Determination of polarization states in (K,Na)NbO3 lead-free piezoelectric crystal

Polarization switching in lead-free (K0.40Na0.60)NbO3 (KNN) single crystals was studied by switching spectroscopy piezoresponse force microscopy (SS-PFM). Acquisition of multiple hysteresis loops on a closely spaced square grid enables polarization switching parameters to be mapped in real space. Piezoresponse amplitude and phase hysteresis loops show collective symmetric/asymmetric characteristics, affording information regarding the switching behavior of different domains. As such, the out-of-plane polarization states of the domains, including amplitudes and phases can be determined. Our results could contribute to a further understanding of the relationships between polarization switching and polarization vectors at the nanoscale, and provide a feasible method to correlate the polarization hysteresis loops in a domain under an electric field with the polarization vector states.


Introduction 
Spontaneous polarization that can be switched by an electric field from one direction to another is the defining feature of ferroelectric crystals, which has long provided the functional foundation for various applications including modern non-volatile memories [1,2], sensor and actuators [3,4], and infrared imaging systems [5]. Domains are coherent regions with uniform polarization directions and significantly contribute to the electromechanical properties of ferroelectrics [6][7][8][9]. Characterization of the responses of domains to external electric stimuli is necessary for a better understanding of local electromechanical functionalities and enables a correlation between microscopic order and macroscopic properties, which is significant to develop high-performance next-generation ferroelectrics.
Piezoresponse force microscopy (PFM) has emerged as a powerful tool to probe local piezoelectric and ferroelectric properties of ferroelectrics at the nanoscale [10][11][12][13][14][15][16][17]. In a typical PFM setup, an AC electrical voltage is applied to the sample surface with a conductive cantilever tip, which induces a structural change as a result of piezoelectricity and in turn, the deflection of the cantilever. This provides local deformation responses that can be interpreted in terms of the piezoelectric properties. The invention of PFM has enabled sub-10 nm resolution imaging of domain structures and local polarization control [18,19].
Polarization vectors consisting of polarization directions and magnitudes are intrinsic properties of domains, which respond to electric stimuli and can be probed by PFM. Characterization of local polarization vectors is of significance to better understand the macroscopic properties of the piezoelectrics. Polarization orientations can be identified by poling experiments, i.e., applying a positive or negative pulsed bias to see how phase contrast changes or conducting switching hysteresis loops. However, only polarization direction rather than magnitude can be identified during poling experiments. And the response of domains to electric stimuli that encoded in the switching hysteresis loops is also missing.
Here, we report an approach to determine the polarization vector states based on mapping of switching behavior obtained using switching spectroscopy piezoresponse force microscopy (SS-PFM). This recognized technique enables quantitative characterization of the local switching behavior of ferroelectrics and a detailed description is given by Refs. [20][21][22]. In this study, polarization vectors are qualitatively determined based on hysteresis loops (amplitude and symmetry) of the mapping results. Considering the shapes of hysteresis loops are subjected to other contributing mechanisms including electrostatic charge, mechanical clamping, and substrate, high quality lead-free potassium sodium niobate (K 0.40 Na 0.60 )NbO 3 (KNN) single crystals are adopted in this study to guarantee hysteresis loops are mainly contributed by the polarization direction and magnitude of the domains. The crystals in our study offer a playground to demonstrate our approach, which is impractical in polycrystalline piezoelectrics where polarization states are randomly distributed and unknown. Also, lead-free materials are chosen with the consideration of environmental concerns over leadbased piezoelectrics [23][24][25][26].

Experimental
The preparation process of the [001] c -oriented KNN single crystal was described by Ref. [27]. The crystal is in orthorhombic structure and the domain wall shown in Fig. 1(b) orients along [001] c . The crystal was polished with diamond paste down to 0.25 μm particle size and the thickness of the crystal is 0.4 mm. The crystal was annealed at 400 ℃ for 2 h afterwards. PFM and SS-PFM were implemented on a commercial Cypher AFM (Asylum Research, Santa Barbara, CA, USA), using Pt and Ir coated cantilever (NanoWorld EFM, force constant 2.8 N/m, resonance frequency 75 kHz). Domain structures were acquired using vertical dual amplitude resonance tracking (DART) mode, where an AC voltage of 0.5 V at a frequency of 300 kHz was applied to the cantilever. Local ferroelectric switching behavior was mapped by SS-PFM, where a TriangleSquare function with a maximum value of 20 V at 0.2 Hz, was applied to facilitate ferroelectric domain switching. Phase of the drive wave is 1 (from 0 to 1) and the period of one square wave pulse is 0.10. A modulated AC voltage of 0.5 V was simultaneously superimposed to acquire data. Contact resonance peaks show symmetric behavior and the piezoresponse hysteresis loops obtained using DART mode were then corrected via simple harmonic oscillator (SHO) model [12,28]. Only off-field hysteresis loops were analyzed   Fig. 2 Fig. 3(d), which can be used to estimate the degree of asymmetry of hysteresis curves. Note that there is a region in the bottom part of the middle domains showing inconsistent coercive bias results. This is due to the shapes of hysteresis loops from this region are not well defined (Figs. S1 and S2 in the Electronic Supplementary Material). And the FMapCalcPFMoff function we used in the Igor program cannot correctly recognize bias values from poorly defined hysteresis loops, leading to inconsistent results. Hence, hysteresis results shown in Fig. 2 do not include results from this region. The origins of these results are unclear. Considering there are only 30 points showing poorly shaped hysteresis loops and the remaining more than 600 points showing consistent switching behavior, the results from this region do not preclude the determination of the collective switching behavior of the domains.
Based on the above results, the OP polarization vector states can be qualitatively determined based on the amplitudes and symmetry of the hysteresis loops. If there is no OP polarization component within a domain, hysteresis curves should be symmetric, i.e., no shift along either positive or negative half axis direction. Once there is an OP spontaneous polarization component, there is a strong unwillingness of the polarization switching along the opposite direction of the spontaneous polarization and in turn, asymmetric curves will be developed, as observed in Fig. 2.
The directions of OP spontaneous polarization components can be determined from the shifts of hysteresis loops. For the middle domain, hysteresis loops shift along the positive half axis direction, indicating that it is easier to induce polarization component to orient upwards under an upwards electric field. Thus, OP spontaneous polarization component is upwards for the middle domain, as shown in Fig. 4(a). For the side domains, in contrast, the shifts of hysteresis loops along the negative half axis direction indicate a downwards OP spontaneous polarization component (Fig. 4(a)). The amplitudes of OP spontaneous polarization components can be estimated from the amplitudes of hysteresis loops. For the middle domain, the difference in amplitudes on the positive and negative axes is limited, indicating a low degree of anisotropy. This can be explained by the presence of a small magnitude of OP spontaneous polarization component for the middle domain. Under an upwards electric field (−20 V), the amplitude of the middle domain is slightly larger because electric field and spontaneous polarization are in the same direction ( Fig. 4(b)). Under a downwards electric field (+20 V), the amplitude of the middle domain is smaller as a result of the opposite direction of polarization to that of electric field (Fig. 4(c)). For the side domains, the amplitude on the positive axis is much higher than that on the negative axis. This is due to the presence of a large magnitude of OP spontaneous polarization component. Similarly, amplitude will be increased or decreased when the direction of OP spontaneous polarization component is in the same or opposite direction to that of electric field. Based on the above analyses, schematics of OP polarization component for the KNN single crystals under different states are shown in Fig. 4.

Conclusions
To summarize, SS-PFM mapping was performed for the KNN single crystals and a number of 625 hysteresis loops were obtained. The collective asymmetric features of the loops are due to different polarization directions of the domains. Based on the collective polarization switching behavior, the initial OP polarization states can be determined. Our results reveal the relationships between polarization switching and polarization vectors.
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