Anisotropic antiferromagnets in an external magnetic field show a rich variety of different ground states meeting in transition lines and multicritical points. We study the dependence of the ground states of these systems in the three dimensional space on physical parameters as exchange, single ion and cubic anisotropy.
One identifies four different ground states: the paramagnetic (PM), the antiferromagnetic (AF), the spin flop (SF) and the biconical (BC) ground state. In the case of absence of a cubic anisotropy the transition lines separating the different ground states can be calculated analytically, otherwise they have to be calculated numerically. We also considered the behavior of the staggered magnetization which characterizes the different ground states. From its behavior the order of the transition from one state to the other is determined. But also the order of the transition changes along the transition lines when including the cubic anisotropy, especially at the reeentrant region where a transition from SF to BC and back to SF by increasing the external field $H$ occurs. Multicritical points are founded which are assumed to be tricritical or critical endpoints. The results obtained may be relevant for other systems since the antiferromagnetic model can be mapped to a lattice gas model where the biconical ground state is interpreted as supersolid phase. Recent renormalization group calculations show that such a phase would indicate the existence of a tetracritical point.
Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy
本文研究了具有立方各向异性的二维N分量Landau-Ginzburg哈密顿量。计算并分析了重整化群函数到四个环的定维微扰展开式。讨论了这些模型与N色Ashkin-Teller模型、离散立方模型、四阶各向异性平面模型以及吸附单分子膜结构相变的关系。对于N=2（XY模型，具有立方各向异性），我们的结果与存在一条连接Ising和O（2）不动点的不动点线是相容的.沿着这条线，指数$η$具有常数值1/4，而指数$ν$以连续和单调的方式从1到$\infty$（从Ising到O（2））。对于\geq 3，我们发现一个三次不动点的区域$u, v \geq 0$，这是边际稳定或不稳定，根据扰动的符号。对于N=3的物理相关的情况下，我们发现指数$η=0.17(8)$和$ν=1.3(3)$在立方过渡。
We present a dynamical mean-field study of antiferromagnetic magnons in one-, two- and three-orbital Hubbard model of square and bcc cubic lattice at intermediate coupling strength. Weinvestigate the effect of anisotropy introduced by an external magnetic field or single-ion anisotropy.For the latter we tune continuously between the easy-axis and easy-plane models. We also analyzea model with spin-orbit coupling in cubic site-symmetry setting. The ordered states as well as themagnetic excitations are sensitive to even a small breaking ofSU(2)symmetry of the model andfollow the expectations of …
We study a frustrated antiferromagnetic Heisenberg model on a triangular lattice with the Dzyaloshinskii-Moriya interaction (DMI) in the presence of an external magnetic field and a single-ion anisotropy. Phase diagrams in the temperature-field plane for both easy-axis and easy-plane anisotropy of a varying strength are constructed in the regimes of a moderate and strong DMI by parallel tempering Monte Carlo simulations. For the considered range of parameters the phase diagrams featuring up to four ordered phases are identified. A skyrmion lattice (SkX) phase is found to be stabilized within s…
Phase diagram of a three-dimensional antiferromagnet with random magnetic anisotropy
具有随机磁各向异性（RMA）的三维（3D）反铁磁体的实验研究至今没有随机的单离子各向异性，而是有竞争的二维和三维交换相互作用，可以掩盖真实的影响RMA。利用磁测量和中子散射测量，推导出了Fe $_{x}$ Ni $_{1-x}$ F $_{2}$外延薄膜的磁相图，并利用平均场论进行了分析。确定了单轴、倾斜和易平面各向异性区域。发现了一个RMA诱导的玻璃区，在那里发生了类似格里菲斯的长程自旋序击穿。
The six-loop expansions of the renormalization-group functions of $φ^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4 - \varepsilon$ dimensions. The $\varepsilon$ expansions for the cubic fixed point coordinates, critical exponents corresponding to the cubic universality class and marginal order parameter dimensionality $n_c$ separating different regimes of critical behavior are presented. Since the $\varepsilon$ expansions are divergent numerical estimates of the quantities of interest are obtained employing proper resummation technique…
Interplay of anisotropy and frustration: triple transitions in a triangular-lattice antiferromagnet
本文研究了三角晶格上单离子易轴各向异性的经典海森堡反铁磁体。构造了外磁场中的平均场相图。通过零场蒙特卡罗模拟，发现了三个有限温度Berezinskiii-Kosterlitz-无相变。两个上部的过渡与离散的${\mathbb Z}_{6}$对称群的破缺有关，而最低的过渡与横向分量的准长程有序有关。第一和第二转变之间的中间共线相位是由J. V. José { \it et al}预测的滑动相位。[Phys. Rev. B { \bf 16}，1217（1977）]。
Analytical solution has been found for the second-order effective anisotropy of magnetic nanoparticles of a cubic shape due to the surface anisotropy (SA) of the Néel type. Similarly to the spherical particles, for the simple cubic lattice the grand-diagonal directions $\left(\pm1,\pm1,\pm1\right)$ are favored by the effective cubic anisotropy but the effect is twice as strong. Uniaxial core anisotropy and applied magnetic field cause screening of perturbations from the surface at the distance of the domain-wall width and reduce the effect of SA near the energy minima. However, screening disap…
Phase diagrams of a classical two-dimensional Heisenberg antiferromagnet with single-ion anisotropy
二维各向异性Heisenberg模型的经典变形再现了La_5Ca_9Cu_24O_41的非弹性中子散射实验[M. Matsuda等人，Phys.Rev. B 68，060406（R）（2003）]主要使用蒙特卡罗技术进行分析。确定了具有平行和垂直于各向异性相互作用的易磁化轴的外场的相图，包括反铁磁相和自旋翻转相。发现移动的无自旋缺陷或空穴形成条纹，这些条纹在相变时聚束、散束和破裂。平行场可以导致自旋翻转相。
