Study of the superconducting and magnetic properties of single crystals grown using the high-temperature solution method

The high-temperature solution growth method is a powerful tool for creating single crystalline samples that then enable the exploration of the superconductivity and magnetization of novel materials. This dissertation presents work that uses the solution growth method to synthesize CaK(Fe$_{1-x}$$T$$_{x}$)$_{4}$As$_{4}$ and LaCrGe$_3$ single crystals. By measuring these single crystals, we study the relations or competition between superconductivity and magnetic transition, try to understand the unconventional superconductors, and explore the magnetic domain wall dynamics. Composition-transition temperature phase diagrams of CaK(Fe$_{1-x}$$T$$_{x}$)$_{4}$As$_{4}$, $T$ = Cr and Mn, are constructed by elemental analysis, thermodynamic and transport measurements. As the substitution level increases, the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K. Kink-like features appear in thermodynamic and transport measurements, which can be associated with antiferromagnetic transitions, and the transition temperature increases as the substitution level increases. Compared with electron-doped CaKFe$_4$As$_4$, the Cr and Mn phase diagrams are not overlapped as a function of hole doping, which indicates that the band-filling behavior is not the primary factor controlling the transition temperature in the Cr and Mn substitution samples. However, phase diagrams of Mn- and Cr- 1144 are overlapped as a function of substitution level, $x$, which reveals the bi-modal responses of the phase diagram to transition metal substitution: on the side of Ni and Co substitution, the rigid band is observed with electron doping, and on the side of Mn and Cr substitution, compounds behave as ionic compounds and local moments substitution seems to be dominated instead of hole doping. Elastoresistivity coefficients, $2m_{66}$ and $m_{11}-m_{12}$, as a function of temperature, are also measured in Mn substituted 1144. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. This may indicate that the magnetic order in Mn substituted system may still be the same as CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. A clear change in $H^\prime_{c2}$($T$)/$T_c$, coherence length, and the London penetration near the crossing of magnetic transition and superconducting transition as a function of substitution level is observed and probably is related to change of the Fermi surface due to magnetic order. LaCrGe$_3$ is an itinerant, metallic ferromagnet with a Curie temperature ($T_C$) of $\sim$ 86 K. Anisotropic $M$($H$) isotherms, coupled with anisotropic AC susceptibility data is presented, and show a remarkable low-temperature coercivity associated with exceptionally sharp, complete magnetization reversals to and from fully polarized states. The behavior of coercivity is temperature dependent and was first discovered in bulk single crystalline samples, which may be due to very low bulk pinning, strong uniaxial anisotropy, and, possibly, strong surface pinning.