The frustrated magnetic structure of hexagonal RMnO3 (R=Sc,Y,Ho,Er,Tm,Yb,Lu) is analyzed by optical second-harmonic (SH) spectroscopy. It is found that in all compounds the Mn3+ spins form antiferromagnetic triangles in the xy easy plane with parallel coupling between adjacent layers at z=0 and c/2 in the unit cell (α-type ordering). Some earlier conclusions on the magnetic structure of RMnO3 should be revised.

Optical second-harmonic (SH) spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic X-ray diffraction experiments are overcome. As an example, various antiferromagnetic compounds of the Mn3+ and Cr3+ ions are discussed.

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites RMnO3 ( R = Sc, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.

We show that by analysing nonlinear spectra of second-harmonic generation we can confirm magnetic structures known from other experiments or distinguish magnetic structures which cannot be distinguished by neutron diffraction or other experiments. Experimental data for the hexagonal rare-earth manganite HoMnO3 are presented.

A new method for the determination of spatially resolved phase differences of nonlinear susceptibilities is presented. The technique is based on the interference of the signal field with a reference field. A phase-shifting element that directly changes the phase difference between the two second-harmonic fields is introduced. The reliability of the method is tested by an experiment with two quartz crystals. As a first application, a measurement of the phase difference between domains in antiferromagnetic YMnO(3) is presented.

Hexagonal manganites RMnO3 (R=Sc, Y, Ho, Er, Tm, Yb) are compounds in which a ferroelectric and an antiferromagnetic order may coexist. The ferroelectric crystal structure is well known but theoretical studies show that there are different possibilities for the spin structure. By means of polarization- and temperature-dependent second-harmonic spectroscopy it is possible to determine the magnetic structure of RMnO3 compounds.

A coexistence of electric and magnetic order in hexagonal YMnO3 gives rise to an unusual nonlinear optical polarization P(2 omega) which contains two contributions defined by the two order parameters. The two contributions overlap over a wide frequency range thus opening up new possibilities to study the electronic structure of crystals. The magnitude and phase of P(2 omega) can be changed by varying the ratio between the two contributions. We show that 180 degrees ferroelectric and antiferromagnetic domains, which are indistinguishable in linear optics, can be visualised with a high contrast using the second harmonic light.

and on their phase. One of the hexagonal manganites, YMnO3 is chosen to demonstrate in detail the experimental methods for obtaining this information. The interference of different contributions is utilized to study domain topography.

We have observed two types of optical second harmonic spectra of Mn3+ ions in hexagonal YMnO3, one of which is caused by the noncentrosymmetric ferroelectric ordering of charges, whereas the other is due to the centrosymmetric antiferromagnetic ordering of spins. Partial overlapping between the electronic transitions gives rise to a new kind of nonlinear optical polarization P(2 omega) = P-FE(2 omega) + P-AFM(2 omega), which depends on two order parameters. The magnitude and phase of P(2 omega) can be changed by varying the ratio between the two contributions, as demonstrated by changing the contrast between 180 degrees antiferromagnetic domains, which are indistinguishable in linear optics. [S0031-9007(98)07311-6].

A novel technique for the visualization of antiferromagnetic domains making use of second harmonic generation is used to study the easy-plane antiferromagnet YMnO3. Domain states characterized by small, medium, or large domains are observed. Switching from one state to another can be achieved by a heat treatment above TN and subsequent cooling below TN. Contributions to the mechanism of this unusual behavior of domains are discussed.

O3, in which the time-invariant second-harmonic reference can be generated either intrinsically by the crystal or externally by use of the new technique, so that both methods may be compared. The technique is then used to visualize the domain structure of YMnO3, an antiferromagnetic crystal which does not provide the time-invariant reference wave intrinsically. The experiments demonstrate the wide applicability of the method.

Summary form only given. Nonreciprocal effects are caused by breaking of time-inversion symmetry. Nonlinear spectroscopy is an excellent tool to study nonreciprocal effects as, for example, antiferromagnetic (afm) ordering, as was recently shown for Cr/sub 2/O/sub 3/. The sign of the nonlinear optical susceptibility tensor can be measured by second harmonic generation (SHG) if there is at the same time a SH-contribution from a time invariant susceptibility tensor.