Universal Alternating Order around Impurities in Antiferromagnets

The study of impurities in antiferromagnets is of considerable interest in condensed matter physics. In this Letter we address the elementary question of the effect of vacancies on the orientation of the surrounding magnetic moments in an antiferromagnet. In the presence of a magnetic field, alternating magnetic moments are induced, which can be described by a universal expression that is valid in any ordered antiferromagnet and turns out to be independent of temperature over a large range. The universality is not destroyed by quantum fluctuations, which is demonstrated by quantum Monte Carlo simulations of the two-dimensional Heisenberg antiferromagnet. Physical predictions for finite doping are made, which are relevant for experiments probing Knight shifts and the order parameter.

Figure 1

Schematic illustration of the effect of a vacancy in an ordered antiferromagnet. The spins ”cant” with an angle $\delta$ towards the field corresponding to a small uniform magnetization. Because of the broken sublattice symmetry the order may be ”tilted” by an angle $\alpha$ relative to the plane normal to the field corresponding to an induced alternating magnetization around the impurity.

Figure 2

The alternating response $m_{\mathrm{alt}}$ as a function of geometrical distance $r$ from a vacancy in a 2DHAF at different fields and $T=0.025\mathrm{J}$ from QMC simulations compared to the universal theoretical prediction $m_{\max }{n}_z$ in Eq. (16) without any adjustable parameters (dashed black lines). Inset: $m_{\mathrm{alt}}$ at $B=0.2\mathrm{J}$. Even at higher $T=0.1\mathrm{J}$ no deviations from Eq. (16) can be seen on a logarithmic scale. At still higher $T$ the induced order first increases for $0.3\mathrm{J}\gtrsim T\gtrsim 0.2\mathrm{J}$ and then decreases again for $T\gtrsim 0.3\mathrm{J}$. Inner inset: magnetic moments at $B=0.1\mathrm{J}$ and $T=0.1\mathrm{J}$ alternating between the extrapolated amplitudes on even and odd sublattices.