We report a 75-As single crystal NMR investigation of LaFeAsO, the parent phase of a pnictide high Tc superconductor. We demonstrate that spin dynamics develop a strong two-fold anisotropy within each orthorhombic domain below the tetragonal-orthorhombic structural phase transition at T[TO]~156 K. This intermediate state with a dynamical breaking of the rotational symmetry freezes progressively into a spin density wave (SDW) below T[SDW]~142 K. Our findings are consistent with the presence of a spin nematic state below T[TO] with an incipient magnetic order.
Doping dependence of Normal-state Property in the Iron-based Oxypnictide Superconductors LaFeAsO1-y probed by 57Fe-NMR and 75As-NMR/NQR
本文报道了贫氧铁基氧氮族化合物超导体LaFeAsO_{1-y} $. A microscopic phase separation between superconducting domains and magnetic domains is shown to take place in the underdoped sample, indicating a local inhomogeneity in association with the density distribution of oxygen deficiencies. As a result, 1/T_1T in the normal state of the superconducting domain decreases significantly upon cooling at both the Fe and As sites regardless of the electron-doping level in LaFeAsO_{1-y}. On the basis of this result, we claim that $ 1/T_1 T $ is not always enhanced by antiferromagnetic fluctuations close to an antiferromagn…
We present $^{75}$As Nuclear Magnetic and Quadrupole Resonance results (NMR, NQR) on a new set of LaFeAsO$_{1-x}$F$_x$ polycrystalline samples. Improved synthesis conditions led to more homogenized samples with better control of the fluorine content. The structural$\equiv$nematic, magnetic, and superconducting transition temperatures have been determined by NMR spin-lattice relaxation rate and AC susceptibility measurements. The so-determined phase diagram deviates from the published one especially for low F-doping concentrations. However, if the doping level is determined from the NQR spectra…
Nematicity in LaFeAsO single crystals studied by elastoresistance, high-resolution thermal expansion and shear-modulus measurements
Leibniz-Institut für Festkörper u. Werkstoffforschung (IFW) Dresden（德累斯顿莱布尼茨固体与材料研究所）；Bergische Universität Wuppertal（伍珀塔尔大学）；Kirchhoff Institute for Physics, Heidelberg University（海德堡大学基尔霍夫物理研究所）
Raman scattering experiments on LaFeAsO with splitted antiferromagnetic (T_AFM = 140 K) and tetragonal-orthorhombic (T_S = 155 K) transitions show a quasi-elastic peak (QEP) in B2g symmetry (2 Fe tetragonal cell) that fades away below ~T_AFM and is ascribed to electronic nematic fluctuations. A scaling of the reported shear modulus with the T-dependence of the QEP height rather than the QEP area indicates that magnetic degrees of freedom drive the structural transition. The large separation between T_S and T_AFM in LaFeAsO compared with their coincidence in BaFe2As2 manifests itself in slower …
Orbital ordering has recently emerged as another important state in iron based superconductors, and its role for superconductivity as well as its connection to magnetic order and orthorhombic lattice distortion are heavily debated. In order to search for signatures of this so-called nematic phase in oxypnictides, we revisit the normal state properties of the pnictide superconductor LaFeAsO$_{1-x}$F$_x$ with a focus on resistivity, Nernst effect, thermal expansion, and $^{75}$As NMR data. The transport properties at the underdoped level $x=0.05$ exhibit pronounced anomalies at about the same te…
The electron-doped high-transition-temperature (T_c) iron-based pnictide superconductor LaFeAsO_{1-x}H_x has a unique phase diagram: superconducting (SC) double domes are sandwiched by antiferromagnetic phases at ambient pressure and they turn to a single dome with a maximum T_c that exceeds 45K at a pressure of 3.0 GPa. We studied whether spin fluctuations are involved in increasing T_c under a pressure of 3.0 GPa by using ^{75}As nuclear magnetic resonance (NMR) technique. The ^{75}As-NMR results for the powder samples show that T_c increases up to 48 K without the influence of spin fluctuat…
We determine the phase diagram of LaFe$_{1-x}$Co$_x$AsO single crystals by using nuclear magnetic resonance (NMR). Up to a nominal doping of $x=0.03$, it follows the phase diagram for F-doped polycrystals. Above $x=0.03$, the F-doped samples become superconducting, whereas for Co-doping the structural and magnetic transitions can be observed up to $x=0.042$, and superconductivity occurs only for higher doping levels and with reduced transition temperatures. For dopings up to $x=0.056$, we find evidence for short-range magnetic order. By means of relaxation-rate measurements, we map out the mag…
Evidence for Unconventional Superconductivity in Arsenic-Free Iron-Based Superconductor FeSe : A ^77Se-NMR Study
本文报道了具有与LaFeAsO $_{1-x}$ F $_x$超导体相似的晶体结构的$α$的核磁共振（NMR）结果.核自旋晶格弛豫速率$1/T_1$在超导转变温度$T_c$以下表现出$T^3$行为，没有相干峰。在高于$T_c$的宽温度范围内，可以看到指示费米液态的$T_1T=$恒定行为。$α$ -FeSe的超导电性与LaFeAsO $_{1-x}$ F $_x$及相关材料一样，也是一种非常规的超导电性. FeAs层对非常规超导性的发生不是必需的。
We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperat…
Novel Superconducting Characteristics and Unusual Normal-State Properties in Iron-based Pnictide Superconductors: 57Fe-NMR and 75As-NQR/NMR studies in REFeAsO_1-y (RE=La,Pr,Nd) and Ba0.6K0.4Fe2As2
利用$^{57}$ Fe-NMR和$^{75}$ As-NQR/NMR研究了铁基磷属元素化物超导体REFeAsO $_{1-y}$（RE=La，Pr，Nd）和Ba $_{0.6}$ K $_{0.4}$ Fe $_2$ As $_2$（$T_{c}=$ 38 K）的新颖超导特性和异常正常态性质.在$_{0.7}$的超导态（$T_{c}=$ 28 K），$^{57}$的Fe-Knight位移的自旋分量在低温下几乎为零，这为自旋-单重态Cooper配对形成超导态提供了有力的证据. LaFeAsO $_{0.7}$和Ba $_{0.6}$ K $_{0.4}$ Fe $_2$ As $_2$中的核自旋-晶格弛豫速率$(1/T_{1})$表现出类似$T^{3}$的依赖性，在$T_{c}$以下没有相干峰，表明在这些Fe基磷属元素化合物中通常实现非常规的超导态。所有这些事件$T_c$以下一直认为在扩展的s $_{\pm}$波配对与费米面之间的顺序参数的符号反转。在正常状态下，$1/T_1T$显着减少后冷却的Fe和As位的LaFeAsO $_{0.7}$。相反，在Ba $_{0.6}$ K $_{0.4}$ Fe $_2$ As $_2$中，它在冷却时逐渐增加。尽管这些化合物的超导性质之间的相似性，观察到一个关键的差异，在其正常状态下的属性取决于电子或空穴是否掺杂到FeAs层。这些结果可能为铁基…
The NMR spectrum of FeSe shows a dramatic broadening on cooling towards the bulk nematic phase at $T_s=90$ K, due to the formation of a quasi-static, short-range-ordered nematic domain structure. However, a quantitative understanding of the NMR broadening and its relationship to the nematic susceptibility is still lacking. Here, we show that the temperature and pressure dependence of the broadening is in quantitative agreement with the mean-field Edwards-Anderson parameter of an Ising-nematic model in the presence of random-field disorder introduced by non-magnetic impurities. Furthermore, the…
We performed angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of the nematic phase in LaFeAsO. Degeneracy breaking between the dxz and dyz hole bands near the Γ and M point is observed in the nematic phase. Different temperature dependent band splitting behaviors are observed at the Γ and M points. The energy of the band splitting near the M point decreases as the temperature decreases while it has little temperature dependence near the Γ point. The nematic nature of the band shift near the M point is confirmed through a detwin experiment using a piezo devi…
Hydrogen (H)-doped LaFeAsO is a prototypical iron-based superconductor. However, its phase diagram extends beyond the standard framework, where a superconducting (SC) phase follows an antiferromagnetic (AF) phase upon carrier doping; instead, the SC phase is sandwiched between two AF phases appearing in lightly and heavily H-doped regimes. We performed nuclear magnetic resonance (NMR) measurements under pressure, focusing on the second AF phase in the heavily H-doped regime. The second AF phase is strongly suppressed when a pressure of 3.0 GPa is applied, and apparently shifts to a highly H-do…
We studied the quantum critical behavior of the second antiferromagnetic (AF) phase in the heavily electron-doped high-$T_c$ pnictide, LaFeAsO$_{1-x}$H$_x$ by using $^{75}$As and $^{1}$H nuclear-magnetic-resonance (NMR) technique. In the second AF phase, we observed a spatially modulated spin-density-wave-like state up to $x$=0.6 from the NMR spectral lineshape and detected a low-energy excitation gap from the nuclear relaxation time $T_1$ of $^{75}$As. The excitation gap closes at the AF quantum critical point (QCP) at $x \approx 0.49$. The superconducting (SC) phase in a lower-doping regime …
An iron-based superconductor LaFeAsO$_{1-x}$H$_x$ (0 $\leq x \leq$ 0.6) undergoes two antiferromagnetic (AF) phases upon H doping. We investigated the second AF phase ($x$=0.6) using NMR techniques under pressure. At pressures up to 2 GPa, the ground state is a spin-density-wave state with a large gap; however, the gap closes at 4.0 GPa, suggesting a pressure-induced quantum critical point. Interestingly, the gapped excitation coexists with gapless magnetic fluctuations at pressures between 2 and 4 GPa. This coexistence is attributable to the lift up of the $d_{xy}$ orbital to the Fermi level,…
No anomalous spin fluctuation in optimally doped and overdoped iron-based oxypnictide superconductors LaFeAsO$_{1-x}$F$_x$ probed by muon spin relaxation
在最佳掺杂和过掺杂超导体LaFeAsO $_{1-x}$ F $_x$中进行了零场和纵向场μ子自旋弛豫测量，以研究在较宽的温度和纵向场范围内的磁涨落.在μ子的时间窗（10 $^{-5}\sim$ 10 $^{-9}$ s）内，我们没有观察到磁涨落随温度变化的迹象.考虑到目前的结果和其他结果，即，通过中子散射观察到的自旋涨落、核磁共振和光电子能谱观察到的类赝能隙行为，表明不仅自旋涨落，而且费米表面具有几种不同轨道贡献的多带特征可能在LaFeAsO $_{1-x}$ F $_x$的超导配对机制中发挥重要作用。
We present $^{77}$Se-NMR measurements on FeSe$_{1-x}$S$_x$ samples with sulfur content $x=0,9,15$ and $29\%$. Twinned nematic domains are observed in the NMR spectrum for all samples except $x=29\%$. The NMR spin-lattice relaxation rate shows that magnetic fluctuations are initially enhanced between $x=0\%$ and $x=9\%$, but are strongly suppressed for higher $x$ values. The observed behavior of the magnetic fluctuations parallels the superconducting transition temperature $T_c$ in these materials, providing strong evidence for the primary importance of magnetic fluctuations for superconductivi…
Interrelationships between nematicity, antiferromagnetic spin fluctuations and superconductivity: Role of hotspots in FeSe$_{1-x}$S$_{x}$ revealed by high pressure $^{77}$Se NMR study
The role of nematic fluctuations for unconventional superconductivity has been subject of intense discussions for many years. In iron-based superconductors, the most established probe for electronic-nematic fluctuations, i.e. the elastoresistivity seems to imply that superconductivity is reinforced by electronic-nematic fluctuations, since the elastoresistivity amplitude peaks at or close to optimal $T_C$. However, on the over-doped side of the superconducting dome, the diminishing elastoresistivity suggests a negligible importance in the mechanism of superconductivity. Here we introduce the N…
We report $^{75}$As nuclear magnetic resonance (NMR) / nuclear quadrupole resonance (NQR) and transmission electron microscopy (TEM) studies on LaFeAsO$_{1-x}$F$_{x}$. There are two superconducting domes in this material. The first one appears at 0.03 $\leq$ $x$ $\leq$ 0.2 with $T_{\rm c}$$^{max}$ = 27 K, and the second one at 0.25 $\leq$ $x$ $\leq$ 0.75 with $T_{\rm c}$$^{max}$ = 30 K. By NMR and TEM, we demonstrate that a $C4$-to-$C2$ structural phase transition (SPT) takes place above both domes, with the transition temperature $T_{\rm s}$ varying strongly with $x$. In the first dome, the S…
Two ordering states, antiferromagnetism and nematicity, have been observed in most iron-based superconductors (SCs). In contrast to those SCs, the newly discovered SC CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ exhibits an antiferromagnetic (AFM) state, called hedgehog spin-vortex crystal structure, without nematic order, providing the opportunity for the investigation into the relationship between spin fluctuations and SC without any effects of nematic fluctuations. Our $^{75}$As nuclear magnetic resonance studies on CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (0$\le x\le$ 0.049) revealed that CaKFe$_4$As$_4$ is loc…
Structural and electronic properties of LaFeAsO$_{0.85}$F$_{0.15}$ superconductor modified under neutron irradiation
用X射线衍射和$^{75}$ As NMR研究了中子辐照引起的原子无序对轻过掺杂LaFeAsO $_{0.85}$ F $_{0.15}$（$T_c=21K$）晶体结构和$E_F$附近电子态的影响.在$T=50^{\circ}C$上用“中等”注量的$Φ=(0;0.5;1.6)\cdot10^{19}cm^{-2}$中子辐照多晶样品导致超导性的抑制。结果表明，中子辐照产生的四方晶系晶格的各向异性膨胀几乎是由于Fe-As距离的增加。的FeAs层的2D字符的部分损失是伴随着抑制的自旋磁化率的温度依赖性的间隙状功能。在最无序的状态下，$^{75}$ As的自旋-晶格弛豫速率遵循柯林加定律$^{75}T_1^{-1} \sim T$，热行为对于传导电子的各向同性运动是典型的。
The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{\rm c}$ cuprate superconductors are extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are n…
Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for int…
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
To elucidate the origin of nematic order in FeSe, we performed field-dependent 77Se-NMR measurements on single crystals of FeSe. We observed orbital ordering from the splitting of the NMR spectra and Knight shift and a suppression of it with magnetic field B0 up to 16 T applied parallel to the Fe-planes. There is a significant change in the distribution and magnitude of the internal magnetic field across the orbital ordering temperature Torb while stripe-type antiferromagnetism is absent. Giant antiferromagnetic (AFM) spin fluctuations measured by the NMR spin-lattice relaxation are gradually …
FeSe is arguably the simplest, yet the most enigmatic, iron-based superconductor. Its nematic but non-magnetic ground state is unprecedented in this class of materials and stands out as a current puzzle. Here, our NMR measurements in the nematic state of mechanically detwinned FeSe reveal that both the Knight shift and the spin-lattice relaxation rate 1/T_1 possess an in-plane anisotropy opposite to that of the iron pnictides LaFeAsO and BaFe2As2. Using a microscopic electron model that includes spin-orbit coupling, our calculations show that an opposite quasiparticle weight ratio between the …
Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature $T_{str}=90$K, in stark contrast that the magnetism emerges slightly below $T_{str}$ in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order ($n_{xz}\neq n_{yz}$) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is v…
Review of nuclear magnetic resonance studies on iron-based superconductors
新发现的铁基超导体引发了凝聚态物理学界新的巨大研究兴趣。核磁共振（NMR）是研究强关联电子的低能局域探针，对高$T_{\rm C}$超导体尤其重要。本文综述了几种铁基高$T_{\rm C}$超导体的结构转变、反铁磁序、自旋涨落和超导性质的NMR研究，包括LaFeAsO $_{1-x}$ F $_x$、LaFeAsO $_{1-x}$、BaFe $_2$ As $_2$、Ba $_{1-x}$ K $_x$ Fe $_2$ As $_2$、Ca $_{0.23}$ Na $_{0.67}$ Fe $_2$ As $_2$、BaFe $_2$（作为$_{1-x}$ P $_x$）$_2$，Ba（Fe $_{1-x}$ Ru $_x$）$_2$ As $_2$，Ba（Fe $_{1-x}$ Co $_x$）$_2$ As $_2$，Li $_{1+x}$ FeAs，LiFe $_{1-x}$ Co $_x$ As，NaFeAs，NaFe $_{1-x}$ Co $_x$ As，K $_y$ Fe $_{2-x}$ Se $_2$，和（Tl，Rb）$_y$ Fe $_{2-x}$ Se $_2$。
The sulfur substituted FeSe system, FeSe$_{1-x}$S$_{x}$, provides a versatile platform for studying the relationship between nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe$_{0.91}$S$_{0.09}$, we established the pressure($p$)-temperature($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p$ = 0.5 GPa, two SC regions, separated by the QPT, appear and antiferromagnetic (AFM) phase emerges above $\sim$3.3 GPa. From the…
The recent study of $^{77}$Se nuclear magnetic resonance (NMR) in a $β$-FeSe single crystal proposed that ferro-orbital order breaks the $90^\circ$ $C_4$ rotational symmetry, driving nematic ordering. Here, we report an NMR study of the impact of small strains generated by gluing on nematic state and spin fluctuations. We observe that the local strains strongly affect the nematic transition, considerably enhancing its onset temperature. On the contrary, no effect on low-energy spin fluctuations was found. Furthermore we investigate the interplay of the nematic phase and superconductivity. Our …
In this Rapid Communication, a set of $^{209}$Bi-nuclear magnetic resonance (NMR)/nuclear quadrupole resonance (NQR) measurements has been performed to investigate the physical properties of superconducting (SC) BaTi$_2$Bi$_2$O from a microscopic point of view. The NMR and NQR spectra at 5~K can be reproduced with a non-zero in-plane anisotropic parameter $η$, indicating the breaking of the in-plane four-fold symmetry at the Bi site without any magnetic order, i.e., `the electronic nematic state'. In the SC state, the nuclear spin-lattice relaxation rate divided by temperature, $1/T_1T$, does …
Strong interplay of spin and charge/orbital degrees of freedom is the fundamental characteristic of the iron-based superconductors (FeSCs), which leads to the emergence of a nematic state as a rule in the vicinity of the antiferromagnetic state. Despite intense debate for many years, however, whether nematicity is driven by spin or orbital fluctuations remains unsettled. Here, by use of transport, magnetization, and $^{75}$As nuclear magnetic resonance (NMR) measurements, we show a striking transformation of the relationship between nematicity and spin fluctuations (SFs) in Na$_{1-x}$Li$_x$FeA…
The interplay of orbital and spin degrees of freedom is the fundamental characteristic in numerous condensed matter phenomena, including high temperature superconductivity, quantum spin liquids, and topological semimetals. In iron-based superconductors (FeSCs), this causes superconductivity to emerge in the vicinity of two other instabilities: nematic and magnetic. Unveiling the mutual relationship among nematic order, spin fluctuations, and superconductivity has been a major challenge for research in FeSCs, but it is still controversial. Here, by carrying out 77Se nuclear magnetic resonance (…
The superconducting critical temperature, $T_{\rm c}$, of FeSe can be dramatically enhanced by intercalation of a molecular spacer layer. Here we report on a $^{77}$Se, $^7$Li and $^1$H nuclear magnetic resonance (NMR) study of the powdered hyper-interlayer-expanded Li$_{x}($C$_2$H$_8$N$_2$)$_y$Fe$_{2-z}$Se$_2$ with a nearly optimal $T_{\rm c}=45$~K. The absence of any shift in the $^7$Li and $^1$H NMR spectra indicates a complete decoupling of interlayer units from the conduction electrons in FeSe layers, whereas nearly temperature-independent $^7$Li and $^1$H spin-lattice relaxation rates ar…
We review our recent experimental results on the electronic nematic phase in electron- and hole-doped BaFe$_2$As$_2$ and FeSe. The nematic susceptibility is extracted from shear-modulus data (obtained using a three-point-bending method in a capacitance dilatometer) using Landau theory and is compared to the nematic susceptibility obtained from elastoresistivity and Raman data. FeSe is particularly interesting in this context, because of a large nematic, i.e., a structurally distorted but paramagnetic, region in its phase diagram. Scaling of the nematic susceptibility with the spin lattice rela…
To elucidate the magnetic structure and the origin of the nematicity in FeSe, we perform a high-pressure $^{77}$Se NMR study on FeSe single crystals. We find a suppression of the structural transition temperature with pressure up to about 2 GPa from the anisotropy of the Knight shift. Above 2 GPa, a stripe-order antiferromagnetism that breaks the spatial four-fold rotational symmetry is determined by the NMR spectra under different field orientations and with temperatures down to 50 mK. The magnetic phase transition is revealed to be first-order type, implying the existence of a concomitant st…
Since its discovery, iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm fails in the iron chalcogenide FeSe, whose single-layer version holds the record for the highest superconducting transition temperature in the iron-based superconductors. The striking puzzle that FeSe displays nematic order (spontaneously broken lattice rotational symmetry) while being non-magnetic, has led to several competing proposals for its origin in terms of either the $3d$-electron's orbital degrees of freedom or spin physics in the form of frustrated magnetism.…
Muon Spin Rotation ($μ$SR) and $^{19}$F Nuclear Magnetic Resonance (NMR) measurements were performed to investigate the effect of Mn for Fe substitutions in La$_{1-y}$Y$_{y}$Fe$_{1-x}$Mn$_x$AsO$_{0.89}$F$_{0.11}$ superconductors. While for $y = 0$ a very low critical concentration of Mn ($x = 0.2$%) is needed to quench superconductivity, as $y$ increases the negative chemical pressure introduced by Y for La substitution stabilizes superconductivity and for $y= 20$% it is suppressed at Mn contents an order of magnitude larger. A magnetic phase arises once superconductivity is suppressed both fo…
NMR experiments on superfluid 3He in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why the HQV in the polar phase in nematic aerogels became unstable in a transverse magnetic field upon a field-cooling is explained.
The polar phase of superfluid $^3$He is stable in "nematically ordered" densed aerogel. A rotating vessel with the polar superfluid can be filled either by an array of the single quantum vortices or by an array of the half-quantum vortices. It is shown that the inhomogeneous distribution of the spin part of the order parameter arising in an array of half-quantum vortices in strong enough magnetic field tilted to the average direction of aerogel strands leads to the appearance of a satellite in the NMR signal shifted in the negative direction with respect to the Larmor frequency. The satellite …
