  Counterintuitive order-disorder phenomena emerging in antiferromagnetically
coupled spin systems have been reported in various studies. Here we perform a
systematic effective field theory analysis of two-dimensional bipartite quantum
Heisenberg antiferromagnets subjected to either mutually aligned -- or mutually
orthogonal -- magnetic and staggered fields. Remarkably, in the aligned
configuration, the finite-temperature uniform magnetization $M_T$ grows as
temperature rises. Even more intriguing, in the orthogonal configuration, $M_T$
first drops, goes through a minimum, and then increases as temperature rises.
Unmasking the effect of the magnetic field, we furthermore demonstrate that the
finite-temperature staggered magnetization $M^H_s$ and entropy density -- both
exhibiting non-monotonic temperature dependence -- are correlated.
Interestingly, in the orthogonal case, $M^H_s$ presents a maximum, whereas in
mutually aligned magnetic and staggered fields, $M^H_s$ goes through a minimum.
The different behavior can be traced back to the existence of an "easy
XY-plane" that is induced by the magnetic field in the orthogonal
configuration.
