Crystal Field Anisotropy Research Articles

Ferrimagnetic structures with rare-earth induced spin-reorientation in the Mn self-doped perovskite (Er0.7Mn0.3)MnO3

The search for spin-reorientation (SR) phase transitions, a spontaneous rotation of ordered magnetic moments, in ferrimagnetic (FiM) materials, which carry a net magnetization, is of fundamental and practical interest for applications in the field of spintronics. In this work, we have investigated Mn self-doped (Er0.7Mn0.3)MnO3 solid solution with GdFeO3-type Pnma perovskite structure by combining specific heat, magnetic susceptibility and neutron powder diffraction measurements. We provide experimental evidence for FiM order below TC = 104 K, and a spontaneous SR transition at TSR = 11 K. A FiM structure appears in all (R1-xMnx)MnO3 compounds with R = Dy–Lu for x ≥ 0.2. But in this structural family, R = Er is the only material with a SR transition. FiM order in (Er0.7Mn0.3)MnO3 appears with ferromagnetic (FM) ordering of Mn3+ and Mn4+ cations at the B site along the a-direction, which are antiferromagnetically (AFM) coupled with Er3+ and Mn2+ cations at the A site. At TSR, ordered Er3+ change direction from the magnetically harder a-axis to the magnetically easy b-axis and induce a change of the whole FiM structure, including the direction of all Mn spins from the irreducible representation mGM3+ to mGM4+. We calculated the crystal-field (CF) anisotropy for Ho3+ in (Ho0.8Mn0.2)MnO3 and Er3+ in (Er0.7Mn0.3)MnO3, based on the point charge model; the results revealed large magnetic anisotropies. For the FiM structure of (Ho0.8Mn0.2)MnO3, the magnetically easy a-axis of Ho3+ keeps the high-temperature magnetic directions along the a-axis and gives rise to a pronounced magnetization reversal effect at low temperature because of a significant rise of Ho3+ ordered moments. On the other hand, for the FiM structure of (Er0.7Mn0.3)MnO3, the magnetically easy b-axis of Er3+ gives rise to a SR phase transition at TSR, which does not lead to magnetization reversal even though Er3+ ordered moments rise significantly at low temperatures.

Circularly Polarized Luminescence Without External Magnetic Fields from Individual CsPbBr3 Perovskite Quantum Dots.

Lead halide perovskite quantum dots (QDs), the latest generation of the colloidal QD family, exhibit outstanding optical properties, which are now exploited as both classical and quantum light sources. Most of their rather exceptional properties are related to the peculiar exciton fine-structure of band-edge states, which can support unique bright triplet excitons. The degeneracy of the bright triplet excitons is lifted with energetic splitting in the order of millielectronvolts, which can be resolved by the photoluminescence (PL) measurements of single QDs at cryogenic temperatures. Each bright exciton fine-structure-state (FSS) exhibits a dominantly linear polarization, in line with several theoretical models based on the sole crystal field, exchange interaction, and shape anisotropy. Here, we show that in addition to a high degree of linear polarization, the individual exciton FSS can exhibit a non-negligible degree of circular polarization even without external magnetic fields by investigating the four Stokes parameters of the exciton fine-structure in individual CsPbBr3 QDs through Stokes polarimetric measurements. We observe a degree of circular polarization up to ∼38%, which could not be detected by using the conventional polarimetric technique. In addition, we found a consistent transition from left- to right-hand circular polarization within the fine-structure triplet manifold, which was observed in magnetic-field-dependent experiments. Our optical investigation provides deeper insights into the nature of the exciton fine structures and thereby drives the yet-incomplete understanding of the unique photophysical properties of this class of QDs for the benefit of future applications in chiral quantum optics.

Crystal field anisotropy correlated charge disproportionation in Ruddlesden-Popper Sr3-xCaxFe2O7-δ perovskites

A series of Ca2+-doped Ruddlesden-Popper phase perovskites Sr3-xCaxFe2O7-δ (x = 0∼0.4) were synthesized. Strong asymmetric FeO6 octahedral distortion was confirmed at x = 0.2 owing to the anisotropic chemical pressure applied from preferable occupation of Ca2+ ion at Sr2 site. Unusual high-charged oxidation state of iron ion with enhanced p→d charge transfer was collectively evidenced by X-ray photoelectron spectroscopy and Mössbauer spectroscopy. Combined electron emission spectroscopy further revealed a narrowing of the surface band gap accompanied by an apparent lowering of the conduction band edge at x = 0.2. These observations can be explained by a nontrivial partial charge disproportionated (CD) regime: d5L + d5L → d5L1−n + d5L1+n, which reflects a significant correlation between anisotropic chemical pressure and CD ground state. The d5L1−n ground state, which dominates the conduction band, is largely stabilized by enhancing the d(Fe)-p(O) hybridization along the c-axis. In addition, abrupt changes in both magnetism and dc electrical properties were also observed at x = 0.2. It is believed that the anisotropic crystal field correlated electronic state fluctuation of iron may facilitate magnetic phase competition and carrier transport. This work provides a comprehensive understanding of the crystallographic anisotropy and correlated valence electron behavior in Fe-base Ruddlesden-Popper perovskites, as well as quasi two-dimensional perovskite materials.

Spin dynamic soliton in ferromagnetic materials over the (2 + 1)-dimensional beta fractional HFSC model

Ferromagnetic materials have important exploitation practice in permanent information in electromagnets, electric motors, generators, recording in thin film etc. This research explores spin dynamic soliton in Ferromagnetic materials via the (2 + 1)-D Heisenberg ferro-magnetic Spin Chains (HFSC) model. The Extended (I,R) and Extended Simple schemes treatment are applied to integrate the model. Through the technique, various novel dynamical wave solutions afford as optical dark and bright soliton envelope, spin wave envelope Black soliton, optical bell-shock interaction, optical bell-anti-shock wave, optical Dark-bright bell soliton and optical bright periodic waves from modulus plots, besides these real and imaginary profiles exhibits bright periodic wave with dark bell wave, periodically increasing–decreasing carrier wave, periodic carrier wave increase its amplitude by shock, periodic carrier wave suddenly decrease its amplitude by shock waves. The effect of fractional derivative, neighboring interaction as well as uniaxial crystal field anisotropy parameters is explored on the envelope soliton and amplitude of carrier waves. The changing value of neighboring interaction parameters are exhibited as increases wave height with the increases of parametric values, but while increasing values of the uni-axial crystal arena anisotropy factor causes the reduction of wave heights.

Elucidating ultranarrow 2F7/2 to 2F5/2 absorption in ytterbium(iii) complexes.

Achieving ultranarrow absorption linewidths in the condensed phase enables optical state preparation of specific non-thermal states, a prerequisite for quantum-enabled technologies. The 4f orbitals of lanthanide(iii) complexes are often referred to as "atom-like," reflecting their isolated nature, and are promising substrates for the optical preparation of specific quantum states. To better understand the photophysical properties of 4f states and assess their potential for quantum applications, theoretical building blocks are required for rapid screening. In this study, an atomic-level perturbative calculation (i.e., spin-orbit crystal field, SOCF) is applied to various Yb(iii) complexes to investigate their linear absorption and emission through a fitting mechanism of their experimentally determined transition energies and oscillator strengths. In particular, the optical properties of (thiolfan)YbCl(THF) (thiolfan = 1,1'-bis(2,4-di-tert-butyl-6-thiomethylenephenoxy)ferrocene), a recently reported complex with an ultranarrow optical linewidth, are computed and compared to those of other Yb(iii) compounds. Through a transition energy sampling study, major contributors to the optical linewidth are identified. We observe particularly isolated f-f transitions and narrow linewidths, which we attribute to two distinct factors. Firstly, the ultra-high atomic similarity of the orbitals involved in the optical transition, along with the presence of an anisotropic crystal field, collectively contribute to the observed narrow transitions. Secondly, we note highly correlated excited-ground energy fluctuations that serve to greatly suppress inhomogeneous line-broadening. This article illustrates how SOCF can be used as a low-cost method to probe the influence of crystal field environment on the optical properties of Yb(iii) complexes to assist the development of novel lanthanide series quantum materials.

Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

Understanding Dopant–Host Interactions on Electronic Structures and Optical Properties in Ce‐Doped WS2 Monolayers

AbstractSubstitutional lanthanide doping of 2D transition metal dichalcogenides (TMDs) is expected to be a promising strategy to engineer optical, electronic, and optoelectronic properties of TMDs. Understanding the interactions between lanthanide dopants and 2D TMDs host is one of the key problems to be resolved for their profound research studies. Herein, the interactions between Ce dopants and monolayer WS2 in a physical vapor deposition grown Ce‐doped WS2 monolayer are studied by combining scanning tunneling microscopy with optical characterizations with high spatial and temporal resolution. It is found that the highly anisotropic crystal field can effectively split the energy levels of the Ce dopants’ f orbital. The electrons in the split energy levels can bind the holes in the valence band maximum of the Ce‐doped WS2, forming optical bright excitons. These excitons collide with the free A excitons when increasing the pump fluences, reducing the A exciton's lifetime. This study may be beneficial for the design and fabrication of optical, electronic, and optoelectronic devices based on lanthanide‐doped TMDs.

Crystal field excitation in the chiral helimagnet YbNi3Al9

A crystal field level scheme of a uniaxial chiral helimagnet $\mathrm{Yb}{\mathrm{Ni}}_{3}{\mathrm{Al}}_{9}$, exhibiting a chiral magnetic soliton lattice state by Cu substitution for Ni, has been determined by inelastic neutron scattering. The ground and the first excited doublets are separated by 44 K and are simply expressed as $\ensuremath{\alpha}|\ifmmode\pm\else\textpm\fi{}7/2\ensuremath{\rangle}+\ensuremath{\beta}|\ensuremath{\mp}5/2\ensuremath{\rangle}$, with $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ nearly equal to $\ifmmode\pm\else\textpm\fi{}1/\sqrt{2}$. The easy axis of the crystal field anisotropy is the $c$ axis when the excited levels are populated at high temperatures and high magnetic fields. On the other hand, the magnetism at low temperatures and low magnetic fields, where only the ground doublet is populated, is described by an easy-plane anisotropy which may be treated as an $S=1/2$ system with an anisotropic $g$ factor, ${g}_{xy}=3.02$ and ${g}_{z}=1.14$. An orbital-dependent exchange interaction is also discussed to explain the temperature dependence of the magnetic susceptibility based on this level scheme.

Dielectric effects, crystal field, and shape anisotropy tuning of the exciton fine structure of halide perovskite nanocrystals

We present a theoretical study of the excitonic band edge states applied to the more commonly studied inorganic perovskite nanocrystals: ${\mathrm{CsPbBr}}_{3}$. We highlight the key role played by the electron-hole exchange interaction, including long-range and short range terms, in the positioning and splitting of dark and bright exciton sublevels, and discuss the influence of dielectric confinement, crystal field and shape anisotropy effects on the excitonic fine structure. The electron-hole exchange interaction splits the four excitonic states into three bright excitonic states at higher energy and a singlet dark state at lower energy. We find that, whatever the crystal phase, the bright-dark splitting is weakly sensitive to shape anisotropy. However, a strong enhancement, of about 50%, is obtained at the maximum of the dielectric contrast. For two crystalline symmetries, we particularly analyze how the bright exciton triplet energies vary, taking into account the states polarizations and considering the directions along which shape elongation/contraction applies. The main effect of the dielectric contrast is to increase significantly the exciton energies, for all the configurations. For a cubic crystal---${\mathrm{O}}_{h}$ symmetry---the bright exciton triplet degeneracy can be partially or fully lifted with anisotropic shape along one or two directions, respectively. For a tetragonal crystal---${\mathrm{D}}_{4h}$ symmetry---the partial triplet degeneracy can be completely lifted by a single distortion from the cubic shape along a direction perpendicular to the tetragonal axis but a partial degeneracy is maintained for small distortions along the tetragonal axis. The amplitude of bright exciton splittings are basically driven by the shape anisotropy and is almost insensitive to the dielectric contrast. On the basis of this model, we discuss recent results on ${\mathrm{CsPbBr}}_{3}$ nanocrystals photoluminescence.

Origin and dynamics of umbrella states in rare-earth iron garnets

Rare-earth iron garnets R3Fe5O12 are fascinating insulators with very diverse magnetic phases. Their strong potential in spintronic devices has encouraged a renewal of interest in the study of their low temperature spin structures and spin wave dynamics. A striking feature of rare-earth garnets with R-ions exhibiting strong crystal-field effects like Tb-, Dy-, Ho-, Er-, Tm- and Yb-ions is the observation of low-temperature non-collinear magnetic structures featuring “umbrella-like” arrangements of the rare-earth magnetic moments. In this study, we demonstrate that such umbrella magnetic states are naturally emerging from the crystal-field anisotropies of the rare-earth ions. By means of a general model endowed with only the necessary elements from the crystal structure, we show how umbrella-like spin structures can take place and calculate the canting-angle as a result of the competition between the exchange-interaction of the rare-earth and the iron ions as well as the crystal-field anisotropy. Our results are compared to experimental data, and a study of the polarised spin wave dynamics is presented. Our study improves the understanding of umbrella-like spin structures and paves the way for more complex spin wave calculations in rare-earth iron garnets with non-collinear magnetic phases.

Multiqudit interactions in molecular spins

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

Magnetic hard-direction ordering in anisotropic Kondo systems

We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions that are not favored by the crystal-field anisotropy. Using a renormalization-group (RG) analysis of single-impurity Kondo models with single-ion anisotropy, we demonstrate that strong fluctuations above the Kondo temperature drive a moment reorientation over a wide range of parameters, e.g., for different spin values $S$ and number of Kondo channels $N$. In tetragonal systems, this can happen for both easy-plane or easy-axis anisotropy. The characteristic crossing of magnetic susceptibilities is not an artifact of the weak-coupling RG treatment but can be reproduced in brute-force perturbation theory. Employing the numerical renormalization group (NRG), we show that for an underscreened moment $(S=1,$ $N=1)$ with easy-plane anisotropy, a crossing of magnetic susceptibilities can also occur in the strong-coupling regime (below the Kondo temperature). This suggests that collective magnetic ordering of such underscreened moments would develop along the magnetic hard axis.

Competition between helimagnetic and ferroquadrupolar ordering in a monoaxial chiral magnetDyNi3Ga9studied by resonant x-ray diffraction

Successive phase transitions in a rare-earth monoaxial chiral magnet ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ have been investigated by resonant x-ray diffraction. Magnetic dipole and electric quadrupole degrees of freedom arising from the large angular moment of $J=15/2$, in combination with the symmetric and antisymmetric exchange interactions and the crystal field anisotropy, give rise to competing ordered phases. We show that the antiferromagnetically coupled Dy moments in the $ab$ plane form an incommensurate helimagnetic order with $\mathbit{q}\ensuremath{\sim}(0,0,0.43)$ just below ${T}_{\text{N}}=10$ K, which further exhibits successive first-order transitions to the commensurate helimagnetic order with $\mathbit{q}=(0,0,0.5)$ at ${T}_{\text{N}}^{\ensuremath{'}}=9.0$ K, and to the canted antiferromagnetic order with $\mathbit{q}=(0,0,0)$ at ${T}_{\text{N}}^{\ensuremath{''}}=8.5$ K, both with large coexistence regions. The relation of the magnetic helicity and the crystal chirality in ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ is also uniquely determined. Splitting of the (6,0,0) Bragg peak is observed below ${T}_{\text{N}}^{\ensuremath{''}}$, reflecting the lattice distortion due to the ferroquadrupole order. In the canted antiferromagnetic phase, a spin-flop transition takes place at 5 K when the temperature is swept in a weak magnetic field. We discuss these transitions from the viewpoint of the competing energies described above.

A neutron diffraction investigation of high valent doped barium ferrite with wideband tunable microwave absorption

The barium ferrite BaTixFe12−xO19 (x = 0.2, 0.4, 0.6, 0.8) (BFTO-x) ceramics doped by Ti4+ were synthesized by a modified sol—gel method. The crystal structure and magnetic structure of the samples were determined by neutron diffraction, and confirm that the BFTO-x ceramics were high quality single phase with sheet microstructure. With x increasing from 0.2 to 0.8, the saturation magnetization (Ms) decreases gradually but the change trend of coercivity (Hc) is complex under the synergy of the changed grain size and the magnetic crystal anisotropy field. Relying on the high valence of Ti4+, double resonance peaks are obtained in the curves of the imaginary part of magnetic conductivity (μ″) and the resonance peaks could move toward the low frequency with the increase of x, which facilitate the samples perform an excellent wideband modulation microwave absorption property. In the x = 0.2 sample, the maximum reflection loss (RL) can reach −44.9 dB at the thickness of only 1.8 mm, and the bandwidth could reach 5.28 GHz at 2 mm when RL is less than −10 dB. All the BFTO-x ceramics show excellent frequency modulation ability varying from 18 (x = 0.8) to 4 GHz (x = 0.4), which covers 81% of the investigated frequency in microwave absorption field. This work not only implements the tunable of electromagnetic parameters but also broadens the application of high-performance microwave absorption devices.

Highly Polarized Upconversion Emissions from Lanthanide-Doped LiYF4 Crystals as Spatial Orientation Indicators.

Polarized emission, an inherent characteristic that correlated with structure and morphology, is very sensitive to orientation. For the upconversion (UC) emission of lanthanides, the mechanism of polarization is rarely discussed, and the highly polarized UC emissions are poorly developed. Herein, with the benefit of the strong anisotropic crystal field, well-resolved emissions from lanthanide-doped LiYF4 crystals were studied, and highly polarized UC emissions from Er3+ and Ho3+ were investigated. With multiple sub-energy level transitions, the UC emissions are classified into two sets, with transition dipoles being either parallel or perpendicular to the c-axis of the LiYF4 crystal. An optical three-dimensional orientation sensor was further investigated, in which the in-plane angle is referenced from the orientation of the transition dipoles. In contrast, the out-of-plane angle can be deduced from the change in the degree of polarization. This research deepens our understanding of the polarized photoluminescence, and it opens up an avenue toward unique UC orientation sensors.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound.

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Lumps and rogue waves on the periodic backgrounds for a (2 + 1)-dimensional nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain

Spin excitations for the magnetic materials are used in the nonlinear signal processing devices and microwave communication systems. Under consideration in this paper is a [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which describes the spin dynamics for a Heisenberg ferromagnetic spin chain. Through a reduced transformation, we convert such an equation into the [Formula: see text]-dimensional focusing NLS equation. Via the rogue-periodic solutions associated with two types of the Lie symmetry transformations of the NLS equation, we present the lump- and rogue-periodic solutions. Besides, the lump and mixed lump-soliton solutions are deduced. We graphically investigate the lump- and rogue-periodic waves and find that the amplitudes of the lumps and rogue waves are negatively related to [Formula: see text] and [Formula: see text]; the distances between two valleys of the lumps and widths of the rogue waves are affected by [Formula: see text] and [Formula: see text], where [Formula: see text] is the uniaxial crystal field anisotropy parameter, [Formula: see text] and [Formula: see text] are related to the bilinear exchange interaction, [Formula: see text] is the lattice parameter.

Experimental and theoretical analysis of magnetocaloric behavior ofDy1−xErxNi2intermetallics(x=0.25,0.5,0.75)and their composites for low-temperature refrigerators performing an Ericsson cycle

In the present work, the structural, magnetic, and thermodynamic properties of ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$ $(x=0.25,\phantom{\rule{0.16em}{0ex}}0.5,\phantom{\rule{0.16em}{0ex}}0.75)$ Laves-phase intermetallics, being continuous solid solutions in the ${\mathrm{DyNi}}_{2}\text{\ensuremath{-}}{\mathrm{ErNi}}_{2}$ system, synthesized by arc melting, are experimentally studied and analyzed in accordance with mutual substitution within the rare-earth sublattice. The existence of Laves-phase superstructure (space group $F\overline{4}3m$) in the substituted ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$ compounds was found by x-ray diffraction analysis. Low-temperature magnetic studies showed the ferromagnetic behavior of the compounds; their Curie temperatures correlate with the erbium content; namely, they decrease from 16.8 K for ${\mathrm{Dy}}_{0.75}{\mathrm{Er}}_{0.25}{\mathrm{Ni}}_{2}$ to 10.0 K for ${\mathrm{Dy}}_{0.25}{\mathrm{Er}}_{0.75}{\mathrm{Ni}}_{2}$. Heat capacity measurements performed in magnetic fields of 1 and 2 T allowed us to estimate the isothermal magnetic entropy and adiabatic temperature changes for ${\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Er}}_{x}{\mathrm{Ni}}_{2}$. Independently, a theoretical analysis was performed for a polycrystalline sample in the frame of a model Hamiltonian taking into account the Zeeman exchange interaction and crystal electric field anisotropy and was expanded to experimental results. Composites with optimum proportions of the individual ${\mathrm{Dy}}_{0.75}{\mathrm{Er}}_{0.25}{\mathrm{Ni}}_{2}$, ${\mathrm{Dy}}_{0.5}{\mathrm{Er}}_{0.5}{\mathrm{Ni}}_{2}$, and ${\mathrm{Dy}}_{0.25}{\mathrm{Er}}_{0.75}{\mathrm{Ni}}_{2}$ components were theoretically determined. The results indicate that the proposed composites are good candidates to be used as the refrigerant material in a magnetic refrigerator performing an Ericsson cycle at low temperatures. The relative cooling power RCP, refrigerant capacity RC, temperature averaged entropy change TEC, and the changes of emitted or absorbed quantity of heat \ensuremath{\Delta}Q were calculated for investigated samples. Direct measurements of the adiabatic temperature change in the vicinity of the magnetic transition temperature were carried out in magnetic fields up to 14 T. The regularities found are discussed in terms of Landau's theory of second-order magnetic phase transitions.

A new theoretical approach to the strain dependence of magnetic crystal-field anisotropy

We report on the derivation of analytical equations for ab-initio calculations of the strain dependence of crystal-electric-field (CEF) parameters for arbitrary deformations. The calculation is based on the fundamental assumption that the charge distribution deforms in the same way as the crystal. Based on this deformed-charge model, simple formulas for the practical usage are given for various site symmetries of cubic lattices under uniform strain. These formulas can be used to predict the change of the magnetic crystal-field anisotropy under strain, which is important for the design of magnetic materials and devices. As an example for the power of the method, we present a calculation of the magnetic contribution to the thermal expansion in some rare-earth-based materials.

An entropic simulational study of the spin-1 Baxter–Wu model in a crystal field

We investigate the critical behavior of the two-dimensional spin-1 Baxter–Wu model in a crystal field using entropic sampling simulations, based on the Wang–Landau method, with the joint density of states. We obtain the temperature–crystal field phase diagram, which includes a tetracritical line ending at a pentacritical point. A finite-size scaling analysis of the maximum of the specific heat, while changing the crystal field anisotropy, is used to obtain a precise location of the pentacritical point. Our results give the critical temperature and crystal field as Tpc=0.98030(10) and Dpc=1.68288(62). We also detect that at the first-order region of the phase diagram, the specific heat exhibits a double peak structure as in the Schottky-like anomaly, which is associated with an order–disorder transition.