Longitudinal Field μSR Research Articles

Spin order and dynamics in the topological rare-earth germanide semimetals

The REAl(Si,Ge) (RE = rare earth) family, known to break both the inversion- and time-reversal symmetries, represents one of the most suitable platforms for investigating the interplay between correlated-electron phenomena and topologically nontrivial bands. Here, we report on systematic magnetic, transport, and muon-spin rotation and relaxation (uSR) measurements on (Nd,Sm)AlGe single crystals, which exhibit antiferromagnetic (AFM) transitions at TN = 6.1 and 5.9 K, respectively. In addition, NdAlGe undergoes also an incommensurate-to-commensurate ferrimagnetic transition at 4.5 K. Weak transverse-field µSR measurements confirm the AFM transitions, featuring a ∼90% magnetic volume fraction. Zero-field (ZF) µSR measurements reveal a more disordered internal field distribution in NdAlGe than in SmAlGe, reflected in a larger transverse muon-spin relaxation rate λT at T ≪ TN. This may be due to the complex magnetic structure of NdAlGe, which undergoes a series of metamagnetic transitions in an external magnetic field, while SmAlGe shows only a robust AFM order. In NdAlGe, the topological Hall effect (THE) appears between the first and the second metamagnetic transitions for H ∥ c, while it is absent in SmAlGe. Such THE in NdAlGe is most likely attributed to the field-induced topological spin textures. The longitudinal muon-spin relaxation rate λL, diverges near the AFM order, followed by a clear drop at T < TN. In the magnetically ordered state, spin fluctuations are significantly stronger in NdAlGe than in SmAlGe. In general, our longitudinal-field μSR data indicate vigorous spin fluctuations in NdAlGe, thus providing valuable insights into the origin of THE and of the possible topological spin textures in REAl(Si,Ge) Weyl semimetals.

Quantum spin liquid ground state in the trimer rhodate Ba4NbRh3O12

Frustrated magnets offer a plethora of exotic magnetic ground states, including quantum spin liquids (QSLs), in which enhanced quantum fluctuations prevent a long-range magnetic ordering of the strongly correlated spins down to lowest temperature. Here we have investigated the trimer based mixed valence hexagonal rhodate Ba4NbRh3O12 using a combination of dc and ac magnetization, electrical resistivity, specific heat, and muon spin rotation/relaxation (μSR) measurements. Despite the substantial antiferromagnetic exchange interactions, as evident from the Weiss temperature (θW∼−35 to −45K), among the Rh-local moments, neither long-range magnetic ordering nor spin freezing is observed down to at least 50 mK, in ac-susceptibility, specific heat, and zero-field μSR measurements (down to 0.26 K). We ascribe the absence of any magnetic transition to enhanced quantum fluctuations as a result of geometrical frustration arising out of the edge-sharing equilateral Rh-triangular network in the structure. Our longitudinal-field μSR result evidences persistent spin fluctuations down to 0.26 K, thus stabilizing a dynamic QSL ground state in Ba4NbRh3O12. Furthermore, the magnetic specific heat data at low T reveal a significant T-linear contribution plus a quadratic T dependence, which may indicate the gapless Dirac QSL phenomenology of the spinon excitations with a linear dispersion. Published by the American Physical Society 2024

Probing the strongly correlated magnetic state of Co2C nanoparticles at low temperatures using μSR

Co2C nanoparticles (NPs) are amongst transition metal carbides whose magnetic properties have not been well explored. An earlier study (Roy et al 2021 J. Phys.: Condens. Matter 33 375804) showed that a pellet made from Co2C NPs exhibits exchange bias (EB) effect below a temperature, T EB = 50 K and a spin glass (SG) feature emerges below T SG = 5 K. In the current study we use magnetic, electrical transport, specific heat, and muon spin rotation (μSR) measurements to explore further the magnetic properties of a pellet made with 40 nm diameter pure Co2C NPs. We uncover the onset of Kondo localization at Kondo temperature T K (= 40.1 K), which is close to the onset temperature (T EB) of the EB effect. A crossover from the Kondo-screened scenario to the Ruderman–Kittel–Kasuya–Yosida interaction-dominated regime is also observed for T < T K. Temperature-dependent specific heat measurement further supports the Kondo localization scenario in the pellet and shows the heavy fermionic nature of the strongly correlated electronic state in Co2C. The zero field μSR asymmetry spectra in the low-temperature regime are characterized by two distinct fast and slow relaxation rates. The spectra show the absence of long-range magnetic order in the sample. However, our analysis suggests the NPs-pellet shows the presence of a dominant magnetically disordered fraction and a smaller fraction with short-range order. Muons in the disordered fraction exhibit a slower relaxation rate, while muons in the smaller fraction with short-range order exhibit a faster relaxation rate. We observe an increase in this fast relaxation rate between T EB and T SG. This increase below T EB ∼ 50 K suggests a slowing down of the fluctuating local magnetic environment around muons. Transverse field-μSR asymmetry spectra show the emergence of a stable, multi-peaked local magnetic field distribution in the pellet below T EB. Longitudinal field μSR spectra shows distinct changes in the dynamics of fluctuations suggesting the presence of a frozen glassy like state below 6 K. Based on our results, we suggest that below T EB, the pellet of Co2C NPs develops a magnetic interface that separates the two magnetic fractions; one is a disordered fraction, and the other is a fraction with short-range order. The exchange interaction that sets in below T EB at the interface couples the two fractions, leading to a suppression of the fluctuations. With the suppression of magnetic fluctuations below T EB, strong correlation effects in the electronic state of Co2C lead to Kondo localization.

Muon Spin Relaxation Study of Frustrated Tm3Sb3Mg2O14 with Kagomé Lattice

The structure and magnetic properties of rare-earth ions Tm3+ Kagomé lattice Tm3Sb3Mg2O14 are studied by x-ray diffraction, magnetic susceptibility and muon spin relaxation (μSR) experiments. The existence of a small amount of Tm/Mg site-mixing disorder is revealed. DC magnetic susceptibility measurement shows that Tm3+ magnetic moments are antiferromagnetically correlated with a negative Curie–Weiss temperature of –26.3 K. Neither long-range magnetic order nor spin-glass transition is observed by DC and AC magnetic susceptibility, and confirmed by μSR experiment down to 0.1 K. However, the emergence of short-range magnetic order is indicated by the zero-field μSR experiments, and the absence of spin dynamics at low temperatures is evidenced by the longitudinal-field μSR technique. Compared with the results of Tm3Sb3Zn2O14, another Tm-based Kagomé lattice with much more site-mixing disorder, the gapless spin liquid like behaviors in Tm3Sb3Zn2O14 can be induced by disorder effect. Samples with perfect geometrical frustration are in urgent demand to establish whether QSL exists in this kind of materials with rare-earth Kagomé lattice.

μSR Study with Light Irradiation of P3HT:ZnO Nanoparticles as Active Material of Hybrid Solar Cells

Recently, hybrid solar cell that consists of a combination of organic and inorganic materials offers promise in increasing efficiency. Combination of conjugated polymer of Poly (3-hexyl thiophene)/P3HT which has the highest hole mobility with inorganic materials which has high electron mobility, good physical and chemical stability of inorganic nanocrystals, shows a better performance of hybrid solar cells. We have conducted a measurement to investigate the charge carrier transport in active material of hybrid solar cells by using muon spin relaxation (μSR) with light irradiation. A bulk sample used in this study is hybrid organic-inorganic material consisting of regio-regular P3HT and ZnO nanoparticles. Longitudinal-field μSR measurements were performed in magnetic field ranging from 0 to 395 mT at temperature of 10 K, 15 K and 25 K. Based on μSR measurement with light irradiation, we found that for those temperatures, longitudinal field dependence of λ1 was proportional with C-H0.5 curve indicating three-dimensional inter-chain diffusion. We assume that light irradiation initiates the production of exciton that increases the number of charge carrier in the sample and transports not only along the chain of polymer (one-dimensional) but also perpendicular to other chain of polymer (three-dimensional). With light irradiation, the crossover temperature from one-dimensional to three-dimensional of regio-regular P3HT and ZnO nanoparticles bulk sample was obtained at lower temperature of 10 K compared to previous result at 25 K without light irradiation.

Synthesis, Crystal Structure, and Magnetic Properties of the Highly Frustrated Orthorhombic Li4MgReO6.

In an effort to understand the structure-property relationship in magnetically frustrated systems, an orthorhombic analog of the S = 1/2 Re-based oxide Li4MgReO6 has been successfully synthesized and its physical properties were investigated. Li4MgReO6 had been previously synthesized in a monoclinic system in an ordered NaCl structure type. That system was shown to exhibit spin glass behavior below ∼12 K. The crystal structure of the latter phase was determined using powder X-ray diffraction data. A structural model was refined in the orthorhombic Fddd space group that resulted in cell dimensions of a = 5.84337 (7) Å, b = 8.33995 (9) Å, and c = 17.6237 (2) Å. The magnetic ions, Re6+ (S = 1/2), consist of various arrangements of interconnected triangles and trigonal prisms that offer potential for geometric magnetic frustration. Temperature dependent magnetic susceptibility reveals an AFM transition below ∼2 K along with a ZFC/FC divergence suggestive of spin freezing. The Curie-Weiss fitting parameters to the paramagnetic regime result in θ = -124 (1) K, which is indicative of predominant AFM interactions. A frustration index of ∼62 is in accordance with a highly frustrated magnetic ground state. Zero field (ZF) μSR data provides evidence for the onset of magnetic order below 4 K, along with the evidence for dynamical fluctuations up to 5 K. Moreover, longitudinal field (LF) μSR data reveals a complete decoupling in applied field at 2 K, which is indicative of static order in most or all of the volume fraction at ∼2 K, with partial ordered volumes coexisting with dynamical fluctuations up to 5 K. Estimates of the relative strengths of various magnetic exchange pathways at the level of spin-dimer analysis for this novel system are calculated and are compared to those of the previously reported values for the monoclinic analog.

Time-Reversal Symmetry in the Hidden Order and Superconducting States of URu2Si2

The presence of a time-reversal symmetry-breaking field in the hidden order and superconducting states of URu2Si2 has been studied by muon spin relaxation (μSR) spectroscopy. The development of an internal magnetic field has been observed in the hidden order state. Longitudinal-field μSR experiments have shown that the internal magnetic field is static on the time scale of μSR. The presence of both a- and c-axis components of the internal magnetic field at the muon sites was revealed by transverse-field μSR experiments. This is in contrast to the pressure-induced antiferromagnetic state, where the internal magnetic field is parallel to the c-axis. We also found that the muon spin relaxation rate is further enhanced below the superconducting phase transition temperature, indicating further development of the internal magnetic field.

Quantum spin glass relaxation in UCu4Ni

Strong non-exponential relaxation due to magnetic disorder in UCu4Ni is observed in zero- and longitudinal-field μSR measurements in this material. Zero-field experiments reveal no evidence for spin freezing down to 20 mK. Qualitatively the shape of the muon asymmetry curves in longitudinal fields is strongly affected as the field is increased from zero and less so as the field is increased towards kOe values. Analysis of the time/field scaling (t/Hγ) for the asymmetry data, performed without reference to any specific decay function or model, together with the absence of spin freezing enables one to classify this system as a quantum-spin-glass; i.e., similar to UCu4Pd. However, in contrast with the behavior of the Pd material and similarly to the more conventional spin glass AgMn, UCu4Ni follows (t/Hγ) scaling only above applied fields of order 100 Oe. Unlike UCu4Pd which has been discussed extensively as partially ordered, disorder ought to be randomly distributed in UCu4Ni.

Muonium in nano-crystalline II–VI semiconductors

The effect of quantum confinement on shallow-donor muonium states and their ionization in nanocrystalline colloidal II–VI semiconductors was studied by the transverse- and longitudinal-field μSR techniques. Evidence is found for the formation of surface muon states on nanocrystalline ZnO with hydrogen passivated surfaces. On nanocrystalline CdSe capped with organic molecules the muons probably form states at the surface or substitute for hydrogen in the organic materials. The results obtained so far on nc-CdTe are suggestive of formation of a muonium state inside the nanocrystals, but further studies are needed to find a definitive proof.

μSR study on ferrimagnetic properties of potassium clusters incorporated into low silica X zeolite

Potassium clusters are stabilized in the cages of low silica X zeolite, where the cages with the inside diameter of ∼13 A are arrayed in a diamond structure. The average number of potassium atoms per cage, n, is changed from ∼6.3 to the saturated value of ∼8.8 by controlling the guest potassium loading density. The temperature dependence of magnetization shows the typical behavior of the N-type ferrimagnetism at n∼6.8 and n∼8.3. The zero field μSR spectra show significant increase in the relaxation rate below the Curie temperature, 5 K, in the sample with n∼6.8. The time dependence of asymmetry shows almost full amplitude of decrease, indicating that the internal field below the magnetic phase transition arises in the almost full volume of the sample. The longitudinal field μSR spectra at 1.7 K show the typical decoupling behavior of a static internal field. A model of ferrimagnetism is proposed based on the structure of the zeolite, where a magnetic sublattice of itinerant electron ferromagnetism is assumed.

19F NMR and longitudinal field μSR studies of the spin dynamics in LiY 0.998Ho 0.002F 4

It has recently been demonstrated that quantum tunneling of magnetization occurs between the low-lying electro-nuclear energy levels of Ho 3+ ions doped into LiYF 4. Here, we report 19F NMR and longitudinal field μSR measurements on single crystal LiY 0.998Ho 0.002F 4. We observe that the 19F spin-lattice relaxation rate 1/T 1 is controlled by the fluctuating field of the Ho ion and, consequently, 1/T 1 increases sharply at resonant magnetic field values where the energy levels are predicted to have level crossings/avoided level crossings, in agreement with the magnetization measurements. Complementary to these ongoing NMR studies we have undertaken longitudinal field μSR measurements. At low magnetic fields, the muon depolarization rate is dominated by strong depolarization due to the formation of F–muon–F bonds, while at higher fields the longitudinal field dominates, and any enhancement of the depolarization rate due to the energy level crossings is very weak.

μSR investigation of the magnetic ordering in EuAs 3

We have investigated the magnetic ordering and the incommensurate–commensurate phase transition in EuAs 3 by zero-field (ZF) and longitudinal-field μSR. In the commensurate phase, stable at temperatures below T L=10.3 K, the ZF muon signal exhibits oscillations corresponding to four muon precession frequencies the lowest of which behaves anomalously. The muon signal shows no oscillation but exponential decay in the incommensurate phase stable in temperature range from T L≈10.3 K up to T N≈11 K. The temperature dependence of the fitted relaxation rate shows divergence-like behaviour at the ordering temperature T N≈11 K and also at the lock-in transition T L≈10.3 K. The results are in qualitative agreement with those previously obtained by neutron and X-ray magnetic scattering investigations except for the anomalous temperature dependence of the lowest frequency in the commensurate phase. We propose a model for this anomalous behaviour.

Universal superconducting and magnetic properties of the (Ca xLa 1− x)(Ba 1.75− xLa 0.25+ x)Cu 3O y system: a μSR investigation

The (Ca x La 1− x )(Ba 1.75−xLa 0.25+ x ) Cu 3O y system is ideal for testing theories of high temperature superconductivity, since nearly the full range of doping is controlled by y, and T c max is continuously controlled by x, with minimal structural changes. We investigate this system with both transverse and longitudinal field μSR. This allows us to re-examine the Uemura relation, the nature of the spontaneous magnetic fields below T c, and the relation between their appearance temperature T g and T c max. Our major findings are: (1) the Uemura relation is respected by this system more adequately than by other cuprates, (2) T g and T c are controlled by the same energy scale, (3) the phase separation between hole poor and hole rich regions is a microscopic one, and (4) spontaneous magnetic fields appear gradually with no moment size evolution.

μSR and NMR in f-electron non-Fermi liquid materials

Magnetic resonance (μSR and NMR) studies of f-electron non-Fermi-liquid (NFL) materials give clear evidence that structural disorder is a major factor in NFL behavior. Longitudinal-field μSR relaxation measurements at low fields reveal a wide distribution of muon relaxation rates and divergences in the frequency dependence of spin correlation functions in the NFL systems UCu 5− x Pd x and CePtSi 1− x Ge x . These divergences seem to be due to slow dynamics associated with quantum spin-glass behavior, rather than quantum criticality as in a uniform system, for two reasons: the observed strong inhomogeneity in the muon relaxation rate, and the strong and frequency-dependent low-frequency fluctuation observed in U(Cu,Pd) 5 and CePt(Si,Ge). In the NFL materials CeCu 5.9Au 0.1, Ce(Ru 0.5Rh 0.5) 2Si 2, CeNi 2Ge 2, and YbRh 2Si 2 the low-frequency weight of the spin fluctuation spectrum is much weaker than in the disordered NFL systems.

Spin dynamics in granular Co xCu 1− x by μSR

Co x Cu 1− x samples with x=0.01,0.02,0.05 produced by melt spinning were probed with zero-field and longitudinal field μSR. For x=0.05, freezing into a spin glass state below 15 K is seen. Spectra between 15 and ∼150 K consist of the sum of two relaxation functions: a weakly dynamic Lorentzian Kubo–Toyabe (DLKT) and a root exponential (REX) relaxation. The cause is either a size distribution of precipitates or a strong heterogeneity in the spatial cluster arrangement. Above ∼150 K , relaxation is purely REX with the slow rate of 1.5 μs −1 , nearly independent of temperature. Persistent correlations between the clusters slow down the fluctuations of cluster moments and the state of free cluster moments is not reached in the temperature range investigated. The μSR response of the samples with lower Co concentration (0.2 and 0.1 at%) is characterized mainly by an increase of spin dynamics and a smaller mean field, implying a reduction of cluster–cluster couplings and a reduction of the moment of the precipitates. For x=0.1, a spin glass state is not formed down to 2 K .

Spin dynamics and spin disorder in frustrated TbCo xNi 1− xC 2

The orthogonal dicarbides RTC 2 ( R= rare earth , T= transition metal ) show ferromagnetic (fm) order of the R ions below T C ≈30 K for T=Co with a being the easy axis and antiferromagnetic (afm) order (with about the same transition temperature) for T=Ni with c as easy axis. The spin turning is caused by changes in the crystalline electric field (CEF) interaction. In the mixed TbCo x Ni 1− x C 2 alloys, fm and afm exchange on the one side and different CEF interactions on the other compete as a function of x. These competing interactions are a source of magnetic frustration. They also cause the materials to undergo several magnetic transitions into fm, afm or spin modulated structures which are well documented by neutron diffraction. Zero, longitudinal and transverse field μSR was carried out on TbCo x Ni 1− x C 2 with x=0.3, 0.5 0.7 and 0.85 using the same samples as in the neutron studies. Marked local spin disorder and persistent spin dynamics were seen in all magnetically ordered states as a consequence of frustration, but distinct differences exist for different values of x. Not all reported phase transition show clearly in the μSR data. In TbCo 0.85Ni 0.15C 2, a short-range dynamically correlated spin state having a strong fm polarizability exists above T C =30 K extending for about 50 K .

Spin dynamics in a structurally ordered non-Fermi-liquid compound: YbRh 2Si 2

Muon spin relaxation (μSR) experiments have been carried out at low temperatures in the non-Fermi-liquid heavy-fermion compound YbRh 2Si 2. The longitudinal-field μSR relaxation function is exponential, indicative that the dynamic spin fluctuations are homogeneous. The relaxation rate 1/ T 1 varies with applied field as H −y, y=1.0±0.1 , which implies a scaling law of the form χ″(ω)∝ω −yf(ω/T), lim x→0 f(x)=x for the dynamic spin susceptibility.

Hidden Order and Weak Antiferromagnetism in URu2Si2.

Abstract The origin and nature of the low-temperature phase appearing below 17.5 K (≡T 0 ) in URu2Si2 is still not fully understood. Since the weak antiferromagnetic state (WAF; μord∼0.02–0.04μB) developing below around T0 is not simply reconciled with a large reduction in the magnetic entropy (∼0.2R ln 2) , the existence of some hidden order parameter has been argued, where WAF is considered to be of a secondary nature. The paper reviews recent development of microscopic characterization of WAF based on neutron scattering and 29 Si NMR under high pressure. It is demonstrated that, at least, for pressures ranging from ∼0.3 to ∼0.83 GPa , there are spatially competing two different ordered states in the crystal: a normal-moment (∼0.25μB/U) antiferromagnetic state and some unknown, non-magnetically ordered state. Simple extrapolation to ambient pressure suggests that WAF originates from one percent volume fraction of this antiferromagnetic phase. We also discuss the unusual magnetic properties at ambient pressure, presenting our latest results of zero-field and longitudinal-field μSR experiments.

Hidden order and weak antiferromagnetism in URu2Si2

The origin and nature of the low-temperature phase appearing below 17.5K(≡T0) in URu2Si2 is still not fully understood. Since the weak antiferromagnetic state (WAF; μord∼0.02–0.04μB) developing below around T0 is not simply reconciled with a large reduction in the magnetic entropy (∼0.2Rln2), the existence of some hidden order parameter has been argued, where WAF is considered to be of a secondary nature. The paper reviews recent development of microscopic characterization of WAF based on neutron scattering and 29SiNMR under high pressure. It is demonstrated that, at least, for pressures ranging from ∼0.3 to ∼0.83GPa, there are spatially competing two different ordered states in the crystal: a normal-moment (∼0.25μB/U) antiferromagnetic state and some unknown, non-magnetically ordered state. Simple extrapolation to ambient pressure suggests that WAF originates from one percent volume fraction of this antiferromagnetic phase. We also discuss the unusual magnetic properties at ambient pressure, presenting our latest results of zero-field and longitudinal-field μSR experiments.

Quantum fluctuations of the magnetization in high spin molecules – a μSR study

Using zero field (ZF) and longitudinal field (LF) μSR we study the magnetic properties of high spin molecules (HSM) with spin S= 15 2 and 27 2 . The LF-μSR at very low temperatures suggests that in both our samples dynamical field fluctuations are responsible for the muon relaxation. The relaxation rate λ increases as the temperature decreases and then saturates below T< T c indicating that the dynamics is of quantum nature. The fluctuation rate at T→0 of the different samples is compared.