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Modeling of a magnetic field sensor based on spin Hall magnetoresistance
Authors:
Syeda Farwa Bukhari,
Alessandro Magni,
Witold Skowroński,
Elena Losero,
Vittorio Basso,
Carlo Appino,
Piotr Wiśniowski,
Juergen Langer,
Berthold Ocker,
Dario Daghero,
Michaela Kuepferling
Abstract:
Next-generation spintronic sensors aim to overcome the limitations of traditional tunneling-magnetoresistance (TMR) devices, such as complex manufacturing, high $1/f$ noise, and significant offsets. This work presents a comprehensive modeling and experimental validation of a magnetic field sensor based on Spin Hall Magnetoresistance (SMR) in a Wheatstone bridge configuration. Utilizing a multiphys…
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Next-generation spintronic sensors aim to overcome the limitations of traditional tunneling-magnetoresistance (TMR) devices, such as complex manufacturing, high $1/f$ noise, and significant offsets. This work presents a comprehensive modeling and experimental validation of a magnetic field sensor based on Spin Hall Magnetoresistance (SMR) in a Wheatstone bridge configuration. Utilizing a multiphysics approach, we simulate the interplay between SMR, Anisotropic Magnetoresistance (AMR), and Spin-Orbit Torque (SOT) using a Stoner-Wohlfarth model complemented by a Fuchs-Sondheimer analysis of current distribution. To account for the presence of magnetic domains, we incorporate a modified Stoner-Wohlfarth framework that considers non-uniform magnetization and domain wall motion through a "truncated astroid" approach, allowing for a statistical distribution of single-domain particles. The model is validated against experimental measurements of Pt/$\text{Fe}_{60}\text{Co}_{20}\text{B}_{20}$ and Ta/$\text{Fe}_{60}\text{Co}_{20}\text{B}_{20}$ bilayers patterned into Hall bars and Wheatstone bridges. The model provides critical design guidelines for optimizing material properties, layer thickness, and device layout to minimize power consumption and maximize sensitivity in SMR-based sensing applications.
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Submitted 20 February, 2026;
originally announced February 2026.
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The spontaneous Nernst coefficient of ferromagnets from the interplay of electron scattering and Berry curvature
Authors:
Vittorio Basso,
Adriano Di Pietro,
Alessandro Sola
Abstract:
We employ the Boltzmann transport approach to derive the spontaneous Nernst coefficient for ferromagnetic metals, explicitly treating the transverse current density due to Berry curvature as a Fermi surface property. We find that the spontaneous Nernst coefficient is proportional to the inverse of the scattering time constant, implying that efficient spontaneous Nernst materials should exhibit rel…
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We employ the Boltzmann transport approach to derive the spontaneous Nernst coefficient for ferromagnetic metals, explicitly treating the transverse current density due to Berry curvature as a Fermi surface property. We find that the spontaneous Nernst coefficient is proportional to the inverse of the scattering time constant, implying that efficient spontaneous Nernst materials should exhibit relatively strong scattering, a stark contrast to ordinary Nernst materials. Furthermore, we establish a direct connection between the strength and sign of the spontaneous Nernst coefficient and the itinerant contribution to orbital angular momentum density arising from the Bloch bands. Finally we construct a rigid two-bands model to evaluate the thermoelectric coefficients by which we find a good agreement with the signs and orders of magnitude of the experimental coefficients of magnetic 3d transition metal ferromagnets. We finally propose some practical recipes for maximizing the spontaneous Nernst effect through electronic band structure tailoring.
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Submitted 25 June, 2026; v1 submitted 12 August, 2025;
originally announced August 2025.
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Effect of bismuth crystal orientations in Nernst thermomagnetic devices
Authors:
Alessandro Sola,
Elena Sonia Olivetti,
Adriano Di Pietro,
Luca Martino,
Vittorio Basso
Abstract:
In this work we report Nernst effect measurements in single crystal bismuth samples, with special emphasis on the characterization of the Nernst coefficient when the magnetic field, heat current and generated voltage are aligned along specific directions relative to the crystal axes. We found significant differences between the different orientations, reflecting the highly anisotropic electronic s…
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In this work we report Nernst effect measurements in single crystal bismuth samples, with special emphasis on the characterization of the Nernst coefficient when the magnetic field, heat current and generated voltage are aligned along specific directions relative to the crystal axes. We found significant differences between the different orientations, reflecting the highly anisotropic electronic structure of bismuth and compatible with the Nernst characteristics obtained from polycrystalline samples. These results not only complement the experimental works published in the past but also underline the role of crystalline orientation in the context of transverse thermoelectric effects, towards an efficient design of thermomagnetic devices like the ordinary-Nernst-effect-based energy harvesters.
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Submitted 29 January, 2025;
originally announced January 2025.
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Disentangling electric field effect on spin waves in ferromagnetic insulators
Authors:
Vittorio Basso,
Patrizio Ansalone,
Adriano Di Pietro
Abstract:
In this paper we extend the micromagnetic theory of magnetostatic surface waves in insulating ferromagnetic thin films to include the applied electric field effects. We start by identifying the two main effects on the dispersion relation: the first one is of relativistic nature and emerges as a consequence of the Ahronov-Casher effect, while the second one is a consequence of the electric field in…
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In this paper we extend the micromagnetic theory of magnetostatic surface waves in insulating ferromagnetic thin films to include the applied electric field effects. We start by identifying the two main effects on the dispersion relation: the first one is of relativistic nature and emerges as a consequence of the Ahronov-Casher effect, while the second one is a consequence of the electric field induced symmetry breaking operating at the level of magnetic exchange interactions. We support our theory by comparing its predictions with experimental data on ittrium iron garnet thin films taken from the literature. The main result is to evidence the limitations of using the same value of the applied electric field to address both effects and to emphasize that crystal symmetry breaking due to the applied electric field brings about the contributions of the crystal field and determines different amplitudes for the two effects.
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Submitted 17 June, 2024;
originally announced June 2024.
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Hard Ferromagnets as a New Perspective on Materials for Thermomagnetic Power Generation Cycles
Authors:
Anthony N. Tantillo,
Alexander Barcza,
Volker Zellmann,
Vittorio Basso,
Martino LoBue,
Nora M. Dempsey,
Karl G. Sandeman
Abstract:
We consider the ways in which magnetically hard materials can be used as the working materials in thermomagnetic power generation (TMG) cycles in order to expand the area in the magnetisation vs. applied field ($M-H$) plane available for energy conversion. There are 3 parts to this Perspective. First, experiments on commercially available hard ferrites reveal that, while these materials are not ye…
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We consider the ways in which magnetically hard materials can be used as the working materials in thermomagnetic power generation (TMG) cycles in order to expand the area in the magnetisation vs. applied field ($M-H$) plane available for energy conversion. There are 3 parts to this Perspective. First, experiments on commercially available hard ferrites reveal that, while these materials are not yet good TMG candidates, hard ferromagnets with higher thermal conductivity and a greater change of magnetization with temperature could outperform existing TMG materials. Second, computational results indicate that biasing a soft magnet with a hard ferromagnet is essentially equivalent to shifting the $M-H$ loop by an amount proportional to the field of the biasing magnet. Work outputs under biased conditions show a substantial improvement over unbiased cycles, but experimental verification is needed. Third, we discuss the rationale for exploring artificial spin reorientation materials as novel TMG working materials.
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Submitted 20 January, 2023;
originally announced January 2023.
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Magnetocaloric effect at the reorientation of the magnetization in ferromagnetic multilayers with perpendicular anisotropy
Authors:
Vittorio Basso,
Carlo P. Sasso,
Martino LoBue,
Karl G. Sandeman
Abstract:
We investigate the magnetocaloric effect obtained by the rotation of a magnetic field applied to an exchange-coupled multilayer system composed of two different ferromagnetic (FM) materials. We specifically consider a system in which the two FMs have perpendicular uniaxial anisotropy axes and utilise conditions which yield a reorientation of the total magnetization when compensation between the an…
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We investigate the magnetocaloric effect obtained by the rotation of a magnetic field applied to an exchange-coupled multilayer system composed of two different ferromagnetic (FM) materials. We specifically consider a system in which the two FMs have perpendicular uniaxial anisotropy axes and utilise conditions which yield a reorientation of the total magnetization when compensation between the anisotropies of the two layers occurs. We calculate the consequent entropy change associated with the "artificial" reorientation. By using known parameters from MnBi and Co we predict an entropy change of $Δs = 0.34$ Jkg$^{-1}$K$^{-1}$ for perfect coupling. Lastly, we study the behavior of the multilayer under a rotating magnetic field via a micromagnetic model. When the layer thicknesses are of the order of the local domain wall width, the magnetic field-induced entropy change can be obtained with magnetic fields one order of magnitude lower than in the uncoupled case.
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Submitted 9 June, 2023; v1 submitted 20 November, 2022;
originally announced November 2022.
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Polycrystalline MnBi as a transverse thermoelectric material
Authors:
Alessandro Sola,
Elena Olivetti,
Luca Martino,
Vittorio Basso
Abstract:
To assess the potential of polycrystalline MnBi as a transverse thermoelectric material, we have experimentally investigated its anomalous Nernst effect (ANE) by means of the heat flux method. We prepared MnBi samples by powder metallurgy; this technique allows the preparation of samples in arbitrary shapes with the possibility to tailor their magnetic properties. In the material exhibiting the hi…
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To assess the potential of polycrystalline MnBi as a transverse thermoelectric material, we have experimentally investigated its anomalous Nernst effect (ANE) by means of the heat flux method. We prepared MnBi samples by powder metallurgy; this technique allows the preparation of samples in arbitrary shapes with the possibility to tailor their magnetic properties. In the material exhibiting the highest remanent magnetization, we found a value of the ANE thermopower of -1.1 $μ$V/K at 1 T, after the compensation of the ordinary Nernst effect from pure bismuth present inside the polycrystalline sample. This value is comparable with those reported in the literature for single crystals.
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Submitted 17 November, 2022;
originally announced November 2022.
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Gauge theory applied to magnetic lattices
Authors:
A. Di Pietro,
P. Ansalone,
V. Basso,
A. Magni,
G. Durin
Abstract:
Micromagnetic exchange is usually derived by performing the continuum limit of the Heisenberg model on a cubic lattice, where the exchange integrals are assumed to be identical for all nearest neighbors. This limitation normally imposes the use of a microscopic theory to explain the appearance of higher order magnetic interactions such as the Dzyaloshinskii-Moriya interaction (DMI). In this paper…
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Micromagnetic exchange is usually derived by performing the continuum limit of the Heisenberg model on a cubic lattice, where the exchange integrals are assumed to be identical for all nearest neighbors. This limitation normally imposes the use of a microscopic theory to explain the appearance of higher order magnetic interactions such as the Dzyaloshinskii-Moriya interaction (DMI). In this paper we combine graph- and gauge field- theory to simultaneously account for the symmetries of the crystal, the effect of spin-orbit coupling and their interplay on a micromagnetic level. We obtain a micromagnetic theory accounting for the crystal symmetry constraints at all orders in exchange and show how to successfully predict the form of micromagnetic DMI in all 32 point groups.
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Submitted 9 September, 2022;
originally announced September 2022.
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Temperature dependence of the mean magnon collision time in a spin Seebeck device
Authors:
Vittorio Basso,
Alessandro Sola,
Patrizio Ansalone,
Michaela Kuepferling
Abstract:
Based on the relaxation time approximation, the mean collision time for magnon scattering $τ_c(T)$ is computed from the experimental spin Seebeck coefficient of a bulk YIG / Pt bilayer. The scattering results to be composed by two processes: the low temperature one, with a $T^{-1/2}$ dependence, is attributed to the scattering by defects and provides a mean free path around 10 $μ$m; the high tempe…
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Based on the relaxation time approximation, the mean collision time for magnon scattering $τ_c(T)$ is computed from the experimental spin Seebeck coefficient of a bulk YIG / Pt bilayer. The scattering results to be composed by two processes: the low temperature one, with a $T^{-1/2}$ dependence, is attributed to the scattering by defects and provides a mean free path around 10 $μ$m; the high temperature one, depending on $T^{-4}$, is associated to the scattering by other magnons. The results are employed to predict the thickness dependence of the spin Seebeck coefficient for thin films.
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Submitted 12 January, 2021;
originally announced January 2021.
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Local spin Seebeck imaging with scanning thermal probe
Authors:
Alessandro Sola,
Vittorio Basso,
Massimo Pasquale,
Carsten Dubs,
Craig Barton,
Olga Kazakowa
Abstract:
In this work we present the results of an experiment to locally resolve the spin Seebeck effect in a high-quality Pt/YIG sample. We achieve this by employing a locally heated scanning thermal probe to generate a highly local non-equilibrium spin current. To support our experimental results, we also present a model based on the non-equilibrium thermodynamic approach which is in a good agreement wit…
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In this work we present the results of an experiment to locally resolve the spin Seebeck effect in a high-quality Pt/YIG sample. We achieve this by employing a locally heated scanning thermal probe to generate a highly local non-equilibrium spin current. To support our experimental results, we also present a model based on the non-equilibrium thermodynamic approach which is in a good agreement with experimental findings. To further corroborate our results, we index the locally resolved spin Seebeck effect with that of the local magnetisation texture by MFM and correlate corresponding regions. We hypothesise that this technique allows imaging of magnetisation textures within the magnon diffusion length and hence characterisation of spin caloritronic materials at the nanoscale.
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Submitted 18 May, 2020;
originally announced May 2020.
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Measurement of the heat flux normalised spin Seebeck coefficient of thin films as a function of temperature
Authors:
G. Venkat,
C. D. W. Cox,
A. Sola,
V. Basso,
K. Morrison
Abstract:
The spin Seebeck effect (SSE) has generated interest in the thermoelectric and magnetic communities for potential high efficiency energy harvesting applications, and spintronic communities as a source of pure spin current. To understand the underlying mechanisms requires characterisation of potential materials across a range of temperatures, however, for thin films the default measurement of an ap…
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The spin Seebeck effect (SSE) has generated interest in the thermoelectric and magnetic communities for potential high efficiency energy harvesting applications, and spintronic communities as a source of pure spin current. To understand the underlying mechanisms requires characterisation of potential materials across a range of temperatures, however, for thin films the default measurement of an applied temperature gradient (across the sample) has been shown to be compromised by the presence of thermal resistances. Here, we demonstrate a method to perform low temperature SSE measurements where instead of monitoring the temperature gradient, the heat flux passing through the sample is measured using two calibrated heat flux sensors. This has the advantage of measuring the heat loss through the sample as well as providing a reliable method to normalise the SSE response of thin film samples. We demonstrate this method with an $\text{SiO}_{2}/\text{Fe}_{3}O_{4}/\text{Pt}$ sample, where a semiconducting-insulating transition occurs at the Verwey transition, $T_{\text{V}}$, of $\text{Fe}_{3}\text{O}_{4}$ and quantify the thermomagnetic response above and below $T_{\text{V}}$.
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Submitted 17 March, 2020;
originally announced March 2020.
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Electric field effect on spin waves and magnetization dynamics: role of magnetic moment current
Authors:
Vittorio Basso,
Patrizio Ansalone
Abstract:
We show that a static electric field $E_x$ gives rise to a shift of the spin wave dispersion relation $ω(q_y-q_E)$ in the direction of the wavenumber $q_y$ of the quantity $q_E=-γ_LE_x/c^2$. This effect is caused by the magnetic moment current carried by the spin wave itself that generates an additional phase proportional to the electric field, as in the Aharonov-Casher effect. This effect is inde…
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We show that a static electric field $E_x$ gives rise to a shift of the spin wave dispersion relation $ω(q_y-q_E)$ in the direction of the wavenumber $q_y$ of the quantity $q_E=-γ_LE_x/c^2$. This effect is caused by the magnetic moment current carried by the spin wave itself that generates an additional phase proportional to the electric field, as in the Aharonov-Casher effect. This effect is independent from the possibly present magneto-electric effects of insulating ferromagnets and superimposes to them. By extending this picture to arbitrary magnetization dynamics, we find that the electric field gives rise to a dynamic interaction term which has the same chiral from of the Dzyaloshinskii-Moriya interaction but is fully tunable with the applied electric field.
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Submitted 7 November, 2019;
originally announced November 2019.
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Spincaloritronic measurements: a round robin comparison of the longitudinal spin Seebeck effect
Authors:
A. Sola,
V. Basso,
M. Kuepferling,
M. Pasquale,
D. Meier,
G. Reiss,
T. Kuschel,
T. Kikkawa,
K. Uchida,
E. Saitoh,
H. Jin,
S. Boona,
S. Watzman,
J. Heremans,
M. B. Jungfleisch,
W. Zhang,
J. E. Pearson,
A. Hoffmann,
H. W. Schumacher
Abstract:
The rising field of spin caloritronics focuses on the interactions between spin and heat currents in a magnetic material; the observation of the spin Seebeck effect opened the route to this branch of research. This paper reports the results of a round robin test performed by five partners on a single device highlighting the reproducibility problems related to the measurements of the spin Seebeck c…
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The rising field of spin caloritronics focuses on the interactions between spin and heat currents in a magnetic material; the observation of the spin Seebeck effect opened the route to this branch of research. This paper reports the results of a round robin test performed by five partners on a single device highlighting the reproducibility problems related to the measurements of the spin Seebeck coefficient, the quantity that describes the strength of the spin Seebeck effect. This work stimulated the search for more reproducible measurement methods through the analysis of the systematic effects.
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Submitted 3 December, 2018;
originally announced December 2018.
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Experimental proof of the reciprocal relation between spin Peltier and spin Seebeck effects in a bulk YIG/Pt bilayer
Authors:
Alessandro Sola,
Vittorio Basso,
Michaela Kuepferling,
Carsten Dubs,
Massimo Pasquale
Abstract:
We verify for the first time the reciprocal relation between the spin Peltier and spin Seebeck effects in a bulk YIG/Pt bilayer. Both experiments are performed on the same YIG/Pt device by a setup able to accurately determine heat currents and to separate the spin Peltier heat from the Joule heat background. The sample-specific value for the characteristics of both effects measured on the present…
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We verify for the first time the reciprocal relation between the spin Peltier and spin Seebeck effects in a bulk YIG/Pt bilayer. Both experiments are performed on the same YIG/Pt device by a setup able to accurately determine heat currents and to separate the spin Peltier heat from the Joule heat background. The sample-specific value for the characteristics of both effects measured on the present YIG/Pt bilayer is $(6.2 \pm 0.4)\times 10^{-3} \,\, \mbox{KA$^{-1}$}$. In the paper we also discuss the relation of both effects with the intrinsic and extrinsic parameters of YIG and Pt and we envisage possible strategies to optimize spin Peltier refrigeration.
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Submitted 13 November, 2018;
originally announced November 2018.
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Kinetics of heat flux avalanches at the first order transition in La(Fe-Mn-Si)$_{13}$-H$_{1.65}$ compounds
Authors:
Marco Piazzi,
Cecilia Bennati,
Vittorio Basso
Abstract:
We study heat flux avalanches occurring at the first order transition in La(Fe-Mn-Si)$_{13}$-H$_{1.65}$ magnetocaloric material. As the transition is associated to the phase boundaries motion that gives rise to the latent heat, we develop a non equilibrium thermodynamic model. By comparing the model with experimental calorimetry data available for Mn=0.18, we find the values of the intrinsic kinet…
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We study heat flux avalanches occurring at the first order transition in La(Fe-Mn-Si)$_{13}$-H$_{1.65}$ magnetocaloric material. As the transition is associated to the phase boundaries motion that gives rise to the latent heat, we develop a non equilibrium thermodynamic model. By comparing the model with experimental calorimetry data available for Mn=0.18, we find the values of the intrinsic kinetic parameter $R_L$, expressing the damping for the moving boundary interface, at different magnetic fields. We conclude that by increasing field, thus approaching the critical point, the avalanches increase in number and their kinetics is slowed down.
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Submitted 11 September, 2017;
originally announced September 2017.
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Basics of the magnetocaloric effect
Authors:
Vittorio Basso
Abstract:
This chapter reviews the basic physics and thermodynamics that govern magnetocaloric materials. The thermodynamics of magnetic materials is discussed by introducing relevant free energy terms together with their microscopic origin leading to a discussion of the sources of entropy that can change in an applied magnetic field. Such entropies account for measurable magnetocaloric effects, especially…
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This chapter reviews the basic physics and thermodynamics that govern magnetocaloric materials. The thermodynamics of magnetic materials is discussed by introducing relevant free energy terms together with their microscopic origin leading to a discussion of the sources of entropy that can change in an applied magnetic field. Such entropies account for measurable magnetocaloric effects, especially in the vicinity of magnetic phase transitions. Particular attention is devoted to first order magnetic transitions that involve the coupling of spin, lattice, electronic and anisotropic magneto-crystalline degrees of freedom. The problem of irreversibility and hysteresis, present in magnetocaloric materials with first order phase transitions is discussed in the context of out-of-equilibrium thermodynamics and hysteresis modeling.
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Submitted 27 February, 2017;
originally announced February 2017.
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Longitudinal spin Seebeck coefficient: heat flux vs. temperature difference method
Authors:
A. Sola,
P. Bougiatioti,
M. Kuepferling,
D. Meier,
G. Reiss,
M. Pasquale,
T. Kuschel,
V. Basso
Abstract:
The determination of the longitudinal spin Seebeck effect (LSSE) coefficient is currently plagued by a large uncertainty due to the poor reproducibility of the experimental conditions used in its measurement. In this work we present a detailed analysis of two different methods used for the determination of the LSSE coefficient. We have performed LSSE experiments in different laboratories, by using…
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The determination of the longitudinal spin Seebeck effect (LSSE) coefficient is currently plagued by a large uncertainty due to the poor reproducibility of the experimental conditions used in its measurement. In this work we present a detailed analysis of two different methods used for the determination of the LSSE coefficient. We have performed LSSE experiments in different laboratories, by using different setups and employing both the temperature difference method and the heat flux method. We found that the lack of reproducibility can be mainly attributed to the thermal contact resistance between the sample and the thermal baths which generate the temperature gradient. Due to the variation of the thermal resistance, we found that the scaling of the LSSE voltage to the heat flux through the sample rather than to the temperature difference across the sample greatly reduces the uncertainty. The characteristics of a single YIG/Pt LSSE device obtained with two different setups was $(1.143\pm0.007)\cdot 10^{-7}$ Vm/W and $(1.101\pm0.015)\cdot 10^{-7}$ Vm/W with the heat flux method and $(2.313\pm0.017)\cdot 10^{-7}$ V/K and $(4.956\pm0.005)\cdot 10^{-7}$ V/K with the temperature difference method. This shows that systematic errors can be considerably reduced with the heat flux method.
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Submitted 10 November, 2018; v1 submitted 12 January, 2017;
originally announced January 2017.
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Determining the First Order Character of La(Fe,Mn,Si)13
Authors:
Milan Bratko,
Edmund Lovell,
A. David Caplin,
Vittorio Basso,
Alexander Barcza,
Matthias Katter,
Lesley F. Cohen
Abstract:
Definitive determination of first order character of the magnetocaloric magnetic transition remains elusive. Here we use a microcalorimetry technique in two modes of operation to determine the contributions to entropy change from latent heat and heat capacity separately in an engineered set of La(Fe, Mn, Si)13 samples. We compare the properties extracted by this method with those determined using…
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Definitive determination of first order character of the magnetocaloric magnetic transition remains elusive. Here we use a microcalorimetry technique in two modes of operation to determine the contributions to entropy change from latent heat and heat capacity separately in an engineered set of La(Fe, Mn, Si)13 samples. We compare the properties extracted by this method with those determined using magnetometry and propose a model independent parameter that would allow the degree of first order character to be defined across different families of materials. The microcalorimetry method is sufficiently sensitive to allow observation of an additional peak feature in the low field heat capacity associated with the presence of Mn in these samples. The feature is of magnetic origin but is insensitive to magnetic field, explicable in terms of inhomogeneous occupancy of Mn within the lattice resulting in antiferromagnetic ordered Mn clusters.
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Submitted 3 October, 2016;
originally announced October 2016.
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Heterogeneous nucleation and heat flux avalanches in La(Fe,Si)$_{13}$ magnetocaloric compounds near the critical point
Authors:
C. Bennati,
L. Gozzelino,
E. S. Olivetti,
V. Basso
Abstract:
The phase transformation kinetics of LaFe$_{11.41}$Mn$_{0.30}$Si$_{1.29}$-H$_{1.65}$ magnetocaloric compound is addressed by low rate calorimetry experiments. Scans at 1 mK/s show that its first order phase transitions are made by multiple heat fllux avalanches. Getting very close to the critical point, the step-like discontinuous behavior associated with avalanches is smoothed out and thermal hys…
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The phase transformation kinetics of LaFe$_{11.41}$Mn$_{0.30}$Si$_{1.29}$-H$_{1.65}$ magnetocaloric compound is addressed by low rate calorimetry experiments. Scans at 1 mK/s show that its first order phase transitions are made by multiple heat fllux avalanches. Getting very close to the critical point, the step-like discontinuous behavior associated with avalanches is smoothed out and thermal hysteresis disappears. This result is confirmed by magneto-resistivity measurements and allows to measure accurate values of the zero field hysteresis ($ΔT_{hyst}$ = 0.37 K) and of the critical field (H$_c$ = 1.19 T). The number and magnitude of heat flux avalanches change with magnetic field, showing the interplay between the intrinsic energy barrier between phases and the microstructural disorder of the sample.
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Submitted 1 September, 2016;
originally announced September 2016.
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Thermodynamic transport theory of spin waves in ferromagnetic insulators
Authors:
Vittorio Basso,
Elena Ferraro,
Marco Piazzi
Abstract:
We use the Boltzmann transport theory in the relaxation time approximation to describe the thermal transport of spin waves in a ferromagnet. By treating spin waves as magnon excitations we are able to compute analytically and numerically the coefficients of the constitutive thermo-magnetic transport equations. As a main result, we find that the absolute thermo-magnetic power coefficient $ε_M$, rel…
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We use the Boltzmann transport theory in the relaxation time approximation to describe the thermal transport of spin waves in a ferromagnet. By treating spin waves as magnon excitations we are able to compute analytically and numerically the coefficients of the constitutive thermo-magnetic transport equations. As a main result, we find that the absolute thermo-magnetic power coefficient $ε_M$, relating the gradient of the potential of the magnetization current and the gradient of the temperature, in the limit of low temperature and low field, is a constant $ε_M = -0.6419 \, k_B/μ_B$. The theory correctly describes the low-temperature and magnetic-field dependencies of spin Seebeck experiments. Furthermore, the theory predicts that in the limit of very low temperatures the spin Peltier coefficient $Π_M$, relating the heat and the magnetization currents, tends to a finite value which depends on the amplitude of the magnetic field. This indicates the possibility to exploit the spin Peltier effect as an efficient cooling mechanism in cryogenics.
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Submitted 14 November, 2016; v1 submitted 12 July, 2016;
originally announced July 2016.
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Non-equilibrium thermodynamics of the spin Seebeck and spin Peltier effects
Authors:
Vittorio Basso,
Elena Ferraro,
Alessandro Magni,
Alessandro Sola,
Michaela Kuepferling,
Massimo Pasquale
Abstract:
We study the problem of magnetization and heat currents and their associated thermodynamic forces in a magnetic system by focusing on the magnetization transport in ferromagnetic insulators like YIG. The resulting theory is applied to the longitudinal spin Seebeck and the spin Peltier effects. By focusing on the specific geometry with one YIG layer and one Pt layer, we obtain the optimal condition…
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We study the problem of magnetization and heat currents and their associated thermodynamic forces in a magnetic system by focusing on the magnetization transport in ferromagnetic insulators like YIG. The resulting theory is applied to the longitudinal spin Seebeck and the spin Peltier effects. By focusing on the specific geometry with one YIG layer and one Pt layer, we obtain the optimal conditions for generating large magnetization currents into Pt or large temperature effects in YIG. The theoretical predictions are compared with experiments from the literature permitting to derive the values of the thermomagnetic coefficients of YIG: the magnetization diffusion length $l_M \sim 0.4 \, μ$m and the absolute thermomagnetic power coefficient $ε_M \sim 10^{-2}$ TK$^{-1}$.
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Submitted 5 May, 2016; v1 submitted 30 December, 2015;
originally announced December 2015.
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Ab-initio based analytical evaluation of entropy in magnetocaloric materials with first order phase transitions
Authors:
Marco Piazzi,
Jan Zemen,
Vittorio Basso
Abstract:
We combine spin polarised density functional theory and thermodynamic mean field theory to describe the phase transitions of antiperovskite manganese nitrides. We find that the inclusion of the localized spin contribution to the entropy, evaluated through mean field theory, lowers the transition temperatures. Furthermore, we show that the electronic entropy leads to first order phase transitions i…
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We combine spin polarised density functional theory and thermodynamic mean field theory to describe the phase transitions of antiperovskite manganese nitrides. We find that the inclusion of the localized spin contribution to the entropy, evaluated through mean field theory, lowers the transition temperatures. Furthermore, we show that the electronic entropy leads to first order phase transitions in agreement with experiments whereas the localized spin contribution adds second order character to the transition. We compare our predictions to available experimental data to assess the validity of the assumptions underpinning our multilevel modelling.
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Submitted 10 December, 2015;
originally announced December 2015.
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Thermodynamics of the heat currents in the longitudinal spin Seebeck and spin Peltier effects
Authors:
Vittorio Basso,
Elena Ferraro,
Alessandro Magni,
Alessandro Sola,
Michaela Kuepferling,
Massimo Pasquale
Abstract:
We employ the non-equilibrium thermodynamics of currents and forces to describe the heat transport caused by a spin current in a Pt/YIG bilayer. By starting from the constitutive equations of the magnetization currents in both Pt and YIG, we derive the magnetization potentials and currents. We apply the theory to the spin Peltier experiments in which a spin current, generated by the spin Hall effe…
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We employ the non-equilibrium thermodynamics of currents and forces to describe the heat transport caused by a spin current in a Pt/YIG bilayer. By starting from the constitutive equations of the magnetization currents in both Pt and YIG, we derive the magnetization potentials and currents. We apply the theory to the spin Peltier experiments in which a spin current, generated by the spin Hall effect in Pt, is injected into YIG. We find that efficient injection is obtained when: i) the thickness of each layer is larger than its diffusion length: $t_{Pt} > l_{Pt}$ and $t_{YIG} > l_{YIG}$ and ii) the ratio $(l_{Pt}/τ_{Pt})/(l_{YIG}/τ_{YIG})$ is small, where $τ_i$ is the time constant of the intrinsic damping ($i=Pt, YIG$). We finally derive the temperature profile in adiabatic conditions. The scale of the effect is given by the parameter $ΔT_{SH}$ which is proportional to the electric current in Pt. Using known parameters for Pt and YIG we estimate $ΔT_{SH}/j_e = 4 \cdot 10^{-13}$ K A$^{-1}$m$^2$. This value is of the same order of magnitude of the spin Peltier experiments.
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Submitted 20 December, 2016; v1 submitted 2 December, 2015;
originally announced December 2015.
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Non-equilibrium thermodynamics of the longitudinal spin Seebeck effect
Authors:
Vittorio Basso,
Elena Ferraro,
Alessandro Magni,
Alessandro Sola,
Michaela Kuepferling,
Massimo Pasquale
Abstract:
In this paper we employ non equilibrium thermodynamics of fluxes and forces to describe magnetization and heat transport. By the theory we are able to identify the thermodynamic driving force of the magnetization current as the gradient of the effective field $\nabla H^*$. This definition permits to define the spin Seebeck coefficient $ε_M$ which relates $\nabla H^*$ and the temperature gradient…
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In this paper we employ non equilibrium thermodynamics of fluxes and forces to describe magnetization and heat transport. By the theory we are able to identify the thermodynamic driving force of the magnetization current as the gradient of the effective field $\nabla H^*$. This definition permits to define the spin Seebeck coefficient $ε_M$ which relates $\nabla H^*$ and the temperature gradient $\nabla T$. By applying the theory to the geometry of the longitudinal spin Seebeck effect we are able to obtain the optimal conditions for generating large magnetization currents. Furthermore, by using the results of recent experiments, we obtain an order of magnitude for the value of $ε_{M} \sim 10^{-2}$ TK$^{-1}$ for yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$).
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Submitted 2 December, 2015;
originally announced December 2015.
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Direct calorimetric measurements of isothermal entropy change on single crystal W-type hexaferrites at the spin reorientation transition
Authors:
Martino Lobue,
Vincent Loyau,
Frédéric Mazaleyrat,
Alexander Pasko,
Vittorio Basso,
Michaela Küpferling,
Carlo Paolo Sasso
Abstract:
We report on the magnetic field induced isothermal entropy change, Δs(Ha, T), of W-type ferrite with CoZn substitution. Entropy measurements are performed by direct calorimetry. Single crystals of the composition BaCo$_0.62$Zn$_1.38$Fe$_16$O$_27$, prepared by the flux method, are measured at different fixed temperatures under an applied field perpendicular and parallel to the c axis. At 296 K one…
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We report on the magnetic field induced isothermal entropy change, Δs(Ha, T), of W-type ferrite with CoZn substitution. Entropy measurements are performed by direct calorimetry. Single crystals of the composition BaCo$_0.62$Zn$_1.38$Fe$_16$O$_27$, prepared by the flux method, are measured at different fixed temperatures under an applied field perpendicular and parallel to the c axis. At 296 K one deduces a value of K$_1$ = 8.7 \times 10^{4} J m$^-3$ for the first anisotropy constant, which is in good agreement with the literature. The spin reorientation transition temperature is estimated to take place between 200 and 220 K.
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Submitted 3 October, 2012;
originally announced October 2012.
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Magnetic and structural characterization of nanosized BaCo_xZn_{2-x}Fe_{16}O_{27} hexaferrite in the vicinity of spin reorientation transition
Authors:
Alexander Pasko,
Frédéric Mazaleyrat,
Martino Lo Bue,
Vincent Loyau,
Vittorio Basso,
Michaela Küpferling,
Carlo Sasso,
Lotfi Bessais
Abstract:
Numerous applications of hexagonal ferrites are related to their easy axis or easy plane magnetocrystalline anisotropy configurations. Certain W-type ferrites undergo spin reorientation transitions (SRT) between different anisotropy states on magnetic field or temperature variation. The transition point can be tuned by modifying the chemical composition, which suggests a potential application of h…
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Numerous applications of hexagonal ferrites are related to their easy axis or easy plane magnetocrystalline anisotropy configurations. Certain W-type ferrites undergo spin reorientation transitions (SRT) between different anisotropy states on magnetic field or temperature variation. The transition point can be tuned by modifying the chemical composition, which suggests a potential application of hexaferrites in room temperature magnetic refrigeration. Here we present the results of structural and magnetic characterization of BaCo_xZn_{2-x}Fe_{16}O_{27} (0.7 \leq x \leq 2) doped barium ferrites. Fine powders were prepared using a sol-gel citrate precursor method. Crystal structures and particle size distributions were examined by X-ray diffraction and transmission electron microscopy. The optimal synthesis temperature ensuring complete formation of single W-phase with limited grain growth has been determined. Spin reorientation transitions were revealed by thermomagnetic analysis and AC susceptibility measurements.
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Submitted 23 November, 2011;
originally announced November 2011.
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Is demagnetization an efficient optimization method?
Authors:
S. Zapperi,
F. Colaiori,
L. Dante,
V. Basso,
G. Durin,
A. Magni,
M. J. Alava
Abstract:
Demagnetization, commonly employed to study ferromagnets, has been proposed as the basis for an optimization tool, a method to find the ground state of a disordered system. Here we present a detailed comparison between the ground state and the demagnetized state in the random field Ising model, combing exact results in $d=1$ and numerical solutions in $d=3$. We show that there are important diff…
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Demagnetization, commonly employed to study ferromagnets, has been proposed as the basis for an optimization tool, a method to find the ground state of a disordered system. Here we present a detailed comparison between the ground state and the demagnetized state in the random field Ising model, combing exact results in $d=1$ and numerical solutions in $d=3$. We show that there are important differences between the two states that persist in the thermodynamic limit and thus conclude that AC demagnetization is not an efficient optimization method.
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Submitted 13 July, 2005;
originally announced July 2005.
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Ground state optimization and hysteretic demagnetization: the random-field Ising model
Authors:
Mikko J. Alava,
Vittorio Basso,
Francesca Colaiori,
Lorenzo Dante,
Gianfranco Durin,
Alessandro Magni,
Stefano Zapperi
Abstract:
We compare the ground state of the random-field Ising model with Gaussian distributed random fields, with its non-equilibrium hysteretic counterpart, the demagnetized state. This is a low energy state obtained by a sequence of slow magnetic field oscillations with decreasing amplitude. The main concern is how optimized the demagnetized state is with respect to the best-possible ground state. Exa…
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We compare the ground state of the random-field Ising model with Gaussian distributed random fields, with its non-equilibrium hysteretic counterpart, the demagnetized state. This is a low energy state obtained by a sequence of slow magnetic field oscillations with decreasing amplitude. The main concern is how optimized the demagnetized state is with respect to the best-possible ground state. Exact results for the energy in d=1 show that in a paramagnet, with finite spin-spin correlations, there is a significant difference in the energies if the disorder is not so strong that the states are trivially almost alike. We use numerical simulations to better characterize the difference between the ground state and the demagnetized state. For d>=3 the random-field Ising model displays a disorder induced phase transition between a paramagnetic and a ferromagnetic state. The locations of the critical points R_c(DS), R_c(GS) differ for the demagnetized state and ground state. Consequently, it is in this regime that the optimization of the demagnetized stat is the worst whereas both deep in the paramagnetic regime and in the ferromagnetic one the states resemble each other to a great extent. We argue based on the numerics that in d=3 the scaling at the transition is the same in the demagnetized and ground states. This claim is corroborated by the exact solution of the model on the Bethe lattice, where the R_c's are also different.
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Submitted 12 July, 2004;
originally announced July 2004.
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Study of the connection between hysteresis and thermal relaxation in magnetic materials
Authors:
Vittorio Basso,
Cinzia Beatrice,
Martino LoBue,
Paola Tiberto,
Giorgio Bertotti
Abstract:
The connection between hysteresis and thermal relaxation in magnetic materials is studied from both the experimental and the theoretical viewpoint. Hysteresis and viscosity effects are measured in Finemet-type nanocrystalline materials above the Curie temperature of the amorphous phase, where the system consists of ferromagnetic nanograins imbedded in a paramagnetic matrix. The hysteresis loop d…
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The connection between hysteresis and thermal relaxation in magnetic materials is studied from both the experimental and the theoretical viewpoint. Hysteresis and viscosity effects are measured in Finemet-type nanocrystalline materials above the Curie temperature of the amorphous phase, where the system consists of ferromagnetic nanograins imbedded in a paramagnetic matrix. The hysteresis loop dependence on field rate, the magnetization time decay at different constant fields and the magnetization curve shape after field reversal are all consistent with a single value of the fluctuation field Hf = 8A/m (at 430 C). In addition, it is shown that all data collapse onto a single curve M(Hath), when magnetization is plotted as a function of a properly defined field Hath, dependent on time and field rate. Experimental data are interpreted by assuming that the system consists of an assembly of elementary bistable units, distributed in energy levels and energy barriers. The approximations under which one predicts data collapse onto a single curve M(Hath) are discussed.
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Submitted 7 October, 1999;
originally announced October 1999.
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Functional Integration Approach to Hysteresis
Authors:
G. Bertotti,
I. D. Mayergoyz,
V. Basso,
A. Magni
Abstract:
A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free energy landscapes. Second, the average hysteres…
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A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure m has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure m is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder, and the interpretation of critical state models of superconducting hysteresis.
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Submitted 27 April, 1999;
originally announced April 1999.
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Stochastic Dynamics in Quenched-in Disorder and Hysteresis
Authors:
Giorgio Bertotti,
Vittorio Basso,
Alessandro Magni
Abstract:
The conditions under which relaxation dynamics in the presence of quenched-in disorder lead to rate-independent hysteresis are discussed. The calculation of average hysteresis branches is reduced to the solution of the level-crossing problem for the stochastic field describing quenched-in disorder. Closed analytical solutions are derived for the case where the disorder is characterized by Wiener…
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The conditions under which relaxation dynamics in the presence of quenched-in disorder lead to rate-independent hysteresis are discussed. The calculation of average hysteresis branches is reduced to the solution of the level-crossing problem for the stochastic field describing quenched-in disorder. Closed analytical solutions are derived for the case where the disorder is characterized by Wiener-Levy statistics. This case is shown to be equivalent to the Preisach model and the associated Preisach distribution is explicitly derived, as a function of the parameters describing the original dynamic problem.
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Submitted 3 November, 1998;
originally announced November 1998.