## 1 Introduction  
The development and receiving of materials with desired properties is an important task in condensed matter physics and physical materials' science, in which hydrogen-bonded crystals (HBC) have been widely used in radio electronics, optoelectronics, and laser technology over the past two decades [1,2]. Based on the results of precision measurements of the temperature spectra of thermally stimulated depolarization currents (TSDC) in HBC, using the example of crystals of natural phlogopite \(\mathrm{KMg_{3}(AlSi_{3}O_{10})(OH)}_{2}\), muscovite \(\mathrm{KAl_{2}(AlSi_{3}O_{10})(OH)}_{2}\), onto \(\mathrm{Mg_{3}(Si_{4}O_{10})(OH)}_{2}\) chemically pure chalcanthite \(\mathrm{CuSO_{4}\cdot 5H_{2}O}\), at temperatures above 50-550 K and polarizing field strengths of 0.1-1 MV/m, as a rule, 6-7 monorelaxation maxima are found [1, 2, 3, 4]. The physical nature of these maxima, revealed in combination with the methods of calcination (at temperatures of 373-1373 K) and doping (in solutions of HCl, HF, NH\({}_{4}\)OH), is diverse and occurs in the temperature range (100-450 K) through the relaxation of ionization (\(\mathrm{H_{3}O^{+}}\), \(\mathrm{OH^{-}}\)) and orientational (\(\mathrm{L,D}\)) Bjerrum defects, as well as the rotations of \(\mathrm{H_{2}O}\) in an electric field, with different relaxer activation energies (0.1-0.7 eV) [4]. Of particular scientific interest is the low-temperature (50-100 K) maximum of TSDC density in HBC, shown by the low activation energies of relaxers (0.01-0.1 eV) [1,5]. The temperature position of this maximum in the experiment varies slightly, and the amplitude significantly depends on the concentrations of alloying impurities [4]. When crystals are calcined at temperatures of 873-1373 K, this maximum completely disappears [4]. These circumstances allow for us to assert that the physical nature of this low-temperature maximum significantly differs from the high-temperature maxima (100-450 K) and is caused by the quantum tunneling transitions of protons inside and between the ions of the anionic sublattice in the HBC [1,5,6]. Then, low-temperature, thermally stimulated depolarization in HBC can be defined as nonlinear quantum proton relaxation caused by the heating of the crystal in the absence of an external electric field [7,8]. This effect opens up the possibility of applying the quantum theory of proton conduction [1,5] to the study of nonlinear properties and the development of resonant tunnel diodes and quantum field-effect transistors based on thin films of composite materials (MIS, MSM structures) consisting of HBC-class crystals [9, 10, 11, 12, 13, 14, 15]. From this point of view, the memory elements of high-speed, non-volatile devices (DRAM, FeRAM) based on ferroelectric HBC (or materials similar to them in terms of properties and type of crystal structure) with a rectangular hysteresis loop (triglycine sulfate (TGS), ferric salt) are promising for modern computer technology [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. They are characterized by abnormally high residual polarizations and long relaxation times (from 5 to 10 years), as well as a high thermal stability and mechanical strength [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]. The quantum theory of proton conduction and relaxation [1,5], due to the universality and generality of mathematical models, will simplify the methodology for studying the mechanisms of formation of the spontaneous polarization of ferroelectric HBC from the perspective of protons' quantum tunneling in a hydrogen sublattice near the point of phase transition of the second kind [1]. Materials of this class (KDP, DKDP) have practical application in nonlinear optics and laser technology as regulators of laser radiation parameters, electric gates, etc. [45; 46; 47; 48; 49; 50; 51]. Fiber-optic strain sensors based on KDP and related crystals are promising [52; 53; 54].