Blind deconvolution is the problem of recovering a convolutional kernel and an activation signal from their convolution y = a0 * x0. This problem is ill-posed without further constraints or priors. This paper studies the situation where the nonzero entries in the activation signal are sparsely and randomly populated. We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. With this spherical constraint, every spurious local minimum turns out to be close to some signed shift truncation of the ground truth, under certain hypotheses. This benign property motivates an effective two stage algorithm that recovers the ground truth from the partial information offered by a suboptimal local minimum. This geometry-inspired algorithm recovers the ground truth for certain microscopy problems, also exhibits promising performance in the more challenging image deblurring problem. Our insights into the global geometry and the two stage algorithm extend to the convolutional dictionary learning problem, where a superposition of multiple convolution signals is observed.

Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.

Diluted ferromagnetic semiconductors (DMSs) that combine the properties of semiconductors with ferromagnetism have potential application in spin-sensitive electronics (spintronics) devices. The search for DMS materials exploded after the observation of ferromagnetic ordering in III-V (Ga,Mn)As films. Recently, a series of DMS compounds isostructural to iron-based superconductors have been reported. Among them, the highest Curie temperature $T_C$ of 230 K has been achieved in (Ba,K)(Zn,Mn)$_2$As$_2$. However, most DMSs, including (Ga,Mn)As, are p-type, i.e., the carriers that mediate ferromagnetism are holes. For practical applications, DMS with n-type carriers are also advantageous. Here we report the successful synthesis of a II-II-V diluted ferromagnetic semiconductor with n-type carriers, Ba(Zn,Co)$_2$As$_2$. Magnetization measurements show that the ferromagnetic transition occurs up to $T_{C} \sim$ 45 K. Hall effect and Seebeck effect measurements jointly confirm that the dominant carriers are electrons. Through muon spin relaxation ($\mu$SR), a volume sensitive magnetic probe, we have also confirmed that the ferromagnetism in Ba(Zn,Co)$_2$As$_2$ is intrinsic and the internal field is static.

We present a muon spin relaxation study of the Mott transition in BaCoS_2 using two independent control parameters: (i) pressure p to tune the electronic bandwidth and (ii) Ni-substitution x on the Co site to tune the band filling. For both tuning parameters, the antiferromagnetic insulating state first transitions to an antiferromagnetic metal and finally to a paramagnetic metal without undergoing any structural phase transition. BaCoS_2 under pressure displays minimal change in the ordered magnetic moment S_ord until it collapses abruptly upon entering the antiferromagnetic metallic state at p_cr 1.3 GPa. In contrast, S_ord in the Ni-doped system Ba(Co_1-xNi_x)S_2 steadily decreases with increasing x until the antiferromagnetic metallic region is reached at x_cr 0.22. In both cases, significant phase separation between magnetic and nonmagnetic regions develops when approaching p_cr or x_cr, and the antiferromagnetic metallic state is characterized by weak, random, static magnetism in a small volume fraction. No dynamical critical behavior is observed near the transition for either tuning parameter. These results demonstrate that the quantum evolution of both the bandwidth- and filling-controlled metal-insulator transition at zero temperature proceeds as a first-order transition. This behavior is common to magnetic Mott transitions in RENiO_3 and V_2O_3, which are accompanied by structural transitions without the formation of an antiferromagnetic metal phase.

We present a coordinated study of the paramagnetic-to-antiferromagnetic, rhombohedral-to-monoclinic, and metal-to-insulator transitions in thin-film specimens of the classic Mott insulator V2O3 using low-energy muon spin relaxation, x-ray diffraction, and nanoscale-resolved near-field infrared spectroscopic techniques. The measurements provide a detailed characterization of the thermal evolution of the magnetic, structural, and electronic phase transitions occurring in a wide temperature range, including quantitative measurements of the high- and low-temperature phase fractions for each transition. The results reveal a stable coexistence of the high- and low-temperature phases over a broad temperature range throughout the transition. Careful comparison of temperature dependence of the different measurements, calibrated by the resistance of the sample, demonstrates that the electronic, magnetic, and structural degrees of freedom remain tightly coupled to each other during the transition process. We also find evidence for antiferromagnetic fluctuations in the vicinity of the phase transition, highlighting the important role of the magnetic degree of freedom in the metal-insulator transition.

Shengli Guo,1 Huiyuan Man,1 Kai Wang,1 Cui Ding,1 Yao Zhao,1 Licheng Fu,1 Yilun Gu,1 Guoxiang Zhi,1 Benjamin A. Frandsen,2 Sky C. Cheung,2 Zurab Guguchia,2 Kohtaro Yamakawa,2 Bin Chen,3 Hangdong Wang,3 Z. Deng,4 C. Q. Jin,4 Yasutomo J. Uemura,2 and Fanlong Ning1,5,* 1Zhejiang Province Key Laboratory of Quantum Technology and Device and Department of Physics, Zhejiang University, Hangzhou 310027, China 2Department of Physics, Columbia University, New York, New York 10027, USA 3Department of Physics, Hangzhou Normal University, Hangzhou 310016, China 4Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 5Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

With the support from JAEA REIMEI project, we have developed novel diluted ferromagnetic semiconductors (DMS) isostructural to iron-based superconductors since 2011. We characterized these DMS systems with magnetic susceptibility, transport, photoemission, and MuSR measurements, and developed theories for electronic states. In this article, we report recent progress on development of a point-contact device, subsequent Andreev reflection measurements, theoretical effort towards n-type DMS systems, and discovery and characterization of an n-type DMS Ba(Zn,Co)2As2. Diluted ferromagnetic semiconductors (DMS) have been studied extensively since 1990’s for potential use in spintronics devices. Prototypical systems, (Ga,Mn)As or (In,Mn)As, however, have limitations as (i) spin and charge co-doping resulting in mostly p-type materials; (ii) poor chemical solubility due to hetero-valence doping of Mn2+ to Ga3+ site, leading to availability only as MBE films; (iii) ferromagnetic TC limited to ~ 200 K. Since 2011, with a partial support from the REIMEI funding, part of the present authors developed novel DMS systems, including Li(Zn,Mn)As [1], (Ba,K)(Zn,Mn)2As2 [2] and (La1 xBax)(Zn1 xMnx)AsO [3]. These systems overcome the above-mentioned limitations (i) (iii), with (i) independent spin and charge doping with p-type carriers, (ii) iso-valent doping allowing synthesis of bulk single crystals, and (iii) highest TC already reaching 230 K within several years of initial development, with promising signatures towards room temperature DMS. Furthermore, the “122” DMS systems [2] share the crystal structure with an iron-based superconductor (Ba,K)Fe2As2, semiconductor BaZn2As2 and antiferromagnet BaMn2As2 with an excellent matching of lattice constants, which would enable making junctions and multilayer heterostructures of various combinations of these ground states. Previously, MuSR studies confirmed bulk ferromagnetism developed in the full volume fraction, with nearly linear relationship between the average static internal field and TC in p-type systems [1-3]. Photoemission studies confirmed hole-carriers in the top of the valence band [4] and Mn impurity band located well below the valence band maximum [5]. However, synthesis of n-type materials had been unsuccessful, and development of a device was not attempted before 2016, remaining as major challenges for the present Reimei project. Bo Gu and Maekawa performed density functional theory (DFT) and quantum Monte Carlo calculations on electronic structures of DMS system [6], and found that semiconductors BaZn2As2 and BaZn2Sb2, with very narrow energy gap, may become a good host material to support DMS systems with n-type carriers. In 2017, a part of present authors from Zhejiang University succeeded in synthesizing the first n-type DMS material Ba(Zn,Co)2As2, with ferromagnetic TC up to 50 K [7]. Magnetic moments are doped with Zn2+/Co2+ substitutions while electrons are doped with Zn2+/Co3+ substitutions. The negative sign of charge carriers is confirmed by Hall effect. With the present REIMEI project, we performed MuSR measurements at TRIUMF in 2017. Single crystals of a p-type DMS (Ba,K)(Zn,Mn)2As2 was developed at the Institute of Physics in Beijing by a part of the present authors, and a point contact junction with a Pb electrode was fabricated [8], as shown in the inset of Fig. 1. This was the first case of a device based on the novel DMS systems developed by the present research team. The differential conductance G is shown to decrease below the superconducting Tc of Pb, confirming features expected for Andreev Reflection. Fig. 1. Normalized differential conductance G/G0 and a sketch for a point contact device between the 122 DMS and Pb used in the Andreev reflection studies [8]. Zero-field MuSR measurements were performed at TRIUMF on a poly crystal specimen of an n-type DMS system Ba(Zn0.95Co0.05)2As2. Onset of relaxation due to static random local field was observed below the Curie temperature TC ~ 40 K. In Fig. 2, we plot the internal static field strength at T = 2 K versus TC observed in the present specimen with earlier MuSR results in other p-type DMS systems [7]. The point for the present n-type system lies at a location very different from the linear trend shown by many other p-type DMS systems [1-3]. Since the static internal field parameter is proportional to the concentration multiplied by the average static moment size in dilute spin systems, the trend for the n-type system implies that TC is relatively high for a given size and density of the static ordered moments. Hence the ferromagnetic exchange coupling is much larger in the n-type system compared to the p-type systems. This tendency can be partly ascribed to the difference between the present Co-doped system and Mn-doped p-type 122 DMS systems, which involve frustration because the nearest-neighbor Mn pairs are coupled antiferromagnetically, as can be seen in BaMn2As2 being a strong antiferromagnet with TN 625 K. In contrast, BaCo2As2 is a paramagnet showing a tendency towards ferromagnetic correlation [9]. Therefore, there is no frustration between neighboring Co spins in the Co-doped 122 system. This could lead to the stronger ferromagnetic coupling in the n-type Co-doped 122 DMS as compared to p-type Mn-doped DMS systems. This difference can also explain why the Co-doped 122 DMS system shows a very small coercive field of ~ 20 G, while the p-type Mn doped 122 DMS has a coercive field of ~ 2 T [2]. Fig. 2. Correlation between the static internal field parameter as determined at T = 2 K by ZF-μSR versus the ferromagnetic Curie temperature TC observed in p-type (Ga,Mn)As [10], Li(Zn,Mn)As [1], (La,Ba)(Zn,Mn)AsO [3] , (Ba,K)(Zn,Mn)2As2 [2], and n-type Ba(Zn,Co)2As2 [7]. Using a device shown in Fig. 1, the differential conductance was observed as a function of bias voltage and temperature. The conductance depends on the spin polarization of the up-spin band and the down spin band P, which is defined as P = (N N )/(N + N ) where N /N is the density of state for spin up/down band. The results in Fig. 3 can be fit to a model with Fig. 3. Normalized differential conductance G/G0 spectra (red dot) from a point-contact device of Pb and (Ba,K)(Zn,Mn)2As2 with K 0.096 and Mn 0.195 and their fits to the modified BTK theory (blue line) at selected temperatures from 1.7 K to 7.0 K. [8] the modified Blonder–Tinkham–Klapwijk (BTK) theory, with the spin polarization P of the DMS and the superconducting gap of Pd as parameters. The observed results fits well to P = 0.66, which is consistent with a large spin polarization for a ferromagnetic DMS system [8]. We reported progress of the studies of novel DMS systems, in (1) the formation of a pointcontact device using a single crystal; (2) successful observation of Andreev Reflection; (3) development of theory describing advantage of a narrow-gap 122 system for possible formation of n-type DMS system; and (4) successful synthesis and characterization of the novel n-type DMS Ba(Zn,Co)2As2. [1] Z. Deng et al., Nature Communications 2 (2011) 422. [2] K. Zhao et al., Nature Communications 4 (2013) 1442. [3] C. Ding et al., Phys. Rev. B 88 (2013) 041102(R). [4] H. Suzuki et al., Phys. Rev. B91, 140401 (2015). [5] H. Suzuki et al., Phys Rev. B92, 235120 (2015). [6] Bo Gu and S. Maekawa, Phys. Rev. B94, 155202 (2016). [7] S.L. Guo et al., submitted to Phys. Rev. B (2017). [8] G.Q. Zhao et al., Scientific Reports 7, 14473 (2017). [9] K. Ahilan et al., Phys. Rev. B 90, 14520 (2014). [10] S.R. Dunsiger et al, Nature Materials 9, 299 (2010). [11] G. E. Blonder et al., Phys. Rev. B. 25, 7 (1982).

Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering.

Sky C. Cheung,1 Zurab Guguchia,1 Benjamin A. Frandsen,1 Zizhou Gong,1 Kohtaro Yamakawa,1 Dalson E. Almeida,2 Ifeanyi J. Onuorah,3 Pietro Bonfá,4 Eduardo Miranda,5 Weiyi Wang,6 David W. Tam,6 Yu Song,6 Chongde Cao,6,7 Yipeng Cai,8 Alannah M. Hallas,8 Murray N. Wilson,8 Timothy J. S. Munsie,8 Graeme Luke,8,9,10 Bijuan Chen,11 Guangyang Dai,11 Changqing Jin,11 Shengli Guo,12 Fanlong Ning,12 Rafael M. Fernandes,13 Roberto De Renzi,3 Pengcheng Dai,6 and Yasutomo J. Uemura1,* 1Department of Physics, Columbia University, New York, New York 10027, USA 2UEMG Unidade Passos, Av. Juca Stockler, 1130, CEP 37900-106 Passos, MG, Brazil 3Department of Mathematical, Physical and Computer Sciences, Parco delle Scienze 7A, I-43124 Parma, Italy 4CINECA, Casalecchio di Reno 6/3 40033 Bologna, Italy 5Instituto de Física Gleb Wataghin, Unicamp, Rua Sérgio Buarque de Holanda, 777, CEP 13083-859 Campinas, SP, Brazil 6Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA 7Department of Applied Physics, Northwestern Polytechnical University, Xian 710072, China 8Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1 Canada 9Canadian Institute for Advanced Research, Toronto, ON, Canada M5G 1M1 10TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada, V6T 2A3 11Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, School of Physics, University of Chinese Academy of Sciences, Beijing 100190, China 12Department of Physics, Zhejiang University, Hangzhou 310027, China 13School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

The original version of this article omitted the following from the Acknowledgements: “CAM and AL were supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Additionally, this research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under ‘Contract No. DE-AC02-05CH11231’.” This has now been corrected in both the PDF and HTML versions of the article.

We use neutron diffraction and muon spin relaxation to study the effect of in-plane uniaxial pressure on the antiferromagnetic (AF) orthorhombic phase in BaFe_2As_2 and its Co- and Ni-substituted members near optimal superconductivity. In the low temperature AF ordered state, uniaxial pressure necessary to detwin the orthorhombic crystals also increases the magnetic ordered moment, reaching an 11% increase under 40 MPa for BaFe_1.9Co_0.1As_2, and a 15% increase for BaFe_1.915Ni_0.085As_2. We also observe an increase of the AF ordering temperature (T_N) of about 0.25 K/MPa in all compounds, consistent with density functional theory calculations that reveal better Fermi surface nesting for itinerant electrons under uniaxial pressure. The doping dependence of the magnetic ordered moment is captured by combining dynamical mean field theory with density functional theory, suggesting that the pressure-induced moment increase near optimal superconductivity is closely related to quantum fluctuations and the nearby electronic nematic phase.

We report the successful synthesis and characterization of a new type I-II-V bulk form diluted magnetic semiconductor (DMS) Li(Zn,Mn,Cu)As, in which charge and spin doping are decoupled via (Cu,Zn) and (Mn,Zn) substitution at the same Zn sites. Ferromagnetic transition temperature up to  ∼33 K has been observed with a coercive field  ∼40 Oe for the 12.5% doping level. μSR measurements confirmed that the magnetic volume fraction reaches nearly 100% at 2 K, and the mechanism responsible for the ferromagnetic interaction in this system is the same as other bulk form DMSs.

We present magnetometry and muon spin rotation (mu SR) measurements of the superconducting dichalcogenide Ir0.95Pt0.05Te2. From both sets of measurements, we calculate the penetration depth and thence superfluid density as a function of temperature. The temperature dependence of the superfluid densities from both sets of data indicate fully gapped superconductivity that can be fit to a conventional s-wave model and yield fitting parameters consistent with a BCS weak coupling superconductor. We therefore see no evidence for exotic superconductivity in Ir0.95Pt0.05Te2.

We present muon spin rotation (mu SR) and susceptibility measurements on single crystals of isoelectronically doped URu2-xTxSi2 (T = Fe, Os) for doping levels up to 50%. Zero field (ZF) mu SR measurements show long-lived oscillations demonstrating that an antiferromagnetic state exists down to low doping levels for both Os and Fe dopants. The measurements further show an increase in the internal field with doping for both Fe and Os. Comparison of the local moment-hybridization crossover temperature from susceptibility measurements and our magnetic transition temperature shows that changes in hybridization, rather than solely chemical pressure, are important in driving the evolution of magnetic order with doping.

We report the discovery of a new fluoride-arsenide bulk diluted magnetic semiconductor (Ba,K) F(Zn,Mn) As with the tetragonal ZrCuSiAs-type structure which is identical to that of the "1111" iron-based superconductors. The joint hole doping via (Ba,K) substitution & spin doping via (Zn,Mn) substitution results in ferromagnetic order with Curie temperature up to 30 K and demonstrates that the ferromagnetic interactions between the localized spins are mediated by the carriers. Muon spin relaxation measurements confirm the intrinsic nature of the long range magnetic order in the entire volume in the ferromagnetic phase. This is the first time that a diluted magnetic semiconductor with decoupled spin and charge doping is achieved in a fluoride compound. Comparing to the isostructure oxide counterpart of LaOZnSb, the fluoride DMS (Ba,K) F(Zn,Mn) As shows much improved semiconductive behavior that would be benefit for further application developments.

RENiO 3 (RE=rare-earth element) and V 2 O 3 are archetypal Mott insulator systems. When tuned by chemical substitution (RENiO 3 ) or pressure (V 2 O 3 ), they exhibit a quantum phase transition (QPT) between an antiferromagnetic Mott insulating state and a paramagnetic metallic state. Because novel physics often appears near a Mott QPT, the details of this transition, such as whether it is first or second order, are important. Here, we demonstrate through muon spin relaxation/rotation (μSR) experiments that the QPT in RENiO 3 and V 2 O 3 is first order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value until it is suddenly destroyed at the QPT. These findings bring to light a surprising universality of the pressure-driven Mott transition, revealing the importance of phase separation and calling for further investigation into the nature of quantum fluctuations underlying the transition.

We have employed muon spin relaxation and rotation (mu SR) to investigate the superconducting properties of the noncentrosymmetric superconductor CaIrSi3. Measurements of single-crystal specimens confirm the development of a robust superconducting state below T-c = 3.55 +/- 0.1 K with a ground-state magnetic penetration depth of xi = 288 +/- 10 nm and a coherence length of lambda(L)= 28.8 +/- 0.1 nm. The temperature evolution of the superfluid density indicates a nodeless superconducting gap structure dominated by an isotropic spin-singlet component in the dirty limit with a carrier density of n = (4.6 +/- 0.2) x 10(22) cm(-3) as determined by Hall resistance measurements. We find no evidence of spontaneous time-reversal symmetry breaking in the superconducting state within an accuracy of 0.05 G. These observations suggest that the influence of any spin-triplet pairing component or multiple gap structure associated with noncentrosymmetric physics is very weak or entirely absent in CaIrSi3.