The magnetic and superconducting properties of a series of underdoped ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ (BNFA) single crystals with $0.19\le x\le 0.34$ have been investigated with the complementary muon-spin-rotation ($\mu \mathrm{SR}$) and infrared spectroscopy techniques. The focus has been on the different antiferromagnetic states in the underdoped regime and their competition with superconductivity, especially for the ones with a tetragonal crystal structure and a so-called double-Q magnetic order. Besides the collinear state with a spatially inhomogeneous spin-charge-density wave (i-SCDW) order at $x=0.24$ and 0.26, that was previously identified in BNFA, we obtained evidence for an orthomagnetic state with a “hedgehog”-type spin vortex crystal (SVC) structure at $x=0.32$ and 0.34. Whereas in the former i-SCDW state the infrared spectra show no sign of a superconducting response down to the lowest measured temperature of about 10 K, in the SVC state there is a strong superconducting response similar to the one at optimum doping. The magnetic order is strongly suppressed here in the superconducting state and at $x=0.34$ there is even a partial reentrance into a paramagnetic state at $T\ll T_c$.

中文翻译：

---

Ba1-xNaxFe2As2的Muon自旋旋转和红外光谱研究

一系列掺杂不足的磁和超导性质 ${巴}_{\mathrm{1个}-X}{娜}_X{铁}_2{如}_2$ （BNFA）单晶与 $0.19\le X\le 0.34$ 已经对互补的μon自旋旋转（$\mu \mathrm{SR}$）和红外光谱技术。重点一直放在欠掺杂状态下的不同反铁磁态及其与超导性的竞争，特别是对于具有四方晶体结构和所谓的双Q磁阶的反铁磁态。除了共线状态外，还有一个空间不均匀的自旋电荷密度波（i-SCDW）阶$X=0.24$ 和BNFA先前确定的0.26，我们获得了具有“刺猬”型自旋涡旋晶体（SVC）结构的正磁态证据。 $X=0.32$和0.34。在以前的i-SCDW状态下，红外光谱没有显示出低至约10 K的最低测量温度的超导响应的迹象，而在SVC状态下，存在类似于最佳掺杂时的超导响应。在超导状态和超导状态下，磁阶被强烈抑制$X=0.34$ 甚至有部分折返进入顺磁性状态 $Ť\ll {Ť}_C$。