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The magnetization, polarization, and band-gap energy in pure and ion-doped KNbO 3 (KNO) bulk and nanoparticles (NPs) are investigated theoretically using a microscopic model and Green's function theory. It is shown that KNO NPs are multiferroic. The size dependence of M and P is studied. The magnetization M increases with decreasing NP size, whereas the polarization P decreases slightly. The properties of KNO can be tuned by ion doping, for example, through the substitution of transition metal ions at the Nb site or Na ions at the K site. By ion doping, depending on the relation between the doping and host ion radii, different strains appear. They lead to changes in the exchange interaction constants, which are inversely proportional to the lattice parameters. So, we studied the macroscopic properties on a microscopic level. By doping with transition metal ions (Co, Mn, Cr) at the Nb site, M increases, whereas P decreases. Doped KNO NPs exhibit the same behavior as doped bulk KNO, but the values of the magnetization and polarization in KNO NPs are somewhat enhanced or reduced due to the size effects compared to the doped bulk KNO. In order to increase P, we substituted the K ions with Na ions. The polarization increases with increasing magnetic field, which is evidence of the multiferroic behavior of doped KNO bulk and NPs. The behavior of the band-gap energy E g also depends on the dopants. E g decreases with increasing Co, Mn, and Cr ion doping, whereas it increases with Zn doping. The results are compared with existing experimental data, showing good qualitative agreement. [ABSTRACT FROM AUTHOR]

We have calculated the phonon energy and damping of ω 0 = 264 cm − 1 in Fe, Mn, and Dy doped BaTiO 3 using a microscopic model. By doping with Fe ions, the phonon energy ω and damping γ show anomalies at the two phase transition temperatures. ω increases whereas γ decreases with the increase in the magnetic field and the kink at T C f m vanishes. ω and T C f e decrease or increase with the increase in Mn or Fe dopants, respectively. T C f e and ω of ω 0 = 718 cm − 1 decrease with the increase in Dy ion doping on the Ba site. γ is enhanced for all three ions. The changes in the phonon properties by ion doping are due to the different strain caused by the different ionic radii of the host and doping ions. The effects of Fe, Mn, and Sm doping on the bandgap energy are also discussed. [ABSTRACT FROM AUTHOR]

We have calculated the phonon energy and damping of ω 0 = 264 cm − 1 in Fe, Mn, and Dy doped BaTiO 3 using a microscopic model. By doping with Fe ions, the phonon energy ω and damping γ show anomalies at the two phase transition temperatures. ω increases whereas γ decreases with the increase in the magnetic field and the kink at T C f m vanishes. ω and T C f e decrease or increase with the increase in Mn or Fe dopants, respectively. T C f e and ω of ω 0 = 718 cm − 1 decrease with the increase in Dy ion doping on the Ba site. γ is enhanced for all three ions. The changes in the phonon properties by ion doping are due to the different strain caused by the different ionic radii of the host and doping ions. The effects of Fe, Mn, and Sm doping on the bandgap energy are also discussed. [ABSTRACT FROM AUTHOR]

The multiferroic properties of ion-doped hexagonal and orthorhombic YFeO3 (YFO) nanoparticles (NPs) are studied theoretically. The magnetization M s in h-YFO NPs increases, whereas for o-YFO NPs it decreases with decreasing NP size. In the dielectric constant (DC) both h- and o-YFO have a peak around T C 1 ∼ 4 5 0 and 460 K, respectively, but only in h-YFO an anomaly appears at T C 2 ∼ 3 0 0 K in the DC and the polarization which could be connected with a possible P 6 3 m c – P 6 3 c m phase transition. The polarization in pure and Bi-doped o-YFO NPs increases with increasing magnetic field. M s (x) is studied by doping of a o-YFO NP with Ti 4 + ions at the octahedral Fe 3 + sites. M s (T) in undoped YFO shows a small kink at T C 1 ∼ 4 5 0 K, whereas in the doped YFO it shows at ∼ 480 K. By different ion doping on the Y or Fe sites in YFO there is a transformation from the h- to the o-phase or vice versa. In Mn-doped o-YFO a spin-reorientation transition appears. The bandgap of h-YFO is smaller compared to that of o-YFO. [ABSTRACT FROM AUTHOR]

We have studied the magnetic properties of ion doped MnFe 2 O 4 nanoparticles with the help of a modified Heisenberg model and Green's function theory taking into account all correlation functions. The magnetization M s and the Curie temperature T C increase with decreasing particle size. This is the opposite behavior than that observed in CoFe 2 O 4 and CoCr 2 O 4 nanoparticles. By Co, Mg or Ni doping, M s and T C increase with enhancing the dopant concentration, whereas, by La or Gd doping, the opposite effect is obtained due to the different doping and host ionic radii which change the exchange interaction constants. The band gap energy E g is calculated from the s–d model. It can decrease or increase by different ion doping. The peak observed in the temperature dependence of the specific heat at T C is field dependent. [ABSTRACT FROM AUTHOR]

The magnetic, dielectric and phonon properties of Ca 3 Mn 2 O 7 are investigated using a microscopic model and the Green's function technique. Electrically induced decrease of the magnetization M is observed which is an indirect evidence that Ca 3 Mn 2 O 7 is a multiferroic material. The dielectric function ϵ ′ has an anomaly at the N e ´ el temperature T N and a broad peak at the Curie temperature T C . ϵ ′ increases with increasing magnetic field. M and T N are enhanced by Li ion doping, whereas reduced by Ti ion doping due to different strain caused by the doped ions which changes the exchange interaction constants. T C increases with increasing Ti concentration. The temperature and magnetic field dependence of the phonon energy and damping for the A 1 mode ω 0 = 624 cm − 1 are studied. Both show a kink at T N due to the strong spin–phonon interaction. The kink disappears applying a magnetic field. [ABSTRACT FROM AUTHOR]

The magnetic, dielectric and phonon properties of Ca 3 Mn 2 O 7 are investigated using a microscopic model and the Green's function technique. Electrically induced decrease of the magnetization M is observed which is an indirect evidence that Ca 3 Mn 2 O 7 is a multiferroic material. The dielectric function ϵ ′ has an anomaly at the N e ´ el temperature T N and a broad peak at the Curie temperature T C . ϵ ′ increases with increasing magnetic field. M and T N are enhanced by Li ion doping, whereas reduced by Ti ion doping due to different strain caused by the doped ions which changes the exchange interaction constants. T C increases with increasing Ti concentration. The temperature and magnetic field dependence of the phonon energy and damping for the A 1 mode ω 0 = 624 cm − 1 are studied. Both show a kink at T N due to the strong spin–phonon interaction. The kink disappears applying a magnetic field. [ABSTRACT FROM AUTHOR]

The multiferroic properties of NaCu 2 O 2 (NCO) around the phase transition temperature T N are studied theoretically. The total polarization P is zero without magnetic field h due to the antiferroelectric state induced by the alternate stacking of CuO 2 layer with opposite spin vector chirality. Applying hP increases, goes through a maximum and vanishes at T N . The magnetic field dependence of P (h) is an evidence that NCO is multiferroic. For h = 0 there is no anomaly in the dielectric constant ϵ ′ at T N which is an evidence for the antiferroelectric behavior of the compound. It is observed that P (h) and ϵ ′ (h) in NCO is quite different compared to that of LiCu 2 O 2 . Around the Neel temperature T N we observe in NCO an anomaly in the specific heat and the phonon energy due to strong anharmonic spin-phonon interaction. This kink disappears by applying an external magnetic field h. [ABSTRACT FROM AUTHOR]

The multiferroic properties of NaCu 2 O 2 (NCO) around the phase transition temperature T N are studied theoretically. The total polarization P is zero without magnetic field h due to the antiferroelectric state induced by the alternate stacking of CuO 2 layer with opposite spin vector chirality. Applying hP increases, goes through a maximum and vanishes at T N . The magnetic field dependence of P (h) is an evidence that NCO is multiferroic. For h = 0 there is no anomaly in the dielectric constant ϵ ′ at T N which is an evidence for the antiferroelectric behavior of the compound. It is observed that P (h) and ϵ ′ (h) in NCO is quite different compared to that of LiCu 2 O 2 . Around the Neel temperature T N we observe in NCO an anomaly in the specific heat and the phonon energy due to strong anharmonic spin-phonon interaction. This kink disappears by applying an external magnetic field h. [ABSTRACT FROM AUTHOR]

We propose a microscopic model in order to study the multiferroic properties of Cu2OSeO3 taking into account the ferrimagnetic interaction, frustration, linear magnetoelectric (ME) coupling, and anharmonic spin-phonon interaction. We have shown that the dielectric constant and the phonon energy and damping have a kink near the magnetic phase transition TC = 58K which disappears with increasing of an external magnetic field. This behavior is an evidence for a strong ME coupling and in qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

We propose a microscopic model in order to study the multiferroic properties of Cu2OSeO3 taking into account the ferrimagnetic interaction, frustration, linear magnetoelectric (ME) coupling, and anharmonic spin-phonon interaction. We have shown that the dielectric constant and the phonon energy and damping have a kink near the magnetic phase transition TC = 58K which disappears with increasing of an external magnetic field. This behavior is an evidence for a strong ME coupling and in qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

The temperature and magnetic field dependence of the magnetic and electric properties of LiFeP2O7 (LFPO) and LiCrP2O7 (LCPO) are studied using a microscopic model and the Green's function technique. We have shown that LFPO is antiferromagnetic, but shows a weak ferromagnetism along the b axis which originates from the canted antiferromagnetic order. For LCPO, such a ferromagnetic order along the b axis is not observed. In the temperature dependence of the electrical polarization P b (T) along the b axis there is a kink at T N = 2 2 K which is an indirect evidence for the intrinsic magnetoelectric effect in LFPO. Applying an external magnetic field H b , the polarization P b increases, stronger for small temperatures and the kink at T N disappears. For LCPO, we do not obtain a kink at T N = 6 K. LCPO is polar, but not ferroelectric. We can conclude that the missing magnetoelectric properties in LCPO could be due to the differences in the magnetic orders between LFPO and LCPO. [ABSTRACT FROM AUTHOR]

The temperature and magnetic field dependence of the magnetic and electric properties of LiFeP2O7 (LFPO) and LiCrP2O7 (LCPO) are studied using a microscopic model and the Green's function technique. We have shown that LFPO is antiferromagnetic, but shows a weak ferromagnetism along the b axis which originates from the canted antiferromagnetic order. For LCPO, such a ferromagnetic order along the b axis is not observed. In the temperature dependence of the electrical polarization P b (T) along the b axis there is a kink at T N = 2 2 K which is an indirect evidence for the intrinsic magnetoelectric effect in LFPO. Applying an external magnetic field H b , the polarization P b increases, stronger for small temperatures and the kink at T N disappears. For LCPO, we do not obtain a kink at T N = 6 K. LCPO is polar, but not ferroelectric. We can conclude that the missing magnetoelectric properties in LCPO could be due to the differences in the magnetic orders between LFPO and LCPO. [ABSTRACT FROM AUTHOR]

We have calculated the temperature, magnetic field, and ion doping dependence of the magnetic and electric properties in Fe-doped BaTiO3 using a microscopic model and the Green's function technique. It is shown that the ferromagnetic and multiferroic properties observed at room temperature in Fe doped BaTiO3 could be due to the super exchange interactions between Fe3+ ions in different occupational sites associated with oxygen vacancies and to the exchange coupling of Fe ions with mixed valence, Fe3+ and Fe4+. There is a multiferroic region which depends strongly on the Fe-doping concentration. [ABSTRACT FROM AUTHOR]

The effects of Al, Mg, Co and Zn ion doping on different properties of multiferroic CuCrO2 are studied using a microscopic model and the Green's function technique. The temperature dependence of the dielectric constant shows a kink near TN. For Al ion doping decreases, for Co it increases, whereas for Mg it has a maximum for. decreases with increasing magnetic field hab. The magnetization M is reduced with enhancing the Al and Zn doping concentration, whereas by Mg doping M shows a maximum at. The band gap Eg increases weakly for Zn doping. It decreases strongly with increasing Co and slightly with increasing Mg doping, which is in good quantitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Using a model Hamiltonian and the Green's function technique for the Zn doped Mn-ferrite, Mn1-xZnxO.Fe2O3, and the Gd doped Zn-ferrite, ZnGdxFe(2-x)O4, nanoparticles of different compositions x were studied. The phase transition temperature, TC, and the coercive field, Hc, for different samples dependent upon composition, particle size, and shape were investigated. An attempt was made to enhance or to lower the TC of the nanoparticles to the optimum temperature required in magnetic hyperthermia (42-43°C). [ABSTRACT FROM AUTHOR]

The temperature, magnetic field and ion doping dependence of the phonon properties of CuFeO2 are studied on the basis of a microscopic model and using Green's function technique. The phonon energy decreases with increasing temperature, whereas the phonon damping increases. There is a kink at the phase transition temperature T N 1 which shows the influence of the magnetic field on the phonon properties. The kinks vanish by applying an external magnetic field. By doping of ions with different radius compared to the Fe ion, the phonon energy in CuFeO2 can increase (Ga) or decrease (Sc) with increasing dopant concentration, whereas the damping is always enhanced. The results are compared with those of CuCrO2. Some discrepancies in the literature are discussed. The observed results are in qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

The temperature, magnetic field and ion doping dependence of the phonon properties of CuFeO2 are studied on the basis of a microscopic model and using Green's function technique. The phonon energy decreases with increasing temperature, whereas the phonon damping increases. There is a kink at the phase transition temperature T N 1 which shows the influence of the magnetic field on the phonon properties. The kinks vanish by applying an external magnetic field. By doping of ions with different radius compared to the Fe ion, the phonon energy in CuFeO2 can increase (Ga) or decrease (Sc) with increasing dopant concentration, whereas the damping is always enhanced. The results are compared with those of CuCrO2. Some discrepancies in the literature are discussed. The observed results are in qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Using a microscopic model, taking into account the spin–phonon interactions and the Green’s function technique, we have studied the phonon properties of pure and ion-doped SnO2 nanoparticles (NPs). The phonon energy of SnO2 NPs decreases whereas the damping increases with decreasing particle size. Near the Curie temperature in the NPs, there appears an anomaly in the phonon energy ω ( T ) and damping γ ( T ). The phonon properties are very sensitive to the anharmonic spin–phonon interaction R. They can increase or decrease for R > 0 or R < 0 with increasing of temperature, respectively. In dependence of the radius of the doping ions, the phonon energies ω could be reduced (Co, Fe, Sm, Nd) or enhanced (Cu). The phonon damping is always enhanced in the doped NPs. In summary, due to the size and temperature effects, we obtain changes in the phonon energy and damping in pure SnO2 NPs, whereas in ion-doped ones, the doping effects strengthen these properties. [ABSTRACT FROM AUTHOR]

Using a microscopic model taking into account the spin-phonon interactions we have studied the magnetic properties of pure and ion-doped SnO2 nanoparticles (NPs). The magnetization M in pure SnO2 NPs is due to surface oxygen vacancies. By doping with magnetic Co ion we observe a maximum in M for small Co-concentration, x = 1%, whereas for nonmagnetic Cu ion M increases with x. By Co-doping there is a local distribution for small Co-concentration, whereas by Cu this is not the case. It is shown that there is a strong connection between the lattice and M. The results are in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

We have studied the electric properties of multiferroic BiFeO3 (BFO) using the transverse Ising model in terms of pseudo-spin variables [ABSTRACT FROM AUTHOR]

We have studied the electric properties of multiferroic BiFeO3 (BFO) using the transverse Ising model in terms of pseudo-spin variables [ABSTRACT FROM AUTHOR]

Using a microscopic model and a Green's function technique we calculate the renormalized phonon energy in multiferroic RCrO3 ( R = Sm, Dy, Er, Pr, Gd and Y) compounds as a function of temperature, magnetic field and R-ionic radius. We explain the observed anomalies in the temperature dependence of the phonon spectra based on a detailed analysis of the influence of the magnetic sublattices, the interaction between them and the spin-reorientation (SR) transition on lattice vibrations via spin-phonon interactions. When the rare earth ions are magnetic we investigate their essential role for the anomalies around the SR temperature. For the case when R is nonmagnetic, for example YCrO3, we propose a new microscopic model. We define an induced Dzyaloshinskii-Moriya (IDM) vector as a consequence from the spontaneous polarization. This IDM interaction is responsible for the appearance of a temperature-driven SR transition, which itself is responsible for the phonon anomalies at low temperatures. The numerical calculations are in good qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Using a microscopic model and a Green's function technique we calculate the renormalized phonon energy in multiferroic RCrO3 ( R = Sm, Dy, Er, Pr, Gd and Y) compounds as a function of temperature, magnetic field and R-ionic radius. We explain the observed anomalies in the temperature dependence of the phonon spectra based on a detailed analysis of the influence of the magnetic sublattices, the interaction between them and the spin-reorientation (SR) transition on lattice vibrations via spin-phonon interactions. When the rare earth ions are magnetic we investigate their essential role for the anomalies around the SR temperature. For the case when R is nonmagnetic, for example YCrO3, we propose a new microscopic model. We define an induced Dzyaloshinskii-Moriya (IDM) vector as a consequence from the spontaneous polarization. This IDM interaction is responsible for the appearance of a temperature-driven SR transition, which itself is responsible for the phonon anomalies at low temperatures. The numerical calculations are in good qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]