Equilibrium Spin Configurations Research Articles

Magnetization curling in a disk with a uniaxial anisotropy

To investigate the behavior of the magnetization in a single-domain disk with a uniaxial magnetocrystalline anisotropy, the assumption is made that the magnetization changes its direction by the magnetization curling mode. In this mode, the deviation θ of the spin from the z axis at (r,φ,z) in the cylindrical coordinate is given by θ=a0+a1(r/R)+a2(r/R)2+a3(r/R)3, where R is the radius of the disk and a0–a3 are coefficients. An equilibrium spin configuration is obtained for a given applied field H by finding a set of values of a0–a3 that minimize the magnetic energy of the disk. Carrying out this procedure for various H, a hysteresis loop and the coercive force are obtained. It is found that the configuration in which the spins deviate from the z axis can be stable and, therefore, the hysteresis loop is not rectangular, even though an applied field is along the z axis. The deviation is larger for the spins near the lateral surface of the disk, and the spins near the center do not incline easily. Moreover, for a large magnetocrystalline anisotropy and a large diameter, the magnetization changes its direction upward and downward alternately with r. The nucleation field calculated with the present model agrees well with that of the curling mode in an oblate spheroid.

Cluster Heat Bath Method on a Quasi-One-Dimensional Ising Model

We have proposed a cluster heat bath(CHB) method of a quasi-one dimensional Ising model and demonstrated that it reproduces the exact results of the two dimensional Ising model with axially anisotropic exchange interactions. The point of the method is to select one of the equilibrium spin configurations of each of the chains which are subjected by effective fields of surrounding spins. Thus the chains are always in their equilibrium state during the simulation and the $d$ dimensional model effectively becomes as a $d-1$ dimensional model of fictitious spins with their freedom of $2^N$ and the simulation time is drastically reduced, where $N$ is the number of the spins on the chain.

Magnetic phases of the two-dimensional Hubbard model at low doping.

We study the equilibrium spin configuration of the 2D Hubbard model at low doping, when a long-range magnetic order is still present. We use the spin-density-wave formalism and examine the two suggested candidates for a ground state: the planar spiral $(\pi,Q)$ and $(Q,Q)$ states. In a mean-field theory, each of these two states is a ground state in a certain range of parameters. We however show that both states have negative bosonic modes in a transverse channel which implies that the spiral states are in fact unstable (the $(Q,Q)$ state, in addition, has a negative longitudinal stiffness). We searched for a ground state in a parameter range which on a mean-field level favored the $(\pi,Q)$ phase, and found that the equilibrium spin configuration is noncoplanar. These findings lead to a novel scenario of spin reorientation upon doping in Hubbard antiferromagnets.

Oblique-incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2.

Theoretical and experimental results are presented for high-resolution frequency scans of 45\ifmmode^\circ\else\textdegree\fi{} oblique-incidence far-infrared reflectivity spectra of ${\mathrm{FeF}}_{2}$ in the vicinity of the antiferromagnetic resonance frequency. The magnetic field is vertical and the plane of incidence horizontal. Calculations are presented and illustrated numerically for an arbitrary angle \ensuremath{\theta} between the crystal c axis and the magnetic field ${\mathit{H}}_{0}$. The main point of principle is that the equilibrium spin configuration and therefore the magnetic susceptibility depend on \ensuremath{\theta}. The reflectivity R is nonreciprocal, i.e., R(-${\mathit{H}}_{0}$)\ensuremath{\ne}R(${\mathit{H}}_{0}$). For \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} magnetic features are seen only in s polarization (E field vertical), but otherwise they are seen in both polarizations. Except for \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} weak s to p and p to s reflections are predicted. We discuss the instrumental developments required for the high resolution that is necessary for this spectroscopy. Experimental results for \ensuremath{\theta}=45\ifmmode^\circ\else\textdegree\fi{} are presented (\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} are in a previous publication). The whole range of spectra, including the s to p and p to s reflections, are accounted for with the same set of parameters as were used previously to fit the \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} results.

Spin-dynamics study of the classical anisotropic XY chain.

We have investigated the time-dependent behavior of the classical XY chain in a symmetry-breaking anisotropy field using an ultrafast spin-dynamics method in which we integrate the equation of motion with equilibrium spin configurations determined by Monte Carlo simulations. All three polarizations of the scattering function S(q,\ensuremath{\omega}) were determined for temperature ${\mathit{k}}_{\mathit{B}}$T=0.2J and fields varying from 0.1J to 0.6J. Substantial differences are found as compared with the isotropic ferromagnetic chain in a transverse magnetic field. The soliton contribution, single-spin-wave peaks, and both the sum and difference two-spin-wave contributions are separated. Half-widths and integrated intensities are extracted and compared with theoretical predictions based on mapping onto the sine-Gordon model.

Quasi-one-dimensional hexagonal antiferromagnets in a magnetic field

The equilibrium spin configurations and antiferromagnetic resonance spectra of quasi-one-dimensional 'easy-plane' antiferromagnets on a triangular lattice are calculated. It is shown that in contrast to a simple two-sublattice antiferromagnet the spin reorientation in a transverse magnetic field is accompanied by a magnetic phase transition in relatively small fields, attributed to spin flip of two magnetic sublattices in the basal plane.

Spin-Wave Analysis of the Antiferromagnetic Plane Rotator Model on the Triangular Lattice–Symmetry Breaking in a Magnetic Field

Lowest-order spin-wave analysis is applied to the antiferromagnetic plane rotator model on the triangular lattice in order to study the low-temperature properties in the presence of magnetic fields. Equilibrium spin configuration in the zero-temperature limit is calculated as a function of the magnetic field. It is found that the thermal-fluctuation effect reduces a continuous degeneracy of the ground state to a discrete one at non-zero temperatures.

Dynamics of the fcc Heisenberg antiferromagnet with nearest-neighbor interactions. II. Dilute arrays

We report the results of a study of the dynamics of the site-dilute face-centered-cubic Heisenberg antiferromagnet with nearest-neighbor interactions. Numerical techniques are used to obtain information about the effect of dilution on the distributions of local fields in the various equilibrium spin configurations. Spin excitations are studied within the framework of a linearized magnon theory. The density of magnon modes is determined for 50% dilution and compared with the corresponding results for the fully occupied lattice and an antiferromagnet with type-III long-range order. The equations of motion for the spins are integrated to obtain the dynamic structure factor. The peaks in the dynamic structure factor indicate the existence of damped spin waves which mirror the short-range-order characteristic of the fully occupied lattice. We find no evidence for weakly damped, long-wavelength hydrodynamic spin waves. The relation of the work to experimental studies of the dilute semiconductors ${\mathrm{Cd}}_{1\ensuremath{-}c}{\mathrm{Mn}}_{c}\mathrm{Te}$, ${\mathrm{Hg}}_{1\ensuremath{-}c}{\mathrm{Mn}}_{c}\mathrm{Te}$, and ${\mathrm{Zn}}_{1\ensuremath{-}c}{\mathrm{Mn}}_{c}\mathrm{Te}$ is commented on.

Magnetostriction of antiferromagnetic iron and chromium garnet single crystals

The static magnetostriction of antiferromagnetic garnet single crystals Ca3Fe2Ge3O12 and Ca3Cr2Ge3O12 is measured at 4.2°K. It is shown that the angular dependences of the magnetostriction are characterized by equilibrium spin configurations occurring in cubic antiferromagnets in spin-flop fields. The magnetostriction fields H1 and H2, whose magnitudes confirm the existence of a significant magnetoelastic gap in the AFMR spectrum of the iron and chromium garnets investigated, are computed on the basis of the values obtained for λ100 and λ111.

Exciton Model of Spin Excitations in Magnetic Dielectrics. Biaxial Antiferrodielectrics with One‐Ion Anisotropy

AbstractA generalized exciton model is used to investigate the acoustic and optical spin excitations of magnetic dielectrics in a magnetic field. Equations which determine the equilibrium spin configuration and which are valid for an arbitrary spin magnitude are derived. The frequencies and the polarization properties of the antiferromagnetic resonance (AFMR) for biaxial antiferrodielectrics with one‐ion anisotropy are considered in detail.

Equilibrium Spin Configuration and Antiferromagnetic Resonance of KMnF3 at the Low Temperature Phase

The antiferromagnetic resonance of KMnF 3 at helium temperature has been studied. The equilibrium orientation of magnetic sublattices and the resonance frequencies are calculated from the free energy expression which involves antisymmetric exchange energy and orthorhombic and cubic anisotropy energies. The Dzyaloshinsky-Moriya vector is taken along the b -axis ([\bar110] in the pseudocubic cell). The experimental results are in good agreement with the theory. In the absence of the applied field, the sublattice magnetizations are in the b -plane, making 43.4° with the c -axis ([001]).

Anisotropic Light Absorption in the Crystalline RbMnF3 in the Frequency Region of the 6A1g(6S) → 4E1g(4G) Transition in the Magnetic Ion Mn2+

AbstractA theory of one‐particle collective excitations of the cubic antiferrodielectric RbMnF3 in an external magneticfield is developed for the doubly degenerate 4E1g(4G) state of the magnetic ion Mn2+. The crystal anisotropy is taken into account. It is shown that the change in the equilibrium spin configuration in a magnetic field (which breaks the magnetic symmetry of a crystal) leads to the spin‐orbit splitting of the degenerate 4 Elg(4G) level and to the further splitting of the obtained levels into the Davydov components. The formulas for the above splittings and for the intensities of optical transitions are obtainedfor different directions of a magnetic field. The results of theoretical calculations are used to explain experimental data.

Equilibrium spin configuration of RbMnF

physica status solidi (b)Volume 50, Issue 1 p. K27-K30 Short Note Equilibrium spin configuration of RbMnF E. G. Petrov, E. G. Petrov Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, KievSearch for more papers by this authorV. N. Kharkyanen, V. N. Kharkyanen Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, KievSearch for more papers by this author E. G. Petrov, E. G. Petrov Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, KievSearch for more papers by this authorV. N. Kharkyanen, V. N. Kharkyanen Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, KievSearch for more papers by this author First published: 1 March 1972 https://doi.org/10.1002/pssb.2220500156Citations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume50, Issue11 March 1972Pages K27-K30 RelatedInformation

Equilibrium Spin Configuration and Resonance Behavior of RbMnF3

The equilibrium orientations of the magnetic sublattices of the cubic antiferromagnet RbMn${\mathrm{F}}_{3}$ have been studied. By assuming spatially uniform magnetization and restricting the applied steady magnetic field to lie in a {110} plane, the problem is considerably simplified. The analysis enables the equilibrium spin configurations for the important cases of the magnetizing field applied along any of the three principal crystal axes to be predicted. Each case has more than one solution. The theory predicts that abrupt spin flopping from one equilibrium state to another should occur under certain conditions. An antiferromagnetic-resonance theory is presented which is applicable over a wide range of field and embraces the low- and high-field resonance theories previously reported as restricted examples. Observations of the resonance spectrum at $X$-band frequencies for the applied field range 0 to 12 kOe are presented. The measurements provide excellent verification of the resonance theory and confirm the validity of the equilibrium analysis. The best fit between theory and experiment was obtained by assuming values of the anisotropy field significantly different from the previously published value. Abrupt spin flopping was not observed. The resonance data indicate that the magnetization can switch between equilibrium directions gradually over a range of field and at much lower field strengths than the theoretical flopping field.

Spin-Wave Analysis of the Sublattice Magnetization Behavior of Antiferromagnetic and Ferromagnetic CrCl3

The temperature and magnetic-field dependences of the sublattice magnetization in the hexagonal layertype compound Cr${\mathrm{Cl}}_{3}$ (${T}_{N}=16.8\ifmmode^\circ\else\textdegree\fi{}$K) have been deduced from the $^{53}\mathrm{Cr}$ nuclear magnetic resonance (NMR) for $0.4\ensuremath{\le}T\ensuremath{\le}8.1\ifmmode^\circ\else\textdegree\fi{}$K and $0\ensuremath{\le}H\ensuremath{\le}10$ kOe. The observed zero-field data can be accounted for over the whole temperature range by a renormalized spin-wave model based on isotropic ferromagnetic (${J}_{T}$) intralayer and antiferromagnetic (${J}_{L}$) interlayer exchange interactions in the presence of a weak effective anisotropy field (${H}_{A}$). Appropriate renormalized spin-wave dispersion relations are given for the four-sublattice antiferromagnetic (weak-field) and two-sublattice ferromagnetic (strong-field) equilibrium spin configurations. The validity of the two-dimensional approximation to these states is examined in detail for ${k}_{B}T>2|{J}_{L}|{z}_{L}S$ and $|{J}_{L}|\ensuremath{\ll}{J}_{T}$. It is shown that under these conditions the sublattice magnetizations for ${J}_{L}<0$ and ${J}_{L}>0$ are identical. The three-dimensional zero-field spin-wave fit gives $\frac{{J}_{T}}{{k}_{B}}=5.25\ifmmode^\circ\else\textdegree\fi{}$K, ${H}_{A}(0)=650$ Oe and a 0\ifmmode^\circ\else\textdegree\fi{}K, zero-field $^{53}\mathrm{Cr}$ frequency $\ensuremath{\nu}(0)=63.318$ Mc/sec. Parallel magnetic susceptibilities calculated with these parameters in the range $0.4<T\ensuremath{\le}8.1\ifmmode^\circ\else\textdegree\fi{}$K are in quantitative agreement with experimental values based on measured splittings of the $^{53}\mathrm{Cr}$ NMR in weak fields ($H\ensuremath{\le}100$ Oe). The interlayer constant, $\frac{{J}_{L}}{{k}_{B}}=\ensuremath{-}0.018\ifmmode^\circ\else\textdegree\fi{}$K, used in the spin-wave calculations was obtained from single-crystal bulk magnetization measurements (${\ensuremath{\chi}}_{\ensuremath{\perp}}=9.9$ emu/mole for $T\ensuremath{\le}4\ifmmode^\circ\else\textdegree\fi{}$K), corrected for demagnetizing effects. These measurements show that the net anisotropy in the ferromagnetic state (i.e., $H\ensuremath{\ge}1.68$ kOe) is zero, presumably because of a cancellation of dipolar and single-ion contributions. The sublattice magnetization behavior in the ferromagnetic state appears to be strongly influenced by long-range dipolar interactions, as evidenced by significantly lower values of $\frac{M(T, H)}{M(0)}$ for $\mathrm{M}\ensuremath{\parallel}c$ than for $\mathrm{M}\ensuremath{\perp}c$.