Theory of nonlinear optical susceptibilities of antiferromagnetic Cr2O3

Tanabe, Yukito; Muto, Makiko; Hanamura, Eiichi

doi:10.1016/s0038-1098(97)00073-2

Cited by 17 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, we confirmed that only the real part of the product of the magnetic-and electric-dipole matrix elements contributes to the magnetoelectric susceptibility. 19 From this fact, only the conventional trigonal crystalline fields V axial,g and V axial,u are effective in the present phenomena in contrast to the second-harmonic generation 12 in which only V twist,g and V twist,u lead to finite contribution. Second, two levels ͉ 4 T 2g x ϯ ͘ split by the diagonal component of the spin-orbit interaction contribute with opposite sign to the magnetoelectric susceptibility.…”

Section: Discussionmentioning

confidence: 80%

Magnetoelectric and second-harmonic spectra in antiferromagneticCr2O3

et al. 1998

Self Cite

View full text Add to dashboard Cite

We present a microscopic model to understand the magnetoelectric and second-harmonic spectra of Cr 2 O 3 and the interference effect between the magnetic ( m ) and electric ( e ) second-order optical polarizations. The spin-orbit interaction and the crystalline fields of correct symmetry around the Cr 3ϩ ion, i.e., the axial and twisted crystalline field of C 3 symmetry, are treated as perturbation on the trigonal states of the d 3 system of Cr 3ϩ . By these treatments we attempt to describe the observed phenomena associated with the transitions between 4 A 2g and 4 T 2g states in Cr 2 O 3 . It is possible to reproduce the observed spectra of the polarization rotation and ellipticity, and the second-harmonic generation spectra described by the nonlinear susceptibilities m and e . The estimated theoretical magnitudes of these quantities are in reasonable agreement with the observed magnitudes.

show abstract

Section: Discussionmentioning

confidence: 80%

Magnetoelectric and second-harmonic spectra in antiferromagneticCr2O3

et al. 1998

Self Cite

View full text Add to dashboard Cite

show abstract

“…in Ref. [29]. Another interesting issue is the behavior of the tensor elements with respect to the AF order parameter L (for ferromagnetic phases L should be replaced by the magnetization M), i.e.…”

Section: Appendix On the Group-theoretical Analysis Of Magnetic Systemsmentioning

confidence: 99%

“…In this approximation they explained the SHG from Cr 2 O 3 as observed by Fiebig et al [1] and they were able to give a quantitative estimate for that. Tanabe et al [29], however, pointed out that the occurrence of purely real or imaginary values of the tensor elements plays a decisive role for the existence of SHG from this substance. They found that for a (CrO 6 ) 2 cluster SHG can take place only in the case where the tensor elements are imaginary, and thus should vanish in Muthukumar's approximation.…”

Section: Introductionmentioning

confidence: 99%

Symmetry analysis of second-harmonic generation at surfaces of antiferromagnets

1999

View full text Add to dashboard Cite

Using group theory we classify the nonlinear magneto-optical response at low-index surfaces of fcc antiferromagnets, such as NiO. Structures consisting of one atomic layer are discussed in detail. We find that optical second harmonic generation is sensitive to surface antiferromagnetism in many cases. We discuss the influence of a second type of magnetic atoms, and also of a possible oxygen sublattice distortion on the output signal. Finally, our symmetry analysis yields the possibility of antiferromagnetic surface domain imaging even in the presence of magnetic unit-cell doubling. 78.20.Ls, 75.30.Pd, 75.50.Ee,

show abstract

“…In the context of the antiferromagnetic Cr 2 O 3 it has been observed [3] that χ (ED) ijk exists only in the ordered phase (T < T N ) and it has been shown [5,6] that it is linearly proportional to the antiferromagnetic order parameter, as it should be if we had defined a Ginzburg-Landau free energy for the ordered phase. In the framework of the classical Ginzburg-Landau approach to phase transitions the allowed terms contributing to the free energy follow from the symmetry of the order-parameter and from the symmetry of the lattice [7,9].…”

mentioning

confidence: 98%

“…The study of this dependence is of crucial importance in order to understand the non-reciprocal character of the SHG tensors. The derivation of a micoscopic theory for a specific effect, in our case SHG, can be rather complicated depending on the properties of the material under study [5,6]. Concrete information of the SHG process in materials where a transition takes place, i.e.…”

mentioning

confidence: 99%

A generalized Ginzburg-Landau approach to second harmonic generation

Valentí

Gros

2000

Eur. Phys. J. B

View full text Add to dashboard Cite

We develop a generalized Ginzburg-Landau theory for second harmonic generation (SHG) in magnets by expanding the free energy in terms of the order parameter in the magnetic phase and the susceptibility tensor in the corresponding high-temperature phase. The non-zero components of the SHG susceptibility in the ordered phase are derived from the symmetries of the susceptibility tensor in the high-temperature phase and the symmetry of the order parameter. In this derivation, the dependence of the SHG susceptibility on the order parameter follows naturally, and therefore its nonreciprocal optical properties. We examine this phenomenology for the magnetoelectric compound Cr2O3 as well as for the ferroelectromagnet YMnO3. [3,4] in Cr 2 O 3 were obtained what confirms that these experiments can distinguish between the two magnetic states that are related to each other by the time reversal operation, and therefore its nonreciprocity. These observations can be explained by an interference effect between a time-symmetric magnetic dipole contribution and a time-antisymmetric electric dipole contribution [3]. Soon after these experiments were done, a microscopic theory was proposed [5] which could explain quantitatively the non-reciprocal effects observed in Cr 2 O 3 . It was shown that the electric dipole contributions were linearly proportional to the antiferromagnetic order parameter giving rise to the timeantisymmetric character to the electric dipole tensor. The study of this dependence is of crucial importance in order to understand the non-reciprocal character of the SHG tensors. The derivation of a micoscopic theory for a specific effect, in our case SHG, can be rather complicated depending on the properties of the material under study [5,6]. Concrete information of the SHG process in materials where a transition takes place, i.e. paramagnetantiferromagnet or paraelectric-ferroelectric, can be obtained at a simpler level, i.e. by considering only the symmetry arguments. In particular, we are interested in investigating the dependence of the SHG susceptibilities in the ordered phase on the order parameter.A powerful phenomenological theory suitable to describe phase transitions is the Ginzburg-Landau theory. The Ginzburg-Landau approach is based on the existence of an order parameter in the ordered phase and on symmetry considerations [7]. Pershan in 1963 [8] showed that the tensors for nonlinear electro-and magneto-optic effects could be derived from a phenomenological timeaveraged free energy. It is our purpose in this paper to extend the formulation of Pershan by including the order parameter explicitly in the expansion of the free energy for SHG. We shall show that the non-zero components of the SHG susceptibility tensor in the ordered phase are naturally obtained from the symmetry of the susceptibility tensor in the high-temperature phase and the symmetry of the order parameter. Once the dependence of the SHG susceptibility tensor on the order parameter is known, the non-reciprocal optical properties below the...

show abstract

Theory of nonlinear optical susceptibilities of antiferromagnetic Cr2O3

Cited by 17 publications

References 6 publications

Magnetoelectric and second-harmonic spectra in antiferromagneticCr2O3

Magnetoelectric and second-harmonic spectra in antiferromagneticCr2O3

Symmetry analysis of second-harmonic generation at surfaces of antiferromagnets

A generalized Ginzburg-Landau approach to second harmonic generation

Contact Info

Product

Resources

About