Strong magnetic pair breaking in Mn-substituted $\mathrm{Mg}{\mathrm{B}}_2$ single crystals

Magnetic ions (Mn) were substituted in $\mathrm{Mg}{\mathrm{B}}_2$ single crystals resulting in a strong pair-breaking effect. The superconducting transition temperature, $T_c$, in ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_2$ has been found to be rapidly suppressed at an initial rate of $10\mathrm{K}∕\%\mathrm{Mn}$, leading to a complete suppression of superconductivity at about 2% Mn substitution. This reflects the strong coupling between the conduction electrons and the $3d$ local moments, predominantly of magnetic character, since the nonmagnetic ion substitutions, e.g., with Al or C, suppress $T_c$ much less effectively (e.g., $0.5\mathrm{K}∕\%\mathrm{Al}$). The magnitude of the magnetic moment ($\simeq 1.7{\mu }_B$ per Mn), derived from normal state susceptibility measurements, uniquely identifies the Mn ions to be divalent, and to be in the low-spin state $(S=1∕2)$. This has been found also in x-ray absorption spectroscopy measurements. Isovalent ${\mathrm{Mn}}^{2+}$ substitution for ${\mathrm{Mg}}^{2+}$ mainly affects superconductivity through spin-flip scattering reducing $T_c$ rapidly and lowering the upper critical field anisotropy $H_{c2}^{ab}∕H_{c2}^c$ at $T=0$ from 6 to 3.3 ($x=0.88\%$ Mn), while leaving the initial slope $\mathrm{d}{H}_{c2}∕\mathrm{d}T$ near $T_c$ unchanged for both field orientations.

Figure 1

Lattice parameters $c$ and $a$ vs Mn content $x$ (determined with EDX) for ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_2$ single crystals (closed symbols, solid lines). The crystals are superconducting for $x<0.02$. The solid lines are linear fits to the data. The dashed lines represent the lattice parameters for Al-substituted crystals (Ref. 31).

Figure 2

Normalized magnetic moment $M$ vs temperature for the ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_2$ single crystals with various Mn content $x$. The measurements were performed in a field of $0.5\mathrm{mT}$, after cooling in a zero field. The superconducting transition temperature $T_c$ is marked by a solid arrow and the transition onset temperature $T_{co}$ by a grey arrow. Crystals with a sharp transition (closed circles) were selected for further studies.

Figure 3

Suppression of $T_c$ with Mn substitution for ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_2$ single crystals with a sharp transition to the superconducting state (see Fig. 2). The solid line is a polynomial fit to the experimental points. The dashed line shows $T_c\left(x\right)$ predicted by the A-G pair-breaking theory. The inset shows $T_c$ vs the lattice parameter $c$. For clarity, only two error bars are shown.

Figure 4

Variation of $T_c$ for $\mathrm{Mg}{\mathrm{B}}_2$ single crystals substituted with nonmagnetic (Al, C) and magnetic (Mn) ions. The most striking result is a rapid suppression of $T_c$ due to the substitution of isovalent Mn for Mg. The main part of the results on Al- and C-substituted crystals has been published in Refs. 31, 36, respectively.

Figure 5

Temperature dependence of the magnetic moment $M$ at a constant field ${\mu }_{o}H=5\mathrm{T}$ for $\mathrm{Mg}{\mathrm{B}}_2$ single crystals substituted with 0.88% of Mn. The sample consists of 25 crystals with $T_c\simeq 28(\pm 1)\mathrm{K}$ and a total mass of $847\mu \mathrm{g}$ $(1.61\times {10}^{-7}\mathrm{mol}\mathrm{Mn})$. The inset shows the Curie part $C^{\star }$ of the $M\left(T\right)$ dependence as obtained from the experiment (circles). The lines are the expectations for $C^{\star }$ based on ${\mathrm{Mn}}^{2+}$ (solid lines) or ${\mathrm{Mn}}^{3+}$ (dashed lines) in the high-spin (HS) and low-spin (LS) configuration. The measurements reveal Mn to be divalent in the low-spin configuration. $H$ was oriented either parallel to the $ab$-plane (open circles) or 70° off the $ab$-plane (solid circles).

Figure 6

(a) XAS spectra for the TEY and the TFY experiments on $\mathrm{Mg}{\mathrm{B}}_2$ single crystals substituted with 6.7% of Mn. In the TEY mode, the spectrum is probably dominated by a MnO surface layer, while the TFY mode is more sensitive to the bulk. (b) Atomic model calculations for the $3d^5$ ground state of Mn in the low-spin (LS) and high-spin (HS) configuration. All the curves are shifted for clarity.

Figure 7

Diamagnetic response of the $\mathrm{Mg}{\mathrm{B}}_2$ crystal substituted with 0.88% of Mn. Shown are examples of measurements in constant field or at constant temperature (inset), for the two main orientations of the field. The transition temperature $T_c$ and the transition onset temperature $T_{co}$ are marked by arrows.

Figure 8

Upper critical field $H_{c2}$ vs temperature for the ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{B}}_2$ single crystals with $x=0$ (diamonds), 0.0042 (circles), and 0.0088 (triangles, stars). The $H_{c2}\left(T\right)$ data were obtained by magnetization measurements (solid symbols) or derived from torque measurements (open symbols), for the magnetic field $H$ oriented parallel (solid lines) and perpendicular (dashed lines) to the $ab$-plane. The magnetization measurements were performed at constant $H$ with increasing $T$ (solid triangles) or at constant $T$ with increasing $H$ (stars). The doted lines show the $H_{c2}\left(T\right)$ corresponding to the transition onset temperature $T_{co}$ (see Fig. 7). The lines are a guide for the eye.

Figure 9

Upper critical field anisotropy vs reduced temperature for the $\mathrm{Mg}{\mathrm{B}}_2$ unsubstituted single crystals (diamonds; $T_c=38.2\mathrm{K}$) and substituted with Mn (squares; 0.42% Mn, $T_c=33.9\mathrm{K}$; 0.88% Mn, $T_c=26.8\mathrm{K}$), Al (triangles; 2.4% Al, $35.3\mathrm{K}$; 9.2% Al, $32.0\mathrm{K}$), and C (circles; 5% C, $34.3\mathrm{K}$; 9.5% C, $30.1\mathrm{K}$). The data for Al- and C-substituted crystals were derived from $H_{c2}\left(T\right)$ results published in Refs. 31, 36.