Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice

Abstract

Motivated by recent experiments on Cs _2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> Cu _3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> SnF _{12} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>12</mml:mn> </mml:msub> </mml:math> and YCu _{3} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> (OH) _{6} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>6</mml:mn> </mml:msub> </mml:math> Cl _{3} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> , we consider the {S=1/2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> Heisenberg model on the kagome lattice with nearest-neighbor super-exchange J <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>J</mml:mi> </mml:math> and (out-of-plane) Dzyaloshinskii-Moriya interaction J_D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:math> , which favors (in-plane) {Q=(0,0)} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> magnetic order. By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for J_D/J \gtrsim 0.03 \mathrm{-} 0.04 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mi>/</mml:mi> <mml:mi>J</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>0.03</mml:mn> <mml:mstyle mathvariant="normal"> <mml:mo>−</mml:mo> </mml:mstyle> <mml:mn>0.04</mml:mn> </mml:mrow> </mml:math> ; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for J_D \to 0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . The small value of J_D/J <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mi>/</mml:mi> <mml:mi>J</mml:mi> </mml:mrow> </mml:math> for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu _{3} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> (OH) _{6} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi

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