Spin Hall antiferromagnetic oscillators (AFMO) (1) are a promising candidate for a CMOS-compatible THz-range frequency source. The output power of a nano-scale AFMO is relatively low, and mutual synchronization of AFMOs may be used to increase the power and to reduce the generation linewidth. The first step in understanding AFMO synchronization is to investigate the injection locking of a single oscillator, i.e., synchronization to an external driving signal.
Here, we numerically study the injection locking of AFMOs using the model derived in (1). In contrast with previous studies (2, 3), we study injection locking in a wide range of AFMO frequencies and assume that the driving signal is mixed with the DC bias current, i.e., that the bias and locking spin currents have the same spin polarization, which is more suitable for practical realization.
Figure 1 shows a dependence of the driven AFMO frequency f on the injected frequency fs. Straight segment near the AFMO free-running frequency f0 = 0.23 THz corresponds to the injection locking at the fundamental signal harmonic. The huge locking bandwidth Δf1≈100 GHz is due to strong influence of AFMO nonlinearity related to anisotropy of the antiferromagnet (1). An additional signature of a strongly nonlinear regime is the appearance of higher-order locking bands f=2fs and f=3fs. Synchronization at higher harmonics may be important in practical applications, since it allows one to synchronize THz-range AFMO by a driving signal of a lower frequency.
The synchronization bandwidth Δf1 drastically reduces with the increase of AFMO free-running frequency f0 (Fig. 2). This effect is caused by reduction of AFMO nonlinearity and may be a serious obstacle for practical use of AFMOs in the frequency range f > 1 THz. Therefore, alternative methods of AFMO injection locking should be studied, such as locking to a microwave magnetic field or to a spin current with different spin polarization (2). 

**References:** 
(1) R. Khymyn, et al., “Antiferromagnetic THz-frequency Josephson-like oscillator driven by spin current”, Sci. Rep. 7, 43705 (2017). 
(2) O. Gomonay, T. Jungwirth, and J. Sinova, “Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques”, Phys. Rev. B 98, 104430 (2018). 
(3) R. Khymyn, et al., “Injection-locking of a nonlinear sub-THz antiferromagnetic spin-Hall oscillator”, DE-08, Abstracts of the International Magnetics Conference INTERMAG-18, Singapore, Singapore, April 2018. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ec4067aac578df55127c6b0106a5e127.png)

Injection Locking of Antiferromagnetic Oscillators

The spin-torque magnetic diode (STMD) effect [1] is a quadratic rectification effect of the input microwave current IRF(t) in a magnetoresistive nano-junction, which is commonly observed in the traditional regime of operation of an STMD, when the magnetization of the “free” layer (FL) lies in-plane, and when the frequency fs of the current IRF(t) is close to the ferromagnetic resonance (FMR) frequency f0 of the junction. In this case, the induced resonance oscillations of the junction resistance R(t) can mix with the oscillations of the input microwave current IRF(t) , and produce an output DC voltage UDC = &lt;IRF(t)R(t)&gt; (where "&lt;&gt;" denotes time averaging) across the junction. It was demonstrated theoretically in [2] that in an STMD, biased by an out-of-plane static magnetic field, a different dynamical regime of the STMD operation characterized by large-angle out-of-plane magnetization precession can be realized. The excitation of the large-angle precession has a threshold character, and is possible only for input microwave currents exceeding a certain frequency-dependent critical value, and sufficiently low frequency. In this regime of the out-of-plane precession the output DC voltage of an STMD increases with the frequency of the input signal, but is virtually independent of its power. An STMD working in the regime of large-amplitude out-of-plane precession functions as a non-resonant threshold detector of low frequency microwave signals, due to the large nonlinear shift of its operating frequency. Therefore, this precession regime is particularly suitable for applications in the microwave energy harvesting. It was demonstrated experimentally in [3] that the out-of-plane magnetization precession regime in an STMD operation predicted in [2] can be realized without any bias magnetic field, if an STMD FL has a perpendicular magnetic anisotropy. In such a regime an STMD has the rectification properties that are independent of the input microwave frequency, and the performance of the STMD-based energy harvesting device is comparable to the performance of the state-of-the-art Schottky diode for low-power rectification. It was further shown in [3] that the developed bias-free STMD provides sufficient dc voltage to power a practical nanodevice − a black phosphorus photosensor. Here we present an analytical and numerical theory explaining the performance of a bias-free STMD with perpendicular magnetic anisotropy [4]. We show that in an STMD, having a magnetic FL with perpendicular magnetic anisotropy of the first and second order, and no external bias magnetic field, the out-of-plane regime of magnetization precession can be excited by sufficiently large (exceeding a certain threshold) RF signals with the frequencies smaller than 250 MHz . We also show that such a device can operate as a broadband energy harvester capable of converting incident RF power into a DC power with a conversion efficiency of ∼5%. The developed analytical theory of the bias-free STMD operation can be used for the optimization of high-efficiency RF detectors and energy harvesters based on STMDs. Our results are paving a way for use of spintronic detectors and harvesters as building blocks for self-powered nano-systems, such as implantable biomedical devices, wireless sensors, and portable electronics.

Signal Detector and RF Energy Harvester Based On A Spintronic Diode With Perpendicular Anisotropy

A spin current - a flow of spin angular momentum - can be carried either by spin-polarized free electrons or by magnons, the quanta of spin waves. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces could transfer energy and angular momentum only along its propagation direction. In this talk, using the data of Brillouin light scattering (BLS) spectroscopy in combination with an extended theory of dipole-exchange spin-wave spectra, I show that in obliquely magnetized magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current without any corresponding transverse transport of energy [1]. It is found that in the case of oblique magnetization, the transverse profiles of in-plane-propagating dipole-exchange spin waves are formed by two co-propagating partial waves with opposite group velocities. Their superposition results in a traveling wave pattern, which carries angular momentum and can be treated as a transversal spin current. Its existence is evidenced by the behavior of thermal spectra of magnons in a yttrium iron garnet film measured in a wide range of wavenumbers using our novel wavevector-resolved BLS setup. In the case of an external excitation of the spin-wave modes carrying the transversal spin current, the angular momentum conservation law would lead to mechanical deformations or/and to the rotation of the magnetic film as a whole, which could be detected using the existing methods of spin mechatronics [2]. Furthermore, the presence of the unconventional spin current may be directly electrically detected [1, 3]. We believe that these non-trivial properties of spin-wave modes may be used in the future to control the effects of spin pumping or/and to generate spin currents in nano-scale spintronic signal processing and signal-generating devices. Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Research Unit TRR 173–268565370 “Spin+X” (projects B01 and B04), as well as financial support by the European Research Council within the AdG SuperMagnonics, is gratefully acknowledged. The work was also supported in part by the US National Science Foundation, by the US Air Force Office of Scientific Research, and by the Oakland University Foundation.

**References:**

[1] D. A. Bozhko, H. Yu. Musiienko-Shmarova, V. S. Tiberkevich, A. N. Slavin, I. I. Syvorotka, B. Hillebrands, and A.A. Serga, Unconventional spin currents in magnetic films, Phys. Rev. Research 2, 023324 (2020). [2] M. Matsuo, E. Saitoh, and S. Maekawa, Spin-mechatronics, J. Phys. Soc. Jpn. 86, 011011 (2017). [3] P. M. Gunnink, R. A. Duine, and A. Rückriegel, Electrical Detection of Unconventional Transverse Spin Currents in Obliquely Magnetized Thin Films, Phys. Rev. B 101, 220407 (2020).

**Images:**

 Unconventional spin currents in obliquely magnetized magnetic films

The dynamics of spin waves propagating in thin magnetic films has been studied intensively for several decades, and is relatively well-understood [1,2]. However, investigations have been mainly focused on the cases of either perpendicular or in-plane magnetization, where forward volume, backward volume, and surface magnetostatic (or dipolar) long-wavelength wave modes have been identified [1]. A more general dipole-exchange theory of the spin wave spectrum in magnetic films applicable also to the short-wavelength spin waves has been later developed by the research group of B.A. Kalinikos [2]. The conventional theory led to the understanding that a spin wave in a magnetic film with spin-sink-free surfaces is a non-uniform travelling wave having a stationary distribution of the variable magnetization along the film thickness, and can transfer energy and angular momentum only along the in-plane direction of the spin wave propagation. It turned out, that the situation becomes substantially more complicated in the case when the magnetic film is magnetized obliquely (see Fig.1), and short-wavelength dipole-exchange spin waves are considered. The results of recent experiments [3], performed using Brillouin light-scattering spectroscopy, in combination with the numerical results, based on the theory of dipole-exchange spin-wave spectra [2], have shown two effects: (i) thickness profiles of the propagating spin waves (both in in-plane and obliquely magnetized films) are strongly dependent on the in-plane wavenumber k due to the strong dipolar hybridization between the modes having different thickness profiles, and demonstrate “dipolar pinning” [4] with the increase on the in-plane wavenumber (see Fig.2, top panel); (ii) transverse (thickness) profiles of the spin waves propagating in the film plane in an obliquely magnetized film are non-stationary , i.e. are changing with time in the process of the wave propagation (see Fig.2, bottom panel). This last phenomenon might mean that there could be a transverse (along the film thickness) transfer of spin angular momentum without corresponding transverse transfer of energy. In the end, this issue of transverse spin transport is related to the boundary conditions at the surfaces of the magnetic film. In our simple system Fig. 1, we consider a magnetic film with spin-sink-free surfaces. However, if there is a spin-sink formed by a layer of a heavy metal, such as Pt, present at the film surface, it may be possible to experimentally detect the transfer of spin angular momentum along the film thickness in an obliquely magnetized magnetic film supporting the unidirectional spin wave propagation in the film plane. Further experimental studies are necessary to clarify the issue of possible transverse spin angular momentum transfer in obliquely magnetized magnetic films.

**References:**

[1] R. Damon and J. Eshbach, J. Phys. Chem. Solids, vol. 19, p.308 (1960). [2] B. Kalinikos and A. Slavin, J. Phys. C, vol. 19, p.7013 (1986). [3] D. Bozhko, H. Musiienko-Shmarova, V. Tiberkevich, et al., Phys. Rev. Research, vol. 2, p.023324 (2020). [4] K.Yu. Guslienko, S.O. Demokritov, B. Hillebrands, and A.N. Slavin, Phys. Rev. B , vol.66, 132402 (2002).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2c295c636a8de1bab19ac4b6cee516b.jpg)
Fig. 1. Geometry of an obliquely magnetized (by an internal magnetic field Hi directed at an angle θ to the surface) spin-sink-free magnetic film of the thickness L carrying a propagating spin wave having a wavenumber k. An example of a transverse profile of the dynamic magnetization in a propagating spin wave is shown along the film thickness.

![](https://assets.underline.io/uploads/markdown_image/1/image/81be77679a816fef838e8f4e5180f41f.jpg)
Fig. 2. Numerically calculated transverse dynamic magnetization profiles of spin wave modes propagating in a 5.6 μm thick yttrium-iron garnet (YIG) film. Top panel: profiles in an in-plane magnetized ( θ =0) film , corresponding to three different values of the in-plane wavenumber, and demonstrating the effect of “dipolar pinning”. Bottom panel: profiles of the wave having in-plane wavenumber k =1 rad μm-1 in an obliquely magnetized ( θ =π/4 ) film at three different time moments, demonstrating that the transverse spin wave profile is non-stationary. 
T - is the period of the spin wave frequency.

 Non-Stationary Thickness Profiles of Spin Wave Modes Propagating in Obliquely Magnetized Magnetic Films

Bose-Einstein condensate is a collective phenomenon which takes place when many bosons – particles having integer value of spin – experience transition to the same single quantum state. The famous example is formation of Cooper pairs of electrons, responsible for the superconducting properties of some materials at extremely low temperatures. Magnons – quasi-particles corresponding to spin waves propagating in magnetic media – are bosons as well. Hence, if we describe oscillation of magnetization as a set of magnons, the phenomenon like Bose-Einstein condensation should also exist in this case. Indeed, the Bose-Einstein condensation of magnons at room temperature has been observed under parametric pumping in thick ferrite films [1], and, recently, by rapid cooling in ultra- thin films [2]. The stability of Bose-Einstein condensate of magnons (mBEC) is determined by the nonlinear interaction between magnons. This includes both interaction between magnons in the same spectral minimum (self-interaction), and the interaction between magnons belonging to two different spectral minima (cross-interaction). mBEC can be stable if the coefficient of nonlinear interaction is positive, i.e. if the interaction is repulsive [3]. It is well known that the self-interaction between magnons in relatively thick films is attractive [3]. However, mBEC has been experimentally proven to be stable [1, 2, 4]. It was shown in [5] that coefficient of nonlinear interaction in mBEC is negative, but rather small, so relatively strong repulsive interaction between magnons in different spectral minima may provide stability to mBEC. Recently, it has been also shown [6] that it is possible to separate mBEC in two parts, each containing magnons from only one spectral minimum, which means that mBEC in each of the minima is stable, and this stability is independent of the strong cross-interaction of magnons from different minima. Thus, the theory developed in [5] cannot be used to explain stability of separated mBEC. Also, the theory [5] assumes a uniform profile of a magnon mode across the film thickness, and infinite in-plane sizes of the magnetic film sample. Both these simplifications are, generally, incorrect. Due to the long-range nature of the dipolar interaction, finite-size effects may have a significant impact on the nonlinear interactions of magnons [4]. Here, we present a simple, but rather accurate model of the nonlinear interactions in mBEC that takes into account the finite-size effects. Using Landau-Lifshits equation and vector Hamiltonian approach [7], we derived approximate analytical expressions for the linear dispersion characteristics and nonlinear interaction coefficients of magnons near the minima of the magnon spectrum (i.e. in the mBEC region). We showed that magnons undergoing mBEC can be described as a gas of weakly-interacting bosonic particles in an infinite potential well formed by a ferromagnetic film. The rest energy of the magnons in mBEC is determined by the dipolar interaction inside a film sample. This leads to a strong anisotropy of the effective mass of magnons in the magnetic film. In the direction along the applied in-plane magnetic field, the effective mass is m∥ = hMs/(32πγA) (where Ms is the saturation magnetization, h is the Planck constant, γ is the gyromagnetic ratio, and A is the exchange stiffness). For yttrium-iron garnet (YIG), this “longitudinal” mass is m∥ ≈ 1.5×10-30 kg ≈ 1.6 me (me is the electron mass). In the directions perpendicular to the applied field magnons are described by the “perpendicular” mass m⊥ = (18λ/d)m∥, which depends on the ratio of the exchange length λ = (2A/μ0Ms2)1/2 to the thickness of the film d. For typical experimental conditions m⊥ « m∥; for example, m⊥ ≈ 0.06 m∥ in a YIG film of the thickness d = 5 μm. The huge anisotropy of the effective mass leads to the anisotropy of the dynamical mBEC properties. In particular, the speed of the Bogolyubov waves [8] depends strongly on the direction of the wave propagation. Since the perpendicular mass m⊥ depends on the thickness of the film, it is possible to achieve the inverse mass relation m⊥ &gt; m∥ in ultra-thin YIG films with d &lt; 300 nm. Under the assumption of totally pinned spins, which is an accurate approximation in the mBEC region, we derived approximate analytical expressions for the nonlinear frequency shift due to the self- and cross- interactions in mBEC: Δf = (Fself + 2Fcross)n; Fself = F0 (2Nd – 3πλ/d√2); Fcross = F0. Here F0 = γ2μ0h/4π2 is the normalisation constant, n is the magnon density, Nd is the component of the demagnetization tensor N = diag(Nx, Ny, Nz) corresponding to the direction along the applied in-plane magnetic field. These expressions show that the nonlinear cross-interaction stays large and positive independently of the confinement of the sample in the applied field direction, while the self-interaction coefficient changes its sign when Nd become greater than the critical value Ncr: Ncr = (3π/2√2)(λ/d). The result explains possibility to separate mBEC into two stable components corresponding to the different minima of the mBEC spectrum [4, 6]. The developed model allows one to make simple and accurate predictions about the stability of the mBEC depending on the shape of the sample used, and to describe dynamics of fluctuations and waves of magnon density in the mBEC. Also, it makes possible to directly apply theoretical methods developed to describe condensates of atoms to study the mBEC dynamics, and, therefore, it might be very useful in further investigations of coherent magnonic phenomena.

**References:**

[1] S. O. Demokritov, V. E. Demidov, O. Dzyapko et al., Nature, vol. 443, pp. 430-433, 2006. [2] M. Schneider, T. Brächer, D. Breitbach et al., Nat. Nanotechnol., vol. 15, pp. 457–461, 2020. [3] V. S. L’vov, Wave turbulence under parametric excitation, Springer Series in Nonlinear Dynamics (Springer, Berlin, 1994). [4] I. V. Borisenko, B. Divinskiy, V. E. Demidov et al., Nat. Commun., vol. 11, no. 1691, 2020. [5] O. Dzyapko, I. Lisenkov, P. Nowik-Boltyk et al., Phys. Rev. B, vol. 96, no. 064438, 2017. [6] I. V. Borisenko, V. E. Demidov, V. L. Pokrovsky et al., Sci. Rep., vol. 10, no. 14881, 2020. [7] V. Tyberkevych, A. Slavin, P. Artemchuk, et al., arXiv:2011.13562 (2020). [8] D. A. Bozhko, A. J. E. Kreil, H. Yu. Musiienko-Shmarova et al., Nat. Commun., vol 10, no. 2460, 2019.

**Images:**

 A Model for Description of Linear Properties and Stability of Bose-Einstein Condensate of Magnons at Room Temperature

It has been shown that a rapid cooling of Yttrium-Iron-Garnet (YIG)/Pt nanostructures preheated by a DC electric current pulse sent through the Pt layer leads to an overpopulation of a magnon gas and to the subsequent Bose-Einstein condensation (BEC) of magnons [1]. Hereby, the application of a sufficiently-long DC heating pulse was used to generate a high population of magnons being in equilibrium with the phononic system. The subsequent rapid decrease in the temperature resulted in the break of the equilibrium, in the over-population of magnons over the whole magnon spectrum, and, in the following, in a redistribution of magnons from higher to lower energies. Finally, if the elevated temperature was high enough, and the cooling process fast enough, the chemical potential reached the minimal energy of the system and the BEC was triggered [1]. In these experiments, a Pt or Al layer was used to heat the YIG nanostructure. For a Pt heater, in addition to the Ohmic heating effects, one expects the generation of a spin-polarized current transverse to the YIG/Pt interface due to the spin Hall effect (SHE) [2]. The spin current, consequently, is known to act on the magnetization dynamics in the YIG via spin-transfer torque (STT). Whereas in our previous studies the induced disequilibrium was found to be mainly given by the temperature increase and subsequent rapid cooling, we observe a significant contribution of the spin Hall effect (SHE) in a new set of samples. The larger effect of the SHE-STT was reached by a modification of the structures (see Fig. 1) with respect to those in the original study [1], i.e. by a decrease in the YIG thickness, and via using a sputtered Pt layer instead of an epitaxially grown Pt layer studies to enhance the spin Hall angle [3]. It was found that SHE-induced STT enhances the BEC formation at the bottom of the magnon spectrum – in the minimum frequency of the fundamental spin-wave mode, and excites a nonlinear magnon mode – the spin-wave bullet, located below the linear magnon spectrum [4]. We investigated the dynamics of these magnon states employing Brillouin light scattering (BLS) spectroscopy. A sketch of the experimental setup and SEM images of the investigated structure is depicted in Fig. 1. The application of a 50-ns-long DC-pulse to a 7-nm- thin Pt layer on top of a 34-nm-thin and 2-μm-wide YIG strip results in the SHE-STT. At sufficiently large amplitudes of the DC-pulse applied, the bullet mode is formed during the DC pulse at a frequency around 1.8 GHz below the frequency of the fundamental mode, see Fig. 2b. The pronounced magnon density peak in the left panel in Fig. 2c (solid orange line), measured at the time just before the current pulse is switched off, clearly demonstrates the bullet mode formation. The SHE-STT nature of the mode is confirmed by the variation of the magnetisation orientation with respect to the current direction. The consequent switching of the DC pulse off results in the rapid cooling-induced BEC of magnons at the frequency around 6 GHz - see Fig. 2c. The results of the control experiment with no SHE-STT contribution under periodically changing polarity of the applied current (Fig. 2d) are in agreement with the original findings presented in Ref. [1]. The interplay between the magnon condensate and the SHE-STT bullet mode, after the current pulse was gone, attracts special attention. Initially, in the rapid cooling phase of the process, thermally-induced excess magnons populate both the bullet mode and the condensate, see Fig. 2a. Further, both modes decay slower than expected from their lifteime indicating that they are still pumped from the gas. Finally, about 30 ns after the DC pulse is turned off, a qualitatively new process begins, resulting in the redistribution of magnons from the bullet mode to the condensate. This phenomenon manifests itself in an elevation of the condensate density accompanied by an increased decay of the bullet mode, and apparently occurs when the chemical potential of the magnon gas [1] decreases below the bullet mode frequency. The results suggest a path towards the application of macroscopic quantum states in spintronic devices.

**References:**

[1] M. Schneider, T. Brächer, D. Breitbach, V. Lauer, P. Pirro, D. A. Bozhko, H. Y. Musiienko- Shmarova, B. Heinz, Q. Wang, T. Meyer, F. Heussner, S. Keller, E. T. Papaioannou, B. Lägel, T. Löber, C. Dubs, A. N. Slavin, V. S. Tiberkevich, A. A. Serga, B. Hillebrands, and A. V. Chumak, Bose-Einstein condensation of quasiparticles by rapid cooling, Nature Nanotechnology 15, 457 (2020). [2] L. J. Cornelissen, K. J. H. Peters, G. E. W. Bauer, R. A. Duine, and B. J. van Wees, Magnon spin transport driven by the magnon chemical potential in a magnetic insulator, Phys. Rev. B 94, 014412 (2016). [3] E. Sagasta, Y. Omori, M. Isasa, M. Gradhand, L. E. Hueso, Y. Niimi, Y. Otani, and F. Casanova, Tuning the spin hall effect of pt from the moderately dirty to the superclean regime, Phys. Rev. B 94, 060412 (2016). [4] A. Slavin and V. Tiberkevich, Spin wave mode excited by spin-polarized current in a magnetic nanocontact is a standing self-localized wave bullet, Phys. Rev. Lett. 95, 237201 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/60e5026f5c65e8d34354a4da266411ef.jpg)
Colored SEM images of the investigated structures and sketch of the experimental setup. The structures consists of a 2-μm-wide and 34-nm-thick YIG strip. A 3-μm-long Platinum-heater (7 nm) on top is contacted by Ti/Au leads. The magnon intensity below the Pt-covered region is measured using time-resolved BLS spectroscopy. The shape of the Ti/Au contact pads attached to the Pt injector results in a DC current parallel to the short axis of the strip. Qualitatively the same results were obtained for another set of samples with a DC current flowing parallel to the short axis of the strip.

![](https://assets.underline.io/uploads/markdown_image/1/image/534ab70ea9e9adb9ae113bed737dcfc7.jpg)
(a) Integrated BLS intensity from (b) as a function of the time within the two indicated frequency ranges. (b) BLS intensity color-coded as a function of time and the BLS frequency. During the pulse (0 ns < t < 50 ns and U = 2.0 V) the formation of a bullet mode is visible. The inset shows a sketch of the structure. (c) BLS intensity as a function of the BLS frequency at three different time steps, indicated by the dashed lines in (b). The black dashed lines depict the thermal BLS spectrum without a DC pulse present. (d) Integrated BLS intensity color coded as a function of time and the BLS frequency. In contrast to (b), the current polarity is alternating during the pulse, effectively switching off the contribution of the SHE-STT while kepping the heating constant.

 The interplay between the rapid cooling-induced BEC and SHE-STT-driven bullet mode

EOA: Antiferromagnetic Spintronics I

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SHORT BIO

Presentations

Injection Locking of Antiferromagnetic Oscillators

Signal Detector and RF Energy Harvester Based On A Spintronic Diode With Perpendicular Anisotropy

Unconventional spin currents in obliquely magnetized magnetic films

Non-Stationary Thickness Profiles of Spin Wave Modes Propagating in Obliquely Magnetized Magnetic Films

A Model for Description of Linear Properties and Stability of Bose-Einstein Condensate of Magnons at Room Temperature

The interplay between the rapid cooling-induced BEC and SHE-STT-driven bullet mode

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