Linear Ac Susceptibility Research Articles

Unraveling the origin of the Griffiths phase in Ho2NiMnO6: perspectives from linear and nonlinear AC susceptibility

In this study, we investigated the magnetic ordering and underlying mechanism of the Griffiths phase, observed in Ho2NiMnO6 through AC susceptibility measurements. Our results indicate that the transition around 86 K corresponds to a paramagnetic to ferromagnetic transition characterized by classical magnetic ordering. Notably, nonlinear AC susceptibility measurements revealed the existence of ferromagnetic clusters within a paramagnetic background well above the transition temperature, establishing this as the origin of the Griffiths-like phase within the Ni/Mn sublattice of Ho2NiMnO6. Our study on the Ho2NiMnO6 system provides insight into the intricate magnetic phenomena common to various other strongly correlated electron systems.

Robust cycloid crossover driven by anisotropy in the skyrmion host GaV4S8

We report on the anomalous magnetization dynamics of the cycloidally-modulated spin textures under the influence of uniaxial anisotropy in multiferroic $\mathrm{GaV_4S_8}$. The temperature and field dependence of the linear ac susceptibility [$\chi_{1\omega}^{\prime}(T,H)$], ac magnetic loss [$\chi_{1\omega}^{\prime\prime}(T,H)$], and nonlinear ac magnetic response [$M_{3\omega}(T,H)$] are examined across the magnetic phase diagram in the frequency range $f = 10-10000$ Hz. According to recent theory, skyrmion vortices under axial crystal symmetry are confined along specific orientations, resulting in enhanced robustness against oblique magnetic fields and altered spin dynamics. We characterize the magnetic response of each spin texture and find that the dynamic rigidity of the N\'eel skyrmion lattice appears enhanced compared to Bloch-type skyrmions in cubic systems, even in the multidomain state. Anomalous $M_{3\omega}$ and strong dissipation emerge over the same phase regime where strong variations in the cycloid pitch were observed on lowering temperature in recent small-angle neutron scattering experiments [White et al., Phys. Rev. B 97, 020401(R) (2018)]. Here, we show that strong anisotropy also drives an extended crossover of the zero-field cycloid texture in $\mathrm{GaV_4S_8}$. The frequency dependence of these dynamic signatures is consistent with that of a robust anharmonic spin texture exhibiting a correlated domain arrangement. The results underpin the essential role of magnetic anisotropy in enhancing the rigidity of topological spin textures for diverse applications.

Intrinsic chiral-spin glass and spin glass transitions in compacted Ni5Al3/NiO core/shell nanoparticles

We report the first synthesis of the intermetallic compound ${\mathrm{Ni}}_{5}{\mathrm{Al}}_{3}$ in the nanocrystalline form. At the nanometer length scale, a stable ${\mathrm{Ni}}_{5}{\mathrm{Al}}_{3}$ compound (core) does not form without a NiO shell. Detailed structural and microstructural characterization as well as the compositional analysis indicate the presence of ${\mathrm{Ni}}_{5}{\mathrm{Al}}_{3}/\mathrm{NiO}$ core/shell nanoparticles and log-normal crystallite size distribution with mean size $d\phantom{\rule{4pt}{0ex}}\ensuremath{\simeq}$ 6 nm. ``Zero-field'' (dc magnetic field, $H=0$) linear (${\ensuremath{\chi}}_{1}$) and nonlinear (${\ensuremath{\chi}}_{n}$ with $n=2,3,4,5$) ac-magnetic susceptibilities have been measured as functions of temperature at various ac driving field amplitudes over three decades of frequency on the nanocrystalline samples ${\mathrm{S}}_{1}$ and ${\mathrm{S}}_{2}$ of composition ${\mathrm{Ni}}_{5+x}{\mathrm{Al}}_{3\ensuremath{-}x}/\mathrm{NiO}$ ($x=0.014$) and ${\mathrm{Ni}}_{5\ensuremath{-}x}{\mathrm{Al}}_{3+x}/\mathrm{NiO}$ ($x=0.038$), respectively. ${\ensuremath{\chi}}_{1}(T)$ and ${\ensuremath{\chi}}_{n}(T)$ are shown to provide conclusive evidence for the existence of two spin glass (SG) thermodynamic phase transitions: one at ${T}_{i}(H=0)\ensuremath{\simeq}138$ K and the other at a lower temperature ${T}_{p}(H=0)\ensuremath{\simeq}108$ K in both ${\mathrm{S}}_{1}$ and ${\mathrm{S}}_{2}$. Linear ac-susceptibility in superposed dc magnetic fields demonstrates that the thermodynamic nature of these transitions is preserved in finite fields and the $H\ensuremath{-}T$ phase diagrams for the samples ${\mathrm{S}}_{1}$ and ${\mathrm{S}}_{2}$ conform very well only with the $H\ensuremath{-}T$ phase diagram predicted by the chirality-driven spin glass (SG) ordering model for a three-dimensional nearest-neighbor Heisenberg SG system with weak random anisotropy. A detailed comparison between theory and experiment permits us to unambiguously identify various ``zero-field'' and ``in-field'' SG phase transitions as (i) the simultaneous paramagnetic (PM): chiral-spin glass (CG) and PM-SG phase transitions at ${T}_{i}(H)$ and (ii) the replica symmetry-breaking SG transition at ${T}_{p}(H)$.

Dynamic scaling analysis of the long-range RKKY Ising spin glass DyxY1−xRu2Si2

Dynamic scaling analyses of linear and nonlinear ac susceptibilities in a model magnet of the long-rang Ruderman-Kittel-Kasuya-Yosida (RKKY) Ising spin glass (SG) ${\mathrm{Dy}}_{0.103}{\mathrm{Y}}_{0.897}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ were examined. The obtained set of critical exponents, $\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 1, $\ensuremath{\beta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 1, $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 2, and $z\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 3.4, indicates the SG phase transition belongs to a universality class different from that of either the canonical (Heisenberg) or short-range Ising SGs. The analyses also reveal a finite-temperature SG transition with the same critical exponents under a magnetic field and the phase-transition line ${T}_{\text{g}}(H)$ described by ${T}_{\text{g}}(H)\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}{T}_{\text{g}}(0)(1\ensuremath{-}A{H}^{2/\ensuremath{\phi}})$, with $\ensuremath{\phi}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}$ 2. The crossover exponent $\ensuremath{\phi}$ obeys the scaling relation $\ensuremath{\phi}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}+\ensuremath{\beta}$ within the margin of errors. These results strongly suggest spontaneous replica-symmetry breaking (RSB) with a non- or marginal-mean-field universality class in the long-range RKKY Ising SG.

Evidence of cluster-glass-like state at low temperature in anti-site disordered La1.5Ca0.5CoMnO6 double perovskite

We have investigated structural and magnetic properties having cluster-glass (CG) like ordering at low temperature in a polycrystalline La1.5Ca0.5CoMnO6 double perovskite sample. In this anti-site disordered double perovskite, ferromagnetic (FM) ordering is observed at ∼157 K. From temperature variation linear ac susceptibility measurements, a CG state is clearly observed below a freezing temperature of ∼50.1 K, the origin of which can be best explained through (1) structural disorder and (2) consequence of the coexistence and competition of antiferromagnetic and FM interactions. The linear complex ac susceptibility data near the freezing temperature are best fitted to a critical slowing down model characterized by the dynamic exponents zυ ∼ 4.95(5) and τ0 ∼ 1.23 × 10−7 s. These values are very similar to what is generally observed in a CG system. The glassy transition temperature versus Hdc23 behaviour follows the Almeida-Thouless line. The time dependent slow relaxation dynamics and aging effect have also been investigated to confirm a CG-like state formation in this compound.

Chirality-driven intrinsic spin-glass ordering and field-induced ferromagnetism in Ni3Al nanoparticle aggregates

Weak itinerant-electron ferromagnet Ni3Al is driven to magnetic instability (quantum critical point, QCP, where the long-range ferromagnetic order of the bulk ceases to exist) by reducing the average crystallite size to d=50nm. ‘Zero-field’ (H=0) linear and nonlinear ac-susceptibilities, measured on Ni3Al nanoparticle aggregates, with d=50nm (S1) and d=5nm (S2), provide strong evidence for two spin glass (SG)-like thermodynamic phase transitions: one at Ti(H=0)≃30K (Ti†(H=0)≃230K) and the other at a lower temperature Tp(H=0)≃8K (Th(H=0)≃52K) in S1 (S2). ‘In-field’ (H≠0) linear ac-susceptibility and dc magnetization demonstrate that the thermodynamic nature of these transitions is preserved in finite fields. The presently determined H–T phase diagrams for the samples S1 and S2 are compared with those predicted by the Kotliar–Sompolinsky and Gabay–Toulouse mean-field models and Monte Carlo simulations, based on the chirality-driven spin glass (SG) ordering scenario, for a three-dimensional nearest-neighbor Heisenberg SG system with or without weak random anisotropy. Such a detailed comparison permits us to unambiguously identify various ‘zero-field’ and ‘in-field’ SG phase transitions as: (i) the simultaneous paramagnetic (PM)-chiral glass (CG) and PM-SG phase transitions at Ti(H), (ii) the PM-CG transition at Ti†(H), (iii) the replica symmetry-breaking SG transition at Tp(H), and (iv) the continuous spin-rotation symmetry-breaking SG transition at Th(H). In the presence of random anisotropy, magnetization fails to saturate even at 90kOe in S1 whereas negligibly small anisotropy allows even fields as weak as 1kOe to saturate magnetization and induce ferromagnetism in S2. Due to the proximity to CG/SG-QCP, magnetization and susceptibility both exhibit non-Fermi liquid behavior over a wide range at low temperatures.

Linear and nonlinear ac susceptibilities in polycrystalline low-bandwidth Pr1−xCaxMnO3(x = 0.0 − 0.3) manganite

The complex linear and nonlinear ac susceptibility have been thoroughly investigated in the low bandwidth manganite compound Pr1−xCaxMnO3 (PCMO) for the doping range x = 0.0–0.3 with and without a superimposed background dc field. The dynamical ac response shows substantial differences between the samples. The sample with x = 0.1 is found to have two separate magnetic transition peaks, compared to the single transitions in the samples x = 0.0 and x = 0.2. The nonlinear ac susceptibility measurements were compared between samples, which confirmed that these transition peaks are similar in nature and from the same magnetic origin. Additionally, for sample x = 0.3 a complex transition peak structure with overlapping transition peaks was found. This kind of evolution of the magnetic phases as a function of the Ca concentration is believed to rise from coexisting antiferromagnetic (AFM) and ferromagnetic (FM) orderings, where the Ca concentration controls the amount of FM clusters in the sample. The spin glass characteristics of these complex phase-separated magnetic regimes showed similarities and contradictions with conventional spin glasses, which indicates that this cluster glass behavior arises from the frustration between competing AFM and FM clusters having different magnetic exchange interaction.

Probing magnetic phase separation in manganites by nonlinear susceptibility

At low frequencies ν≤300Hz, nonlinear magnetic susceptibility of polycrystalline La0.7Pb0.3Mn0.8(Co, Ni)0.2O3 samples near the ferromagnetic (FM)–paramagnetic (PM) phase transition reinforces the earlier observation, based on linear ac susceptibility, that these systems behave as a three-dimensional isotropic dipolar ferromagnet in the asymptotic critical regime and exhibit an isotropic dipolar to isotropic Heisenberg crossover. In addition, the nonlinear susceptibility results reveal the phase segregation of the conducting and insulating FM phases (clusters) within the conducting FM regime and existence of conducting FM clusters in the insulating PM matrix at high frequencies.

Investigation of complex magnetic state in [formula omitted

We present here the results of a comprehensive study of the DC magnetization, linear and nonlinear AC susceptibility, DC resistivity and Magnetotransport behavior of the La0.8Bi0.2MnO3 polycrystalline manganite to understand its complex magnetic nature. The sample under study is synthesized by a conventional solid state route and is found to crystallize in rhombohedral structure having R3¯c group. A significant irreversibility between zero-field-cooled and field-cooled magnetization data with a broad peak in ZFC is clearly observed. Temperature variation of first and third order AC susceptibilities is in good agreement with Wohlfarth׳s Model for Superparamagnetism (SPM). The analysis of history dependence of DC magnetization, linear and non-linear AC susceptibility provides evidence of SPM like behavior associated along with weak ferromagnetism in the sample at low temperature. The results are supported by the electrical resistivity and Magnetotransport measurements.

The spin glass behavior in the Heusler alloy Cu2VAl

The magnetic properties of the Heulser alloy Cu2VAl were comprehensively investigated. A broad maximum at low temperature in both zero-field-cooled magnetization and the real part of the linear ac susceptibilities as well as a clear irreversibility between the zero-field-cooled and field-cooled magnetization curves were detected. The absence of the second harmonic ac susceptibility and a negative peak observed in the third harmonic ac susceptibility indicate its spin glass ground state. Fitting of the temperature dependences of the linear ac susceptibilities with different frequencies to the Vogel–Fulcher model and the critical slowing down power law confirms the spin glass nature of the detected magnetic behavior at low temperature in the Heusler alloy Cu2VAl.

Mn12 single molecule magnets deposited on μ-SQUID sensors: the role of interphases and structural modifications

Direct measurements of the linear ac susceptibility and magnetic relaxation of a few Mn12 monolayers deposited on a μ-SQUID sensor are reported. In order to integrate the molecules into the device, DPN has been the technique of choice. It enabled the structuration of the molecules on the most sensitive areas of the sensor without the need for any previous functionalization of the molecule or the substrate, while controlling the number of molecular units deposited on each array. The measurements reveal that their characteristic SMM behaviour is lost, a fact that is attributed to molecular distortions originated by the strong surface tensions arising at the molecular interphases.

Spin-glass and cluster ferromagnetism in RuSr2Y1.5Ce0.5Cu2O10 magneto-superconductor synthesized by HPHT

We report structural, DC magnetization, linear and non-linear AC susceptibility for phase pure RuSr2Y1.5Ce0.5Cu2O10 (YRu-1222) magneto-superconductor. The studied compound is synthesized through HPHT (high pressure high temperature: 6GPa, 1400°C) technique at NIMS-Japan. As synthesized YRu-1222, is crystallized in single phase tetragonal structure with space group I4/mmm. DC magnetic susceptibility showed that studied YRu-1222 is a magneto-superconductor with Ru spins magnetic ordering at around 120K and superconductivity in the Cu-O2 planes below ∼40K. The frequency and field dependent AC susceptibility measurements confirmed the spin-glass (SG) behavior with homogenous/non-homogenous ferromagnetic clusters for the studied system. The frequency variation followed the Vogel–Fulcher law with homogeneous/non-homogenous magnetically interacting ferromagnetic clusters embedded in spin-glass (SG) matrix. Detailed linear and non-linear AC susceptibility measurements are carried out to probe the exact magnetic nature of the studied magneto-superconductor YRu-1222.

Nanophase Separation and Magnetic Spin Glass in Nd<sub>2/3</sub>Ca<sub>1/3</sub>MnO<sub>3</sub>

A study of the low temperature magnetic state of polycrystalline colossal magnetoresistance perovskite Nd2/3Ca1/3MnO3 has been carried out. The data obtained, such as strongly divergent ZFC and FC static magnetizations and frequency dependent ac susceptibility, are evident of the glassy magnetic state of the system. Well defined maxima Tmax in the in-phase linear ac susceptibility χ curves were observed, indicating a spin-glass transition. Clear frequency dependence of the cusp temperature Tmax was found. The frequency dependence of Tmax was successfully analyzed by the dynamical scaling theory of a three-dimensional spin glass. Slow relaxation process and variety of relaxation times found imply a cluster glass magnetic state of the compound at low temperatures rather than a canonical spin glass state. The cluster glass state, accompanied by the multiple magnetic transitions of Nd2/3Ca1/3MnO3, might exist due to the competing interaction between the FM clusters and the AFM matrix induced by the complex nanophase segregated state of the compound.

Cluster glass magnetism in the phase-separated Nd2/3Ca1/3MnO3 perovskite

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd2/3Ca1/3MnO3 perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at Tg∼60K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature Tmax of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole–Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at “macroscopic” time scale. Slow relaxation in the zero-field-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below Tg, associated with its antiferromagnetic–ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature Tg and above it are strongly different. Magnetic field up to about μ0H∼0.4T suppresses the glassy magnetic state of the compound.

Suppression of itinerant ferromagnetism and a spin-glass-like state in Zn substitutedLa0.67Ca0.33MnO3

We examine the magneto-transport, static and dynamic magneticresponses of the single phase glassy insulating compoundLa0.67Ca0.33Mn1 − xZnxO3 (x = 0.10). Thiscompound undergoes a field induced metal–insulator transition and exhibits colossal magnetoresistancefor H ≥ 2 T. Many experimental features, such as a frequency dependent cusp inthe in-phase component of linear ac susceptibility at a temperatureT′f, a broadmaximum (at Ta) in the ZFC cooled thermo-magnetization close toT′f, large thermo-magneticirreversibility below Ta, non-saturation of magnetization at 5 K even under 12 T with a characteristic S shape in the virgincurve, monotonic increase of the coercivity at low fields under ZFC condition as one approaches theT′f, logarithmic relaxation of thermo-magnetization and ageing effects belowTa and a characteristic maximum in the magnetic viscosity below the spin-glass transition temperature(Tg) indicate a spin-glass-like state at low temperatures. This is further substantiated by theabsence of second order non-linear ac susceptibility, a characteristic negative maximum atTg in third order non-linearac susceptibility (χ′3), thecritical divergence of χ′3 as a function of temperature and ac probe field and an unusually large linear term in thelow temperature specific heat.

Effects of A-site disorder on magnetic, electrical and thermal properties of La 0.5− xLn xCa 0.5− ySr yMnO 3manganites

The magnetic, electrical and thermal properties in the La 0.5− x Ln x Ca 0.5− y Sr y MnO 3 (Ln=Pr, Nd, Sm) bulk system were investigated. Detailed dc magnetization and linear ac susceptibility measurements reveal that the samples first undergo phase transition from paramagnetic to ferromagnetic phase and then to an antiferromagnetic phase upon further cooling. It is found that both the Curie and Neel temperatures decrease systematically with increasing A-site disorder in these manganites. The electrical resistivity exhibits semiconducting behavior throughout the temperature range investigated and the electronic conduction mechanism can be conveniently described within the framework of the variable range hopping model above T=150 K. The Seebeck coefficient ( S) in the magnetically ordered regime infers that the complicated temperature dependence of S is an indication of electron–magnon scattering. Specific heat measurements depict a broadened hump in the vicinity of T C , indicating the existence of magnetic ordering and magnetic inhomogeneity in the samples. The temperature dependence of thermal conductivity, κ( T), reveals a positive d κ/d T in the paramagnetic region, which may be related to the local anharmonic lattice distortions associated with small polarons.

Classical and quantum nonlinear phenomena in molecular magnetic clusters

We review recent studies, experimental and theoretical, of the nonlinear magnetic response of Mn12 single-molecule magnets. Compared with the linear ac susceptibility, which has become the standard tool to ascertain whether a molecular cluster possesses magnetic memory (i.e. whether it behaves as a “single-molecule magnet”), the nonlinear susceptibility provides additional information on the relaxation process at a little cost in terms of experimental time and complexity. The nonlinear dynamic susceptibility depends not only on the relaxation times, as the linear susceptibility does, but also on how sensitive the relaxation process is to external magnetic fields. We show that the presence of spin quantum tunneling, and its strong dependence on external bias that detune the tunneling levels, gives rise to a very large contribution to the nonlinear response of Mn12 clusters. Just like tunneling itself, this “quantum nonlinearity” can be “switched off and on” by external magnetic fields. By studying the orientational dependence of the nonlinear susceptibility, we estimate a bound for the decoherence time due to the coupling to the phonon bath. We find that, for tunneling via thermally activated states of Mn12 acetate, decoherence is not limited by the lifetime of the excited states, but by a much shorter timescale of order 10−11 s.

Ordered, Disordered, and Coexistent Stable Vortex Lattices inNbSe2Single Crystals

The peak effect (PE) in the critical current density of type II superconductors has been related to an order-disorder transition in the vortex lattice (VL), but its underlying physics remains a controversial issue. Intrinsic to the PE are strong metastabilities that frequently mask the stationary VL configurations. We follow shaking and thermal protocols in NbSe2 single crystals to access these configurations and examine them by linear ac susceptibility measurements that avoid VL reorganization. We identify three different regions. For T<T1(H), stable VL configurations are maximally ordered. For T>T2(H), configurations are fully disordered and no metastability is observed. In the T1<T<T2 region, we find temperature-dependent stable configurations with an intermediate degree of disorder, possibly associated with the coexistence of ordered and disordered lattices throughout the PE.

Linear and nonlinear susceptibility effects inY2Fe17andEr2Fe17

The thermal dependence of the linear and nonlinear ac susceptibilities of the ferromagnetic ${\mathrm{Y}}_{2}{\mathrm{Fe}}_{17}$ and of the ferrimagnetic ${\mathrm{Er}}_{2}{\mathrm{Fe}}_{17}$ intermetallic compounds is investigated as a function of the amplitude and frequency of the applied ac field. In both compounds, the change of sign at ${T}_{C}$ and the behavior below and above the ferromagnetic or ferrimagnetic transition temperature are well explained in terms of divergence of the nonlinear susceptibility. Low temperature transitions detected by real and imaginary components of the fundamental ac susceptibility are related to the coupling of domain-wall dynamics and mobility defects. The thermal behavior of the linear and third order susceptibilities has been tentatively divided in different regions with different relaxation phenomena. Moreover, nonlinear effects due to the annealing procedure have been analyzed and discussed.

Modes of Periodic Domain Wall Motion in Ultrathin Ferromagnetic Layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.