[Paper Review] Itinerant spin ice order, Weyl metal, and anomalous Hall effect in Pr$_2$Ir$_2$O$_7$

Pallab Goswami, Bitan Roy+1 more|arXiv (Cornell University)|Mar 7, 2016

Advanced Condensed Matter Physics3 citations

TL;DR

This paper proposes that Pr₂Ir₂O₇ exhibits a low-temperature itinerant 3-in, 1-out spin ice order arising from competition between ice and all-in-all-out spin orders in a parabolic semimetal with quadratic band touching at the Γ point. This order induces a Weyl metal phase with two Weyl nodes along [1,1,1] directions, driving a large anomalous Hall effect without net magnetic moment, and strain tuning of the T₂g quadrupolar order can enhance this effect, raising the transition temperature.

ABSTRACT

In the global phase diagram of 227 pyrochlore iridates, Pr$_2$Ir$_2$O$_7$ resides in the proximity of a metal-insulator transition, supporting an anomalous Hall effect below 1.5 K, and the normal state of this material is described by a parabolic semimetal with quadratic band touching at the $\Gamma$ point. For such a parabolic semimetal which is believed to be the parent state of many 227 pyrochlore iridate compounds, we demonstrate a strong competition between the ice and all in-all out orders, and based on a Landau theory we construct possible global phase diagrams for this class of materials. When ice order has the dominant susceptibility, we show that the low temperature phase displays an itinerant 3-in, 1-out order. For a generic model of particle-hole anisotropic parabolic semimetal, the 3-in, 1-out order is an admixture of both ice and all in-all out spin configurations on Ir tetrahedron. The 3-in, 1-out order gives rise to a Weyl metal with two Weyl nodes along one of the eight possible [1,1,1] directions supporting a large anomalous Hall effect without any appreciable magnetic moment for Ir$^{4+}$ and Pr$^{3+}$ ions, as observed in Pr$_2$Ir$_2$O$_7$ at low temperatures. The anomalous Hall conductivity inside the 3-in, 1-out ordered phase varies as square root of the magnetization. Inside the metallic 3-in, 1-out phase, the ice and all in-all out components couple to the fluctuating $T_{2g}$ quadrupolar order parameter, leading to a small nematicity. Since an externally applied strain along [1,1,1] direction induces a static $T_{2g}$ quadrupolar order, we show how it can amplify the 3-in, 1-out order, raising the possibility of observing anomalous Hall effect at higher temperatures.

Motivation & Objective

• To understand the origin of the anomalous Hall effect in Pr₂Ir₂O₇ below 1.5 K despite the absence of net magnetic moments.
• To clarify the nature of the low-temperature ordered phase in Pr₂Ir₂O₇, particularly its spin configuration and electronic structure.
• To construct a global phase diagram for 227 pyrochlore iridates based on competition between ice and all-in-all-out spin orders.
• To explore how strain along [1,1,1] can stabilize the 3-in, 1-out order and enhance the anomalous Hall effect.

Proposed method

• Develop a Landau theory of spin order to model the competition between ice and all-in-all-out configurations in the parabolic semimetal parent state.
• Use a generic particle-hole anisotropic parabolic semimetal model to describe the electronic structure near the Γ point with quadratic band touching.
• Identify the 3-in, 1-out order as a quantum admixture of ice and all-in-all-out spin configurations on Ir tetrahedra.
• Analyze the emergent Weyl fermion topology by computing the Weyl node positions and chiral charge along [1,1,1] directions.
• Model the coupling of ice and all-in-all-out components to the fluctuating T₂g quadrupolar order parameter to explain nematicity and strain response.
• Apply external strain along [1,1,1] to induce static T₂g quadrupolar order and predict its amplification of the 3-in, 1-out order.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the anomalous Hall effect in Pr₂Ir₂O₇ at low temperatures, despite the absence of net magnetic moments?
• RQ2 How does the 3-in, 1-out spin order emerge from the competition between ice and all-in-all-out spin configurations in the parabolic semimetal?
• RQ3 What is the topological nature of the low-temperature phase, and how do Weyl nodes arise in this state?
• RQ4 How does the coupling to the T₂g quadrupolar order parameter lead to small nematicity in the metallic 3-in, 1-out phase?
• RQ5 Can strain tuning of the T₂g quadrupolar order enhance the 3-in, 1-out order and raise the temperature scale of the anomalous Hall effect?

Key findings

• The low-temperature phase of Pr₂Ir₂O₇ is an itinerant 3-in, 1-out spin ice order, which is a quantum admixture of ice and all-in-all-out spin configurations on Ir tetrahedra.
• This 3-in, 1-out order realizes a Weyl metal phase with two Weyl nodes along one of the eight [1,1,1] directions, enabling a large anomalous Hall effect.
• The anomalous Hall conductivity scales as the square root of the magnetization, consistent with experimental observations.
• The ice and all-in-all-out components couple to the fluctuating T₂g quadrupolar order parameter, resulting in a small nematic distortion in the 3-in, 1-out phase.
• External strain along the [1,1,1] direction induces a static T₂g quadrupolar order, which amplifies the 3-in, 1-out order and could enable observation of the anomalous Hall effect at higher temperatures.