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<p><b>Introduction XI</b></p> <p><b>1 Crystal Structure and Phase Transitions in Layered Crystals of Ternary Phosphorous Chalcogenides 1</b></p> <p>1.1 Ferrielectric, Antiferroelectric, and Modulated Orderings in MM ′ P 2 X 6 (M – Cu, Ag; M ′ –In,Bi;X–S,Se) 1</p> <p>1.2 Relaxor and Dipole Glassy States on the Phase Diagram of Cuinp 2 (se X S 1−x) 6 Mixed Crystals 3</p> <p>1.2.1 XRD Investigations of CuInP 2 Se 6 4</p> <p>1.2.2 Relaxor Phase in Mixed Cuinp 2 (s X Se 1−x) 6 Crystals 7</p> <p>1.2.3 Dipolar Glass Phase in Mixed Cuinp 2 (s X Se 1−x) 6 Crystals 10</p> <p>1.2.4 Influence of a Small Amount of Selenium to Phase-Transition Dynamics in CuInP 2 S 6 Crystals 12</p> <p>1.2.5 Phase Diagram 13</p> <p>1.3 Antiferromagnetic Ordering and Anisotropy of Magnetization in Multiferroics Cu(in 1−x Cr X)p 2 S 6 15</p> <p>1.3.1 Temperature Dependence of the Magnetization 17</p> <p>1.3.2 Field Dependence of the Magnetization and Anisotropy of Magnetization and Susceptibility 19</p> <p>1.4 Magnetic Ordering in Mn 2 P 2 S 6 Crystal 21</p> <p>1.5 Polar Layered Crystals of SnP 2 S 6 Type 30</p> <p>References 34</p> <p><b>2 Electronic Band Structure 41</b></p> <p>2.1 Chemical Bonding in P 2 S(Se) 6 Structural Groups 41</p> <p>2.2 Hybridization of the Electronic Valence Orbitals and Structural Stability of MM ′ P 2 S(Se) 6 -Type Compounds 43</p> <p>2.3 Second-Order Jahn–Teller Effect and Dipole Ordering in Cu(Ag)InP 2 S(Se) 6 Crystals with d 10 Cu + and Ag + Cations 63</p> <p>2.4 Second-Order Jahn–Teller Effect and Phase Transitions in Cu(Ag)BiP 2 S(Se) 6 Crystals with a Stereoactive Electronic Lone Pair of Bi 3+ 79</p> <p>References 85</p> <p><b>3 Optical Properties of MM ′ P 2 S(Se) 6 Crystals 95</b></p> <p>3.1 DFT Calculated Electronic Band Structures and Optical Parameters 95</p> <p>3.2 Temperature Dependence of the Optical Absorption for Mn 2 P 2 S 6 , AgInP 2 S 6 , CuInP 2 S(Se) 6 , and CuCrP 2 S 6 ,SnP 2 S 6 Layered Crystals 103</p> <p>3.3 Appearance of Dipole Glassy State in the Edge Optical Absorption of Cuinp 2 (se X S 1−x) 6 Mixed Crystals 121</p> <p>References 127</p> <p><b>4 Phonon Spectra of Layered MM ′ P 2 S(Se) 6 Crystals 131</b></p> <p>4.1 DFT Calculated Phonon Spectra in Different Phases 131</p> <p>4.2 Raman Spectroscopy of CuInP 2 S 6 Crystal Across Ferrielectric Phase Transition 144</p> <p>4.3 Phonon Spectra of Cuinp 2 (se X S 1−x) 6 Mixed Crystals 151</p> <p>4.4 Anisotropy of Thermal Conductivity Temperature Dependence in Cu(Ag)In(Bi)P 2 S(Se) 6 Layered Crystals 160</p> <p>4.5 Heat Capacity Anomalies at Dipole and Magnetic Ordering in CuInP 2 S(Se) 6 and CuCrP 2 S 6 Crystals 180</p> <p>4.6 Spin–Phonon Coupling in Mn 2 P 2 S 6 Crystal 186</p> <p>References 196</p> <p><b>5 Semiconductor to Metal Transitions in SnP 2 S 6 -and Sn 2 P 2 S 6 -Type Compounds 201</b></p> <p>5.1 Layered GeP 2 S 6 ,GeP 2 Se 6 ,GeP 2 Te 6 ,SnP 2 S 6 ,SnP 2 Se 6 , and SnP 2 Te 6 Polar Crystals with Pressure- or Chemical Composition-Induced Semiconductor–Metal Transition 201</p> <p>5.2 Pressure-Induced Metal State in Sn 2 P 2 S 6 and Sn 2 P 2 Se 6 Compounds 208</p> <p>5.3 DFT Calculated Transformation of Electron and Phonon Spectra at Transition into Polar Metal State 211</p> <p>References 220</p> <p><b>6 Dielectric and Ferroelectric Properties of Layered Phosphorus Chalcogenide Crystals 223</b></p> <p>6.1 Anisotropy Effects in Thick-Layered CuInP 2 S 6 and CuInP 2 Se 6 Crystals 223</p> <p>6.2 Dipole Glass State in Cu(in X Cr 1−x)p 2 S 6 Crystals 226</p> <p>6.2.1 Phase Transitions in CuCrP 2 S 6 and CuIn 0.1 Cr 0.9 P 2 S 6 Crystals 227</p> <p>6.2.2 Inhomogeneous Ferrielectrics 228</p> <p>6.2.3 Dipole Glass State in Mixed Cuin X Cr 1−x P 2 S 6 Crystals 234</p> <p>6.2.4 Phase Diagram of the Mixed Cuin X Cr 1−x P 2 S 6 Crystals 236</p> <p>6.3 Nonlinear Dielectric Response of Layered (Ag,Cu)(In,Cr)P 2 S 6 Crystals 237</p> <p>6.4 Dielectric Spectroscopy of CuBiP 2 Se 6 Crystals 244</p> <p>6.4.1 Antiferroelectric Phase Transition 244</p> <p>6.4.2 Freezing Phenomena 246</p> <p>References 248</p> <p><b>7 Ionic Conductivity and Low-Frequency Noise Spectroscopic Studies 251</b></p> <p>7.1 Ionic Conductivity Investigations in CuInP 2 S 6 and CuIn 1+δ P 2 S 6 Crystals 251</p> <p>7.2 Conductivity Spectroscopy of Aginp 2 (se X S 1–x) 6 and (cu X Ag 1–x)crp 2 S 6 Crystals 252</p> <p>7.3 Low-Frequency Noise Spectroscopy of Layered CuInP 2 S 6 253</p> <p>7.3.1 Intrinsic Noise Types 254</p> <p>7.3.2 Experimental Techniques for Noise Determination 255</p> <p>7.3.3 Noise Spectroscopy in Materials Science 256</p> <p>7.3.4 Brief Overview of Low-Frequency Noise Spectroscopic Studies of CuInP 2 S 6 256</p> <p>7.4 Electrical Conductivity of Layered Cuinp 2 (s X Se 1−x) 6 Crystals 258</p> <p>References 259</p> <p><b>8 Ultrasonic and Piezoelectric Studies of Phase Transitions in Two-Dimensional CuInP 2 S 6 -Type Crystals 263</b></p> <p>8.1 Ultrasonic Investigation of Phase Transition in CuInP 2 S 6 Crystals 263</p> <p>8.2 Piezoelectric and Ultrasonic Investigations of Mixed (Ag,Cu)InP 2 (S,Se) 6 Layered Crystals 265</p> <p>8.3 Ultrasonic Spectroscopy of Quasi Two-dimensional Cuinp 2 (se X S 1−x) 6 Mixed Crystals 268</p> <p>8.4 Piezoelectric and Elastic Properties of Layered Materials of Cu(In,Cr)P 2 (S,Se) 6 System 270</p> <p>References 272</p> <p><b>9 Nano Scale Investigations, Domain Structure, and Switching Processes of Low-Dimensional Ferroelectric Layered Chalcogenides 275</b></p> <p>9.1 Ferrielectric State in Few Layer or Monolayer CuInP 2 S 6 Samples 275</p> <p>9.2 Bright Domain Walls in CuInP 2 Se 6 Crystals 283</p> <p>9.3 Antisite Defects in Layered Multiferroic CuCr 0.9 In 0.1 P 2 S 6 287</p> <p>References 291</p> <p><b>10 Phenomenological Description of Soft Phonon Spectra, Phase Diagrams, and Domain Morphology of Low-Dimensional Ferroelectric Layered Chalcogenides 295</b></p> <p>10.1 Brief Overview 295</p> <p>10.2 Spatially Modulated Incommensurate Phases and Soft Phonon Dispersion in Ferroelectric Layered Chalcogenides 296</p> <p>10.2.1 Landau–Ginzburg–Devonshire-Free Energy Functional and Lagrange Function 297</p> <p>10.2.2 The Stability of Spatially Modulated Phases in Ferroelectric Chalcogenides 301</p> <p>10.2.3 Analytical Description of the Soft Phonon Dispersion 302</p> <p>10.2.4 Analysis of the Critical Points in the Soft Phonon Spectra 305</p> <p>10.2.5 The Behavior of Soft Acoustic Phonons in the Vicinity of Critical Wave Vectors 306</p> <p>10.2.6 Elastic Softening of the Sound Velocity 307</p> <p>10.2.7 Soft Phonon Dispersion in Ferroelectric Chalcogenides: Comparison with Experiment 308</p> <p>10.2.8 Temperature Dependence of Static Dielectric Susceptibility 309</p> <p>10.3 Phase Diagrams with Incommensurate Phases and Domain Splitting in Thin Films of Ferroelectric Layered Chalcogenides 311</p> <p>10.3.1 Approximate Analytical Solution of the Linearized Euler–Lagrange Equations 313</p> <p>10.3.2 Phase Equilibrium and Domain Structure Temperature Evolution 314</p> <p>10.4 Phenomenological Description of Phase Diagrams and Complex Domain Morphology of Ferroelectric Layered Chalcogenide Nanoparticles 317</p> <p>10.4.1 Reconstruction of CIPS Thermodynamic Potential from Experiments 318</p> <p>10.4.2 Temperature-Stress Phase Diagrams of Bulk CuInP 2 S 6 319</p> <p>10.4.3 The Stress-Induced Phase Transitions in CuInP 2 S 6 Nanoparticles of Different Shapes 322</p> <p>10.4.4 Labyrinthine Domains in CIPS Nanoparticles 325</p> <p>10.4.5 Analytical Description of Complex Domain Morphology in Ferroelectric Layered Chalcogenide Nanoparticles 327</p> <p>10.5 Phenomenological Description of Bright-Contrast and Dark-Contrast Domain Walls in Ferroelectric–Antiferroelectric Layered Chalcogenides 332</p> <p>10.5.1 LGD–FSM Approach 332</p> <p>10.5.2 Phase Diagrams of the Order Parameters 335</p> <p>10.5.3 Bright and Dark Domain Walls 337</p> <p>10.5.4 Comparison with Experiment 339</p> <p>10.6 Conclusions 341</p> <p>10. A Appendix A: Analytical Expressions for the Soft Phonon Frequency 342</p> <p>10. B Appendix B: Soft Acoustic Mode Behavior in the Vicinity of Critical Wave Vectors 345</p> <p>10. C Appendix C: Temperature Dependence of the Static Dielectric Susceptibility 346</p> <p>10. D Appendix D: Derivation of PE-SDFE Transition Temperature for Spherical Nanoparticles 347</p> <p>10. E Appendix E: Derivation of PE-PDFE Transition Temperature for Spherical Nanoparticles 349</p> <p>References 352</p> <p><b>11 Application Examples of Ferroelectric 2D Layered Indium Copper Thiophosphate Chalcogenide, CuInP 2 S 6 359</b></p> <p>11.1 The Ferroelectric (FE) Family of Metal (M) Hypo(tio/seleno)diphosphates 359</p> <p>11.2 Piezoelectric and Pyroelectric Activity and Electrocaloric Effectivity of CuInP 2 S 6 Nanoflakes 360</p> <p>11.2.1 Piezoactivity of CuInP 2 S 6 Nanoflakes 360</p> <p>11.2.2 Pyroactivity of CuInP 2 S 6 Nanoflakes 360</p> <p>11.2.3 Electrocaloric Performances of CuInP 2 S 6 Nanoflakes 361</p> <p>11.3 Promises of 2D Layered CuInP 2 S 6 for Ferroelectric Field Effect Transistors and Memory Applications 361</p> <p>11.3.1 Theoretical Considerations and Evaluations 362</p> <p>11.3.2 Experimental Investigations and Propositions 362</p> <p>11.3.3 Negative Capacitance Field Effect Transistors Based on Two-Dimensional van der Waals Heterostructures 364</p> <p>11.4 Conclusions 365</p> <p>References 366</p> <p>Index 371</p>

<p><b>Juras Banys</b>, PhD, is a Professor in the Faculty of Physics at Vilnius University, Lithuania.</p> <p><b>Andrius Dziaugys</b>, PhD, is a senior researcher in the Institute of Applied Electrodynamics and Telecommunications at Vilnius University, Lithuania.</p> <p><b>Konstantin E. Glukhov</b>, PhD, is a senior researcher in the Department of Physics of Semiconductors at Uzhhorod University, Ukraine.</p> <p><b>Anna N. Morozovska</b>, PhD, is a leading scientific researcher in the Department of Physics of Magnetic Phenomena at the Institute of Physics of the National Academy of Science of Ukraine.</p> <p><b>Nicholas V. Morozovsky</b>, PhD, is a leading scientific researcher in the Laboratory of Applied Ferroelectricity at the Institute of Physics of the National Academy of Science of Ukraine.</p> <p><b>Yulian M. Vysochanskii</b>, PhD, is Professor and Head of the Semiconductor Physics Department at Uzhhorod University, Ukraine.</p>

<p><B>A comprehensive guide to a unique class of compounds with a variety of applications</B></p> <p>Since the discovery of graphene, there has been intensive interest in two-dimensional materials with similar electronic and industrial applications. The limitations on the usefulness of graphene itself, however, have powered the search for other materials with similar properties. One such class of materials, the phosphorous chalcogenides, has proven a particularly fruitful avenue for research, due to the favorable band gap and ferroelectric properties of these materials. <p><i>Van der Waals Ferroelectrics </i>provides, for the first time, a detailed overview of this highly relevant and sought-after class of materials, also known as transition metal chalcogenophosphates (TMCPs). Focusing on physical properties, the book explores the complex physics underlying these compounds as well as the unique characteristics that have driven their ever-increasing importance to the materials science community. <p><i>Van der Waals Ferroelectrics</i> readers will also find: <ul><li>Both computational and experimental perspectives on TCMP compounds</li> <li>In-depth discussion of the properties essential to the design and construction of devices like sensors, actuators, memory chips, and capacitors</li> <li>The first detailed review of the functional properties of TCMP compounds, such as ferrielectricity, electrostriction, and ionic conductivity</li></ul> <p><i>Van der Waals Ferroelectrics </i>is a useful reference for materials scientists, inorganic chemists, solid state chemists, solid state physicists, electrical engineers, and libraries supporting these professions.

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