R = (n-1) 2 /(n + 1) 2 .At 700-1400 nm waveband, the transmittance was found to be almost not affected by the sample thickness, which indicated the α value was relatively small at this waveband.So Eq. ( 1) could be simplified as T = (1-R)/(1 + R), according to the transmission coefficient T, the refractive index of TTO crystal at 1064 nm was estimated to 2.31.The absorption coefficient calculated through the data of transmittance and sample thickness includes the reflection loss and weak host absorption loss.Usually, anti-reflection coatings is used to eliminate the reflection loss for optical isolators in practical application.So the weak host absorption really reflect the optical quality of magneto-optical material.The weak absorption at 1064 nm for TTO crystal was measured by the PCI technique.The typical curve of the weak absorption is given in Fig. 4. The peak is close to 9600 ppm/cm.Usually, the weak absorption of a good optical quality TGG sample is less than 3000 ppm/cm at 1064 nm.Faraday effect of paramagnetic materials is relevant to its magnetic properties.Figure 5 shows the magnetization curves of TTO and TGG crystals, the applied magnetic fields are parallel and vertical to the [111] direction, respectively (In fact, magnetic field paralleled to [100] and [110] directions of TTO also were measured).No magnetic anisotropy is found between these directions.Volume magnetic susceptibilities of TTO are determined to be χ = 9.68 × 10 −3 emu•cm −3 •T −1 , while the χ of TGG is 8.16 × 10 −3 emu•cm −3 •T −1 , The ratio of two χ values is 1.19, which is consistent with the ratio of Tb 3+ ions unit volume concentration in the two kinds of crystals.As is well known, Faraday rotation in a paramagnetic material is given by the equation θ = VHL, where θ is the rotation angle, L is the length of the light path in a medium, H is the magnetic field applied along the light beam and V is the Verdet constant.Faraday rotation angles at a specified wavelength are proportional to the magnetic field.The straight lines were fitted using the least square method, as demonstrated in Fig. 6.The Verdet constants can be calculated by the slope of straight lines, as shown in Table 1.Verdet constants of TTO are about 1.7 times as large as those of TGG.It is well known that Faraday magneto-optical effect of rare earth ions is mainly caused by the transitions of 4f-4f5d, but the 4f-4f transitions also have significant contributions to the magneto-optical activity (MOA) [34].Through MCD spectrum measurement, the absorbing transitions associated with MOA can be observed.Figure 7 shows the MCD spectra of TTO crystal (0.1mm thickness) at different magnetic fields.At the 350-500 nm waveband, MCD signal of TTO only shows a peak centred at 357.5 nm, which may be assigned to the Tb 3+ transition of 7 F 6 → 5 L 9 [35] .The peak intensity is proportional to the magnetic field.Due to the strong absorption of Ti 4+ ions at ultraviolet region, the difference between the right-handed and left-handed light below 350nm could not be detected.As for MCD signal of TGG (0.1mm thickness), the peaks centred at 278.5, 307.9, 352.5, 377.2 and 484.5 nm can be found, but its intensities are obviously lower than that of TTO at 357.5 nm.The integral paramagnetic MOA of a transition is determined by the equation [36]: Here, <Δk(ω)> 0 and <k(ω)> 0 are integral intensities of the MCD and Tb 3+ ions absorption bands, respectively.A is adimensionless parameter of the MOA, μ B and k B represent the Bohr magneton and Boltzmann constant, respectively.T C is the Curie-Weiss constant.The Eq. ( 2) is valid both for a single line and for a complex band.Due to the strong absorption of Ti 4+ ions covering all the absorption bands of Tb 3+ ions at ultraviolet region, the <k(ω)> 0 could not be accurately measured and calculated, but it is related with the concentration of Tb 3+ ions.By comparing the integral intensities of the MCD of TTO and TGG at 357.5 (352.5)nm, we consider that the contribution of concentration to MOA is relatively small, the main contribution to MOA is that Ti 4+ absorption may be transfer energy to Tb 3+ , which enhances the 4f-4f transition intensities of Tb 3+ .Under the action of pump beam at different elliptically polarized states, transient lightinduced polarization and magnetization of TTO could be detected by the time-resolved ΔI θ (variation of rotation signal)and ΔI η (variation of ellipticity signal), as shown in Fig. 8.In this case, the energy density of the pump beam is 12mJ/cm 2 , after normalization, all the width at half signals are ~500 fs.Most signals have a Gaussian-like shape and have opposite signs for the opposite pump helicities.Thus, the interpretation of experimental data is based on the assumption that the rotation and ellipticity of the signal beam comes from the spin magnetization.
The peak intensities (signal amplitude) of I θ and I η in Fig. 8 are denoted as I θ,max and I η,max , respectively, and plotted as a function of Ф.Then, the experimental points is displayed in Fig. 9.Under the approximation of continuous wave and near coaxial, the relationship between I θ (I η ) and Ф can be expressed by Eq. ( 3 Where I pump is the power density of pump beam, n is the complex refractive index, c is the speed of light, χ xxyy and χ xyyx are the incoherent part of polarized tensor of isotropic material. Equation (3) showed that I θ and I η are determined by the contribution of two parts, the first term and the second term at the right of the equal sign representing the contribution of OKE and IFE with the change of Φ.The period of OKE contribution is π/2, when Φ = ± 22.5°, ± 67.5°, OKE contribution is most significant, whereas Φ = ± 45° or pump beam is parallel (perpendicular) to the polarized plane of the probe beam, OKE contribution is zero.The period of IFE contribution is π, when the pump beam is circularly polarized, IFE contribution is most significant, and when the pump beam is linearly polarized, it is zero.If the pump beam is an arbitrary elliptically polarized, OKE and IFE contributions will exist.Fitting the experimental data according to Eq. ( 3), the results are shown in Fig. 9, the twofold (dashed) and fourfold (dotted) lines represent the OKE and IFE contributions with a change of Ф, respectively, and the solid line represents the superposition of two contributions.The good fit confirms the assumptions about the origins of each contribution.Indeed, the IFE is maximized, whereas, the contribution from the OKE decreases to zero, when the pump is circularly polarized.Figure 10 shows the amplitude of rotation and elliptictiy signals as a function of the pump intensity together with a linear fit.The linear intensity dependence indicates that the observed signal is a second-order nonlinear effect with respect to the electric-field amplitude of the pump beam.Compared with that of TGG, TTO has larger rotation and elliptictiy signals at the same pump intensity.The previous idea thought Faraday effects and inverse Faraday effects were described by the same parameters that characterized the magneto-optical properties of the medium-the Verdet constant V, but recently, R.V. Mikhaylovskiy et al. [31] think ultrafast magneto-optical signal is determined by the instantaneous diamagnetic response rather than the paramagnetic alignment of spins by a light-induced effective magnetic field based on the investigation of ultrafast inverse Faraday effect in TGG crystal.In our case, combined the experimental results of non-cubic structure NaTb(WO 4 ) 2 [30] and analyzed the data in Table 2, we initially speculate that the value of IFE have a more direct relationship with the magnetic susceptibility of paramagnetic materials.

Conclusions
Tb 2 Ti 2 O 7 single crystal has been grown by the Czochralski method.It displays strong growth habit with {111} facets easily exposed.The transmittance of TTO was about 73% at wavelengths of 700-1400 nm.The crystal has larger specific Faraday rotations than those of TGG at 532, 633 and1064 nm wavelengths.Besides the large concentration of Tb 3+ ions and refraction index contribute to the large Faraday effect of TTO, MCD spectra show the absorption of Ti 4+ ions at ultraviolet region may transfer energy to Tb 3+ , which has contributions to the magneto-optical activity (MOA) of the Tb 3+ ions 4f-4f transitions.In the time-resolved pump-probe spectroscopy, when the pump beam is arbitrary elliptically polarized, OKE and IFE contributions will exist, whereas the pump beam is circularly polarized, the IFE is maximized, the contribution from the OKE decreases to zero.Paramagnetic properties of TTO crystal determines its tens of femtoseconds spin relaxation time, the FWHM of the probe beam rotation and elliptical signals are close to 500 fs, its strength increases linearly with the increase of the pump energy density.At present, compared with the commercial TGG, our TTO crystal displays relatively large absorption coefficient, may be not suitable as a Faraday isolator used in the high continuous power laser systems.
Improving the purity of raw materials and the crystal growth technique are helpful for obtaining TTO crystals with low absorption coefficient.Therefore, we think the high optical quality Tb 2 Ti 2 O 7 crystal can be a good candidate material for magneto-optical devices and ultrafast all-optical magnetic switching at the 700-1400 nm regions.

Fig. 4 .
Fig. 4. Curve of the weak absorption of TTO crystal at 1064 nm.

Fig. 5 .
Fig. 5.The applied magnetic field dependence of magnetization response for TTO and TGG crystals.

Fig. 8 .
Fig. 8.The amount of rotation and ellipticity signal change induced by the pump beam with different polarized states (Φ represents the angle between the linearly polarized plane of pump beam and the fast axis of quarter-wave plate).

Fig. 9 .
Fig. 9. (a)The dependence of ΔI θ , max (rotation signal amplitude) upon Φ ; (b)The dependence of ΔI η , max (ellipticity signal amplitude) upon Φ.The fitting curve (solid) shown on the graph consists of the twofold (dashed) and fourfold (dotted) sinusoidal contributions, which correspond to the OKE and IFE, respectively.

Fig. 10 .
Fig. 10.Control pulse fluence dependence of the peak rotation and ellipticity signals of TTO and TGG crystals.