**6. Magneto-optical CeF3 crystal**

Frequency instabilities and parasitic oscillations in optical sources are deleterious to a civilization increasingly dependent on the transfer of optical information with light. An optical isolator is an optical diode that allows light to pass in only one direction. The functions of optical isolators are based on the non-reciprocal magnetooptical rotation of polarization of light, long known as the Faraday rotation (FR). The crystals investigated and employed as optical isolators to date include only isotropic crystals or uniaxial crystals with well-defined isotropic directions (*i.e.*, along the optic axis). Otherwise, optically anisotropic crystals are complicated by LB and LD.

Like OA, FR in anisotropic crystals cannot be accurately measured conventionally, except along high-symmetry directions. Therefore, low-symmetry directions in anisotropic crystals have been avoided in magneto-optical research.

A sample subjected to a magnetic field applied parallel and anti-parallel to the wave vector of the light can manifest FR and magnetic circular dichroism (MCD) that can be analyzed by the G-HAUP method. A Nd-Fe-B (NIB) magnet introduced for this purpose is shown in **Figure 10**. In this configuration, we measured the dispersion of FR and MCD in CeF3 single crystal along the optic axis (*c*-axis) as well as *perpendicular* to the optic axis (*a*-axis) with the G-HAUP.

Single crystals of CeF3 were grown by the modified Czochralski technique [58–60]. We prepared two types of samples: (001) and (100) plates of single-crystal CeF3. The smooth flat sample surfaces were obtained by polishing machines with a diamond slurry (3.0 μm) and colloidal silica (32.5 nm) abrasive, successively. We polished a 307 μm thick (001) plate of a single crystal of CeF3 [58–60] with point symmetry *D*3*d*. When the magnetic field was applied parallel to the light propagation direction, FR occurs only along <001>. In this direction, the measurement is conventional, but here, we implemented the rotating analyzer mode of G-HAUP. The sample was sandwiched between two permanent NIB magnets and illuminated through a 0.5 mm pinhole (**Figure 10**). The longitudinal field of 0.5 Tesla (T) was homogeneous [60]. The wavelength dependence of the Verdet constant, the quantity in deg./mm. T that describes the strength of FR along the *c*-axis at 25°C, is plotted as black rhombuses in **Figure 11c**. Positive Verdet constants along the *c*-axis indicated that the right-handed

**Figure 10.**

*Photograph of the Nd-Fe-B (NIB) magnet with the magnetic field applied parallel or anti-parallel to the light propagation direction. The sample was mounted on a plate with a 0.5 mm pinhole sandwiched between two identical NIB permanent magnet rings. The black scale bar = 1 cm. Reproduced from ref. [9] with permission from Springer Nature.*

*Chiroptical Studies on Anisotropic Condensed Matter: Principle and Recent Applications… DOI: http://dx.doi.org/10.5772/intechopen.108721*

circularly polarized light propagates faster than its left-handed counterpart across the spectrum.

A (100) plate just 58.0 μm thick was polished. The extinction directions were determined accurately with an Ehringhaus compensator fitted to a polarized light microscope. We first determined with G-HAUP in the extended mode the dispersion of LD, OA, and CD along the *a*-axis in the absence of the magnetic field at 25°C (blue rhombuses in **Figure 11**). LB was comparable to that of *α*-quartz (**Figure 11a**). LD was almost zero over the wavelength examined (**Figure 11b**), consistent with the absence of absorption bands at wavelengths longer than 282 nm. The OA and CD values were also close to zero, consistent with the *D*3*<sup>d</sup>* symmetric crystal structure. The dispersion of LB, LD, FR, and MCD along <100> was established, while the magnetic field was propagated parallel and anti-parallel to the wave vector at 25°C (red rhombuses in **Figure 11**). LB and LD were indifferent to the sign of the magnetic field. Reversing the magnetic field direction inverted the signs of FR and MCD. The values of LB and LD hardly changed with and without the magnetic field (**Figure 11a** and **b**). The Verdet constants along the *a*-axis were positive throughout the wavelength region (**Figure 11c**).

CeF3 is paramagnetic at room temperature. Therefore, the magnetic interactions such as ferromagnetism, anti-ferromagnetism, or ferrimagnetism, which are often observed in low-temperature regions, do not affect the G-HAUP measurements.

#### **Figure 11.**

*Wavelength dependences of LB (a), LD (b), Verdet constant (c), and MCD (d) in single-crystal CeF3 at 25°C. the black, blue, and red rhombuses represent the data along <001>, along <100> without a magnetic field, and along <100> under an applied magnetic field, respectively. We eliminated points in spectral regions where G-HAUP is less sensitive. The Verdet constant spectra were fitted to a simple Drude oscillator. The error bars represent the standard deviations. The error along <100> given in (c) ranged from 0.32 to 1.40 deg./mmT. reproduced from ref. [9] with permission from Springer Nature.*

Cerium is usually in the 3+ oxidation state in condensed matter; the electronic configuration of Ce3+ is 1*s* 2 2*s* 2 2*p*<sup>6</sup> … 4*d*104*f* 1 5*s* 2 5*p*<sup>6</sup> . Transitions from 4*f* ➔ 5*d* confer the magneto-optical properties in the UV–Vis-IR region [61]. The Verdet constants were positive along the *c-* and *a*-axes at all measured wavelengths, and their magnitudes along both axes were nearly equal (**Figure 11c**). The magnetic susceptibilities, measured with SQUID (superconducting quantum interference device), were nearly identical in both directions. The magnitude of Verdet constants at an arbitrary frequency depends on the magnetic susceptibility and the transition probabilities. Therefore, we may surmise that the anisotropy of the summed 4*f* ➔ 5*d* transition probabilities is zero.

#### **7. Conclusions**

In this review, principles and recent applications of G-HAUP method are concisely introduced. New CD peaks in photomechanical crystals originating from photochromism were observed. According to the G-HAUP results of alanine crystals, we discuss the relationship between the absolute structure and OA. In addition, we found by benzil measurements and quantum chemical calculations that the intermolecular interactions are decisive even though comparatively weak dispersion forces dominate the interactions between molecules. Moreover, the first application of G-HAUP to a magneto-optical material was presented by applying magnetic field with NIB magnets. These results strongly indicate the usefulness of the HAUP method for evaluating the chiroptical and magneto-optical properties of ordered specimens. More recently, a rapid HAUP system was developed by using dispersive detection technique with a CCD array spectrometer [62]. Very thin crystalline sample, *ca.* less than several dozen micrometers, were prepared to accommodate the G-HAUP transmission requirement. A reflection-mode HAUP system can contribute to the significant increase in the number of HAUP-applicable specimen because of the simplification of sample preparation. In addition, the extension of wavelength coverage to the infrared and/or vacuum UV region results in the significant increase in the information related to the electronic structure and/or conformation of optically active specimens [63].

#### **Acknowledgements**

This review is cordially dedicated to Prof. Jinzo Kobayashi, who is an inventor of HAUP and has opened a new way to solid-state dissymmetry from a spectroscopic point of view. We thank Prof. Dr. Hidehiro Uekusa, Prof. Dr. Tadashi Mori, Dr. Alexander T. Martin, Dr. Shane M. Nichols, and Dr. Veronica L. Murphy for their fruitful discussions and comments. This study was financially supported by the JSPS Scientific Research in the Challenging Exploratory Research, the High-Tech Research Center (TWIns), the Consolidated Research Institute for Advanced Science and Medical Care (ASMeW), the Global COE for Practical Chemical Wisdom, the Leading Graduate Program in Science and Engineering, the Top Global University Project, Waseda University, from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and the grant-in-aid from the Mitsubishi Materials Corporation and the Mizuho Foundation for the Promotion of Sciences.

*Chiroptical Studies on Anisotropic Condensed Matter: Principle and Recent Applications… DOI: http://dx.doi.org/10.5772/intechopen.108721*
