Flat Band Phase Transition in Gadolinium Gallium Garnet

钆石榴石，Gd 3Ga 5 O 12（GGG），是一种受抑反铁磁体，基态不显示长程有序。Gd位置上的局部（S = 7/2）矩之间的相互作用被认为是最近邻交换和长程偶极相互作用的良好描述[1]。高场相（B>1.8T）表现出显著的性质：作为最低的自旋波激发，它具有几乎无色散的带，对应于10格点环上的激发（它们在无偶极相互作用的极限下是完全无色散的）。磁场通过塞曼能量耦合到这些自旋波激发，因此对这些（弱相互作用）玻色子激发起化学势的作用。当这个化学势接近零时，基态的确切性质尚不清楚，但将由激发之间的相互作用和来自偶极相互作用的小色散之间的相互作用决定。该项目完全符合EPSRC对“磁性基础物理学和磁性材料”的研究。它将研究在（B 1.8T）以上的磁场下从纯铁磁相到部分反铁磁相的转变。跃迁只能由两种效应控制--偶极相互作用对自旋波色散的影响和玻色子自旋波之间的相互作用（自旋翻转可以用玻色子表示，但具有排斥相互作用）。实验给出了一个明确的目标，理论解释，即出现了一个无公度的弹性磁布拉格峰。这项工作将从计算自旋波能量开始，考虑到长程偶极项和随之而来的总自旋不守恒。还有其他石榴石，例如涉及Al代替Ga或过渡金属离子代替Gd。长期目标是在理解石榴石和其他开放磁性结构的挫折方面取得进展。目的：理解GGG的相位作为磁场的函数。目标：-模拟铁磁到反铁磁转变上下的自旋波激发;-计算中子散射（准弹性和非弹性）的材料;-为了验证涉及软化的一个完整的激发带的过渡的性质。方法：自旋结构及其激发的分析和数值模拟的结合。我们将使用自旋波的经典模型和量子模型。[1]N.d'Ambrumenil，O.A.Petrenko，H.Mutka，and P.P.Deen，Phys. Rev. Lett.，114：227203，2015.

Gadolinium garnet, Gd3Ga5O12 (GGG), is a frustrated antiferromagnet with a ground state which does not show long-range order. The interaction between local (S = 7/2) moments on the Gd sites is thought to be well described by a nearest neighbour exchange together with the long-range dipole interaction [1]. The high field phase (B>1.8T) shows remarkable properties: It has, as lowest lying spin wave excitations, almost dipersionless bands corresponding to excitations localized on 10 site rings (they are completely dispersionless in the limit of no dipole interaction). A magnetic field couples to these spin wave excitations via the Zeeman energy and hence acts like a chemical potential for these (weakly interacting) bosonic exci-tations. When this chemical potential approaches zero, the exact nature of the ground-state is unclear but will be determined by the interplay between the interactions between the excitations and the small dispersion coming from the dipole interaction. The project sits well within EPSRC's research into the `fundamental physics of magnetism and into magnetic materials'. It will study the transition from pure ferromagnet at fields above (B 1.8T) to partly antiferromagnetic phase. The transition can only be controlled by two effects-the effect of the dipole interaction on the spin wave dispersion and the interaction between bosonic spin waves (spin flips can be represented as bosons but with a repulsive interaction). Experiments gives one clear target for theory to explain, namely the appearance of an incommensurate elastic magnetic Bragg peak. The work would start by computing the spin wave energies taking account of the long-range dipole terms and the consequent non-conservation of the total spin. There are other garnets, involving for example Al instead of Ga or transition metal ions instead of Gd. A long-term aim would be to make progress on the understanding of frustration in garnets and other open magnetic structures. Aim: To understand the phases of GGG as a function magnetic field.Objectives: - To model the spin wave excitations above and below the transition from ferromagnetic to antiferromagnet;- To compute the neutron scattering (quasi-elastic and inelastic) of the material;- To characterise the nature of a transition involving the softening of a complete band of excitations.Methodology: A combination of analytic and numerical modelling of the spin structures and their excitations. We will use both classical and quantum models of spin waves.[1] N.d'Ambrumenil, O.A.Petrenko, H.Mutka, andP.P.Deen, Phys.Rev.Lett.,114:227203, 2015.