Session A15: Focus Session: Spins in Metals - Thermal Effects on Magnons and Spin Currents

Theory of phonon-driven spin Seebeck effect

Spin Seebeck effect refers to a thermal spin injection occurring over millimeter scales from a ferromagnet into an attached nonmagnetic metal [Uchida et al., Nature 455, 778 (2008)]. We discuss the importance of the phonon-drag process in the spin Seebeck effect. Our theory of phonon-drag spin Seebeck effect [Adachi et al., Appl. Phys. Lett. 97, 252506 (2010)] explains simultaneously the local nature of the spin Seebeck effect [Jaworski et al., Nature Materials 9, 898 (2010); Uchida et al., Nature Materials 10, 737 (2011)] and the signal enhancement at low temperatures [Jaworski et al., Phys. Rev. Lett. 106, 186601 (2011)]. We also discuss the difference between our approach and that developed in Xiao et al., Phys. Rev. B 81, 214418 (2010).   

Spin Seebeck Effect Measurements on Ferromagnetic Thin Films Using Micromachined Thermal Isolation Platforms

The newly discovered thermoelectric effect, called the spin Seebeck effect (SSE), refers to a spin imbalance generated by a thermal gradient. This spin imbalance, capable of driving a pure spin current into a contact, is detected by measuring the conversion of the spin current into a transverse voltage ($V_{T}$) via the inverse spin Hall effect. A robust theoretical treatment of the SSE has so far eluded the community at large, and more experimental data are needed to understand the underlying physics. In this talk we present $V_{T}$ measurements associated with the SSE and AMR measurements for Ni, Fe, and Ni-Fe alloy thin films, along with Au as a control, made using our micromachined thermal isolation platforms. The sensitive thermal transport measurements we make using these platforms offer several advantages including concurrent measurements at hot and cold ends of the sample, equal heating of the sample ends to isolate traditional thermoelectric effects, and a large reversible thermal gradient. Additionally, the substrate thickness results in a virtually 2-D thermal platform that dramatically reduces the likelihood of thermal gradients perpendicular to the sample.   

Search For Spin Seebeck effect in in situ grown thin films

The Spin Seebeck Effect (SSE) is a phenomenon in which the application of a temperature gradient cross a ferromagnet causes a measurable electric potential difference transverse to the gradient when a normal metal is grown onto the ferromagnet. The spin current diffusing into the normal metal is transduced to a voltage via the Inverse Spin Hall Effect. Measuring the SSE accurately is challenging due to presence of other effects, possibly including regular Seebeck effect and anomalous thermo-magnetic phenomena. Here we report on our efforts to measure the SSE in thin films of NiFe and Co, using Au and Ta as the electrodes. All samples were grown on Si/SiOx substrates by magnetron sputtering through contact masks. The mask exchange was done in situ in a chamber where the base pressure was 2.0x10-7 Torr in order to limit contamination of the interfaces. The samples were measured using a rig with a reversible temperature gradient of 15K/cm and the resultant voltage was measured at the hot and cold ends of the sample using nanovoltmeters. The voltage signal we observe is strongly correlated with the magnetic hysteresis loops measured by Magneto-Optical Kerr Effect magnetometer.   

Intrinsic spin-dependent thermal transport

Spin caloritronic effect, such as spin Seebeck effect, has attracted a great deal of attention recently. In most cases such studies have been made on patterned ferromagnetic thin films on substrates. The mechanism of spin Seebeck effect has evolved from intrinsic difference in the spin chemical potentials to magnon-phonon interaction through the substrate. We use patterned ferromagnetic thin film to demonstrate the profound effect of a substrate on the spin-dependent thermal transport. With different sample patterns and on varying the direction of temperature gradient, both longitudinal and transverse thermal voltages exhibit asymmetric instead of symmetric spin dependence. This unexpected behavior is due to an out-of-plane temperature gradient imposed by the thermal conduction through the substrate and the mixture of the anomalous Nernst effects. Only with substrate-free samples have we determined the intrinsic spin-dependent thermal transport with characteristics and field sensitivity similar to those of anisotropic magnetoresistance effect.   

Thermoelectric coating based on the spin Seebeck effect

Thermoelectric (TE) technologies have been drawing great interest, since they can directly generate electricity from thermal energy that is available in various places. However, their complicated module structure, which is based on a number of thermocouples, still makes it difficult to fabricate large-area TE devices at low cost. In this work, we show a novel concept based on the spin Seebeck effect (SSE) called TE coating, which is characterized by a simple film structure, convenient scaling capability, and easy fabrication. We fabricated a TE-coating film with a bismuth-substituted yttrium iron garnet (Bi:YIG) by a highly productive spin-coating-based process on a nonmagnetic substrate, and demonstrated the SSE-induced TE conversion. The TE-coating layer amounts to only 0.01 {\%} of the total sample thickness, suggesting that such an ultrathin magnetic film can work as a useful thermal-energy collector. This new concept may enable us to implement low-cost and large-area TE functions on various objects, opening opportunities for innovative energy harvesting applications.   

Linear response theory for magnon transport in ferromagnetic insulators

We study transverse response of magnons in ferromagnetic insulators within linear response theory. In analogy with the corresponding theory for electrons [1], magnon transverse response is described, including the Hall effect, Nernst effect, and thermal Hall effect. As is also the case for electrons [1], the response functions for magnons consist of the Kubo-formula term, and the term corresponding to the orbital angular momentum. We can rewrite the response functions in terms of the Berry curvature in momentum space [2]. We apply this theory to the (quantum-mechanical) magnons and to the classical magnetostatic waves. For the magnetostatic waves, the eigenmodes are given by a generalized eigenvalue problem, giving rise to the special form of the Berry curvature [2]. We explain various properties of this Berry curvature for the generalized eigenvalue problem, and discuss its implications for the physical properties of magnetostatic modes. [1] L. Smrcka and P. Streda, J. Phys. C, 10, 2153 (1977); H. Oji, P. Streda, Phys. Rev. B 31, 7291 (1985); [2] R. Matsumoto and S. Murakami, Phys. Rev. Lett. 106, 197202 (2011); Phys. Rev. B 84, 184406 (2011).   

Thermally-assisted magnetization reversal in nanomagnets with spin-transfer torque: a GPU approach

Spin transfer magnetization reversal has a direct impact on magnetic information storage technologies. The probability that a nanomagnet switches under an applied magnetic field is expected to follow a simple thermally activated LLG model\footnote{M. L. N\'eel, Ann. Geophys. 5, 99 (1949); W. F. Brown, Phys. Rev. B 130, 1677 (1963).}. However, a direct current applied to a nanomagnet produces a spin-transfer torque that drives the magnetization out of equilibrium\footnote{J. C. Slonczewski, JMMM. 159, L1 (1996)}. Such dynamics have been studied in limits where both the low and high current regimes allow analytical treatment\footnote{J. Sun, Phys. Rev. B 62 1 (2000)}. Nonetheless, the inability to study numerically the long time behavior has tampered with theoretical verification and comparison to current experimental data\footnote{D. Bedau et al. Appl. Phys. Lett. 97, 262502 (2010)}. In this talk, we present results obtained by employing modern GPU computational techniques to massively parallelize the Langevin equations of the model. We test the numerics by considering a simplified uniaxial case. The full current spectrum is reviewed, verified and compared to the present literature. We then proceed to break the symmetries in the problem and explore the general macrospin model.   

Can heat flow induced spin currents move a magnetic domain wall?

It has been established in the past few years that heat flow within a ferromagnet can induce a spin current and an associated voltage. This Spin Seebeck effect, initially reported in ferromagnetic metals, has also been observed in magnetic semiconductors as well as magnetic insulators. An open question has been whether heat flow induced spin currents can also move magnetic domain walls in 'racetrack' magnetic nanowires. In order to answer this question, we investigate the interaction of a magnetic domain wall with spin currents induced by sharp temperature gradients in magnetic nanowire spin valves. We use optical as well as electrical techniques to create sharp temperature gradients on the order of 1-10 K/nm on nanosecond timescales. We will describe our experimental setup and present data that show the various roles that temperature plays on the saturation magnetization of the material as well as on the induced spin currents that influence magnetic domain wall motion.   

Observation of spin-wave cooling effect in magnets

We focused on utilizing a surface spin wave (Damon-Eshbach mode); traveling on top and bottom surfaces in a non reciprocal manner, as a good carrier of heat. As a sample, Yttrium iron garnet (YIG) was chosen because the spin waves excited in the YIG is known to have a long coherence length propagating distances even a few millimeters. By exciting the surface spin wave of only one side, heat transportation was successfully observed by measuring sample temperature with an infrared thermocamera. More interestingly, the temperature where the spin wave is initially excited shows cooling effect to drop its temperature just after the excitation of the surface spin wave. Here we call this effect as microwave cooling effect which is introducing a new cooling principle.   

Thermodynamics of magnetic systems from first principles

Density functional calculations have proven to be a useful tool in the study of ground state properties of many materials. The investigation of finite temperature magnetism on the other hand has to rely usually on the usage of empirical models that allow the large number of evaluations of the system's Hamiltonian that are required to obtain the phase space sampling needed to obtain the free energy, specific heat, magnetization, susceptibility, and other quantities as function of temperature. We have demonstrated a solution to this problem that harnesses the computational power of today's large massively parallel computers by combining a classical Monte-Carlo calculations with our first principles multiple scattering electronic structure code (LSMS) for constrained magnetic states. Here we will present recent advances in our method that improve the convergence as well as applications to 3d element based ferromagnets. This research was performed at Oak Ridge National Lab and sponsored in parts by the Center for Nanophase Material Sciences, Scientific User Facilities Division, the Center for Defect Physics, an Energy Frontier Research Center funded by the US DOE Office of Basic Energy Sciences and the Division of Materials Science and Engineering, Office of Basic Energy Science of   

Effect of Temperature and Spin Torque on the Stoner-Wohlfarth Astroid of a Nanomagnet

We report measurements of the Stoner-Wohlfarth switching astroid curves of the free layer nanomagnet in CoFeB/MgO/CoFeB/Ru/CoFe/PtMn elliptical nanoscale magnetic tunnel junctions made as a function of applied voltage and temperature. Measurements of the astroid area as a function of temperature allow us to determine the magnetic anisotropy energy barrier of the free layer and thereby quantify its thermal stability - an important performance parameter of spin torque nonvolatile magnetic memory. Measurements of the astroid as a function of voltage (V) applied to the junction at the bath temperature of 4 K reveal significant voltage-induced deformations of the astroid curve. We observe a decrease of the hard-axis length of the astroid, which arises from ohmic heating of the junction. Comparison of the hard-axis astroid length measured at T = 4 K and |V| > 0 to the hard-axis astroid length measured at T > 4 K and V = 0 allows us to quantify ohmic heating of nanoscale tunnel junctions by the applied voltage. The applied voltage reduces the easy-axis length of the astroid as well, but the reduction is asymmetric for positive and negative easy-axis directions. This easy-axis asymmetry reverses upon the applied voltage sign reversal and thus it can be attributed to spin transfer torque.   

Magnetization dynamics at elevated temperatures

The conventional Landau-Lifshitz (LL) equation is the basis for simulation of magnetic structure and dynamics as long as the temperature is not too close to Curie temperature. In order to model the magnetization dynamics at elevated temperatures, one needs to extend the LL equation by including a finite longitudinal relaxation. Here within the self-consistent mean-field treatment of ferromagnetism, we propose an effective equation which is capable of addressing magnetization dynamics for a wide range of temperatures. At low temperatures, the equation reduces to the Landau-Lifshitz equation, namely, the transverse relaxation governs the dynamics. At high temperatures, it reduces to paramagnetic Block equation. Near the Curie temperature, the longitudinal relaxations play a more important role on the magnetization reversal. We present numerical calculations to simulate a heat-assisted-magnetic-recording process when the temperature is heated and cooled through the Curie temperature.   

Temperature dependence of magnetic losses in GMR and TMR devices

Thermally induced magnetization fluctuations in the free and reference magnetic layers of giant and tunneling magnetoresistance (GMR and TMR) spin valves (SV) devices typically give rise to a low-frequency 1/f power spectral density that has been related to local dissipative processes [1]. Understanding the origin of these magnetic losses is essential for increasing the magnetic field sensitivity of GMR and TMR sensors. The low-frequency magnetic losses can be parameterized through a loss angle, $\varepsilon $(T, H). $\varepsilon $(T) for the reference layer in our GMR SV is non-monotonic: first decreasing with increasing T, then exhibiting a minimum near 50K and what may be the onset of a plateau or peak near 300K. The peak and minimum shift to lower temperatures when the applied field is oriented perpendicular to the exchange pinning direction. Data for TMR devices show similar trends. The measurements will be described in the context of a model involving thermally activated kinetics and a field-dependent distribution of activation energies for the nanoscale magnetic fluctuators. \\[4pt] [1] Z. Diao et al., PRB \textbf{84}, 094412 (2011)