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Öğe Determination of the steady-state kinetics in a spin-1 Ising model using path probability method(World Scientific Publ Co PTE Ltd, 2020) Özüm, Songül; Erdem, RızaAs a continuation of our previously published work, we propose a theoretical framework for the determination of steady-state kinetics in a spin-1 Ising model by the path probability method. The framework is based on the principles of non-equilibrium statistical physics and is quite different from the phenomenological approach. We construct a set of linear kinetic equations for the order parameters using the non-linear dynamic (or rate) equations in the presence of external magnetic field. From the steady-state solutions of the linear equations, an expression for the complex (or dynamic) magnetic susceptibility (chi = chi(1) - i chi(2)) is derived. The temperature dependence of the magnetic dispersion relation (chi(1)) and magnetic absorption factor (chi(2)) has been studied in the ferromagnetic (FM) and paramagnetic (PM) phases as well as near the critical regime.Öğe Dipolar and Quadrupolar Hysteresis in Core-Surface Magnetic Nanoparticles(2019) Özüm, Songül; Yalçın, Orhan; Erdem, RızaBlume-Emery-Griffiths (BEG) model [1] is used to investigate the hysteretic behaviour of dipole (M) and quadrupole ordering (Q) properties peculiar to core/surface (C/S) type hexagonal Ising nanoparticles (HINPs) [2-3]. The bond energy parameters ( ij ? ) and bond variables ( Pij ) are computed using the BEG Hamiltonian for HINPs. Dipole and quadrupole order parameters are calculated from numerical solutions of Pij . It has also been shown that the dipole order parameter as a function magnetic field (M-h) and quadrupole order parameter as a function single-ion isotropy parameter (Q-D) has ‘‘hysteresis’’ character which is generally called quadrupole hysteresis (QD). Shifted QD loops with an asymmetry are observed in the increasing of K and magnetic field (h) values one by one. The observed M?h hysteresis loops depend on T and D values while Q?D hysteresis loops depend on T and h values. These are also discussed in relation with the experimental and theoretical findings [4, 5].Öğe Dynamic susceptibility for a spin-1 Isingmodel using the path probability method(Niğde Ömer Halisdemir University, 2019) Özüm, Songül; Erdem, RızaThe nonlinear rate equations based on the path probability method is used to derive the dynamic (or complex) susceptibility ( ? ) for a spin-1 Ising model with bilinear and biquadratic interactions when the external magnetic field exists. Firstly, the rate equations are linearized. Then, these are solved in the presence of an oscillating external magnetic field. From the real and imaginary parts of ? , the magnetic dispersion and absorption factors are found. Temperature dependence of these quantities in the ferromagnetic and paramagnetic phase regions (as well as their critical properties) are presented. Finally, the theoretical results are compared with those obtained using irreversible thermodynamicsÖğe Hysteretic behavior of quadrupolar ordering in a 2D magnetic spin?1 Ising nanoparticle(Physical Society of the Republic of China, 2021) Erdem, Rıza; Yalçın, Orhan; Özüm, Songül; Şahin, Ayşe; Demirer, NazlıPair approximation technique has been used to study the quadrupolar ordering properties for the 2D magnetic spin-1 Ising nanoparticles, consisting of core and surface parts with an interface coupling. Similar to the magnetic hysteresis, it has been shown that the quadrupole order parameter (Q) as a function of single-ion anisotropy (D) has a ‘hysteresis’ character which is generally called quadrupole (or QD) hysteresis. The observed QD loops strongly depend on temperature (T), external magnetic field (H) and biquadratic exchange interaction (K). Shifted QD loops with an asymmetry are found when H and K values are increased. These behaviors are also discussed in relation to other theoretical findings.Öğe Hysteretic dipolar and quadrupolar properties of the spin-1 Blume-Emery-Griffiths model under pair approximation(World Scientific, 2021) Özüm, Songül; Erdem, Rıza; Yalçın, Orhan; Görgülüer, ÖmerAs a continuation of previously published work [A. Erdinç and M. Keskin, Int. J. Mod. Phys. B 18, 1603 (2004), doi:10.1142/S0217979204024823] the hysteretic properties of magnetization (m) and quadrupolar moment (q) have been investigated for the spin-1 Blume-Emery-Griffiths model using pair approximation. The magnetic field (h) dependence of m is produced for different values of the lattice coordination number (z), biquadratic interaction (k) and single-ion anisotropy (d). The (m,h) loops show different and novelty properties when d < 0. We also observed the hysteresis cycles in the (q,d), (q,h) and (m,d) planes. These curves strongly depend on biquadratic interaction k. Our results are found to be in good agreement with the other theoretical findings. © 2021 World Scientific Publishing Company.Öğe Hysteretic properties of magnetization and quadrupolar moment in the blume-emery-griffiths model under the pair approximation(L.N. Gumilyov Eurasian National University, 2020) Özüm, Songül; Görgülüer, Ömer; Erdem, Rıza; Yalçın, OrhanThe magnetic hysteresis (M-H) and quadrupole hysteresis (Q-D) loops have been investigated for the Blume-Emery-Griffiths (BEG) model using the pair approximation. The observed curves strongly depend on biquadratic exchange interaction (K). Especially, M-H loops show different and novelty properties from those which depend on negative D values. Besides, we presented the M-D and Q-H behaviors which are in good agreement with the other theoretical findings.Öğe Ising-like model for the two-step spin-crossover systems: Static properties with magnetic field effects using cluster variation method(Institute of Molecular Physics, Polish Academy of Sciences Faculty of Physics, Adam Mickiewicz University, Pozna?, 2021) Veliu, Valon; Erdem, Rıza; Özüm, Songül; Yalçın, OrhanWe investigate the static properties of a two?sublattice Ising?like Hamiltonian for spin-crossover (SCO) systems in the presence of an external magnetic field. Self?consistent equations are obtained using cluster variation method in the lowest approximation. From the solutions of these equations, we present high?spin state fraction vs. temperature and magnetic field variations for various values of the degeneracy ratio between high?spin and low?spin states (r). It is shown that two metastable and one unstable (or saddle) branches in the SCO region are displayed in the r > 1 case while the metastable states disappear and only one saddle point occurs when r = 1. However, only stable states are obtained at high temperatures outside the SCO region. The comparison of our results to other theoretical treatments is also givenÖğe Nanosized Monolayer on Square Lattice within Spin-1 Ising Model: Hysteretic Properties with Odd Interactions(Polish Acad Sciences Inst Physics, 2021) Özüm, Songül; Kavlak, Ramazan; Erdem, Rıza; Yalçın, OrhanThe hysteretic properties of a nanosized monolayer on the square lattice have been studied based on the spin-1 Ising model, including a single-ion anisotropy (D) and dipolar-quadrupolar (or odd, L) interaction parameters using the pair approximation. The nanosized monolayer is divided into the core, core-surface, and surface parts as introduced in J. Mugn. Magn. Mater. 373, 217 (2015). The dipolar (or magnetization M) and quadrupolar (Q) order parameters are calculated. We have investigated M vs. magnetic field H behaviors for different values of L, temperatures T, and monolayer sizes R. We also observed Q-D, M-D and Q-H hysteresis loops. These results are discussed in relation to other theoretical findings.Öğe Nanosized monolayer on the square lattice within spin-1 ising Model: Hysteretic properties with odd interactions(L.N. Gumilyov Eurasian National University, 2020) Kavlak, Ramazan; Özüm, Songül; Erdem, Rıza; Yalçın, OrhanWe propose a theoretical framework for the investigation of M-H and Q-D hysteresis loops for the nanosized monolayer on the square lattice within spin-1 Ising model Hamiltonian with dipolar (J), quadrupolar (K), dipolar-quadrupolar (odd, L) interactions and single-ion anisotropy parameter (D) in pair approximation. We observed that the shift of these loops depends on K, D, temperature (T) and monolayer size (R). These are also discussed in relation with the experimental and theoretical findings.Öğe Nanosized Monolayer on the Square Lattice within Spin-1 Ising Model: Magnetic Properties with odd Interactions(2020) Kavlak, Ramazan; Özüm, Songül; Erdem, Rıza; Yalçın, OrhanBased on the spin-1 Ising model Hamiltonian with dipolar (bilinear, J), quadrupolar, (biquadratic, K), dipolar-quadrupolar (odd, L) interactions and single-ion anisotropy parameter (D), magnetic properties of the nanosized monolayer within the square lattice are studied in pair approximation [1-3]. The monolayer is divided into the core (C), coresurface (CS) and surface (S) parts as introduced by Özüm and co-workers [4]. The dipolar order parameter (or magnetization m) and quadrupolar order parameter (q) are calculated. We have investigated the thermal behaviours of m and q for different values of magnetic field (H), monolayer sizes (R) and L. The results of numerical calculations are in agreement with the available theoretical works.Öğe Relaxation times obtained from the rate equations using path probability method for the spin-1 Ising model(World Scientific Publishing Co. Pte Ltd, 2019) Erdem, Rıza; Özüm, SongülWe have presented the time-dependent behaviors of a spin-1 Ising model (with both bilinear and biquadratic interactions) in the neighborhood of the equilibrium states via the path probability method. The rate equations as introduced by Keskin and co-workers (1989) have been linearized to obtain the characteristic relaxation times. The temperature variations of these times were produced in accordance with the Tanaka and Mannari's work (1976) on the equilibrium properties. Results are compared to one using Onsager's phenomenological theory and a good agreement is achieved. © 2019 World Scientific Publishing CompanyÖğe Spin-1 Ising modelinde manyetik dağılganlık bağıntısı ve manyetik sönüm faktörünün yol olasılık metodu ile hesaplanması(2019) Özüm, Songül; Erdem, RızaBu çalışmada, önceki çalışmamızın [1] devamı olarak, manyetik alan altında bilineer (J) ve bikuadratik (K) etkileşme Hamiltonyenli spin-1 Ising Modeli [2, 3] için dinamik (yani kompleks) alınganlık ifadesi X= X¹ iX²[4, 5] denge dışı istatistik mekaniksel yaklaşımlardan yol olasılık metodu (PPM) kullanılarak bulunduÖğe Spin-1 Ising sisteminde Manyetizasyon ve Kuadrupol Moment durulma sürelerinin Yol Olasılık Metodu ile hesaplanması(Bilkent Üniversitesi, 2018-12-21) Özüm, Songül; Erdem, RızaBu çalışmada, bilineer (J) ve bikuadratik (K) etkileşme Hamiltonyenli spin-1 Ising sistemi [1] için-durulma (dinlenme veya gevşeme olarak ta adlandırılır) süreleri denge-dışı istatistik meka-niksel-yaklaşımlardan yol olasılık metodu (PPM) kullanılarak hesaplandı. Birçok çalışma-da [2, 3] PPM ile-elde edilen ve dinamik denklemler olarak adlandırılan diferansiyel denklem sistemi lineer forma-dönüştürüldü. Lineer denklem sisteminin çözümü sonucu iki zaman sabiti ( S ? , F ? ) türetildi. Bunlar-sırasıyla dipol (mıknatıslanma) ve kuadrupol düzen para-metrelerinin denge durumlarına doğru üstel-azalma şeklindeki gelişimini (durulma) karak-terize etmektedir. ? ? J / K ?1.2 için S ? ve F ? ’nin-indirgenmiş sıcaklıkla (? ) değişimi özellik le kritik sıcaklık civarındaki davranışı farklı hız sabiti-değerleri ( k ) dikkate alınarak incelendi. S ? süresinin ikinci-derece faz geçiş sıcaklığının ( c-? ) her iki-tarafında hızlı bir artışa paralel olarak sonsuza doğru ıraksadığı gözlendi (Şekil 1). Bu davranışa-literatürde “kritik yavaşlama” adı verilir. Diğer taraftan, F ? zamanının c-? sıcaklığında sivri uç (kasp)-şeklinde bir süreksizlik sergilediği tespit edildi (Şekil 2). k sabitindeki artışın (yukarıdaki davranışları-etkilememekle birlikte) sadece düzenli ve düzensiz faz bölgelerindeki durulma sürecini hızlandırdığı-görüldü. Sonuçlar, Onsager teorisine dayalı tersinmez termodinamik (ORT) kullanılarak elde-edilenlerle [4] karşılaştırıldı ve aralarında tam bir uyumun olduğu anlaşıldı.-Şekil 1:-Öğe Static and dynamic properties of two-sublattice spin-crossover systems(Elsevier B.V., 2022) Yalçın, Orhan; Veliu, Valon; Özüm, Songül; Erdem, RızaWe investigate the static and dynamic properties of spin-crossover systems in the presence of an external magnetic field using two-sublattice Ising-like Hamiltonian. At low temperatures both sublattices are in the LS state, and in the HS state at high temperatures. The new feature of spin-crossover is depicted for our model when we take the non-equivalent sublattices , the two-step spin-crossover phase transition is obtained with the presence of the hysteresis loop. In order to study the properties of two-step spin-crossover, we use the lowest approximation of the cluster variation method for static properties. The dynamic properties of the system with bilinear interactions are studied by the path probability method. We present high-spin state fraction vs temperature and magnetic field variations for constant values of the degeneracy ratio between high-spin and low-spin states. In the present model, we obtained the relaxation curves of the order parameters and using different temperature values. Finally, the flow diagram of the order parameters is depicted for different values of rate constant and temperature, which displays the stable, metastable, and unstable properties. Static and dynamic self-consistent equations of the system were performed by using Newton-Raphson and Runge-Kutta methods.Öğe Static properties of spin-crossover with magnetic interaction of Spin-1 Blume-Emery-Griffiths model for two-sublattices(2022) Veliu, Valon; Özüm, Songül; Yalçın, Orhan; Erdem, RızaThe static properties of the spin-1 Blume-Emery-Griffiths (BEG) model for two-sublattices with the presence of an external magnetic field for spin-crossover (SCO) and magnetic ordering are presented. To study the static properties of SCO and magnetic ordering we use the cluster variation method in the lowest approximation (CVMLA). The obtained self-consistent equations are solved using the Newton Raphson method. From these solutions of the self-consistent equations, we present the thermal behaviors of the high-spin fraction (nHS = QA+QB 2 ) state and magnetizations (MF = MA+MB 2 ) for different values of magnetic interaction and quadrupolar interaction parameters. Also, the properties of SCO and magnetic ordering for varying external magnetic fields are presented. It is shown some properties that magnetization is zero and SCO exhibits a first-order phase transition when the temperature increases for different value of magnetic interaction and when temperature decreases both magnetization and SCO are exhibiting the first-order phase transition with the absence of the external magnetic. SCO is different when the temperature is decreasing. However, different states appear for magnetization and SCO with varying external magnetic field for fixed temperature. Our results were compared with other theoretical investigations also given.
