Exchange Striction Model Research Articles

Critical Point in the Curve of First-Order Magnetic Phase Transition

A magnetic state diagram for ferromagnets exhibiting a first-order phase transition in a magnetic field has been calculated. Calculations have been made using the exchange-striction model of a ferromagnet. It has been shown that the curve of first-order magnetic phase transition ends up at a critical point (Hcr, Tcr) that is similar to the critical point of the liquid–gas transition on the (T, P) plane. Analytical expressions for thermodynamic quantities, namely, magnetic susceptibility, specific heat, and compressibility, which anomalously grow near the critical point, have been derived. Calculation results have been compared with available experimental data for La(Fe0.88Si0.12)13 ferromagnet, which experiences the first-order magnetic phase transition.

Tricritical fluctuations and elastic properties of the Ising antiferromagnet UIrSi3

Elastic constants, thermal expansion, magnetostriction, and heat capacity measurements were performed with and without applied magnetic field on a single crystal of ${\mathrm{UIrSi}}_{3}$. The elastic properties were interpreted within the theory of the strain-exchange effect. The exchange-striction model together with the Ising model for the behavior of magnetic localized $5f$ electrons and itinerant electrons of uranium correctly reproduces the main features of our magneto-acoustic experiments in ${\mathrm{UIrSi}}_{3}$. Data on thermal expansion and magnetostriction confirm the conclusion that the dominant contribution of the measured temperature and field change in the speed of sound comes from the change in the elastic modulus itself. Based on the analysis of heat capacity measurements in the magnetic field, we explain the significant anomalies at the second-order branch of the phase transition boundary as a manifestation of the tricritical fluctuations, dominating the region below the tricritical point. The outcome confirms the three-dimensional Ising model, at zero and low magnetic fields, with a crossover to the mean-field tricritical behavior at fields close to the tricritical point, where tricritical fluctuations dominate the temperature evolution of the given property.

Microstructural, dielectric, magneto-electric and optical properties of single phase Ca3CoMnO6

Type II intrinsic multiferroics oxide Ca3CoMnO6 (CCMO) having collinear spin ordering and non-zero polarization is a fascinating compound from the view point of fundamental and technological applications. Room temperature properties of Ca2.7Sr0.3CoMn1-xFexO6 ceramics with dilute Fe doping (x) have been investigated. Rietveld refinements of X-ray diffraction data confirmed single rhombohedral phase with R-3c space group for all the samples. Frequency dependent dielectric properties with low loss tangents measured in frequency range of 1 MHz to 1 GHz, showed an increase in the real permittivity upon Fe doping within the entire frequency range; which is attributed to doping induced optimal modification in Co/Mn ratios. Room temperature ME coupling coefficient of the order of 1.7 mV/cm Oe for pure CCMO is achieved and the mechanism is explained through exchange striction model. It suggested that the dilute Fe substitution (or Mn deficiency) break the inter chain interactions to some extent, in otherwise, quasi collinear magnetic chain structure. Kubelka-Munk function was applied to analyse the optical measurements, which revealed an increase in reflectance and refractive indices with doping of Fe into pure CCMO. Consequently, the optical band gaps were found to systematically decrease from 2.25 eV to 1.80 eV upon Fe doping at the Mn-site.

Magnetoelastic couplings in the deformed kagome quantum spin lattice of volborthite

Microscopic spin interactions on a deformed Kagom\'{e} lattice of volborthite are investigated through magnetoelastic couplings. A negative longitudinal magnetostriction $\Delta L<0$ in the $b$ axis is observed, which depends on the magnetization $M$ with a peculiar relation of $\Delta L/L \propto M^{1.3}$. Based on the exchange striction model, it is argued that the negative magnetostriction originates from a pantograph-like lattice change of the Cu-O-Cu chain in the $b$ axis, and that the peculiar dependence arises from the local spin correlation. This idea is supported by DFT+$U$ calculations simulating the lattice change and a finite-size calculation of the spin correlation, indicating that the recently proposed coupled-trimer model is a plausible one.

Application of the exchange-striction model for the calculation of the FeRh alloys magnetic properties

Application of the exchange-striction model for the calculation of the magnetic properties of antiferro (AFM) - and ferromagnetic (FM) phases of the iron-rhodium alloy is proposed. The following properties of the antiferromagnetic phase have been calculated and compared with the experimental data: the temperature dependences of the sublattice magnetization, the relative change in volume and entropy, and the pressure dependence of the Néel temperature. For the ferromagnetic phase, the temperature dependence of the magnetization, the dependence of the volume and entropy on temperature, and the dependence of the Curie temperature on pressure were calculated. A satisfactory agreement between the results of calculations and experiment has been obtained. The reasons for the AFM-FM phase transition in the iron-rhodium alloy are discussed.

Magnetostriction of the spin-ice system Yb2Ti2O7

Low temperature magnetostriction effects have been studied at Yb2Ti2O7 which is characterized by a geometric magnetic frustration. The experimental finding and the developed theory suggest that Yb2Ti2O7 is a quantum spin ice. Most of the magnetoelastic effects can be explained by an exchange striction model. The external magnetic field together with the temperature govern the transition between the collective paramagnetic behavior of the classical spin ice and the magnetically ordered state.

Entropy and magnetocaloric effect in ferrimagnets RCo2

The equations of state for the magnetic and elastic subsystems of a ferrimagnet are obtained in terms of the exchange–striction model. In the formulas derived for magnetic entropy, it is represented as the sum of the contributions of two magnetic sublattices of the ferrimagnet. One of the main characteristics of the magnetocaloric effect, viz., isothermal variation ΔS iso of the entropy in a magnetic field, is calculated for compounds RCo2 (R = Er, Ho, Dy) that experience a first-order magnetic phase transition and TbCo2 that experiences a second-order magnetic phase transition. It is shown that the calculated values of ΔS iso for these compounds are in satisfactory quantitative agreement with experimental results. The change in the entropy of a ferrimagnet in a strong magnetic field upon a transition from the ferrimagnetic to ferromagnetic ordering is calculated. The peculiarities in the magnetic field dependences of the magnetic entropy of a two-sublattice ferrimagnet are analyzed.

Recognition of exchange striction as the origin of magnetoelectric coupling in multiferroics

The magnetoelectric coupling, a phenomenon inducing magnetic (electric) polarization by application of an external electric (magnetic) field and first conjectured by Curie in 1894, is observed in most of the multiferroics and used for many applications in various fields such as data storage or sensing. However, its microscopic origin is a long-standing controversy in the scientific community. An intense revival of interest developed in the beginning of the 21st century due to the emergence of multiferroic frustrated magnets in which the ferroelectricity is magnetically induced and which present an inherent strong magnetoelectric coupling. The Dzyaloshinskii-Moriya interaction (DMI) well accounts for such ferroelectricity in systems with a noncollinear magnetic order such as the ${\mathrm{RMnO}}_{3}$ manganites. The DMI effect is, however, inadequate for systems presenting ferroelectricity induced by quasicollinear spin arrangements such as the prominent ${\mathrm{RMn}}_{2}{\mathrm{O}}_{5}$ manganites. Among different microscopic mechanisms proposed to resolve this incompatibility, the exchange-striction model stands as the most invoked candidate. In this scenario, the polar atomic displacements originate from the release of a frustration caused by the magnetic order. Despite its theoretical description 15 years ago, this mechanism had yet to be unambiguously validated experimentally. The breakthrough finally comes from ${\mathrm{SmMn}}_{2}{\mathrm{O}}_{5}$ presenting a unique magnetic order revealed by powder neutron diffraction. The unique orientation of its magnetic moment establishes the missing element that definitely validates the exchange striction as the effective mechanism for the spin-induced ferroelectricity in this series. More generally, this is a proof of concept that validates this model on actual systems, facilitating the development of a new generation of multiferroics with unrivaled magnetoelectric properties.

Magnetic properties of RCo2 compounds in the exchange-striction model of ferrimagnets

The original version of the exchange-striction model of a ferrimagnet has been employed for calculating a number of magnetic properties of RCo2 ferrimagnets, where R = Er, Ho, Dy, Tb, and Gd are rareearth ions. The following magnetic properties are calculated: pressure dependence of the Curie temperature (ТС), temperature dependences of magnetization in sublattices of cobalt and rare-earth atoms, and isotherms of magnetization of these lattices at Т > ТС. For an ErСо2 sample, the Н–Т phase diagram has been constructed and the magnetization in the magnetic fields Н = 0–70 Т has been calculated. The calculated and experimental results have been compared. Based on the exchange-striction model, the qualitative explanation of the difference in the type of the magnetic phase transformation in the intermetallic compounds with R = Tb and Gd and R = Er, Ho, and Dy is given.

Magnetovolume effects and effect of pressure on the temperature dependence of sublattice magnetization in Ho(Co0.9Ga0.1)2 compounds

The temperature dependence of the magnetic moments of cobalt and holmium ions in the temperature range of 5–300 K at pressures of P = 0 and 5 kbar was determined based on neutron diffraction data on Ho(Co0.9Ga0.1)2 intermetallide. The temperature dependence of the lattice parameter was established, and the spontaneous bulk magnetostriction was determined. These quantities were calculated using the exchange striction model of a ferrimagnet, and good agreement with the experiment was obtained. The parameters of the exchange interaction between pairs of atoms of this compound and the magnetoelastic coupling constant were estimated. An original interpretation of the nature of the first-order magnetic phase transition in HoCo2 is proposed.

Microscopic mechanism of spin-order induced improper ferroelectric polarization

Type-II multiferroic is an important area in the big family of multiferroics, in which its polarization originates from the spin order, resulting in a strong magnetoelectric coupling. Here we briefly review the previous mechanisms of the spin-order induced polarization, including the Katsura–Nagaosa–Balatsky (KNB) model, inverse Dzyaloshinskii-Moria (DM) interaction model, exchange striction model, and the bond polarization model. Then our unified polarization model is discussed in detail, which contains pure electronic, ion displacement and lattice deformation contributions. And a feasible approach for constructing the unified model based on the first-principles calculations is presented. With this model, we unravel the microscopic mechanisms of the ferroelectricity in several typical multiferroics. New type-II multiferroics with strong magnetoelectric coupling and giant polarization are expected to be discovered and/or designed through the use of this model.

Novel phase transition and metastable regions in the frustrated magnetCdCr2O4

A new magnetic phase transition, which we assign to the separation of two different spiral phases, has been observed by ultrasound studies below the N\'eel temperature (${T}_{N}=7.8$ K) in the frustrated antiferromagnet ${\mathrm{CdCr}}_{2}{\mathrm{O}}_{4}$. This transition renormalizes the velocity and amplitude of the transverse acoustic mode ${c}_{T}$ whereas the longitudinal mode ${c}_{L}$ is not affected. The specific heat does not show any significant change in the entropy at this transition. Furthermore, in an applied magnetic field, the mode ${c}_{T}$ exhibits extended metastable magnetostructural states neighboring the one-half magnetization plateau in ${\mathrm{CdCr}}_{2}{\mathrm{O}}_{4}$. By applying an exchange-striction model we can quantitatively describe the field dependence of the sound velocity below and above the one-half magnetization plateau.

Irreversible transitions in the exchange-striction model of spin-glass state

Based on the assumption of a negative volume dependence of random exchange integrals, it is possible to switch to a compressible Sherrington–Kirkpatrick spin-glass model. Within the proposed model, temperature–pressure phase diagrams were calculated and pressure- and magnetic-field-induced first-order phase transitions from the initial paramagnetic and spin-glass states to the ferromagnetic state were predicted. It was shown that the application of pressure in the spin-glass state not only increases and shifts magnetic susceptibility, but also reduces the critical magnetic fields of irreversible induced phase transitions from the spin-glass to the ferromagnetic state. The obtained results are used to describe the spin-glass state in (Sm1–xGdx)0.55Sr0.45MnO3.

Exchange-striction associated with the elliptical proper helical magnetic structure in the ferroelectric phase of CuFe1−yGayO2

Recently, the detail magnetic structure in the ferroelectric phase of CuFe1−yGayO2 has been determined to be the proper helical structure with the ellipticity of ~ 0.9 by the comprehensive neutron diffraction study.[Nakajima et al. Phys. Rev. B 79 214423 (2009)] In the present study, we have investigated the lattice modulation associated with the elliptical magnetic structure, using the resonant X-ray diffraction measurements on CuFe0.965Ga0.035O2. We observed the superlattice reflection indexed as (0 1 + 2qm 0), where qm is the wave number of the magnetic modulation. The energy spectrum near the Fe-K absorption edge for the (0 1 + 2qm 0) intensity conforms with that for the fundamental (0 2 0) intensity within experimental accuracy, suggesting that the superlattice modulation is at least associated with displacements of the Fe ions. We discuss the origin of the superlattice modulation with the exchange striction model.

Entropy and magnetocaloric effects in ferromagnets undergoing first- and second-order magnetic phase transitions

The exchange striction model is invoked to derive an expression for the entropy of ferromagnetic materials undergoing first- and second-order magnetic phase transitions. The magnetocaloric and barocaloric effects are calculated for the ferromagnet La(Fe0.88Si0.12)13 undergoing a first-order phase transition. The calculated results are in fair agreement with experimental data. The ferromagnet La(Fe0.88Si0.12)13 is used as an example to predict the changes in magnetic and magnetocaloric properties associated with gradual increase in the magnetoelastic coupling constant (i.e., with passage from first- to second-order magnetic transition region). It is shown that stronger magnetoelastic coupling leads to stronger magnetocaloric effects and changes their dependence on magnetic field and pressure. Expressions are obtained for the maximum field- and pressure-induced entropy changes. An analysis is presented of the mechanism responsible for the increase in magnetocaloric and barocaloric effects associated with change from the second- to first-order magnetic phase transition.

Pressure-induced polarization reversal in multiferroicYMn2O5

The low-temperature ferroelectric polarization of multiferroic ${\text{YMn}}_{2}{\text{O}}_{5}$ is completely reversed at a critical pressure of 10 kbar and the phase transition from the incommensurate to the commensurate magnetic phase is induced by pressures above 14 kbar. The high-pressure data correlate with thermal-expansion measurements, indicating a significant lattice strain at the low-temperature transition into the incommensurate phase. The results support the exchange striction model for the ferroelectricity in multiferroic ${R\text{Mn}}_{2}{\text{O}}_{5}$ compounds and they show the importance of magnetic frustration as well as the spin-lattice coupling.

Spin-flop transition in samarium metal investigated by capacitance dilatometry in a steady magnetic field of45T

The longitudinal and transversal forced magnetostrictions of a single crystal of samarium metal have been investigated in a static magnetic field up to $45\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The data show pronounced features of a spin-flop transition initiating at an applied field of about $30\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The measured forced magnetostriction is about 1 order of magnitude smaller than the spontaneous magnetostriction. Based on a model calculation of the magnetic phase diagram these features have been interpreted within the exchange striction model. The moments of the quasicubic Sm sites enter a spin-flop phase at about $30\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and ferromagnetic saturation is predicted at $60\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Similarly the model predicts a spin-flop phase for the hexagonal Sm sites at $140\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ and ferromagnetic saturation at $390\phantom{\rule{0.3em}{0ex}}\mathrm{T}$.

The magnetoelastic paradox in [formula omitted] and [formula omitted

For isotropic systems the only source of magnetostriction is believed to be the exchange striction (ES). In many cases large magnetostrictive effects have been observed in Gd 3 + based systems ( S = 7 2 , L = 0 ), but in no case a significant symmetry breaking lattice distortion has been found. For ferromagnetic (fm) order this is in line with the ES model. However, for antiferromagnetic (afm) large symmetry breaking distortions of the lattice are expected from theory. This contrasts to all available experimental data on several Gd-based antiferromagnets. We demonstrate examples for this magnetoelastic paradox and discuss in detail experimental evidence for GdAg 2 and GdRu 2 Si 2 .

Exchange striction model for the spin configuration in the antiferromagnetic YMn 2 with the cubic Laves phase structure

By making use of the Luttinger–Tisza method for the classical spin Heisenberg model, we examine how the exchange striction affects the highly frustrated pyrochlore-type spin system in YMn 2 with the cubic Laves phase (C15) structure. The distance dependence of the exchange parameter between the nearest neighboring spin pair is taken into account. The complicated spin configuration observed in YMn 2 is deduced through energy change due to the exchange striction.

Pressure-induced changes in transport properties of layeredLa1.2Ca1.8Mn2O7

The transport properties of a single crystal of ${\mathrm{La}}_{1.2}{\mathrm{Ca}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ with the layered ${\mathrm{Sr}}_{3}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$-type perovskite structure have been studied under hydrostatic pressures of up to \ensuremath{\sim}9 kbar. It is found that ${\mathrm{La}}_{1.2}{\mathrm{Ca}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ undergoes a first-order phase transition from a paramagnetic insulating to a low-temperature ferromagnetic metallic state which is accompanied by a large decrease in the electrical resistivity. At ambient pressure the magnetic phase transition takes place at ${T}_{c}=242 \mathrm{K}$ and as the external pressure is applied the critical temperature increases linearly at a rate of 1.1 K/kbar. The present results reflect the competition between double and superexchange resulting from two-dimensional Mn-O-Mn networks and can be interpreted in terms of the exchange striction model.