As-Grown Domain Structure in Calcium Orthovanadate Crystals

: An as-grown domain structure in nominally pure and Mn-doped calcium orthovanadate (CVO) crystals was studied by several methods of domain imaging: optical microscopy, piezoelectric force microscopy, and Cherenkov-type second harmonic generation. The combination of imaging methods provided an opportunity for comprehensive study of the domain structure on the polar surface and in the bulk of the samples. It was shown that, in nominally pure CVO crystals, an irregular 3D maze of rounded domains, with charged walls, essentially tilted from the polar direction, was present. It was proposed that the domain structure was formed just below the phase transition temperature and persisted during subsequent cooling. Such behavior is due to effective bulk screening of the depolarization ﬁeld and a low value of the pyroelectric ﬁeld which appears during cooling. The revealed formation of triangular domains and ﬂat fragments of domain walls in Mn-doped CVO was attributed to polarization reversal under the action of the polar component of the pyroelectric ﬁeld, above the threshold value for domain switching. This fact represents the ﬁrst observation of the domain switching in CVO crystals. Author Contributions: Conceptualization, V.S. and E.S.; methodology, E.S.; software, E.L.; investigation, M.N., V.Y. and E.S.; resources, L.I.; writing—original draft preparation, E.S. and V.S.; writing—review and editing, V.S. and E.P.; visualization, M.N., V.Y. and E.S.; supervision, V.S.; project administration,


Introduction
The single crystals of calcium orthovanadate (Ca 3 (VO 4 ) 2 ) (CVO) are considered as a laser host material [1]. It has been shown that the high optical damage threshold [2] and nonlinear optical coefficients of CVO are comparable to those of potassium dihydrophosphate (KH 2 PO 4 ) (KDP) [3]; therefore, these crystals are potentially useful for frequency conversion of tunable laser sources. CVO possesses the trigonal space group R3c [2], and, being acentric, demonstrates intense second harmonic generation. Recently, nominally pure CVO crystals, and those doped by Mn and rare earth elements (Tm, Ho), have become of special interest due to their potential application as a new active medium for 2 µm lasers [4][5][6][7].
Ferroelectricity in CVO single crystals was discovered by Glass et al. in 1978 [2]. The ferroelectric phase transition temperature (Tc = 1383 K) was determined by differential thermal analysis and dielectric studies. The spontaneous polarization value (P S = 68 µC/cm 2 ) was calculated using an empirical dependence of T C , because high conductivity prevented direct hysteresis measurements [2]. It was claimed that the observations of electrical domains, pyroelectric behavior, and dielectric and thermal evidence of a phase transition "leave little doubt that this material is correctly classified as ferroelectric" [2]. As-grown domain structure, revealed by etching, represented the shapeless domains up to millimeter size.
The domains at the surface of CVO plates, revealed by etching in a 0.5% boric acid solution, are usually imaged by optical microscopy [2,4,5,7]. Recently, it has been demon-strated that confocal Raman microscopy (CRM) [8] and piezoelectric force microscopy (PFM) [9] could be used for detail analysis of as-grown domain structure in CVO [10]. Nevertheless, domain structure in the bulk of CVO single crystals is still unstudied.
In this paper, we present the results of an experimental study of as-grown domain structure in CVO by several methods of domain imaging: optical microscopy, PFM, and Cherenkov-type second harmonic generation (CSHG) [11,12]. The combination of imaging methods provided a unique opportunity for the comprehensive study of domain structure in the bulk, and allowed the revelation of the domain switching during cooling, under the action of the pyroelectric field.

Materials and Methods
The studied nominally pure CVO single crystals, and those doped with Mn ions (at 0.05% and 0.1%), were grown from the melt, in air, by the Czochralski method with pulling in [100] directions [7]. The grown crystals were about 12 mm in diameter and up to 45 mm in length. Then, 0.6-mm-thick plates were cut perpendicular to the polar axis. A final surface treatment was done by mechanochemical polishing, using a PM5 machine (Logitech Ltd., Glasgow, UK) with 50 nm colloidal silica suspension (Allied High Tech Products, Inc., Compton, CA, USA). The polishing procedure revealed a shallow relief corresponding to the surface domain pattern, with a step height of about 100 nm, which was enough for obtaining optical contrast.
Both polar surfaces of the sample were studied by optical microscopy and PFM. Various imaging optical modes (transmitted and reflected light, phase contrast, and bright and dark fields) were realized by means of an optical microscope BX-61 (Olympus, Tokyo, Japan). PFM imaging was performed using an NTEGRA Aura scanning probe microscope (NT-MDT, Moscow, Russia) with silicon NSC-16 tips (MikroMasch, Sofia, Bulgaria), conductive platinum coating, and a typical curvature radius about 25 nm. AC modulation voltage with amplitude U mod = 10 V and frequency f mod = 20 kHz was applied between the tip and the silver-paste solid-bottom electrode. The obtained contrast of piezoelectric response proved that the optical images correspond to ferroelectric domains on the polar surface ( Figure 1). grown domain structure, revealed by etching, represented the shapeless domains up to millimeter size.
The domains at the surface of CVO plates, revealed by etching in a 0.5% boric acid solution, are usually imaged by optical microscopy [2,4,5,7]. Recently, it has been demonstrated that confocal Raman microscopy (CRM) [8] and piezoelectric force microscopy (PFM) [9] could be used for detail analysis of as-grown domain structure in CVO [10]. Nevertheless, domain structure in the bulk of CVO single crystals is still unstudied.
In this paper, we present the results of an experimental study of as-grown domain structure in CVO by several methods of domain imaging: optical microscopy, PFM, and Cherenkov-type second harmonic generation (CSHG) [11,12]. The combination of imaging methods provided a unique opportunity for the comprehensive study of domain structure in the bulk, and allowed the revelation of the domain switching during cooling, under the action of the pyroelectric field.

Materials and Methods
The studied nominally pure CVO single crystals, and those doped with Mn ions (at 0.05% and 0.1%), were grown from the melt, in air, by the Czochralski method with pulling in [100] directions [7]. The grown crystals were about 12 mm in diameter and up to 45 mm in length. Then, 0.6-mm-thick plates were cut perpendicular to the polar axis. A final surface treatment was done by mechanochemical polishing, using a PM5 machine (Logitech Ltd., Glasgow, UK) with 50 nm colloidal silica suspension (Allied High Tech Products, Inc., Compton, CA, USA). The polishing procedure revealed a shallow relief corresponding to the surface domain pattern, with a step height of about 100 nm, which was enough for obtaining optical contrast.
Both polar surfaces of the sample were studied by optical microscopy and PFM. Various imaging optical modes (transmitted and reflected light, phase contrast, and bright and dark fields) were realized by means of an optical microscope BX-61 (Olympus, Tokyo, Japan). PFM imaging was performed using an NTEGRA Aura scanning probe microscope (NT-MDT, Moscow, Russia) with silicon NSC-16 tips (MikroMasch, Sofia, Bulgaria), conductive platinum coating, and a typical curvature radius about 25 nm. AC modulation voltage with amplitude Umod = 10 V and frequency fmod = 20 kHz was applied between the tip and the silver-paste solid-bottom electrode. The obtained contrast of piezoelectric response proved that the optical images correspond to ferroelectric domains on the polar surface ( Figure 1). Application of CSHG allowed us to obtain a set of 2D domain images at different depths, with spatial resolution of about 500 nm. This method was realized by means of a homemade setup based on an NTEGRA Spectra scanning probe microscope (NT-MDT SI, Moscow, Russia) with a Yb fiber laser (1064 nm, 40 mW). Treatment of the obtained data Application of CSHG allowed us to obtain a set of 2D domain images at different depths, with spatial resolution of about 500 nm. This method was realized by means of a homemade setup based on an NTEGRA Spectra scanning probe microscope (NT-MDT SI, Moscow, Russia) with a Yb fiber laser (1064 nm, 40 mW). Treatment of the obtained data by the Blender 3D computer graphics software toolset allowed the construction of 3D domain images.

Surface Domain Structure
As-grown domain structure, imaged on the polar surface of all the studied samples by optical microscopy, mostly consisted of rounded shapeless domains ( Figure 2). Bright-field transmitted-light optical microscopy allowed imaging of the domain walls on both polar surfaces simultaneously (Figure 2a). The significant difference in the domain wall positions on the opposite polar surfaces proved the existence of charged domain walls in the bulk. Moreover, rounded isolated domains, with diameter below the sample thickness, reached, typically, only one surface, which indicated the absence of essential domain elongation in the polar direction. The typical domain size on the surface ranged from 50 µm to 1 mm. by the Blender 3D computer graphics software toolset allowed the construction of 3D domain images.

Surface Domain Structure
As-grown domain structure, imaged on the polar surface of all the studied samples by optical microscopy, mostly consisted of rounded shapeless domains ( Figure 2). Brightfield transmitted-light optical microscopy allowed imaging of the domain walls on both polar surfaces simultaneously (Figure 2a). The significant difference in the domain wall positions on the opposite polar surfaces proved the existence of charged domain walls in the bulk. Moreover, rounded isolated domains, with diameter below the sample thickness, reached, typically, only one surface, which indicated the absence of essential domain elongation in the polar direction. The typical domain size on the surface ranged from 50 μm to 1 mm.

Bulk Domain Structure
Complete information about domain shape in the bulk was obtained by CSHG. The 3D images of domains in CVO crystals were more complicated than those of domains formed during polarization reversal in lithium niobate (LN) and lithium tantalate (LT) crystals, which typically demonstrate a small tilt of the domain walls from the polar direction [13,14]. The domain wall images in the bulk of CVO crystals represent interferometric patterns (Figure 3), which, according to Kampfe et al. [15], correspond to abnormally tilted charged domain walls.
We used CSHG to image as-grown domains in the bulk of CVO crystals by recording XY scans at different focal depths with 13 μm steps ( Figure 3). According to [15], every bright line in the images represents a cross-section of the domain wall at different depths. The axial displacement between cross sections was equal to 5.8 μm, for the used fundamental wavelength (λ = 1064 nm). The depth of independent cross sections, recorded in a single XY scan, was defined by numerical aperture of the used objective. The local topology of the domain wall was calculated from the obtained XY scans. 3D reconstruction of the domain structure from Figure 3 was obtained by deconvolution ( Figure 4) (see the rotated image in Video S1 in Supplementary Materials).

Bulk Domain Structure
Complete information about domain shape in the bulk was obtained by CSHG. The 3D images of domains in CVO crystals were more complicated than those of domains formed during polarization reversal in lithium niobate (LN) and lithium tantalate (LT) crystals, which typically demonstrate a small tilt of the domain walls from the polar direction [13,14]. The domain wall images in the bulk of CVO crystals represent interferometric patterns (Figure 3), which, according to Kampfe et al. [15], correspond to abnormally tilted charged domain walls.  Analysis of domain wall position in the bulk allowed us to observe that the domain wall tilt from the polar direction ranged from 11.2° to 71.4°, with an average value of about 35°.
It was demonstrated that as-grown domain structure in CVO crystals represented a 3D maze, with randomly oriented charged domain walls, strongly tilted from the polar direction. According to bulk imaging, isolated rounded domains rarely occurred. This fact indicates that optical images of rounded domains, observed on the polar surfaces, usually correspond to cross-sections of a large irregular domain maze. We used CSHG to image as-grown domains in the bulk of CVO crystals by recording XY scans at different focal depths with 13 µm steps (Figure 3). According to [15], every bright line in the images represents a cross-section of the domain wall at different depths. The axial displacement between cross sections was equal to 5.8 µm, for the used fundamental wavelength (λ = 1064 nm). The depth of independent cross sections, recorded in a single XY scan, was defined by numerical aperture of the used objective. The local topology  Analysis of domain wall position in the bulk allowed us to observe that the domain wall tilt from the polar direction ranged from 11.2° to 71.4°, with an average value of about 35°.
It was demonstrated that as-grown domain structure in CVO crystals represented a 3D maze, with randomly oriented charged domain walls, strongly tilted from the polar direction. According to bulk imaging, isolated rounded domains rarely occurred. This fact indicates that optical images of rounded domains, observed on the polar surfaces, usually correspond to cross-sections of a large irregular domain maze. The optically observed as-grown domain structure in both Mn-doped CVO crystals (Figure 2b,c) looked similar to that of nominally pure ones (Figure 2a). However, the essential difference between the shapes of isolated domains and domain walls of these crystals was revealed. In nominally pure CVO, all domains were rounded (Figure 2a), whereas in 0.05% Mn-doped (Figure 5a-c) and 0.1% Mn-doped CVO (Figure 5d), single crystals sometimes showed triangular isolated domains and oriented flat fragments of domain walls, appearing together with rounded domains. It was demonstrated that as-grown domain structure in CVO crystals represented a 3D maze, with randomly oriented charged domain walls, strongly tilted from the polar direction. According to bulk imaging, isolated rounded domains rarely occurred. This fact indicates that optical images of rounded domains, observed on the polar surfaces, usually correspond to cross-sections of a large irregular domain maze.
The optically observed as-grown domain structure in both Mn-doped CVO crystals (Figure 2b,c) looked similar to that of nominally pure ones (Figure 2a). However, the essential difference between the shapes of isolated domains and domain walls of these crystals was revealed. In nominally pure CVO, all domains were rounded (Figure 2a

Discussion
The obtained results can be discussed in terms of kinetic approach [16] to formation of as-grown domain structure during phase transition and subsequent cooling [17]. The geometry of the domain structure, formed during slow cooling just below TC, is determined by spatial distribution of the internal field, produced by bulk defects and composition inhomogeneities. The obtained absence of the quasi-regular layered domain struc-

Discussion
The obtained results can be discussed in terms of kinetic approach [16] to formation of as-grown domain structure during phase transition and subsequent cooling [17]. The geometry of the domain structure, formed during slow cooling just below T C , is determined by spatial distribution of the internal field, produced by bulk defects and composition inhomogeneities. The obtained absence of the quasi-regular layered domain structure justifies random spatial distribution of the defects, without pronounced growth striations [18][19][20][21][22][23]. Formation of charged domain walls is caused by low value of the depolarization field and high bulk conductivity, near T C . The fast bulk screening of the depolarization field at high temperature stabilizes the formed domain pattern and provides its permanence during slow cooling [17].
During fast cooling to the room temperature, the domain structure can change under the action of the pyroelectric field [17,24,25], for implementation of the following relation: where E pyr.z (T, dT/dt) is the polar component of the pyroelectric field, which depends on temperature and cooling rate, and E th (T) is the temperature-dependent threshold field for domain switching.
It is important to point out that the shape of the isolated ferroelectric domains that arise during polarization reversal is defined by the crystal's symmetry [26]. A triangular or hexagonal shape in isolated domains is typical for uniaxial ferroelectric crystals of C 3 symmetry [21,27,28]. The formation of flat domain walls is a result of determined step generation and kink motion along the wall [26].
Thereby, it is possible to claim that, in nominally pure CVO crystals, the geometry of the as-grown domain structure, with rounded domains formed near T C , persists during subsequent cooling due to effective bulk screening of the depolarization field. The flat oriented fragments of domain walls and triangular domains in Mn-doped CVO appear during switching, under the action of the polar component of the pyroelectric field, above the threshold value. This fact represents the first observation of the domain switching in CVO crystals.

Conclusions
The domain structure formed after crystal growth in the paraelectric phase and cooling to room temperature, through the ferroelectric phase transition, was studied experimentally in nominally pure and Mn-doped calcium orthovanadate (CVO) crystals. Several methods were used for domain imaging: at the surface-optical microscopy and piezoelectric force microscopy, and in the bulk-Cherenkov-type second harmonic generation. Formation of an irregular 3D maze of rounded domains with charged walls, essentially tilted from the polar direction, was revealed in nominally pure and Mn-doped CVO crystals. The geometry of the domain structure formed during slow cooling, just below T C , is determined by spatial distribution of the internal field produced by bulk defects and composition inhomogeneities. The obtained absence of the quasi-regular layered domain structure justifies random spatial distribution of defects, without pronounced growth striations. The persistence of the domain structure with charged walls during cooling can be attributed to effective bulk screening of the depolarization field, and low value of the pyroelectric field. The rare formation of triangular domains and flat fragments of domain walls revealed in Mn-doped CVO was attributed to the action of the excess polar component of the pyroelectric field, above the threshold value for domain switching. This fact represents the first observation of domain switching in CVO crystals. Therefore, we plan to study domain switching in pure and Mn-doped CVO crystals under the action of the pyroelectric field, which arises during heating and cooling with controlled rates.