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We re-investigate the magnetically frustrated, {\itdiamond-lattice-antiferromagnet} spinels FeAl$_2$O$_4$ and MnAl$_2$O$_4$ usingmagnetization measurements and diffuse scattering of polarized neutrons. InFeAl$_2$O$_4$, macroscopic measurements evidence a "cusp" in zero field-cooledsusceptibility around 13~K. Dynamic magnetic susceptibility and {\it memoryeffect} experiments provide results that do not conform with a canonicalspin-glass scenario in this material. Through polarized neutron scatteringstudies, absence of long-range magnetic order down to 4~K is confirmed inFeAl$_2$O$_4$. By modeling the powder averaged differential magnetic neutronscattering cross-section, we estimate that the spin-spin correlations in thiscompound extend up to the third nearest-neighbour shell. The estimated value ofthe Land\'{e} $g$ factor points towards orbital contributions from Fe$^{2+}$.This is also supported by a Curie-Weiss analysis of the magneticsusceptibility. MnAl$_2$O$_4$, on the contrary, undergoes a magnetic phasetransition into a long-range ordered state below $\approx$ 40~K, which isconfirmed by macroscopic measurements and polarized neutron diffraction.However, the polarized neutron studies reveal the existence of prominentspin-fluctuations co-existing with long-range antiferromagnetic order. Themagnetic diffuse intensity suggests a similar short range order as inFeAl$_2$O$_4$. Results of the present work supports the importance of spin-spincorrelations in understanding magnetic response of frustrated magnets like$A$-site spinels which have predominant short-range spin correlationsreminiscent of the "spin liquid" state.

Approaching the Ground State of Frustrated A-site Spinels: A Combined Magnetization and Polarized Neutron Scattering Study