Thin Yttrium Iron Garnet (YIG) is a promising material for integrated magnonics. In order to introduce YIG into nanofabrication processes it is necessary to fabricate very thin YIG films with a thickness well below 100 nm while retaining the extraordinary magnetic properties of the material, especially its long magnon lifetime and spin wave propagation length. Here, we give a brief introduction into the topic and we review and discuss the various results published over the last decade in this area. Especially for ultrathin films it turns out that pulsed layer deposition and sputtering are the most promising candidates. In addition, we discuss the application of room temperature deposition and annealing for lift-off based nanopatterning and the properties of nanostructures obtained by this method over the past years.
A platinum (Pt)/yttrium iron garnet (YIG) bilayer system with a well-controlled interface has been developed; spin mixing conductance at the Pt/YIG interface has been studied. Crystal perfection at the interface is experimentally demonstrated to contribute to large spin mixing conductance. The spin mixing conductance is obtained to be $1.3\times10^{18} \rm{m^{-2}}$ at the well-controlled Pt/YIG interface, which is close to a theoretical prediction.
Using femtosecond optical pulses, we have investigated the ultrafast magnetization dynamics induced in a dielectric film of bismuth-substituted yttrium iron garnet (Bi-YIG) buried below a thick Cu/Pt metallic bilayer. We show that exciting the sample from Pt surface launches an acoustic strain pulse propagating into the garnet film. We discovered that this strain pulse induces a coherent magnetization precession in the Bi-YIG at the frequency of the ferromagnetic resonance. The observed phenomena can be explain by strain-induced changes of magnetocristalline anisotropy via the inverse magnetos…
The dependence of the spin pumping efficiency and the spin mixing conductance on the surface processing of yttrium iron garnet (YIG) before the platinum (Pt) deposition has been investigated quantitatively. The ferromagnetic resonance driven spin pumping injects a spin polarized current into the Pt layer, which is transformed into an electromotive force by the inverse spin Hall effect. Our experiments show that the spin pumping effect indeed strongly depends on the YIG/Pt interface condition. We measure an enhancement of the inverse spin Hall voltage and the spin mixing conductance of more tha…
We investigated the spin-wave propagation in a micro-structured yttrium iron garnet waveguide of $40$ nm thickness. Utilizing spatially-resolved Brillouin light scattering microscopy, an exponential decay of the spin-wave amplitude of $(10.06 \pm 0.83)$ $μ$m was observed. This leads to an estimated Gilbert damping constant of $α=(8.79\pm 0.73)\times 10^{-4}$, which is larger than damping values obtained through ferromagnetic resonance measurements in unstructured films. The theoretically calculated spatial interference of waveguide modes was compared to the spin-wave pattern observed experimen…
Spin waves can probe the Dzyaloshinskii-Moriya interaction (DMI) which gives rise to topological spin textures, such as skyrmions. However, the DMI has not yet been reported in yttrium iron garnet (YIG) with arguably the lowest damping for spin waves. In this work, we experimentally evidence the interfacial DMI in a 7~nm-thick YIG film by measuring the nonreciprocal spin wave propagation in terms of frequency, amplitude and most importantly group velocities using all electrical spin-wave spectroscopy. The velocities of propagating spin waves show chirality among three vectors, i.e. the film no…
We carried out a concerted effort to determine the absolute sign of the inverse spin Hall effect voltage generated by spin currents injected into a normal metal. We focus on yttrium iron garnet (YIG)|platinum bilayers at room temperature, generating spin currents by microwaves and temperature gradients. We find consistent results for different samples and measurement setups that agree with theory. We suggest a right-hand-rule to define a positive spin Hall angle corresponding to with the voltage expected for the simple case of scattering of free electrons from repulsive Coulomb charges.
Spin information carried by magnons is attractive for computing technology and the development of magnon-based computing circuits is of great interest. However, magnon transport in insulators has been challenging, different from the clear physical picture for spin transport in conductors. Here we investigate the lateral transport properties of thermally excited magnons in yttrium iron garnet (YIG), a model magnetic insulator. Polarity reversals of detected spins in non-local geometry devices have been experimentally observed and are strongly dependent on temperature, YIG film thickness, and in…
Pure spin current, a flow of spin angular momentum without flow of any companying net charge, is generated in two common ways. One makes use of the spin Hall effect in normal metals (NM) with strong spin-orbit coupling, such as Pt or Ta. The other utilizes the collective motion of magnetic moments or spin waves with the quasi-particle excitations called magnons. A popular material for the latter is yttrium iron garnet, a magnetic insulator (MI). Here we demonstrate in NM/MI/NM trilayers that these two types of spin currents are interconvertible across the interfaces, predicated as the magnon-m…
We have investigated the unidirectional spin wave heat conveyer effect in sub-micron thick yttrium iron garnet (YIG) films using lock-in thermography (LIT). Although the effect is small in thin layers this technique allows us to observe asymmetric heat transport by magnons which leads to asymmetric temperature profiles differing by several mK on both sides of the exciting antenna, respectively. Comparison of Damon-Eshbach and backward volume modes shows that the unidirectional heat flow is indeed due to non-reciprocal spin-waves. Because of the finite linewidth, small asymmetries can still be …
Yttrium iron garnet is a complex ferrimagnetic insulator with 20 magnon modes which is used extensively in fundamental experimental studies of magnetisation dynamics. As a transition metal oxide with moderate gap (2.8 eV), yttrium iron garnet requires a careful treatment of electronic correlation. We have applied quasiparticle self-consistent GW to provide a fully ab initio description of the electronic structure and resulting magnetic properties, including the parameterisation of a Heisenberg model for magnetic exchange interactions. Subsequent spin dynamical modelling with quantum statistics…
We report the magnetic properties of yttrium iron garnet (YIG) thin films grown by pulsed laser deposition technique. The films were deposited on Si (100) substrates in the range of 15-50 nm thickness. Magnetic characterizations were investigated by ferromagnetic resonance spectra. Perpendicular magnetic easy axis was achieved up to 50 nm thickness. We observed that the perpendicular anisotropy values decreased by increasing the film thickness. The origin of the perpendicular magnetic anisotropy (PMA) was attributed to the texture and the lattice distortion in the YIG thin films. We anticipate…
We present a comprehensive investigation of propagating spin waves in nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas on top of continuous and patterned YIG films to characterize spin waves with wave vectors up to 10 rad/$μ$m. All films are grown by pulsed laser deposition. From spin-wave transmission spectra, parameters such as the Gilbert damping constant, spin-wave dispersion relation, group velocity, relaxation time, and decay length are derived and their dependence on magnetic bias …
As a thin layer of palladium (Pd) is directly deposited on an yttrium iron garnet or YIG (Y3Fe5O12) magnetic insulator film, Pd develops both low- and high-field magneto-transport effects that are absent in standalone Pd or thick Pd on YIG. While the low-field magnetoresistance peak of Pd tracks the coercive field of the YIG film, the much larger high-field magnetoresistance and the Hall effect do not show any obvious relationship with the bulk YIG magnetization. The distinct high-field magneto-transport effects in Pd are shown to be caused by interfacial local moments in Pd.
We show that using maskless photolithography and the lift-off technique, patterned yttrium iron garnet thin films possessing ultra-low Gilbert damping can be accomplished. The films of 70 nm thickness were grown on (001)-oriented gadolinium gallium garnet by means of pulsed laser deposition, and they exhibit high crystalline quality, low surface roughness, and the effective magnetization of 127 emu/cm3. The Gilbert damping parameter is as low as 5x10-4. The obtained structures have well-defined sharp edges which along with good structural and magnetic film properties pave a path in the fabrica…
We report strong damping enhancement in a 200 nm thick yttrium iron garnet (YIG) film due to spin inhomogeneity at the interface. The growth-induced thin interfacial gadolinium iron garnet (GdIG) layer antiferromagnetically (AFM) exchange couples with the rest of the YIG layer. The out-of-plane angular variation of ferromagnetic resonance (FMR) linewidth $ΔH$ reflects a large inhomogeneous distribution of effective magnetization $Δ4 πM_{eff}$ due to the presence of an exchange springlike moments arrangement in YIG. We probe the spin inhomogeneity at the YIG-GdIG interface by performing an in-p…
Yttrium Iron Garnet is the prototypical material used to study pure spin currents. It is a complex material with 20 magnetic atoms in the unit cell. Almost all theories and experimental analysis approximates this complicated material to a simple ferromagnet with a single spin wave mode. We use the method of atomistic spin dynamics to study the temperature evolution of the full 20 mode exchange spin wave spectrum. Our results show a strong frequency dependence of the modes in quantitative agreement with neutron scattering experiments. We find this causes in a reduction in the net spin pumping d…
Temperature dependence of the magnon-phonon coupling in yttrium iron garnet/gadolinium gallium garnet high overtone bulk acoustic resonators
Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学，自然科学学院，物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Centre for Quantum Engineering (ZQE), Technical University of Munich（量子工程中心，慕尼黑工业大学）；Institute for Theoretical Solid State Physics, RWTH Aachen University（亚琛工业大学理论固体物理研究所）
We show that in ferromagnetic (FM)/normal metal (NM) bilayers the dynamic coupling at the interface transfers an additional magnetic relaxation from the heavily damped motion of the conduction electron spins in the NM layer to the FM spins. While the FM relaxation rates due to two-magnon scattering and spin pumping decrease rapidly with increasing FM film thickness, the damping due to the dynamic coupling does not depend on the FM film thickness. The proposed mechanism explains the very large broadening of ferromagnetic resonance lines in thick films of yttrium iron garnet after deposition of …
The exceptional magnetic, optical and phononic properties of Yttrium Iron Garnet (YIG) make it unique for spin-wave based and photonic applications. Yet, nanostructuring crystalline YIG and manipulating its magnetism in a non-destructive way is an outstanding challenge, and so far mostly limited to two-dimensional capabilities. Here, we show that irradiation of single-crystal YIG films with a focused UV laser drives a stable, giant enhancement of the perpendicular magnetic anisotropy, preserving the crystalline quality. This modulation is highly confined at the nanoscale in both the lateral an…
We report thermal control of mode hybridization between the ferromagnetic resonance (FMR) and a planar resonator (notch filter) working at 4.74 GHz. The chosen magnetic material is a ferrimagnetic insulator (Yttrium Iron Garnet: YIG) covered by 6 nm of platinum (Pt). A current induced heating method has been used in order to enhance the temperature of the YIG/Pt system. The device permits us to control the transmission spectra and the magnon-photon coupling strength at room temperature. These experimental findings reveal potentially applicable tunable microwave filtering function.
Yttrium Iron Garnet is the ubiquitous magnetic insulator used for studying pure spin currents. The exchange constants reported in the literature vary considerably between different experiments and fitting procedures. Here we calculate them from first-principles. The local Coulomb correction (U - J) of density functional theory is chosen such that the parameterized spin model reproduces the experimental Curie temperature and a large electronic band gap, ensuring an insulating phase. The magnon spectrum calculated with our parameters agrees reasonably well with that measured by neutron scatterin…
We discuss threshold field-dependence of the decay rate of the uniform magnon mode in yttrium iron garnet (YIG) thin films. We demonstrate that decays must cease to exist in YIG films of thickness less than 1 μm, the lengthscale defined by the exchange length. We show that due to the symmetry of the three-magnon coupling the decay rate is linear in ΔH=(Hc-H) in the vicinity of the threshold field Hc instead of the step-like ΓΘ(ΔH) expected from the two-dimensional character of magnon excitations in such films. For thicker films, the decay rate should exhibit multiple steps due to thresholds fo…
Cerium substituted yttrium iron garnet (Ce:YIG) epitaxial thin films are prepared on gadolinium gallium garnet (GGG) substrate with pulsed laser deposition (PLD). It is observed that the films grown on GGG(111) substrate exhibit perpendicular magnetic anisotropy (PMA) as compared to films grown on GGG(100) substrate. The developed PMA is confirmed from magneto-optical Kerr effect, bulk magnetization and ferromagnetic resonance measurements. Further, the magnetic bubble domains are observed in the films exhibiting PMA. The observations are explained in terms of the growth direction of Ce:YIG fi…
30-80 nm thick yttrium iron garnet (YIG) films are grown by pulsed laser deposition on a 5 nm thick sputtered Pt atop gadolinium gallium garnet substrate (GGG) (110). Upon post-growth rapid thermal annealing, single crystal YIG(110) emerges as if it were epitaxially grown on GGG(110) despite the presence of the intermediate Pt film. The YIG surface shows atomic steps with the root-mean-square roughness of 0.12 nm on flat terraces. Both Pt/YIG and GGG/Pt interfaces are atomically sharp. The resulting YIG(110) films show clear in-plane uniaxial magnetic anisotropy with a well-defined easy axis a…
Spin currents are generated within the bulk of magnetic materials due to heat flow, an effect called intrinsic spin-Seebeck. This bulk bosonic spin current consists of a diffusing thermal magnon cloud, parametrized by the magnon chemical potential ($μ_{m}$), with a diffusion length of several microns in yttrium iron garnet (YIG). Transient opto-thermal measurements of the spin-Seebeck effect (SSE) as a function of temperature reveal the time evolution of $μ_{m}$ due to intrinsic SSE in YIG. The interface SSE develops at times < 2 ns while the intrinsic SSE signal continues to evolve at times >…
We investigate the temperature dependent microwave absorption spectrum of an yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic resonance linewidth increases linearly with temperature and shows a Gilbert-like linear frequency dependence. At lower temperatures, the temperature dependence of the resonance linewidth at constant external magnetic fields exhibits a characteristic peak which coincides with a non-Gilbert-like frequency dependence. The complete temperature and frequency evolution of the li…
We experimentally study the transient voltage response of yttrium iron garnet/platinum bilayer samples subject to periodic heating up to gigahertz frequencies. We observe an intrinsic cutoff frequency of the induced thermopower voltage, which characteristically depends on the thickness of the yttrium iron garnet film. The cutoff frequency reaches values of up to 350 MHz in a 50 nm thick yttrium iron garnet film, but drops to below 1 MHz for several-micrometer-thick films. These data corroborate the notion that the magnon spectrum responsible for the spin current emission in the spin Seebeck ef…
The magnetostatic mode (MSM) spectrum of a 300$μ$m diameter single crystalline sphere of yttrium iron garnet is investigated using broadband ferromagnetic resonance (FMR). The individual MSMs are identified via their characteristic dispersion relations and the corresponding mode number tuples $(nmr)$ are assigned. Taking FMR data over a broad frequency and magnetic field range allows to analyze both the Gilbert damping parameter~$α$ and the inhomogeneous line broadening contribution to the total linewidth of the MSMs separately. The linewidth analysis shows that all MSMs share the same Gilbert…
We combine the theoretical method of calculating spin wave excitation with the finite-temperature modeling and calculate the magnon-phonon relaxation time in the technologically important material Yttrium iron garnet (YIG) from first principles. The finite lifetime of magnon excitation is found to arise from the fluctuation of the exchange interaction of magnetic atoms in YIG. At room temperature, the magnon spectra have significant broadening that is used to extract the magnon-phonon relaxation time quantitatively. The latter is a phenomenological parameter of great importance in YIG-based sp…
Spin-orbit effects [1-4] have the potential of radically changing the field of spintronics by allowing transfer of spin angular momentum to a whole new class of materials. In a seminal letter to Nature [5], Kajiwara et al. showed that by depositing Platinum (Pt, a normal metal) on top of a 1.3 $μ$m thick Yttrium Iron Garnet (YIG, a magnetic insulator), one could effectively transfer spin angular momentum through the interface between these two different materials. The outstanding feature was the detection of auto-oscillation of the YIG when enough dc current was passed in the Pt. This finding …
We study the magnetic properties of Gadolinium-Yttrium Iron Garnet ($\text{Gd}_{x}\text{Y}_{3-x}\text{Fe}_5\text{0}_{12}$, $x=3,1.8$) ferrite ceramics. The complex initial permeability is measured in the temperature range 2 K to 295 K at frequency of 1 kHz, and in the frequency range 100 Hz to 200 MHz at temperatures 4 K, 77 K, and 295 K. The magnetic viscosity-induced imaginary part of the permeability is observed at low frequencies. Measurements of the magnetization noise are made at 4 K. Using the fluctuation-dissipation theorem, we find that the observed magnetization fluctuations are cons…
For longitudinal spin Seebeck effect (LSSE) devices, a multilayer structure comprising ferromagnetic and nonmagnetic layers is expected to improve their thermoelectric power. In this study, we developed the fabrication method for alternately stacked yttrium-iron-garnet (YIG)/Pt multilayer films on a gadolinium gallium garnet (GGG) (110) substrate, GGG/[YIG(49 nm)/Pt(4 nm)]$_n$ ($n =$ 1 - 5) based on room-temperature sputtering and $ex$-$situ$ post-annealing method and we evaluated their structural and LSSE properties. The fabricated [YIG/Pt]$_n$ samples show flat YIG/Pt interfaces and almost i…
A dense system of independent oscillators, connected only by their interaction with the same cavity excitation mode, will radiate coherently, which effect is termed superradiance. In several cases, especially if the density of oscillators is high, the superradiance may dominate the intrinsic relaxation processes. This limit can be achieved, e.g., with cyclotron resonance in two-dimensional electron gases. In those experiments, the cyclotron resonance is coupled to the electric field of light, while the oscillator density can be easily controlled by varying the gate voltage. However, in the cas…
Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbor exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for exper…
We study the temperature dependence of the longitudinal spin-Seebeck effect (LSSE) in a yttrium iron garnet Y3Fe5O12 (YIG) / Pt system for samples of different thicknesses. In this system, the thermal spin torque is magnon-driven. The LSSE signal peaks at a specific temperature that depends on the YIG sample thickness. We also observe freeze-out of the LSSE signal at high magnetic fields, which we attribute to the opening of an energy gap in the magnon dispersion. We observe partial freeze-out of the LSSE signal even at room temperature, where kBT is much larger than the gap. This suggests tha…
We investigate the Goos-Hanchen (G-H) shifts reflected and transmitted by a yttrium-iron-garnet (YIG) film for both normal and oblique incidence. It is found that the nonreciprocity effect of the MO material does not only result in a nonvanishing reflected shift at normal incidence, but also leads to a slab-thickness-independent term which breaks the symmetry between the reflected and transmitted shifts at oblique incidence. The asymptotic behaviors of the normal-incidence reflected shift are obtained in the vicinity of two characteristic frequencies corresponding to a minimum reflectivity and…
The nuclear and magnetic structure and full magnon dispersions of yttrium iron garnet Y$_3$Fe$_5$O$_{12}$ have been studied by neutron scattering. The refined nuclear structure is distorted to a trigonal space group of $R\bar{3}$. The highest-energy dispersion extends up to 86 meV. The observed dispersions are reproduced by a simple model with three nearest-neighbor-exchange integrals between 16$a$ (octahedral) and 24$d$ (tetrahedral) sites, $J_{aa}$, $J_{ad}$, and $J_{dd}$, which are estimated to be 0.00$\pm$0.05, $-$2.90$\pm$0.07, and $-$0.35$\pm$0.08 meV, respectively. The lowest-energy dis…
We have investigated recrystallization of amorphous Yttrium Iron Garnet (YIG) by annealing in oxygen atmosphere. Our findings show that well below the melting temperature the material transforms into a fully epitaxial layer with exceptional quality, both structural and magnetic.\\ In ferromagnetic resonance (FMR) ultra low damping and extremely narrow linewidth can be observed. For a 56 nm thick layer a damping constant of $α$=(6.63$\pm$1.50)$\cdot$10$^{-5}$ is found and the linewidth at 9.6 GHz is as small as 1.30$\pm$0.05 Oe which are the lowest values for PLD grown thin films reported so fa…
Vanadium ions charge states and their incorporation in the yttrium aluminum garnet Y3Al5O12 (YAG) lattice were studied by the correlated optical absorption and electron paramagnetic resonance (EPR) measurements. In as-grown crystals, the occupation of the V3+ at both the octahedral and tetrahedral aluminum sites was proven. The V3+ to V4+ charge transformation was observed after annealing in air, whereas annealing in the hydrogen atmosphere resulted exclusively in a slight weakening of the V3+ absorption bands due to partial recharge of these ions. Spin Hamiltonian parameters of the V3+ and V4…
Using liquid phase epitaxy (LPE) technique (111) yttrium iron garnet (YIG) films with thicknesses of ~100 nm and surface roughnesses as low as 0.3 nm have been grown as a basic material for spin-wave propagation experiments in microstructured waveguides. The continuously strained films exhibit nearly perfect crystallinity without significant mosaicity and with effective lattice misfits of delta a(perpendicular)/a(substrate) ~10-4 and below. The film/substrate interface is extremely sharp without broad interdiffusion layer formation. All LPE films exhibit a nearly bulk-like saturation magnetiza…
Modern-days CMOS-based computation technology is reaching its fundamental limitations. The emerging field of magnonics, which utilizes spin waves for data transport and processing, proposes a promising path to overcome these limitations. Different devices have been demonstrated recently on the macro- and microscale, but the feasibility of the magnonics approach essentially relies on the scalability of the structure feature size down to an extent of a few 10 nm, which are typical sizes for the established CMOS technology. Here, we present a study of propagating spin-wave packets in individual y…
The first observation of microwave magnetoelectric (ME) interactions through ferromagnetic resonance (FMR) in bilayers of single crystal ferromagnetic-piezoelectric oxides and a theoretical model for the effect are presented. An electric field E produces a mechanical deformation in the piezoelectric phase, resulting in a shift dHE in the resonance field for the ferromagnet. The strength of ME coupling is obtained from data on dHE vs E. Studies were performed at 9.3 GHz on bilayers of (111) yttrium iron garnet (YIG) films and (001) lead magnesium niobate-lead titanate (PMN-PT). The samples were…
Spin waves are promising candidates for information processing and transmission in a broad frequency range. In the realization of magnonic devices, the frequency depended division of the spin wave frequencies is a critical function for parallel information processing. In this work, we demonstrate a proof-of-concept spin-wave frequency division multiplexing method by magnetizing a homogenous magnetic microstripe with an inhomogeneous field. The symmetry breaking additional field is introduced by a permalloy stripe simply placed in lateral proximity to the waveguide. Spin waves with different fr…
The spin Peltier effect (SPE), heat-current generation due to spin-current injection, in various metal (Pt, W, and Au single layers and Pt/Cu bilayer)/ferrimagnetic insulator (yttrium iron garnet: YIG) junction systems has been investigated by means of a lock-in thermography (LIT) method. The SPE is excited by a spin current across the metal/YIG interface, which is generated by applying a charge current to the metallic layer via the spin Hall effect. The LIT method enables the thermal imaging of the SPE free from the Joule-heating contribution. Importantly, we observed spin-current-induced tem…
Spin current -- a flow of the spin degree of freedom in matter -- has vital importance in spintronics. Propagation of the spin current ranges over a whole momentum space; however, generated spin currents are mainly detected in the long-wavelength limit. To facilitate practical uses of spintronics and magnonics, microscopic understanding of the spin current is necessary. We here address yttrium iron garnet, which is a well-employed ferrimagnet for spintronics, and review {\it in re} the momentum- and energy-resolved characteristics of its magnetism. Using {\it unpolarized} neutrons, we refined …
We analyze the structural and magnetic characteristics of (111)-oriented lutetium iron garnet (Lu$_3$Fe$_5$O$_{12}$) films grown by molecular-beam epitaxy, for films as thin as 2.8 nm. Thickness-dependent measurements of the in- and out-of-plane ferromagnetic resonance allow us to quantify the effects of two-magnon scattering, along with the surface anisotropy and the saturation magnetization. We achieve effective damping coefficients of $11.1(9) \times 10^{-4}$ for 5.3 nm films and $32(3) \times 10^{-4}$ for 2.8 nm films, among the lowest values reported to date for any insulating ferrimagnet…
