Measurements of temperature dependent magnetization associated with trapped magnetic flux in single crystals of CaKFe₄As₄, CaK(Fe_0.983Mn_0.017)₄As₄and MgB₂using zero-field-cooled and field-cooled protocols are presented. The results allow for the determination of the values of superconducting transition temperature, lower critical field and self-field critical current density. These are compared with the literature data. Possible experimental concerns are briefly outlined. Our results, on these known superconductors at ambient pressure, are qualitatively similar to those recently measured on superhydrides at megabar pressures (Minkovet al2023Nat. Phys.https://doi.org/10.1038/s41567-023-02089-1) and, as such, hopefully serve as a baseline for the interpretation of high pressure, trapped flux measurements.

In order to study the effects of Mn substitution on the superconducting and magnetic ground state of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ $(T_c=35 \mathrm{K})$, members of the $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by elemental analysis, thermodynamic, and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as $x$ is increased from 0 to 0.036. For $x$ values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kinklike features allow for the determination of the transition temperature $T^{*}$ that increases as Mn substitution increases. A temperature-composition $\left(T\text{−}x\right)$ phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature $T^{*}$ appearing near 26 K for $x\sim 0.017$ and rising slowly up to 33 K for $x\sim 0.036$. In addition to the creation of the $T\text{−}x$ phase diagram for $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$, specific-heat data are used to track the jump in specific heat at $T_c$; the $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ data do not follow the scaling of $\mathrm{\Delta }{C}_p$ with $T_c^3$ as many of the other Fe-based superconducting systems do. These data suggest that, as magnetic pair breaking is present, the jump in $C_p$ for a given $T_c$ is reduced. Elastoresistivity coefficients $2m_{66}$ and $m_{11}-m_{12}$ as a function of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$. This may indicate that the magnetic order in Mn-substituted system may be still the same as $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$. Superconductivity of $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ is also studied as a function of magnetic field. A clear change in $H_{c2}^{\prime }(T)/T_c$, where $H_{c2}^{\prime }(T)$ is $d{H}_{c2}(T)/dT$, at $x\sim 0.015$ is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also show the changes near $x=0.015$, again consistent with Fermi-surface changes associated with the magnetic ordering seen for higher-$x$ values.

Members of the $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x\right)}_4{\mathrm{As}}_4$ series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by x-ray diffraction, elemental analysis, and magnetic and transport measurements. The effects of Cr substitution on the superconducting and magnetic ground states of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ ($T_c=35$ K) have been studied. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as $x$ is increased from 0 to 0.038. For $x$-values greater than 0.012, signatures of a magnetic transition can be detected in magnetic measurements with the associated features in the transport measurements becoming detectable for $x\ge 0.038$. The magnetic transition temperature increases in a roughly linear manner as Cr substitution increases. A temperature-composition ($T-x$) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, $T^{*}$, appearing near 22 K for $x\sim 0.017$ and rising slowly up to 60 K for $x\sim 0.077$. The $T-x$ phase diagrams for $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{T}_x\right)}_4{\mathrm{As}}_4$ for $T=\text{Cr}$ and Mn are essentially the same despite the nominally different band filling; this is in marked contrast to $T=\text{Co}$ and Ni series for which the $T-x$ diagrams scale by a factor of 2, consistent with the different changes in band filling Co and Ni would produce when replacing Fe. Superconductivity of $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x\right)}_4{\mathrm{As}}_4$ is also studied as a function of magnetic field. A clear change in $H_{c2}^{\prime }\left(T\right)/T_c$, where $H_{c2}^{\prime }\left(T\right)$ is $d{H}_{c2}\left(T\right)/dT$, at $x\sim 0.012$ is observed and probably is related to a change of the Fermi surface due to magnetic order. Coherence length and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Both of them as a function of $x$ show changes near $x=0.012$, again consistent with Fermi surface changes associated with the magnetic ordering seen for higher $x$-values.

${\mathrm{LaCrGe}}_3$ is an itinerant, metallic ferromagnet with a Curie temperature $\left(T_C\right)$ of $\sim$86 K. Whereas ${\mathrm{LaCrGe}}_3$ has been studied extensively as a function of pressure as an example of avoided ferromagnetic quantum criticality, questions about its ambient pressure-ordered state remain: specifically, whether there is a change in the nature of the ferromagnetically ordered state below $T_C\sim$ 86 K. We present anisotropic $M\left(H\right)$ isotherms, coupled with anisotropic AC susceptibility data, and demonstrate that ${\mathrm{LaCrGe}}_3$ has a remarkable, low temperature coercivity associated with exceptionally sharp, complete magnetization reversals to and from fully polarized states. This coercivity is temperature dependent; it drops to zero in the 40–55 K region and reappears in the 70–85 K regions. At low temperatures ${\mathrm{LaCrGe}}_3$ has magnetization loops and behavior that has been previously associated with micromagnetic/nanocrystalline materials, not bulk macroscopic samples.

In an extension of our previous work, (Bud’ko et al 2023 Supercond. Sci. Technol. 36 115001) the measurements of temperature dependent magnetization associated with trapped magnetic flux in a small single crystal of CaKFe₄As₄, using zero—field—cooled and field—cooled protocols were performed, on the same crystal, at ambient pressure without a pressure cell and at 2.2 GPa in a commercial diamond anvil cell (DAC), showing comparable results. The data show that with a proper care and understanding, trapped flux measurements in superconductors indeed can be performed on samples in DACs under pressure, as was done on superhydrides (Minkov et al 2023 Nat. Phys. 19 1293).

An amendment to this paper has been published and can be accessed via a link at the top of the paper.