## 1 Introduction  
Among intelligent materials, a special place is occupied by ferroelectric ceramics with a perovskite-type structure, which play a key role in modern technologies due to their unique electrical, dielectric, and piezoelectric properties [1, 2, 3]. Among them, materials based on lead zirconate titanate (PZT) enjoy particular interest. This is attributed to their elevated Curie temperature (T\({}_{c}\)), high dielectric constant (\(\epsilon_{r}\)), and significant electromechanical coupling coefficient (k) [4]. These characteristics make these materials suitable for a broad spectrum of applications, including sensors, actuators, transducers, and ferroelectric memories [5, 6, 7, 8, 9, 10]. However, the need to limit the content of lead in materials, resulting from environmental regulations, has led researchers to search for new materials and doping PZT, which would allow for the modification of its properties and their improvement [11, 12, 13, 14, 15, 16, 17]. In addition, it is well established that modifying PZT ceramics by substituting a small amount of isovalent or heterovalent elements for Pb or Zr/Ti sublattices significantly enhances their properties [18, 19, 20, 21, 22, 23]. Numerous studies have suggested that these dopants affect the temperatures of structural phase transitions between phases with different electric orders (FE, AFE, and PE) and influence various parameters, including dielectric, pyroelectric, piezoelectric, and electro-optic properties [24; 25; 26].  
The Ba-modified Pb(Zr\({}_{1-x}\)Ti\({}_{x}\))O\({}_{3}\) (PBZT) ceramic composition has been of great interest for a long time due to its exceptional ferroelectric properties, such as its high electrical permittivity, which shows minimal dependence on temperature [27; 28; 29]. The creation of the (Pb,Ba)(Zr,Ti)O\({}_{3}\) (PBZT) system was initiated by [PERSON] et al. [30]. Structural analysis of these ceramic materials was later conducted by [PERSON] [31], who established the phase diagram for this system. [PERSON] and [PERSON] [32] continued these investigations, discovering that ceramics with compositions near the phase boundaries between the ferroelectric (FE) rhombohedral, tetragonal, and paraelectric (PE) cubic phases exhibit characteristics typical of ferroelectric relaxors. In this context, the development of La-doped PBZT ceramics represents a promising direction in the quest for high-performance, environmentally friendly materials. By carefully selecting the doping concentration and optimizing the synthesis process, researchers aim to achieve a balance between performance and sustainability, paving the way for next-generation ferroelectric materials with minimized environmental impact.  
The aim of this study was to understand the effect of La\({}^{3+}\) doping on the impedance properties of (Pb\({}_{0.75}\)Ba\({}_{0.25}\))(Zr\({}_{0.70}\)Ti\({}_{0.30}\))O\({}_{3}\) ceramics. The substitution of Ba\({}^{2+}\) or Pb\({}^{2+}\) ions with La\({}^{3+}\) ions leads to the creation of oxygen vacancies, which can significantly influence the concentration and distribution of space charge in the material. Comprehensive analysis of the material's impedance response, examined across a wide range of temperatures and frequencies and correlated with the results of the DC conductivity measurements and thermally stimulated depolarization currents described in a previous article, provided the answer to the question of the actual role of lanthanum doping and the associated oxygen vacancies in shaping the material's electrical properties. Understanding this issue is essential for tuning the material's electrical response to meet the demands of various applications, such as capacitors, sensors, and actuators. Furthermore, the insights gained from this research could guide the design of new, high-performance ceramic materials with tailored properties for advanced electronics.