Magnetism and spin dynamics of the $S$=$\frac{3}{2}$ frustrated trillium lattice compound $K_2\mathrm{CrTi}({\mathrm{PO}}_4{)}_3$

Competing magnetic interactions, frustration-driven quantum fluctuations, and spin correlations offer an ideal route for the experimental realization of emergent quantum phenomena with exotic quasiparticle excitations in three-dimensional frustrated magnets. In this context, trillium lattice, wherein magnetic ions decorate a three-dimensional chiral network of corner-shared equilateral triangular motifs, provides a viable ground. Herein, we present the crystal structure, dc and ac magnetic susceptibilities, specific heat, electron spin-resonance (ESR), muon spin-relaxation ($\mu \mathrm{SR}$) results on the polycrystalline samples of $K_2\mathrm{CrTi}{\left({\mathrm{PO}}_4\right)}_3$ wherein the ${\mathrm{Cr}}^{3+}$ ions form a two-coupled trillium lattice. The Curie-Weiss fit of the magnetic susceptibility data above 100 K yields a Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ = $-23$ K, which indicates the presence of dominant antiferromagnetic interactions between $S=3/2$ moments of ${\mathrm{Cr}}^{3+}$ ions. For temperatures below 40 K, the Curie-Weiss temperature is reduced to ${\theta }_{\mathrm{CW}}$ = $-3.5$ K, indicative of the appearance of subdominant ferromagnetic interactions. The specific heat measurements reveal the occurrence of two consecutive phase transitions, at temperatures $T_L=4.3$ K and $T_H=8$ K, corresponding to two different magnetic phases. Additionally, it unveils the existence of short-range spin correlations above the ordering temperature $T_H$. The power-law behavior of ESR linewidth suggests the persistence of short-range spin correlations over a relatively wide critical region $(T-T_H)/T_H>0.25$ in agreement with the specific heat results. The $\mu \mathrm{SR}$ results provide concrete evidence of two different phases corresponding to two transitions, coupled with the critical slowing down of spin fluctuations above $T_L$ and persistent spin dynamics below $T_L$, consistent with the thermodynamic results. Moreover, the $\mu \mathrm{SR}$ results reveal the coexistence of static and dynamic local magnetic fields below $T_L$, signifying the presence of complex magnetic phases owing to the entwining of spin correlations and competing magnetic interactions in this three-dimensional frustrated magnet.