arXiv subjects

Hung T. Diep

Publications and source records attributed to Hung T. Diep.

At least 19 recordsLinked to original sources

arXiv2025

Is the hyperscaling relation violated below the upper critical dimension in some particular cases?

In this review, we show our results with new interpretation on the critical exponents of thin films obtained by high-performance multi-histogram Monte Carlo simulations. The film thickness $N_z$ consists of a few layers up to a dozen of layers in the $z$ direction. The free boundary condition is applied in this direction while in the $xy$ plane periodic boundary conditions are used. Large $xy$ plane sizes are used for finite-size scaling. The Ising model is studied with nearest-neighbor (NN) interaction. When $N_z=1$, namely the two-dimensional (2D) system, we find the critical exponents given by the renormalization group. While, for $N_z>1$, the critical exponents calculated with the high-precision multi-histogram technique show that they deviate slightly but systematically from the 2D values. If we use these values of critical exponents in the hyperscaling relation with $d=2$, then the hyperscaling relation is violated. However, if we use the hyperscaling relation and the critical exponents obtained for $N_z>1$ to calculate the dimension of the system, we find the system dimension slightly larger than 2. This can be viewed as an "effective" dimension. More discussion is given in the paper. We also show the cross-over between the first- and second-order transition while varying the film thickness in an antiferromagnetic FCC Ising frustrated thin film. In addition, we will show evidence that when a 2D system has two order parameters of different symmetries with a single transition, the critical exponents are new, suggesting a universality class of coupled two-symmetry breakings. In this case, the 2D hyperscaling does not hold. Another case is the 3D Ising model coupled to the lattice vibration: the critical exponents deviate from the 3D Ising ones, the results suggest the violation of the hyperscaling.

cond-mat.stat-mech↗

arXiv2025

Frustrated Spin Systems: History of the Emergence of a Modern Physics

In 1977, Gérard Toulouse has proposed a new concept termed as "frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention the Villain's model, the fully frustrated simple cubic lattice, the antiferromagnetic triangular lattice. The former models are systems with mixed ferromagnetic and antiferromagnetic bonds, while in the latter containing only an antiferromagnetic interaction, the frustration is caused by the lattice geometry. These frustrated spin systems have novel properties that we will review in this paper. One of the striking aspects is the fact that well-established methods such as the renormalization group fail to deal with the nature of the phase transition in frustrated systems. Investigations of properties of frustrated spin systems have been intensive since the 80's. I myself got involved in several investigations of frustrated spin systems soon after my PhD. I have learned a lot from numerous discussions with Gérard Toulouse. Until today, I am still working on frustrated systems such as skyrmions. In this review, I trace back a number of my works over the years on frustrated spin systems going from exactly solved 2D Ising frustrated models, to XY and Heisenberg 2D and 3D frustrated lattices. At the end I present my latest results on skyrmions resulting from the frustration caused by the competition between the exchange interaction and the Dzyaloshinskii-Moriya interaction under an applied magnetic field. A quantum spin-wave theory using the Green's function method is shown and discussed.

cond-mat.stat-mech↗

arXiv2024

Physics of 2D magnets and magnetic thin films: Surface structure and surface phase transition, criticality and skyrmions

Recently, there is an increasing renewed interest in 2D magnetism such as Van der Waals magnets. The physics of 2D magnetism and ultra-thin magnetic films has a long history. This chapter is a review devoted to some fundamental theoretical properties of 2D magnets and and magnetic thin films including frustrated systems and topological spin textures. These properties allow to understand macroscopic behaviors experimentally observed in thin films and superlattices where the surface and the interface play a crucial role. The chapter begins with a review on 2D magnets, their spin structures and phase transitions. Next, the case of thin films is considered. The theory of surface spin waves is discussed in various situations with and without surface reconstruction of spin ordering. Various interactions are taken into account: surface interaction different from the bulk one, competing interactions, Dzyaloshinskii-Moriya interaction. Surface phase transitions are shown in some particularly striking cases. Finally, some cases of topological spin textures called "skyrmions" are reviewed. All the results shown in this chapter have been published in various research papers cited in the text. Therefore, we will discuss some important results but avoid to enter complicated methods. Instead, the reader is referred to original papers for detailed demonstrations.

cond-mat.stat-mech↗

arXiv2024

First-Order Phase Transition in Perovskites Pr$_{0.67}$Sr$_{0.33}$MnO$_{3}$ - Magneto-Caloric Properties -- Effect of Multi-Spin Interaction

We show by extensive Monte Carlo simulations that we need a multi-spin interaction in addition to pairwise interactions in order to reproduce the temperature dependence of the experimental magnetization observed in the perovskite compound Pr$_{0.67}$Sr$_{0.33}$MnO$_{3}$. The multi-spin interaction is introduced in the Hamiltonian as follows: each spin interacts simultaneously with its four nearest-neighbors. It does not have the reversal invariance as in a pairwise interaction where reversing the directions of two spins leaves the interaction energy invariant. As a consequence, it competes with the pairwise interactions between magnetic ions. The multi-spin interaction allows the sample magnetization $M$ to increase, to decrease or to have a plateau with increasing $T$. In this paper we show that $M$ increases with increasing $T$ before making a vertical fall at the transition temperature $T_C$, in contrast to the usual decrease of $M$ with increasing $T$ in most of magnetic systems. This result is in an excellent agreement with the experimental data observed in Pr$_{0.67}$Sr$_{0.33}$MnO$_{3}$. Furthermore, we show by the energy histogram taken at $T_C$ that the transition is clearly of first order. We also calculate the magnetic entropy change $|ΔS_m|$ and the Relative Cooling Power (RCP) by using the set of curves of $M$ obtained under an applied magnetic field $H$ varying from 0 to 5 Tesla across the transition temperature region. We obtain a good agreement with experiments on $|ΔS_m|$ and the values of RCP. This perovskite compound has a good potential in refrigeration application due to its high RCP.

cond-mat.str-el↗

arXiv2024

Phase Transition and Magneto-caloric Properties of Perovskites Pr$_{0.55}$Sr$_{0.45}$MnO$_{3}$: Modeling versus Experiments

Experimental data obtained with the perovskite compounds Pr$_{0.55}$Sr$_{0.45}$MnO$_{3}$ show that the magnetization decreases with increasing temperature $T$ and undergoes a very sharp phase transition to the paramagnetic phase. The sharp transition in a system with a strong disorder is very rare, if not non-existent, in the theory of phase transition in systems of short-range pairwise exchange interactions. To understand this remarkable property, we introduce a model including a multispin (cluster-like) interaction between Mn ions, in addition to the usual pairwise exchange terms between these ions and the Mn-Pr interactions. We carry out Monte Carlo (MC) simulations. Due to the doping, Mn$^{4+}$ with $S=3/2$ has the concentration of Pr$^{3+}$ ($S=1$) and Mn$^{3+}$ with $S=2$ has the Sr concentration. After attempts with different spin models and various Hamiltonians, we find that the many-state Ising spin model reproduces most of the experimental results. For the Hamiltonian, we find that pairwise interactions alone between ions cannot reproduce the sharp transition and the magnetization below $T_C$. We have to include a multispin interaction as said above. We fit the MC results with experimental data, and we estimate values of various exchange interactions in the system. These values are found to be in the range of those found in perovskite manganite compounts. We also study the applied-field effect on the magnetization in the temperature region below and above the transition temperature $T_C$. We calculate the magnetic entropy change $|ΔS_m|$ and the Relative Cooling Power, for magnetic field from 1 to 3 Tesla. Our simulation results are in good agreement with experiments.

cond-mat.mtrl-sci↗

arXiv2023

Monte Carlo Study of Agent-Based Blume-Capel Model for Political Depolarization

In this paper, using Monte Carlo simulations we show that the Blume-Capel model gives rise to the social depolarization. This model borrowed from statistical physics uses the continuous Ising spin varying from -1 to 1 passing by zero to express the political stance of an individual going from ultra-left (-1) to ultra-right (+1). The particularity of the Blume-Capel model is the existence of a $D$-term which favors the state of spin zero which is a neutral stance. We consider the political system of the USA where voters affiliate with two political groups: Democrats or Republicans, or are independent. Each group is composed of a large number of interacting members of the same stance. We represent the general political ambiance (or degree of social turmoil) with a temperature $T$ similar to thermal agitation in statistical physics. When three groups interact with each other, their stances can get closer or further from each other, depending on the nature of their inter-group interactions. We study the dynamics of such variations as functions of the value of the $D$-term of each group. We show that the polarization decreases with increasing $D$. We outline the important role of $T$ in these dynamics. These MC results are in excellent agreement with the mean-field treatment of the same model.

physics.soc-ph↗

arXiv2023

Spin Transport in Magnetically Ordered Systems: Ferromagnets, Antiferromagnets and Frustrated Systems

In this review, we outline the important results on the resistivity encountered by an electron in magnetically ordered materials. The mechanism of the collision between the electron and the lattice spins is shown. Experiments on the spin resistivity in various magnetic materials as well as theoretical background are recalled. We focus on our works since 15 years using principally Monte Carlo simulations. In these works, we have studied the spin resistivity in various kinds of magnetic systems ranging from ferromagnets and antiferromagnets to frustrated spin systems. It is found that the spin resistivity shows a broad peak at the transition temperature in systems with a second-order phase transition, while it undergoes a discontinuous jump at the transition temperature of a first-order transition. New results on the hexagonal-close-packed (HCP) antiferromagnet are also shown in extended details for the Ising case in both the frustrated and non-frustrated parameter regions.

cond-mat.stat-mech↗

arXiv2022

Quantum Spin-Wave Theory for non-collinear Spin Structures, a Review

In this review, we trace the evolution of the quantum spin-wave theory treating non-collinear spin configurations. Non-collinear spin configurations are consequences of the frustration created by competing interactions. They include simple chiral magnets due to competing nearest-neighbor (NN) and next-NN interactions and systems with geometry frustration such as the triangular antiferromagnet and the Kagomé lattice. We review here spin-wave results of such systems and also systems with the Dzyaloshinskii-Moriya interaction. Accent is put on these non-collinear ground states which have to be calculated before applying any spin-wave theory to determine the spectrum of the elementary excitations from the ground states. We mostly show results obtained by the use of a Green's function method. These results include the spin-wave dispersion relation and the magnetizations, layer by layer, as functions of $T$ in 2D, 3D and thin films. Some new unpublished results are also included. Technical details and discussion on the method are shown and discussed.

cond-mat.mtrl-sci↗

arXiv2022

Bifurcation of a Topological Skyrmion String

Manipulation of three-dimensional (3D) topological objects is of both fundamental interest and practical importance in many branches of physics. Here, we show by spin dynamics simulations that the bifurcation of a 3D skyrmion string in a layered frustrated system could be induced by the dampinglike spin-orbit torque. The bifurcation of a skyrmion string happens when the skyrmion string carries a minimal topological charge of $Q=2$. We demonstrate that three types of bifurcations could be realized by applying different current injection geometries, which lead to the transformation from I-shaped skyrmion strings to Y-, X-, and O-shaped ones. Besides, different branches of a bifurcated skyrmion string may merge into an isolated skyrmion string spontaneously. The mechanism of bifurcation should be universal to any skyrmion strings with $Q\geq 2$ in the layered frustrated system and could offer a general approach to manipulate 3D stringlike topological objects for spintronic functions.

cond-mat.mes-hall↗

arXiv2022

The stability of 3D skyrmions under mechanical stress studied via Monte Carlo calculations

Using Monte Carlo (MC) simulations, we study the skyrmion stability/instability as a response to uniaxial mechanical stresses. Skyrmions emerge in chiral magnetic materials as a stable spin configuration under external magnetic field $\vec{B}$ with the competition of ferromagnetic interaction and Dzyaloshinskii-Moriya interaction (DMI) at low temperature $T$. Skyrmion configurations are also known to be stable (unstable) under a compressive stress applied parallel (perpendicular) to $\vec{B}$. To understand the origin of such experimentally confirmed stability/instability, we use the Finsler geometry modeling technique with a new degree of freedom for strains, which plays an essential role in DMI being anisotropic. We find from MC data that the area of the skyrmion state on the $B$-$T$ phase diagram increases (decreases) depending on the direction of applied stresses, in agreement with reported experimental results. This change in the area of the skyrmion state indicates that skyrmions become more (less) stable if the tensile strain direction is parallel (perpendicular) to $\vec{B}$. From the numerical data in this paper, we find that the so-called magneto-elastic effect is suitably implemented in the effective DMI theory with the strain degree of freedom without complex magneto-elastic coupling terms for chiral magnetic materials. This result confirms that experimentally-observed skyrmion stability and instability are caused by DMI anisotropy.

cond-mat.str-el↗

arXiv2021

Dynamic transformation between a skyrmion string and a bimeron string in a layered frustrated system

Frustrated topological spin textures have unique properties that may enable novel spintronic applications, such as helicity-based information storage and computing. Here, we report the statics and current-induced dynamics of two-dimensional (2D) pancake skyrmions in a stack of weakly coupled frustrated magnetic monolayers, which form a three-dimensional (3D) skyrmion string. The Bloch-type skyrmion string is energetically more stable than its Néel-type counterpart. It can be driven into translational motion by the dampinglike spin-orbit torque and shows the damping-dependent skyrmion Hall effect. Most notably, the skyrmion string can be transformed to a dynamically stable bimeron string by the dampinglike spin-orbit torque. The current-induced bimeron string rotates stably with respect to its center, which can spontaneously transform back to a skyrmion string when the current is switched off. Our results reveal unusual physical properties of 3D frustrated spin textures, and may open up different possibilities for spintronic applications based on skyrmion and bimeron strings.

cond-mat.mes-hall↗

arXiv2021

Finsler geometry modeling and Monte Carlo study of skyrmion shape deformation by uniaxial stress

Skyrmions in chiral magnetic materials are topologically stable and energetically balanced spin configurations appearing under the presence of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI). Much of the current interest has focused on the effects of magneto-elastic coupling on these interactions under mechanical stimuli, such as uniaxial stresses for future applications in spintronics devices. Recent studies suggest that skyrmion shape deformations in thin films are attributed to an anisotropy in the coefficient of DMI, such that $D_{x}\!\not=\!D_{y}$, which makes the ratio $λ/D$ anistropic, where the coefficient of FMI $λ$ is isotropic. It is also possible that $λ_{x}\!\not=\!λ_{y}$ while $D$ is isotropic for $λ/D$ to be anisotropic. In this paper, we study this problem using a new modeling technique constructed based on Finsler geometry (FG). Two possible FG models are examined: In the first (second) model, the FG modeling prescription is applied to the FMI (DMI) Hamiltonian. We find that these two different FG models' results are consistent with the reported experimental data for skyrmion deformation. We also study responses of helical spin orders under lattice deformations corresponding to uniaxial extension/compression and find a clear difference between these two models in the stripe phase, elucidating which interaction of FMI and DMI is deformed to be anisotropic by uniaxial stresses.

cond-mat.mtrl-sci↗

arXiv2021

Vortex Structure in Magnetic Nanodots: Dipolar Interaction, Mobile Spin Model, Phase Transition and Melting

We study in this article properties of a nanodot embedded in a support by Monte Carlo simulation. The nanodot is a piece of simple cubic lattice where each site is occupied by a mobile Heisenberg spin which can move from one lattice site to another under the effect of the temperature and its interaction with neighbors. We take into account a short-range exchange interaction between spins and a long-range dipolar interaction. We show that the ground-state configuration is a vortex around the dot central axis: the spins on the dot boundary lie in the $xy$ plane but go out of plane with a net perpendicular magnetization at the dot center. Possible applications are discussed. Finite-temperature properties are studied. We show the characteristics of the surface melting and determine the energy, the diffusion coefficient and the layer magnetizations as functions of temperature.

cond-mat.stat-mech↗

arXiv2021

Dynamics of the Price Behavior in Stock Market: A Statistical Physics Approach

We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter $T$ which plays the role of the temperature in physics. We show that there is a critical value of $T$, say $T_c$, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. We have considered three models: $q=3$ ( sell, buy, wait), $q=5$ (5 states between absolutely buy and absolutely sell), and $q=\infty$. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time $t_1$ and removed at the time $t_2$. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. Many striking results are obtained. In particular we show that the price strongly fluctuates near $T_c$ and there exists a critical value $H_c$ above which the boosting effect remains after $H$ is removed. This happens only if $H$ is applied in the critical region. Otherwise, the effect of $H$ lasts only during the time of the application of $H$. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time.

q-fin.GN↗

arXiv2021

A Frustrated Bimeronium: Static Structure and Dynamics

We show a topological spin texture called "bimeronium" in magnets with in-plane magnetization. It is a topological counterpart of skyrmionium in perpendicularly magnetized magnets and can be seen as a combination of two bimerons with opposite topological charges. We report the static structure and spin-orbit-torque-induced dynamics of an isolated bimeronium in a magnetic monolayer with frustrated exchange interactions. We study the anisotropy and magnetic field dependences of a static bimeronium. We also explore the bimeronium dynamics driven by the damping-like spin-orbit torque. We find that the bimeronium shows steady rotation when the spin polarization direction is parallel to the easy axis. Moreover, we demonstrate the annihilation of the bimeronium when the spin polarization direction is perpendicular to the easy axis. Our results are useful for understanding fundamental properties of bimeronium structures and may offer an approach to build bimeronium-based spintronic devices.

cond-mat.mes-hall↗

arXiv2020

Current-driven skyrmionium in a frustrated magnetic system

Magnetic skyrmionium can be used as a nanometer-scale non-volatile information carrier, which shows no skyrmion Hall effect due to its special structure carrying zero topological charge. Here, we report the static and dynamic properties of an isolated nanoscale skyrmionium in a frustrated magnetic monolayer, where the skyrmionium is stabilized by competing interactions. The frustrated skyrmionium has a size of about $10$ nm, which can be further reduced by tuning perpendicular magnetic anisotropy or magnetic field. It is found that the nanoscale skyrmionium driven by the damping-like spin-orbit torque shows directional motion with a favored Bloch-type helicity. A small driving current or magnetic field can lead to the transformation of an unstable Néel-type skyrmionium to a metastable Bloch-type skyrmionium. A large driving current may result in the distortion and collapse of the Bloch-type skyrmionium. Our results are useful for the understanding of frustrated skyrmionium physics, which also provide guidelines for the design of spintronic devices based on topological spin textures.

cond-mat.mes-hall↗

arXiv2019

Skyrmions on 2D Elastic Surfaces with Fixed Boundary Frame

We report simulation results of skyrmions on fluctuating 2D lattices, where the vertices ${\bf r}_i (\in {\bf R}^3)$ are treated as a dynamical variable and, hence, there is no crystalline structure. On the fluctuating surfaces, an external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov Hamiltonian for membranes. The surface (or frame) tension $τ$ is calculated under both isotropic and uniaxial strain conditions, and this calculation clarifies a non-trivial dependence of $τ$ on the skyrmion, stripe, and ferromagnetic phases. We find that the variation of $τ$ with respect to the applied magnetic field in the skyrmion phase is accompanied by a variation of the total number of skyrmions. Moreover, we find that this total number variation is qualitatively consistent with a recent experimental result for the creation/annihilation of skyrmions of 3D crystalline material under uniaxial stress conditions. It is also found that the stripe phase is significantly influenced by uniaxial strains, while the skyrmion phase remains unchanged. These results allow us to conclude that the skyrmion phase is stable even on fluctuating surfaces.

cond-mat.str-el↗

arXiv2016

Partial phase transition and quantum effects in helimagnetic films under an applied magnetic field

We study the phase transition in a helimagnetic film with Heisenberg spins under an applied magnetic field in the c direction perpendicular to the film. The helical structure is due to the an-tiferromagnetic interaction between next-nearest neighbors in the c direction. Helimagnetic films in zero field are known to have a strong modification of the in-plane helical angle near the film surfaces. We show that spins react to a moderate applied magnetic field by creating a particular spin configuration along the c axis. With increasing temperature (T), using Monte Carlo simulations we show that the system undergoes a phase transition triggered by the destruction of the ordering of a number of layers. This partial phase transition is shown to be intimately related to the ground-state spin structure. We show why some layers undergo a phase transition while others do not. The Green's function method for non collinear magnets is also carried out to investigate effects of quantum fluctuations. Non-uniform zero-point spin contractions and a crossover of layer magnetizations at low T are shown and discussed.

cond-mat.stat-mech↗