Magnetostriction Measurements Research Articles

Origin of the uniaxial magnetic anisotropy in cobalt ferrite induced by spark plasma sintering

Cobalt ferrite (CFO) is a promising candidate for magnetostrictive applications like actuators or sensors. We have recently shown that uniaxial magnetic anisotropy can be induced in CFO by reactive sintering using spark plasma sintering (SPS), which leads to an improvement of its magnetostrictive properties. However, the origin of the anisotropy and the formation mechanism remain unexplained so far. In this study, different SPS processes have been conducted to determine which parameter is responsible for the induced uniaxial anisotropy. We demonstrate that the magnetic anisotropy arises during the cooling step when done under SPS’s uniaxial compression. In addition, we also investigate the fundamental origin of the magnetic anisotropy induced during the SPS process. We show that the polycrystalline anisotropic cobalt ferrite obtained after SPS exhibits no texture. However, the SPS samples turn isotropic after being annealed in air at 400 °C/2 h, as shown by magnetic and magnetostrictive measurements. A change in ionic distribution after the annealing is also observed by Mössbauer spectroscopy. Our findings suggest that the induced magnetic anisotropy results from the ionic distribution of the Co2+ in the CFO’s spinel lattice, a mechanism previously observed in magnetic annealed CFO. This study advances the in-depth understanding of the relationship between SPS processing and magnetic properties of cobalt ferrite.

Elastic response of U3Cu4Ge4 to spontaneous and field-induced phase transitions

${\mathrm{U}}_{3}{\mathrm{Cu}}_{4}{\mathrm{Ge}}_{4}$ is a uniaxial ferromagnet that displays a first-order magnetization process (FOMP) at 25 T for field applied along the hard $b$ axis. Here, we report on ultrasound and magnetostriction measurements of ${\mathrm{U}}_{3}{\mathrm{Cu}}_{4}{\mathrm{Ge}}_{4}$ in static and pulsed magnetic fields up to 40 T. The FOMP causes stepwise anomalies in the magnetoelastic properties. ${\mathrm{U}}_{3}{\mathrm{Cu}}_{4}{\mathrm{Ge}}_{4}$ elongates along the $a$ and $c$ axes and shrinks along the $b$ axis, leading to an almost zero volume effect. The sound velocities of the longitudinal and transverse acoustic waves decrease sharply at the FOMP, whereas the sound attenuation shows pronounced peaks. An analysis of the ultrasound data using a mean-field theory suggests the existence of quadrupolar interactions and crystal-electric-field effects. The $5f$ electronic states are between itinerant and localized, typical of uranium-based intermetallic compounds.

Complex magnetic phase diagram with a small phase pocket in a three-dimensional frustrated magnet CuInCr4S8

Frustrated magnets with a strong spin-lattice coupling can show rich magnetic phases and the associated fascinating phenomena. A promising platform is the breathing pyrochlore magnet ${\mathrm{CuInCr}}_{4}{\mathrm{S}}_{8}$ with localized $S=3/2\phantom{\rule{4pt}{0ex}}{\mathrm{Cr}}^{3+}$ ions, which is proposed to be effectively viewed as an $S=6$ Heisenberg antiferromagnet on the face-centered-cubic lattice. Here we unveil that ${\mathrm{CuInCr}}_{4}{\mathrm{S}}_{8}$ exhibits a complex magnetic phase diagram with a small phase pocket ($A$ phase) by means of magnetization, magnetostriction, magnetocapacitance, and magnetocaloric-effect measurements in pulsed high magnetic fields of up to 60 T. Remarkably, the appearance of $A$ phase is accompanied by anomalous magnetostrictive and magnetocapacitive responses, suggesting the emergence of helimagnetism in contrast to the neighboring commensurate magnetic phases. Besides, the high-entropy nature is confirmed in the high-temperature side of $A$ phase. These features are potentially related to a thermal fluctuation-driven multiple-$q$ state caused by the magnetic frustration, which has been theoretically predicted but yet experimentally undiscovered in insulating magnets.

Study on high damping L12/D03 biphase Fe-27Ga alloys with near-zero magnetostriction and its damping mechanism

A novel L12/D03 biphase Fe-27Ga alloy with both high damping (0.007, equivalent to a specific damping capacity (SDC) of 0.04) and the near-zero (∼−4 ppm) magnetostriction has been prepared by using an appropriate heat treatment process: annealing at 480 °C for 1 h. Here the L12 phase proportion is about 44.8%. More importantly, the damping mechanism of L12/D03 biphase Fe-27Ga alloy has been deeply studied based on the experiments of amplitude-dependent IF measurements with and without magnetic field, combined with the magnetostriction measurements. All the results indicate that for the L12/D03 biphase Fe-27Ga alloy, D03 phase with a magnetic damping plays a dominant role under a lower strain amplitude while L12 phase with a non-magnetic damping plays a main role under a higher strain amplitude. At the same time, the L12/D03 biphase Fe-27Ga alloy with more L12 phase has a higher damping capacity under a higher strain amplitude, which is mainly the non-magnetic damping contribution originated from the twin boundaries movement. This can provide a new way and design concept for high damping Fe-Ga alloys to satisfy more application requirements, such as micro-vibration field, strong vibration field, magnetic or non-magnetic field.

Structural and magnetoelastic properties of non-stoichiometric TbFe2Mnx Laves phase

In this paper, we studied TbFe2Mnx alloys using x-ray powder diffraction, x-ray fluorescent analysis, differential scanning calorimetry, scanning electron microscopy, and magnetostriction measurements. It was established that single phase non-stoichiometric TbFe2Mnx compounds are formed up to Mn concentration x = 0.25. The non-stoichiometric TbFe2Mnx compounds possess huge spontaneous magnetostriction in [111] direction (up to 2550 ppm) which result to distortion cubic MgCu2-type structure to rhombohedral (R3¯m) at room temperature. The formation of non-stoichiometric TbFe2Mnx compounds results from partial substitution of Tb by Mn in (6c) positions. It was found a characteristic value for the cubic MgCu2-type lattice parameter ac ≈ 7.2 Å. If binary RT2 (R is a rare-earth metal, T – 3d transitional metal) compounds have lattice parameter smaller than 7.2 Å, we can expect large values of Mn concentration (x > 0.4) in non-stoichiometric RT2Mnx compounds. The Mn doping in TbFe2Mn0.25 compound led to significant increase of magnetostriction at liquid nitrogen temperature (λ|| ≈ 2400 ppm in magnetic field 18 kOe) which is 25 % larger than that of initial TbFe2. It also preserve large magnetostriction at room temperature (λ|| ≈ 1530 ppm in magnetic field 18 kOe). This make non-stoichiometric TbFe2Mn0.25 compound promising material for various magnetostrictive applications in wide temperature range.

Giant magnetostriction in low-concentration magnetorheological elastomers

Magnetorheological elastomers (MREs) are smart composite materials that can vary their mechanical properties under the influence of an external magnetic field. In the present work, we report the giant magnetostriction of low-concentration isotropic and anisotropic MREs, by combining a soft elastomer matrix with helicoidal-shaped particles. Magnetic characterization has shown high magnetic sensitivity of the anisotropic MREs near H ≅ 0, which can be up to 400% larger comparing to the isotropic counterparts. The determination of tensile elastic modulus (E) of the MREs indicates that the anisotropic samples become softer when the magnetic field is increased from H = 0 to H = 200 Oe. Due to the higher field sensitivity of the anisotropic composites, the magneto-induced elongation contributes to the increase in the overall strain when measuring the elastic modulus at low deformation. This compliance of the MRE explains the decrease in E from H = 0 to H = 200 Oe. Magnetostriction measurements were performed and giant strain values up to 3731 ppm were obtained for isotropic samples with 3.4 vol% of Hiperco particles under a field of H = 3500 Oe. This result stands out from the literature due to the giant induced elongation, with reduced volume fraction of particles. The developments of this work are a step forward on improving smart and efficient composites, that can have many applications, such as switches, controllable valves, and vibration attenuators.

Detection of relativistic fermions in Weyl semimetal TaAs by magnetostriction measurements

Thus far, a detection of the Dirac or Weyl fermions in topological semimetals remains often elusive, since in these materials conventional charge carriers exist as well. Here, measuring a field-induced length change of the prototype Weyl semimetal TaAs at low temperatures, we find that its c-axis magnetostriction amounts to relatively large values whereas the a-axis magnetostriction exhibits strong variations with changing the orientation of the applied magnetic field. It is discovered that at magnetic fields above the ultra-quantum limit, the magnetostriction of TaAs contains a linear-in-field term, which, as we show, is a hallmark of the Weyl fermions in a material. Developing a theory for the magnetostriction of noncentrosymmetric topological semimetals and applying it to TaAs, we additionally find several parameters characterizing the interaction between the relativistic fermions and elastic degrees of freedom in this semimetal. Our study shows how dilatometry can be used to unveil Weyl fermions in candidate topological semimetals.

New method to optimize no-load noise of power transformers based on core design & transformer operating conditions

This paper introduces a new algorithm to calculate and optimize no-load noise (sound pressure) of power transformers, and to identify iron sheet parameters. The calculation consists of two steps: the 1st step consists in calculating an initial sound pressure level (A-Evaluation) which has approx. 70 % accuracy within a tolerance interval of ±2dB (A). The 2nd step consists in estimating the expected deviation from the initial calculation to reach 90 % accuracy in the final results. This deviation could be due to material handling, quality tolerance, core manufacturing, etc. The optimization process consists of two parts: the 1st part takes place before choosing a certain iron sheet for calculation to identify the sheet parameters required for computational accuracy (“Sheet Optimization”). The 2nd part consists in considering a core design with an undesirable sound pressure level in order to reduce it to an acceptable limit. This part takes into account the other limitations such as no-load losses and transformer dimensions (“Design Optimization”). For new iron sheets in the market, there is no measurement history to rely on. However, the algorithm is also capable of identifying the sheet parameters for calculation based on the available algorithm data base and the magnetostriction measurements of the iron sheet manufacturer.

Magnetovolume Effect on the First-Order Metamagnetic Transition in UTe2

The link between the metamagnetic transition and novel spin-triplet superconductivity of UTe$_2$ was discussed thermodynamically through magnetostriction measurements in a pulsed-magnetic field. We revealed a discontinuous magnetostriction across the metamagnetic transition at $\mu_0H_{\rm m}\approx 35$~T for the applied magnetic fields along the crystallographic $b$ axis in the orthorhombic structure. The resultanting volume magnetostriction of $\Delta V/V \approx-5.9\times 10^{-4}$ gives the initial pressure dependence of $H_{\rm m}$ by employing the Clausius-Clapeyron's equation, which agrees with previous pressure experiments. Further, significant anisotropic magnetostriction (AMS), derived by subtracting the averaged linear magnetostriction, was revealed. Contrary to the weakly field-dependent AMS along the $a$ axis, those along the $b$ and $c$ axes show strong field dependences with a similar magnitude but with opposite signs, indicating its lattice instability. The relationship between characteristic energy scales of magnetic fields and temperatures was discussed in terms of the Gr\"uneisen parameters compared to the other $f$-electron systems. The volume shrinkage in UTe$_2$ at $H_{\rm m}$, contrary to the volume expansion in typical heavy fermion metamagnets, pushes to invoke the link with the valence instability related to the itinerant-localized dual nature of the U magnetism.

Linear magnetoelastic coupling and magnetic phase diagrams of the buckled-kagomé antiferromagnet [Formula: see text

Single crystals of Cu_3Bi(SeO_3)_2O_2Cl were investigated using high-resolution capacitance dilatometry in magnetic fields up to 15 T. Pronounced magnetoelastic coupling is found upon evolution of long-range antiferromagnetic order at T_{mathrm {N}} = 26.4(3) K. Grüneisen analysis reveals moderate effects of uniaxial pressure on T_{mathrm {N}}, of 1.8(4) K/GPa, -0.62(15) K/GPa and 0.33(10) K/GPa for p parallel a, b, and c, respectively. Below 22 K Grüneisen scaling fails which implies the presence of competing interactions. The structural phase transition at T_{mathrm {S}} = 120.7(5) K is much more sensitive to uniaxial pressure than T_{mathrm {N}}, with strong effects of up to 27(3) K/GPa (p parallel c). Magnetostriction and magnetization measurements reveal a linear magnetoelastic coupling for Bparallel c below T_{mathrm {N}}, as well as a mixed phase behavior above the tricritical point around 0.4 T. An analysis of the critical behavior in zero-field points to three-dimensional (3D) Ising-like magnetic ordering. In addition, the magnetic phase diagrams for fields along the main crystalline axes are reported.

Tricritical fluctuations and elastic properties of the Ising antiferromagnet UIrSi3

Elastic constants, thermal expansion, magnetostriction, and heat capacity measurements were performed with and without applied magnetic field on a single crystal of ${\mathrm{UIrSi}}_{3}$. The elastic properties were interpreted within the theory of the strain-exchange effect. The exchange-striction model together with the Ising model for the behavior of magnetic localized $5f$ electrons and itinerant electrons of uranium correctly reproduces the main features of our magneto-acoustic experiments in ${\mathrm{UIrSi}}_{3}$. Data on thermal expansion and magnetostriction confirm the conclusion that the dominant contribution of the measured temperature and field change in the speed of sound comes from the change in the elastic modulus itself. Based on the analysis of heat capacity measurements in the magnetic field, we explain the significant anomalies at the second-order branch of the phase transition boundary as a manifestation of the tricritical fluctuations, dominating the region below the tricritical point. The outcome confirms the three-dimensional Ising model, at zero and low magnetic fields, with a crossover to the mean-field tricritical behavior at fields close to the tricritical point, where tricritical fluctuations dominate the temperature evolution of the given property.

Elastic study of electric quadrupolar correlation in the paramagnetic state of the frustrated quantum magnet Tb2+δTi2−δO7

The electric quadrupolar state in the frustrated quantum magnet ${\mathrm{Tb}}_{2+\ensuremath{\delta}}{\mathrm{Ti}}_{2\ensuremath{-}\ensuremath{\delta}}{\mathrm{O}}_{7}$ has been studied by means of ultrasonic and magnetostriction measurements. A single crystal showed an elastic anomaly around 0.4 K, manifesting a long-range quadrupole ordering. By investigating the anisotropy of the magnetoelastic responses, we found a crossover temperature for the strongly correlated quadrupole state, below which the experimental data of the elastic constant and magnetostriction become qualitatively different from their calculations based on a single-ion model. We suppose that relatively high onset temperature of the quadrupole correlation compared with the transition temperature is ascribed to the geometrical frustration effect, and this correlated state seems to be responsible for the unusual properties in the paramagnetic state of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$.

Study on magnetostriction characteristics under different measurement conditions under an externally compressive stress

The measurement of magnetostriction characteristics of grain-oriented electrical steel strip under an external compressive stress has always been a main focus in the process of magnetostriction measurement. There are difficulties in the measurement of magnetostriction, especially under compressive stress, mainly because the thickness of test specimen is small, and the test specimen is very easy to deform under the compressive stress. A weight should be placed on the test specimen to prevent a deformation of the test specimen when the measurement of magnetostriction characteristics under an externally compressive stress according to the IEC/TR 62581:2010. But how much weight and how to place aren’t concerned in IEC standard. In this paper, different weights were placed on the grain-oriented electrical steel test specimen under external compressive stress and zero stress. Through analyzed the measured magnetostriction data under different weights to determine the optimal measurement method of grain-oriented electrical steel strip under compressive stress and zero stress. The purpose of this paper is to find the most accurate and high reproducibility measurement method of magnetostriction, which can truly reflect the magnetostriction performance of grain-oriented electrical steel.

Stress-dependent nonlinear magnetoelectric effect in press-fit composites: A numerical and experimental study

Magnetoelectric (ME) composites have posed an immense research interest over the past few decades. Their multifunctional capabilities enable a wide array of applications like field and pressure sensors, energy harvesters, gyrators, etc. The voltage developed under applied magnetic fields in these composites is governed strongly by the stress and magnetization state of the magnetostrictive phase, which needs to be characterized effectively. Towards this end, magnetostriction measurements are carried out under applied stresses in Nickel to understand its magnetomechanical response. A three-dimensional magnetostrictive constitutive model is used to predict the magnetostrictive behavior, which is later implemented in COMSOL Multiphysics® using the external material module. The FE solutions obtained are validated against analytical solutions. The model is subsequently used to obtain FE solutions for the magnetoelectric response of press-fit composites subjected to general magneto-thermo-mechanical loading. Experiments are performed on the press-fit composite to validate the voltage response predicted by the developed model, which shows a good agreement. The developed FE model is used to conduct a parametric study to quantify the effect of external loading conditions, the shape of inclusion, and the field orientation with an effort to optimize the ME response in press-fit ME composites.

Origin of Metamagnetic Transition (MMT) in the Spin-Triplet Superconductivity in UTe2

State-of-the-art magnetostriction measurements in a pulsed-magnetic field reveal the origin of a metamagnetic transition of spin-triplet superconductor UTe2. We propose that the uranium valence fluctuation plays a crucial role in its metamagnetic and superconducting transitions.

Phase diagram of CeSb2 from magnetostriction and magnetization measurements: Evidence for ferrimagnetic and antiferromagnetic states

Cerium diantimonide ($\mathrm{Ce}{\mathrm{Sb}}_{2}$) is one of a family of rare-earth-based magnetic materials that exhibit metamagnetism, enabling control of the magnetic ground state through an applied magnetic field. At low temperatures, $\mathrm{Ce}{\mathrm{Sb}}_{2}$ hosts a rich phase diagram with multiple magnetically ordered phases for many of which the order parameter is only poorly understood. In this paper, we report a study of its metamagnetic properties by scanning tunneling microscopy (STM) and magnetization measurements. We use STM measurements to characterize the sample magnetostriction with subpicometer resolution from magnetic field and temperature sweeps. This allows us to directly assess the bulk phase diagram as a function of field and temperature and relate spectroscopic features from tunneling spectroscopy to bulk phases. Our magnetostriction and magnetization measurements indicate that the low-temperature ground state at zero field is ferrimagnetic. Quasiparticle interference mapping shows evidence for a reconstruction of the electronic structure close to the Fermi energy upon entering the magnetically ordered phase.

Possible antiferroquadrupolar order in the Kondo semiconductor CeOs4Sb12

We report the results of dc magnetization, thermal expansion, and magnetostriction measurements of the Kondo semiconductor ${\mathrm{CeOs}}_{4}{\mathrm{Sb}}_{12}$. These results provide a magnetic-field--temperature phase diagram for the three principal axes of the cubic crystal [100], [110], and [111] and reveal the magnetic anisotropy of the three ordered phases A, B, and C. The magnetic anisotropy of the transition temperature ${T}_{\mathrm{C}}$ from the paramagnetic phase to the C phase is ${T}_{\mathrm{C}}^{[111]}>{T}_{\mathrm{C}}^{[110]}>{T}_{\mathrm{C}}^{[100]}$. At low temperatures, the magnetization has a distinct magnetic anisotropy in high magnetic fields: ${M}^{[100]}>{M}^{[110]}>{M}^{[111]}$. This ratio of magnetization is in good agreement with that of the magnetically anisotropic ${\mathrm{\ensuremath{\Gamma}}}_{67}$ quartet. The observation indicates that the crystalline electric field ground state is a ${\mathrm{\ensuremath{\Gamma}}}_{67}$ quartet and that the $c\text{\ensuremath{-}}f$ hybridization effect is nearly isotropic. In addition, comparison of the present experimental results with numerical calculations of a two-sublattice model using the mean-field approximation suggests that the C phase is a ${\mathrm{\ensuremath{\Gamma}}}_{5}$-type antiferroquadrupolar ordered state despite the presence of strong $c\text{\ensuremath{-}}f$ hybridization effects. In this case, the increase in ${T}_{\mathrm{C}}$ due to the external field is mainly caused by the ${\mathrm{\ensuremath{\Gamma}}}_{2}$-type antiferro-octupolar interaction.

Phase transition in the 5d1 double perovskite Ba2CaReO6 induced by high magnetic field

Magnetic properties of an antiferromagnetic double perovskite oxide Ba2CaReO6, where Re6+ (5d1) ions with large spin-orbit coupling are arranged on the face-centered-cubic lattice, are investigated using pulsed high magnetic field up to 66 T. Magnetization and magnetostriction measurements have revealed a magnetic field induced phase transition at around 50 T. The phase transition accompanies a jump of magnetization and longitudinal magnetostriction of approximately 2 10^(-4) with the change of power law behavior, indicating sizable coupling between the electronic degrees of freedom and the lattice. The high field phase exhibits a magnetic moment approximately 0.2 {\mu}B, which is close to the values observed in 5d1 double perovskite oxides with non-collinear magnetic structure. We argue that Ba2CaReO6 is an antiferromagnet that sits close to the phase boundary between the collinear and non-collinear phases, providing the target material for investigating the interplay between spin-orbital entangled electrons and magnetic field.

Magnetization and thermal expansion measurements on the Ising magnet SmPt2Si2 : Potential coexistence of spin glass and antiferromagnetic states

The Ising magnet $\mathrm{Sm}{\mathrm{Pt}}_{2}{\mathrm{Si}}_{2}$ undergoes an antiferromagnetic (AFM) transition at ${T}_{\mathrm{N}1}$ = 5.6 K, but the magnetic moments of some Sm ions remain disordered even below ${T}_{\mathrm{N}1}$. Here, we report the results of measurements of thermal expansion, magnetostriction, and dc magnetization of $\mathrm{Sm}{\mathrm{Pt}}_{2}{\mathrm{Si}}_{2}$ in the temperature range from 0.26 to 7 K. The magnetization and thermal expansion results show clear irreversible phenomena at temperatures below ${T}_{\mathrm{g}}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}$ 2.4 K. These results suggest that the partially disordered state of the Sm ions becomes a cluster spin glass below ${T}_{\mathrm{g}}$ and coexists with the AFM long-range order. However, unlike the conventional coexistence of spin glass and antiferromagnetism, the isothermal magnetization process at 0.26 K shows a hysteresis curve with almost no remanent magnetization. This observation suggests that the cluster spin glass state is an unusual state with a short relaxation time at zero field.

Field-induced anomalous magnetic state beyond the magnetically ordered state in the slightly distorted triangular S=12 rare-earth antiferromagnet CeZn3P3

Magnetic properties of ${\mathrm{CeZn}}_{3}{\mathrm{P}}_{3}$, which has been believed to have the same hexagonal ${\mathrm{ScAl}}_{3}{\mathrm{C}}_{3}$-type crystal structure as that of a spin dimer system of ${\mathrm{YbAl}}_{3}{\mathrm{C}}_{3}$ at room temperature, have been investigated by magnetization, magnetostriction, specific heat ($C$), and magnetocaloric effect measurements. In this research, we have found that ${\mathrm{CeZn}}_{3}{\mathrm{P}}_{3}$ certainly has a slightly deformed crystal structure from the hexagonal one even at room temperature, which is in contrast to the structural phase transition of ${\mathrm{YbAl}}_{3}{\mathrm{C}}_{3}$ occuring at around 80 K, although the very slight deformation along the $c$ plane, i.e., slightly deformed triangular lattice, and the formation of the multidomain structure are common to both compounds. ${\mathrm{CeZn}}_{3}{\mathrm{P}}_{3}$ is thought to maintain its deformed structure from a high-temperature region above room temperature to an extremely low-temperature region and shows a magnetic order below ${T}_{\mathrm{N}}=0.8$ K. The analysis of the temperature dependence of the magnetic susceptibility ($\ensuremath{\chi}$) and $C$ has revealed that a Kramers doublet ground state with an easy-plane type anisotropy on the $c$ plane is well isolated from the excited states by the crystal field splitting energy of more than 300 K. Above ${T}_{\mathrm{N}}, \ensuremath{\chi}$ makes a broad peak at around 2 K, which certainly originates from the dimer formation due to the slight deformation of the triangular lattice. On the other hand, below ${T}_{\mathrm{N}}$, a magnetic phase diagram reminiscent of a magnetic flower blooming on the $c$ plane was observed, which may have a close relation to a quantum effect of a quasi $S=\frac{1}{2}$ spin system and a contribution of the orbital component. With increasing magnetic field, we have found an anomalous magnetic state beyond the usual magnetically ordered state, where $C/T$ is anomalously enhanced. This anomalous magnetic state is similar to that observed in ${\mathrm{YbAl}}_{3}{\mathrm{C}}_{3}$ induced by the field, although the magnetic ground state in ${\mathrm{YbAl}}_{3}{\mathrm{C}}_{3}$ is a nonmagnetic dimer state different from the normal magnetically ordered state in ${\mathrm{CeZn}}_{3}{\mathrm{P}}_{3}$.