Field-induced multi-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo></mml:mo></mml:mover></mml:math> states in a pyrochlore Heisenberg magnet

We construct exact ground states of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>J</a:mi><a:mn>1</a:mn></a:msub><a:mtext>−</a:mtext><a:msub><a:mi>J</a:mi><a:mrow><a:mn>3</a:mn><a:mi>b</a:mi></a:mrow></a:msub></a:mrow></a:math> classical Heisenberg model on the pyrochlore lattice in the presence of a magnetic field. They are noncoplanar multi-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mover accent="true"><b:mi>Q</b:mi><b:mo>⃗</b:mo></b:mover></b:math> spin configurations with a large magnetic unit cell that generalize the previously found coplanar sublattice pairing states. Using linear spin-wave theory, we show that entropy favors these multi-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mover accent="true"><d:mi>Q</d:mi><d:mo>⃗</d:mo></d:mover></d:math> states at low temperatures in high magnetic fields. This is confirmed by Monte Carlo simulations, and a phase diagram is constructed. We also calculate the zero-temperature dynamical structure factor. Besides the usual Goldstone modes associated with the ordering <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mover accent="true"><f:mi>Q</f:mi><f:mo>⃗</f:mo></f:mover><f:mi mathvariant="normal">s</f:mi></f:mrow></f:math>, we find high intensity gapless modes at momenta where there are no Bragg peaks.