It has been proposed recently \cite{son} that excitations in Spin Ice can be of the form of magnetic monopoles that does not obey the Dirac Quantization Condition. It is also well known \cite{rj} that the above scenario leads to non-associativity among translation generators. It will be interesting to see how the monopole picture in Spin Ice survives in the light of the latter observation.
While there is compelling evidence for the existence of magnetic monopoles in spin ice, the direct observation of a point-like source of magnetic field in these systems remains an open challenge. One promising approach is electron holography, which combines atomic-scale resolution with extreme sensitivity to magnetic vector potentials, through the Aharonov-Bohm effect. Here we explore what holography can teach us about magnetic monopoles in spin ice, through experiments on artificial spin ice, and numerical simulations of pyrochlore spin ice. In the case of artificial spin ice, we show that ho…
Thermal Conductivity and Specific Heat of the Spin-Ice Compound Dy$_2$Ti$_2$O$_7$: Experimental Evidence for Monopole Heat Transport
自旋冰化合物Dy $_2$ Ti $_2$ O $_7$中的基元激发可以描述为在由磁性Dy离子形成的烧绿石晶格内独立传播的磁单极子。我们研究了B的热导率κ（B）与磁场的关系||[001]并观察到源自磁激发的磁热传输的明显证据。磁贡献κ mag与磁场有很强的相关性，并与磁化强度M（B）有关。由κ mag与磁比热之比得到的扩散系数在低于1K时大大增强，表明自旋冰态的自旋激发具有高的迁移率.
Evidence for the Confinement of Magnetic Monopoles in Quantum Spin Ice
磁单极子是由狄拉克弦连接起来的基本粒子，它们的行为就像无限薄的弦。尽管经过几十年的研究，自由磁单极子和它们的狄拉克弦仍然无法在实验中被探测到，尽管有大量证据表明自旋冰材料中存在非受限的磁单极子准粒子。在这里，我们报告的检测层次的不等间距磁激发\emph{via}高分辨率非弹性中子光谱测量的量子自旋冰候选人Pr $_{2}$ Sn $_{2}$ O $_{7}$。这些激发可以用一个简单的模型来描述，该模型是由一个有效张力为0.642（8）K~ $\cdot$/$^{-1}$（1.65 K）的线性势所束缚的电子对。线性势模型的成功表明，这些低能磁激发是量子自旋冰候选体Pr $_{2}$ Sn $_{2}$ O $_{7}$中磁束缚准粒子的直接光谱证据.
Extremely slow non-equilibrium monopole dynamics in classical spin ice
本文报道了用高分辨磁致伸缩测量方法探测到的经典自旋冰Dy $_2$ Ti $_2$ O $_7$中的非平衡磁致伸缩动力学。显著的晶格变化发生在过渡期从戈薇冰饱和冰相，可见的纵向和横向磁致伸缩。在低于0.6 K的温度下的滞后开放表明一个一阶跃之间的戈薇和饱和状态。观察到由磁场变化触发的极慢的晶格弛豫。这些晶格弛豫效应来自于非平衡态的电子形成或湮灭过程。从我们的实验中提取的弛豫时间与理论预测的$10{^4}$ s量级的衰减常数在0.3 K时是很好的一致。
Dipolar spin ice states with fast monopole hopping rate in CdEr$_2$X$_4$ (X = Se, S)
自旋冰中的激发表现为磁单极子，它们的数量和迁移率控制着自旋冰在低温下的动力学。CdEr $_2$ Se $_4$被报道具有自旋冰的鲍林熵特征，但其动力学比规范自旋冰Dy $_2$ Ti $_2$ O $_7$快三个数量级。在这封信中，我们使用扩散中子散射表明，这两个CdEr $_2$ Se $_4$和CdEr $_2$ S $_4$支持偶极自旋冰态-主相的库仑气体的新兴磁单极子。这些库仑气体具有与Dy $_2$ Ti $_2$ O $_7$类似的参数，即稀释且不相关，因此无法单独通过更大的单极群提供三阶更快的动力学。我们用交流阻抗法和中子自旋回波谱研究了Er离子的晶体动力学，并用中子非弹性散射验证了Er $^{3+}$离子的晶体电场哈密顿量。利用库仑气体和晶体电场参数对CdEr的双光子跃迁速率进行了定量计算，结果表明CdEr $_2$ X $_4$（X = Se，S）中的快动力学主要是由于快得多的双光子跃迁。我们的工作表明，CdEr $_2$ X $_4$提供了研究替代自旋冰基态和动力学的可能性，平衡可能在比稀土烧绿石的例子低得多的温度。
Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
虽然磁场的来源--磁单极子--到目前为止被证明是难以捉摸的基本粒子，但最近在凝聚态物理中已经提出了几种类似单极子的新兴准粒子的方案。一个特别简单的命题涉及到在高度受挫的烧绿石晶格上旋转冰。自旋冰态被认为可以用类似螺线管的偶极子网络来描述--经典的、可观测的狄拉克弦。在这些管子结束的地方，产生的缺陷看起来像一个磁性磁铁。我们证明，通过漫中子散射，存在这样的字符串在自旋冰Dy 2 Ti 2 O 7。这是通过施加一个破磁磁场来实现的，我们可以用它来操纵弦的密度和方向。反过来，热容量由磁单极子通过磁库仑相互作用相互作用的气体描述。
We consider quantum spin ice in a temperature regime in which its response is dominated by the coherent motion of a dilute gas of monopoles. The hopping amplitude of a monopole is sensitive to the configuration of its surrounding spins, taken to be quasi-static on the relevant timescales. This leads to well-known blocked directions in the monopole motion; we find that these are sufficient to reduce the coherent propagation of monopoles to quantum diffusion. This result is robust against disorder, as a direct consequence of the ground-state degeneracy, which disrupts the quantum interference pr…
Critical speeding-up near the monopole liquid-gas transition in magnetoelectric spin-ice
在所谓的自旋冰化合物中，相互竞争的相互作用稳定了一个具有有限零点熵的受抑基态，有趣的是，还出现了磁共振激发。这些单极子的性质是最近研究的焦点，特别强调它们的量子动力学。据预测，每个电介质也具有电偶极矩，这允许通过介电函数ε（ν）来研究它们的动力学。在这里，我们报告的宽带光谱测量的ε（ν）在Dy 2 Ti 2 O 7下降到200 mK的温度与特定的重点上的关键端点存在的磁场沿晶体[111]方向。当磁单极子的密度以临界方式变化时，类似于在液-气转变中，在介电响应中揭示出明确的临界特征。令人惊讶的是，介电弛豫时间τ表现出临界加速，随着温度向临界温度降低，介电弛豫时间τ显著增加1/τ。除了展示了紧急的双激发的磁电特性，我们的结果揭示了独特的临界动力学附近的双凝聚转变。
A Measure of Monopole Inertia in the Quantum Spin Ice Yb$_2$Ti$_2$O$_7$
现代固体物理学的一个重要和持续的主题是在材料（例如准粒子）中实现奇异激发，这些材料在自由空间的实际物理真空中没有类似物（或尚未被观察到）。尽管它们不是基本粒子，但此类准粒子确实构成了它们所处的“真空”的激发态的最基本描述。在这方面的激发态的自旋冰，占主导地位的伊辛相互作用的磁性烧绿石氧化物的磁性纹理，提出了建模为有效的磁荷单极。最近的非弹性中子散射实验已经确定烧绿石材料Yb $_2$ Ti $_2$ O $_7$（YbTO）作为量子自旋冰，其中除了伊辛相互作用之外，还有大量的横向项可以诱导量子动力学和-原则上-相干的自旋运动。在这里，我们报告了相结合的时域太赫兹光谱（THEMS）和微波腔的研究YbTO探测其复杂的动态磁化率。我们发现磁化率的形式与自旋运动相一致，并且可以定义和测量磁自旋电导率。使用这些技术的独特的相敏能力，我们观察到的磁响应的反应部分的符号变化。在惯性运动的一般模型中，这只能通过引入惯性效应（例如，质量相关项）到运动方程中来实现。类似于传统的电荷系统，测量电导率的光谱权重使我们能够推导出磁致伸缩质量的值，我们发现该值约为1800电子质量。我们的结果建立了磁单极子的量子自旋冰作为真正的相干传播准粒子的这个系统。
A magnetic monopole in spin ice is a novel quasiparticle excitation in condensed matter physics, and we found that the ac frequency dependent magnetic susceptibility $χ(ω)$ in the two-dimensional (2D) spin ice (so-called kagomé ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG) systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge correlation length $ξ(\propto1/\sqrt{ω_1})$, where $ω_{1}$ is a characteristic frequency proportional to the peak position of the imaginary part of $χ(ω)…
Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
International Center for Quantum Materials, Peking University（北京大学量子材料中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；The University of Hong Kong, Shenzhen Institute of Research and Innovation（香港大学深圳研究院）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
Frustration in magnetic systems is fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles in spin-ice systems is yet to be found. Here, using measurements on single crystals of Ho$_{2}$Ir$_{2}$O$_{7}$ in combination with dipolar Monte Carlo simulations, we show that the magnetoresistance is highly s…
The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength ($J_{eff}$) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho$_2$Ti$_2$O$_7$, and show that the magneto-chemical potential depends on the spin-sublattice ($α$ or $β$), i.e.,…
Anisotropic Monopole Heat Transport in the Spin-Ice Compound Dy$_2$Ti$_2$O$_7$
本文报道了自旋冰材料Dy $_2$ Ti $_2$ O $_7$的热导率$κ$的研究。从κ $ and by additional measurements on the phononic reference compounds Y$ _2 PDMATHABMQ_2 PDMATHABMR_7 PDMATHABMS_2 PDMATHABMR_7 $, we are able to separate the phononic and the magnetic contributions to the total heat transport, i.e. $ κ_{ph} $ and $ κ_{mag} $, respectively, which both depend on the magnetic field. The field dependent $ κ_{ph} $ arises from lattice distortions due to magnetic-field induced torques on the non-collinear magnetic moments of the Dy ions. For $ κ_{mag} $, we observe a highly anisotropic magnetic-field dependence, which co…
Exploring possible magnetic monopoles-induced magneto-electricity in spin ices
University of Geneva（日内瓦大学）；Institut Néel, CNRS and Université Grenoble Alpes（内勒研究所，法国国家科学研究中心与格勒诺布尔阿尔卑斯大学）；ICMMO, Université Paris-Saclay, CNRS（物质化学与分子和超分子研究所，巴黎萨克雷大学，法国国家科学研究中心）
Correlated Quantum Tunnelling of Monopoles in Spin Ice
自旋冰材料Ho $_{2}$ Ti $_{2}$ O $_{7}$和Dy $_{2}$ Ti $_{2}$ O $_{7}$可能是目前研究得最好的经典阻挫磁体。理解它们的低温行为的关键一步-无论是关于它们不同寻常的动力学性质还是观察它们的量子相干时间演化的可能性-是对支撑磁单极子跳跃的自旋翻转过程的定量理解。我们攻击这个问题的框架中的一个单离子的量子治疗受到晶体，交换和偶极场从邻近的离子。通过研究基本的量子力学机制，我们发现了一个双峰分布的跳跃率依赖于本地的自旋配置，在广泛的协议从实验中提取的速率。对Pr $_{2}$ Sn $_{2}$ O $_{7}$和Pr $_{2}$ Zr $_{2}$ O $_{7}$进行同样的分析，我们发现时间尺度的分离更加明显，表明了相干多体动力学的可能性。
We investigate thermal transport in square ice, a two-dimensional analogue of spin ice, exploring the role played by emergent magnetic monopoles in transporting energy. Using kinetic Monte Carlo simulations based on energy preserving extensions of single-spin-flip dynamics, we explicitly compute the (longitudinal) thermal conductivity, $κ$, over a broad range of temperatures. We use two methods to determine $κ$: a measurement of the energy current between thermal baths at the boundaries, and the Green-Kubo formula, yielding quantitatively consistent values for the thermal conductivity. We inte…
The multiple symmetry sustaining phase transitions of spin ice
我们提出了完整的相图的哑铃模型的自旋冰作为温度，化学势和交错的化学势的函数，打破了有利于电荷晶体有序的平移晶格对称性。我们观察到一个双翅结构，有五种可能的相，螺旋流体（自旋冰），破碎的单晶体相和双螺旋晶体，锌的混合物结构。我们的模型提供了一个框架的液-液相变和观察到的流动磁体在压力和外场的翼结构。我们将我们的研究结果与最近的实验Ho $_2$ Ir $_2$ O $_7$，并提出了广泛的一套新的实验，利用相图，包括高压协议，动态缩放的Kibble-Zurek形式和普遍违反的波动耗散定理。
Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7
在Ho 2 Ti 2 O 7自旋冰的基态，磁矩的无序遵循相同的规则，在水冰的质子无序。激发采用磁单极子的形式，其通过磁库仑相互作用相互作用。本文用μ子自旋转动研究了Ho_（2-x）Y_xTi_2 O_7（x=0，0.1，1，1.6和2）单晶的低温磁性。在非常低的温度下，在x=0和0.1的样品中观察到μ子旋进λ（B）的弛豫速率与线性场的依赖关系，在以前的一些实验中，Dy 2 Ti 2 O 7自旋冰与μ子电流有关。从磁场穿透到银样品板由于晶体的磁化的信号被观察到所有的样品含有Ho，使我们能够研究不寻常的磁性动力学的Y掺杂自旋冰。
Spin ice systems display a variety of very nontrivial properties, the most striking being the existence in them of magnetic monopoles. Such monopole states can also have nontrivial electric properties: there exist electric dipoles attached to each monopole. A novel situation is encountered in the moment fragmentation (MF) state, in which monopoles and antimonopoles are perfectly ordered, whereas spins themselves remain disordered. We show that such partial ordering strongly modifies the electric activity of such systems: the electric dipoles, which are usually random and dynamic, become paired…
Ising models on a pyrochlore oxide lattice are usually associated with spin ice materials and "magnetic monopoles". Ever more often effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O$^{-2}$ ions mediating superexchange; we call it the Magnetoelastic Spin Ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite…
Magnetic charge injection in spin ice: a new way to fragmentation
凝聚态物质中的复杂性为新物质状态的发现提供了养分，而挫折感等因素则丰富了新物质状态。磁性系统的例子有Kitaev自旋液体、Skyrmions相或自旋冰。这些非传统的基态支持奇异的激发，例如自旋冰中的磁荷，也称为单极子。除了发现它们之外，一个重要的挑战是能够控制和操纵它们。在这里，我们提出了一种新的机制，通过交错磁场注入单极子的自旋冰。我们从理论上表明，并在实验中证明，在Ho $_2$ Ir $_2$ O $_7$烧绿石铱酸盐，它的结果在一个稳定的晶体，表现出磁性碎片。在这种新的物质状态下，磁矩分裂成一个有序的部分和一个持续波动的部分。与传统的自旋冰相比，在这种分裂状态下的不同性质的激发开辟了新的可调场诱导和动力学行为的道路。
