Isolated and isothermal susceptibilities of a pseudospin-phonon system

V. L. Aksenov   ; Yu. Shraiber

Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 112-120

Résumé

A study is made of the model of a phonon system coupled to a two-level subsystem containing a substitutional impurity. It is shown that the isolated and isothermal susceptibilities may have different forms in both the ferrophase and the paraphase. As a result, there is an additional concentration dependence of the energy of the coupled pseudospin-phonon excitations and a central peak in the neutron or light scattering cross sections. The results are discussed for the example of the ferroelectric $\operatorname{K(H_{1-x}D_x)_2PO_4}$.

Bibliographie

[1] Yamada Y., “Lattice instabilities in coupled pseudospin-phonon systems”, Ferroelectrics, 16:1/2/3/4 (1977), 49–58 | DOI

[2] Ngai K. L., Reinicke T. L., “Dynamic instabilities in high-$T_c$ superconductors”, Phys. Rev., B16:3 (1977), 1077–1085 ; Vujičič G., Aksenov V. L., Plakida N. M., Stamenkovič S., “On the role of quasilocal excitations in the lattice of high-$T_c$ superconductors”, Phys. Lett., 73A:5, 6 (1979), 439–441 | DOI

[3] Villain J., Stamenkovič S., “Atomic motion in hydrogen-bond Ferroelectrics”, Phys. Stat. Sol., 15:2 (1966), 585–596 ; Стасюк И. В., Левицкий Р. Р., “Связанные колебания протон-ионной системы в сегнетоэлектриках с водородными связями типа $\mathrm{KH}_2\mathrm{PO}_4$”, УФЖ, 15:3, 459–469 | DOI

[4] Konsin P. I., Kristofel N. N., “O fazovykh perekhodakh v segnetoelektrikakh s vodorodnymi svyazyami”, FTT, 14:10 (1972), 2873–2879; “Динамическая теория фазовых переходов в сегнетоэлектриках с водородными связями”, Изв. АН СССР, сер. физ., 39:4 (1975), 650–654

[5] Lage E. J. S., Stinchcombe R. B., “Pressure and deuteration dependence of static and dynamic properties of KDP - DKDP mixed crystals”, J. Phys., C9:24 (1976), 3681–3690

[6] Pirc R., Prelovšek P., “Coupled tunneling-lattice modes in partially deuterated hydrogen-bounded ferroelectrics”, Phys. Rev., B15:9 (1977), 4303–4308 | DOI

[7] Levitskii R. R., Sorokov S. I., Dinamika chastichno deiterirovannykh segnetoaktivnykh soedinenii s vodorodnymi svyazyami. I: Modeli segnetoelektrikov s asimmetrichnoi vodorodnoi svyazyu i $\mathrm{PbH}_{1-x}\mathrm{D}_x\mathrm{PO}_4$, Preprint ITF-78-152R, ITF, Kiev, 1979 | MR

[8] Bogolyubov N. N., Tyablikov S. V., “Zapazdyvayuschie i operezhayuschie funktsii Grina v statisticheskoi fizike”, DAN SSSR, 126:1 (1959), 53–56 ; Зубарев Д. Н., “Двухвременные функции Грина в статистической физике”, УФН, 71:1 (1960), 71–116 | Zbl | DOI | MR

[9] Pirc R., Dick B. G., “Exact isolated and isothermal susceptibilities for an interacting dipole-lattice system”, Phys. Rev., B9:6 (1974), 2701–2710 | DOI

[10] Kalashnikov V. P., Dinamicheskaya teoriya izotermicheskogo otklika na mekhanicheskoe vozmuschenie i funktsii Grina, Soobschenie R4-7803, OIYaI, Dubna, 1974

[11] Thomas H., “Soft modes at first and second order phase transitions”, Anharmonic lattices structural transitions and melting, ed. T. Riste, Noordhoff Int. Publ., Noordhoff-Leiden, 1974, 231–244 | DOI

[12] Rudoi Yu. G., “Sovremennoe sostoyanie metoda dvukhvremennykh funktsii Grina v kvantovoi teorii magnetizma”, Statisticheskaya fizika i kvantovaya teoriya polya, ed. N. N. Bogolyubov, Nauka, M., 1973, 97–164 | MR

[13] Aksenov V. L., Shraiber Yu., “Fazovyi perekhod v modeli svyazannykh psevdospinfononnykh sistem”, Izv. AN SSSR, ser. fiz., 43:8 (1979), 1593–1597

[14] Vaks V. G., Zein N. E., “Segnetoelektricheskie svoistva tverdykh rastvorov tipa $\mathrm{K}(\mathrm{H}_x\mathrm{D}_{1-x})_2\mathrm{PO}_4$”, FTT, 17:6 (1975), 1617–1626

[15] Aksenov V. L., Plakida N. M., “Fluktuatsionnye effekty v modeli segnetoelektrika tipa smescheniya”, TMF, 35:1 (1978), 104–112

[16] Velicky B., Kirkpatrick S., Ehrenreich H., “Single-site approximation in the electronic theory of simple binary alloys”, Phys. Rev., 175:3 (1968), 747–766 | DOI

[17] Kwok P. C., Schultz T. D., “Correlation functions and Green functions: zero-frequency anomalies”, J. Phys., ser. 2, 2:7 (1969), 1196–1206

[18] Suzuki M., “Ergodicity, constants of motion, and bounds for susceptibilities”, Physica, 51:2 (1971), 277–291 | DOI | MR

[19] Kubo R., “Statistical-mechanical theory of irreversible processes. I: General theory and simple applications to magnetic and conduction problems”, J. Phys. Soc. Jap., 12:6 (1957), 570–786 | DOI | MR

[20] Aksenov V. L., Stamenkovich S., “Teoriya neuprugogo rasseyaniya neitronov na segnetoelektrikakh s vodorodnymi svyazyami”, FTT, 19:8 (1977), 1366–1372 | MR

[21] Kascheev V. N., Rol tsentralnogo pika v fononnoi relaksatsii dlya modeli Izinga v poperechnom pole, Preprint LAFI-009, IF AN LatvSSR, Salaspils, 1979