Nonlinear 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.

Influence of the Azimuthal Angle on the Dynamic Forced Response of the Magnetization of Nanoparticles in Superimposed Ac and Dc Bias Field

A consistent study of the consequence of the azimuthal angle φ on the susceptibility and the hysteresis of the nanoparticles is performed, we treat the problem with Brown’s magnetic equation thereby extending the statistical moment method. The (DMH) loops are obtained, the principal-axis of the magnetization is oriented to the direction of the field under an any azimuthal angle. It’s demonstrated that the hysteresis and the nonlinear ac susceptibility powerfully depend on the Azimuthal angle φ.

Nonlinear Magnetic Properties of Magnetic Fluids for Automotive Applications

The external magnetic field required to activate a magnetic fluid in an industrial application is sufficiently large that magnetization is no longer a linear function of the external field strength, i.e. magnetic fluids exhibit nonlinear characteristics. The aim of our research was to develop a measuring system which is capable of determining the nonlinear AC susceptibility of magnetic fluids at discrete frequencies and in the presence of a high-intensity driving magnetic field. The measurement of susceptibility is based on the determination of the change in frequency of a low-intensity field, which is generated by an LC oscillator. The application of sinusoidal excitation to the material results in a variation in the susceptibility that modulates the frequency of the measured low-intensity field and in the appearance of higher-order harmonics of the driving field. The higher-order components of the nonlinear AC susceptibility are extracted from the measured response by Fourier analysis. By applying the measuring system, the nonlinear susceptibility of water-based ferrofluids (Ferrotec’s EMG 700) and its dependence on the magnetic field strength were investigated.

Geometrical surface pinning in the nonlinear AC susceptibility of HTS tapes

The analytic expression for the nonlinear magnetic susceptibility of a thin disk derived from Bean’s model with a uniform J C for predicts a peak-peak ratio of 7.1 (5.4) for the real (imaginary) components of the third harmonic χ 3 susceptibility. Our measurements show a peak-peak ratio closer to 1.1 in the real component and a noise limited lower estimate of ≈ 7 in the imaginary component. The anomalous third harmonic can be explained by the presence of a geometrical surface barrier for flux entry and exit which we have included as a small region of enhanced current density, J C,G, close to the surface of the disk. The geometrical surface current density is predicted to be approximately equal to J C,G ≈ 2B C1/μ 0 d. In 2G HTS tapes with d ≈ 1μm and B C1 ≈ 5mT this is J C,G ≈ 8GAm−2. We have measured both J C,B and J C,G using the nonlinear susceptibility of a Superpower tape without artificial pinning in fields orthogonal to the tape up to 35T. We find a geometrical surface current of J C,G ≈ 10GAm−2 and an average critical current density J C which is in good agreement with transport measurements performed on material from the same reel of tape.

Magnetic glassy behaviour coupled with long range non-collinear magnetic order in Tb3Co

Detailed and systematic study of rare earth rich intermetallic compound Tb3Co, using dc magnetisation, neutron powder diffraction, and linear and non-linear ac-susceptibilities, shows the presence of an unexpected magnetic glassy state along with complex non-collinear or modulated antiferromagnetic (AFM) order. Our neutron diffraction study shows that the magnetic structure remains more or less the same except for a decrease in moment values in the temperature range of 2 K–70 K and rules out any phase transition around 30 K. However, it reveals sharp changes in structural parameters around 30 K, which indicates strong spin-lattice coupling and change in strength. It appears to be mainly responsible for the observed increase in ZFC magnetisation on warming around 30 K. Another important unexpected result of this study is the strong frequency dispersion in linear and non-linear (higher order harmonics) ac-susceptibilities below K. The analysis in terms of various spin glass theoretical formulisms and even stronger frequency dispersion in non-linear susceptibilities provides evidence for the presence of a spin glass like state in Tb3Co. The final picture that emerges out of this study is that a spin glass like state coexists with the long range modulated AFM order below 72 K.

Cluster-glass dynamics of the Griffiths phase in Tb5−xLaxSi2Ge2

The static magnetization and dynamic susceptibility responses of the cluster system within a Griffiths phase of the magnetocaloric compound ${\mathrm{Tb}}_{5\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Si}}_{2}{\mathrm{Ge}}_{2}$ ($x=0.075$) have been investigated. A novel cluster-glass state within the Griffiths phase is formed at a characteristic freezing temperature where short-range ferromagnetic correlations set in the paramagnetic regime. Ferromagneticlike correlations are built up at around 155 K, which suddenly become frozen at a lower temperature $\ensuremath{\sim}140\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, thus in analogy with a reentrant spin glass behavior. The ac susceptibility near the freezing temperature follows a critical slowing down process characterized by ${\ensuremath{\tau}}_{0}={10}^{\ensuremath{-}13}s$ and dynamic exponents $\mathrm{z}\ensuremath{\nu}\ensuremath{\sim}6$ and $\ensuremath{\beta}\ensuremath{\sim}0.4$, similar to well-known spin glass systems. The nonlinear ac susceptibility analysis shows clearly the existence of a transition associated to the reentrant behavior. The origin of the intermediate cluster-glass phase inside the Griffiths phase is proposed to be the result of a combination of short-ranged RKKY intralayer positive exchange interactions between rare-earth ${\mathrm{Tb}}^{3+}$ ions and antiferromagnetic exchange between adjacent interlayers involving Si and Ge atoms in connection to the ${\mathrm{Tb}}^{3+}$ atoms.

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.

Anomalous re-entrant glassy magnetic phase in LaMn0.5Co0.5O3 single crystals

We report an anomalous re-entrant glassy magnetic phase in (l00) oriented ferromagnetic LaMn0.5Co0.5O3 single crystals. The characterization is fortified with conventional magnetometry, like linear as-well-as non-linear ac susceptibility and specific heat. As the sample is cooled below the ferromagnetic transition temperature, it reenters a glassy magnetic phase whose dynamics have little resemblance with the conventional response. The glassy transition shifts to a higher temperature with increasing frequency of the applied ac field. But it does not respond to the dc biasing or memory experiment. Specific heat as well as nonlinear ac susceptibility data also do not relate to the conventional glassy response. Unusually low magnetic entropy indicates the lack of long range magnetic ordering. The results demonstrate that the glassy phase in LaMn0.5Co0.5O3 is not due to any of the known conventional origins. We infer that the competing ferromagnetic and antiferromagnetic interaction due to high B-site disorder is responsible for this anomalous re-entrant glassy phase.

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.

Co-existence of Griffiths phase and ferromagnetic insulating state in electron doped nanomanganite

Detailed temperature dependent magnetic and transport properties of electron doped Sm0.09Ca0.91MnO3 nanomanganite exhibiting Griffiths phase (GP) have been investigated. A GP-like behavior having ferromagnetic spin correlation above ferromagnetic transition temperature (TC) without any spontaneous magnetization has been observed in this nanomanganite. Moreover, in this electron doped nanomanganite, the experimental large effective magnetic moment and deviation of the inverse susceptibility from Curie–Weiss law clearly indicate the possible existence of GP. The complex non-linear ac susceptibilities (2nd and 3rd harmonics) have also been studied to explore the role of nature of disorder in the GP phenomenon. The transport measurements yield a ferromagnetic insulating ground state exhibiting colossal magneto resistance (CMR) near the ferromagnetic transition temperature. It has also been reported that the temperature dependent average spin moment at the hopping site and the ferromagnetic phase fraction bear the signature of the onset of GP.

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.

Correspondence between neutron depolarization and higher order magnetic susceptibility to investigate ferromagnetic clusters in phase separated systems

It is a tough task to distinguish a short-range ferromagnetically correlated cluster-glass phase from a canonical spin-glass-like phase in many magnetic oxide systems using conventional magnetometry measurements. As a case study, we investigate the magnetic ground state of La0.85Sr0.15CoO3, which is often debated based on phase separation issues. We report the results of two samples of La0.85Sr0.15CoO3 (S-1 and S-2) prepared under different conditions. Neutron depolarization, higher harmonic ac susceptibility and magnetic relaxation studies were carried out along with conventional magnetometry measurements to differentiate subtle changes at the microscopic level. There is no evidence of ferromagnetic correlation in the sample S-2 attributed to a spin-glass phase, and this is compounded by the lack of existence of a second order component of higher harmonic ac susceptibility and neutron depolarization. A magnetic relaxation experiment at different temperatures complements the spin glass characteristic in S-2. All these signal a sharp variance when we consider the cluster-glass-like phase (phase separated) in S-1, especially when prepared from an improper chemical synthesis process. This shows that the nonlinear ac susceptibility is a viable tool to detect ferromagnetic clusters such as those the neutron depolarization study can reveal.

Coexistence of interacting ferromagnetic clusters and small antiferromagnetic clusters in La0.5Ba0.5CoO3

We report detailed dc magnetization and linear and nonlinear ac susceptibility measurements on the hole doped disordered cobaltite La0.5Ba0.5CoO3. Our results show that the magnetically ordered state of the system consists of coexisting non-ferromagnetic phases along with percolating ferromagnetic clusters. The percolating ferromagnetic clusters possibly start a magnetic ordering at the Curie temperature of 201.5(5) K. The non-ferromagnetic phases mainly consist of antiferromagnetic clusters with size smaller than the ferromagnetic clusters. Below the Curie temperature the system exhibits an irreversibility in the field cooled and zero field cooled magnetization and a frequency dependence in the peak of ac susceptibility. These dynamical features indicate the possible coexistence of spin-glass phase along with ferromagnetic clusters similar to La1−xSrxCoO3 (x ≥ 0.18), but the absence of field divergence in the third harmonic of ac susceptibility and zero field cooled memory clearly rule out any such possibility. We argue that the spin-glass phase in La1−xSrxCoO3 (x ≥ 0.18) is associated with the presence of incommensurate antiferromagnetic ordering in non-ferromagnetic phases, which is absent in La0.5Ba0.5CoO3. Our analysis shows that the observed dynamical features in La0.5Ba0.5CoO3 may be due to progressive thermal blocking of ferromagnetic clusters, which is further confirmed by Wohlfarth’s model of superparamagnetism. The frequency dependence of the peak of ac susceptibility obeys the Vogel–Fulcher law with τ0 ≈ 10−9 s. This together with the existence of an AT-line in H–T space indicates the presence of significant inter-cluster interaction among these ferromagnetic clusters.

Nonlinear susceptibility and dynamic hysteresis loops of magnetic nanoparticles with biaxial anisotropy

The nonlinear ac susceptibility and dynamic magnetic hysteresis (DMH) of a single domain ferromagnetic particle with biaxial anisotropy subjected to both external ac and dc fields of arbitrary strength and orientation are treated via Brown's continuous diffusions model [W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963)] of magnetization orientations. The DMH loops and nonlinear ac susceptibility strongly depend on the dc and ac field strengths, the polar angle between the easy axis of the particle, the external field vectors, temperature, and damping. In contrast to uniaxial particles, the nonlinear ac stationary response and DMH strongly depend on the azimuthal direction of the ac field and the biaxiality parameter Δ.

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.

Physical and Magnetic Properties of Sm<sub>0.2</sub>Gd<sub>0.8</sub>Ni<sub>4</sub>B Compound

Physical properties of theSm0.2Gd0.8Ni4Bcompound have been investigated by means of theX-ray powder diffraction, DC and AC-susceptibility techniques. The compound studied crystallizes in CeCo4B type structure withP6/mmmspace group. The unit-cell parametersaand c are determined as 5.01 and 6.95 Å, respectively, and the unit-cell volumeVis calculated as 151.08 Å3. DC and AC magnetic measurements present the visible magnetic phase transition from paramagnetic to ferromagnetic, around definite transition temperature. The magnetic phase transition temperature of the compound is obtained from DC magnetization, AC-susceptibility and the well known Kouvel-Fisher method as 36.6, 35.7 and 35.2 K, respectively. The saturation magnetization (Ms) and the coercive fields (Hc) of the compound are found to be 3.7µB/f.u and 277 Oe, respectively, by using the hysteresis loops at 9.5 K. We have also investigated the non-linear AC-susceptibility of the compound, around its ferromagnetic transition temperature, as a function of temperature, frequency and amplitude of the AC-driving field. In order to explain the measured experimental results, we have used the theory developed for ferromagnetic, based upon the mean field model. The measurements exhibit both frequency and amplitude dependencies. Observed dependencies are compared with the existing theories of linear and nonlinear susceptibilities with reference to short- and long-range interactions. In Kouvel-Fisher method, one plots1/χ1*(dχ-1/dT)againstT,obtaining a straight line. The slope of this line gives the critical exponent γ,and it intersects theTaxis atTc.In order to obtaindχ-1/dTand the best straight line, we used a two-point numerical differentiation program and linear regression method, respectively. The critical exponent γ of the sample is calculated to be 2.78 ± 0.05. The value of the critical exponent β, which is characteristic of static phase transition to a ferromagnetic state, is estimated as 2.41±0.3 from the slope of the line obtained the plot of the absolute third-harmonic values versus the reduced temperature on a log–log scale.

Evidence of glassy ferromagnetic phase and kinetic arrest of electronic phase in Sm0.35Pr0.15Sr0.5MnO3 manganites

The effect of doping of rare earth Pr3+ ion as a replacement of Sm3+ in Sm0.5Sr0.5MnO3 is investigated. Temperature dependent dc and ac magnetic susceptibility, resistivity, magnetoresistance measurements on chemically synthesized (Sm0.5−xPrx)Sr0.5MnO3 show various unusual features with doping level x=0.15. The frequency independent ferromagnetic to paramagnetic transition at higher temperature (∼191K) followed by a frequency dependent reentrant magnetic transition at lower temperature (∼31K) has been observed. The nature of this frequency dependent reentrant magnetic transition is described by a critical slowing down model of spin glasses. From non-linear ac susceptibility measurements it has been confirmed that the finite size ferromagnetic clusters are formed as a consequence of intrinsic phase separation, and undergo spin glass-like freezing below a certain temperature. There is an unusual observation of a 2nd harmonic peak in the non-linear ac susceptibility around this reentrant magnetic transition at low temperature (∼31K). Arrott plots at 10 and 30K confirm the existence of glassy ferromagnetism below this low temperature reentrant transition. Electronic- and magneto-transport measurements show a strong magnetic field—temperature history dependence and strong irreversibility with respect to the sweeping of magnetic field. These results are attributed to the effect of phase separation and kinetic arrest of the electronic phase in this phase separated manganite at low temperatures.

Magnetic phase diagrams based on static and dynamic magnetic behaviour in Ru-based superconducting ferromagnets

In this work, we present magnetic phase diagrams of a RuSr2Eu1.5Ce0.5Cu2O10−δ (Ru-1222) superconducting ferromagnet derived from its static and dynamic magnetic responses, measured by temperature and field dependences of dc magnetization and nonlinear ac susceptibility in both low and high magnetic fields. Comparison of magnetic phase diagrams of phase pure and impure samples singles out the intrinsic and extrinsic magnetic features, naturally proposing a unified model of Ru-1222 magnetic behaviour. The results considered within the proposed interpretation indicate full agreement between static and dynamic properties which, if measured in combination, effectively complement each other, uncovering existing ambiguities.

Determination of the magnetic ground state in the martensite phase of Ni–Mn–Z (Z = In, Sn and Sb) off-stoichiometric Heusler alloys by nonlinear AC susceptibility

DC and AC magnetic measurements were carried out to clarify thedifference in the magnetic ground state depending on the kinds ofZ element used in the martensite phase in Ni–Mn–Z (Z = In,Sn and Sb) off-stoichiometric Heusler alloys. Magnetic field cooling effects were observed in theDC thermomagnetization curves in the low temperature regions, and a frequency dependenceon AC susceptibility was also observed in both real and imaginary parts of the susceptibility.Negative divergence was clearly observed in nonlinear AC susceptibility only for theNi50Mn40Sb10 alloy, suggesting that the magnetic feature of its ground state is the spin-glass state. Themagnetic ground state of the martensite phase in these alloys would relate to themagnetic configuration of the Mn atoms in the ferromagnetic austenite phase.