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Magnetic materials showing perpendicular magnetic anisotropy (PMA) and low damping are of great importance in spintronics. Co/Ni multilayers have been known to exhibit large tunable PMA [1], high spin polarization [2] and relatively low intrinsic damping [3]. In this study we investigated a series of Pt/[Co/Ni]N/Ir multilayers grown on Si/SiO2 with a Ta/Pt seed adhesion layer and the multilayer stack was capped with an Ir/Pt/Ta capping layer. Broadband ferromagnetic resonance (FMR) and polar angle dependent FMR measurements reveal the presence of a strong fourth-order contribution to the perpendicular anisotropy. Polar angle dependent data are fitted using the Smit-Beljers relation [4] to extract both the second and fourth-order anisotropy constants (shown in Fig.1). This model explains the data qualitatively and we observe systematic deviations for samples near or in the easy cone state of the phase diagram. We find that the effective Gilbert damping scales with the inverse multilayer thickness, indicating a significant interfacial contribution to the damping process.References: 1. G. Daalderop, P. Kelly and F. D. Broeder, Physical Review Letters., vol 68, p:682-685 (1992) 2. S. Mangin, D. Ravelsona, J. A. Katine, et.al., Nature Materials., vol 5, p:210-215 (2006) 3. J. M. Shaw, H. T. Nembach and T. J. Silva, Journal of Applied Physics., vol 108, p: 093922 (2010) 4. J. Smith and H. Beljers, Philips Research Reports., vol 10, p:113 (1955) 



MMM 2020

Higher-order contribution to perpendicular anisotropy and interfacial damping of Co/Ni multilayers

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

In geometrically frustrated magnetism, the very nature of the ground state of Tb2Ti2O7, has remained a long standing conundrum. In this pyrochlore material, no conventional spin-ice or long-range magnetic order is stabilized, even at very low temperatures [1]. Quantum fluctuations are suspected of being at the origin of such an exotic quantum phase, yet so far no complete description is available. Using neutron scattering [2] and synchrotron-based terahertz spectroscopy [3], it has been shown that spin/lattice couplings are present in form of hybrid Tb crystal-field / phonon modes that are present across a broad temperature range from 200 K down to 6 K. This so called vibronic process affects the electronic ground state that can no longer be described solely by electronic wave functions and involve quadrupolar degrees of freedom associated with the rare earth magnetic element in its local environnement. We present here new magneto-optical investigation of vibronic spin-lattice coupling effects. We apply a static magnetic field along the cubic <111> direction while probing with linearly polarized THz radiation. Through the Zeeman effect, the magnetic field enhances splitting within the low-energy Tb crystal field transitions revealing new details in our THz spectra. Complementary magneto-optical quantum calculations including quadrupolar terms show that indeed vibronic effects are required to describe our observations at 3 K. A further prediction of our theoretical model is the presence of a novel magneto-optical birefringence as a result of this vibronic process. Together, our results [4] reveal the significance of considering quadrupolar spin-lattice effects when describing the spin-liquid ground state of Tb2Ti2O7. They also highlight the potential for future magneto-optical investigations to probe complex materials where spin /lattice couplings are present and unravel new magneto-optical activity in the THz range.References: [1] J. S. Gardner, B. D. Gaulin, A. J. Berlinsky et al., Phys. Rev. B 64, 224416 (2001) [2] T. Fennell, M. Kenzelmann, B. Roessli et al., Phys. Rev. Lett. 112, 017203 (2014) [3] E. Constable, R. Ballou, J. Robert et al., Phys. Rev. B 95, 020415(R) (2017) [4] K. Amelin, Y. Alexanian, U. Nagel et al, to be published 

THz Magneto-Optical Investigation of Quadrupolar Spin-Lattice Effects in Magnetically Frustrated Tb2Ti2O7

The spin nematic phase, which is a kind of multipole phases, has attracted a lot of interest in the field of the strongly correlated electron systems, as well as the quantum spin liquid phase. Using the numerical exact diagonalization, the density matrix renormalization group (DMRG) calculation, and the finite-size scaling analysis, it is found that some spin nematic and spin liquid phases are induced by external magnetic field in the anisotropic and frustrated quantum spin systems. In our previous work[1], it was found that a field-induced nematic phase appears at some critical field in the anisotropic spin ladder. The nematic phase is characterized by the power-law decay in the correlation function of the second-order spin moment. In addition at some higher critical field a quantum phase transition can occur to the conventional field-induced Tomonaga-Luttinger liquid. Several typical magnetization curves calculated by DMRG are presented. Recently the field-induced nematic phase was observed on the frustrated spin ladder system[2]. So we studied on a frustrated spin ladder system[3], using the numerical diagonalization and DMRG. As a result, it was found that several exotic quantum phases, including the spin-nematic liquid phase. We also reported several interesting phase diagrams of this model and some related systems[4,5]. In the present paper, we investigate the S=1 antiferromagnetic chain with the biqadratic interaction, as another candidate that exhibits the field-induced spin nematic liquid pahse. The numerical diagonalization study of finite-size clusters indicates that the spin nematic liquid pahse appears in this model under sufficiently strong magnetic field. The phase diagram in the plane of the magnetic field and the biquadratic interaction is presented.References: [1] T. Sakai, T. Tonegawa and K. Okamoto, Physica Status Solidi B 247, 583 (2010) . [2] N. Buttgen et al., Phys. Rev B 90, 134401 (2014) . [3] T. Hikihara, T. Tonegawa, K. Okamoto and T. Sakai, J. Phys. Soc. Jpn. 86, 054709 (2017). [4] T. Tonegawa, T. Hikihara, K. Okamoto, S. C. Furuya, and T. Sakai, J. Phys. So. Jpn. 87, 104002 (2018). [5] T. Sakai, K. Okamoto and T. Tonegawa, Phys. Rev. B 100, 054407 (2019) 

Quantum Spin Nematic Liquid in the S=1 Antiferromagnetic Chain with the Biquadratic Interaction

Spin liquids are disordered states of matter that still fluctuate at low temperature. In many cases, the ground state of spin liquids is expected to be ordered, for example because the dipolar interaction lifts the (quasi)degeneracy between low-energy spin configurations. However, this is not what is observed experimentally, and many systems dynamically freeze in a liquid phase [1] before the ordering takes place. In spin ice compounds or artificial magnets, ground state configurations are then generally out of reach for practical reasons. In this presentation, we will show how dynamical freezing can be bypassed in an artificial kagome ice. We will illustrate the efficiency of our method by demonstrating that the a priori dynamically inaccessible ordered ground state of the dipolar kagome ice is imaged reproducibly in real space, and at room temperature. The central idea of this work is to replace the spin degree of freedom by a micromagnetic knob, which can be adjusted by a proper design of the vertex geometry. Our strategy is to imprint the desired spin configuration, vertex by vertex, in a kagome array made of connected nanomagnets, with a notch at each vertex site. Each notch locally lifts the energy degeneracy between the six states of a given vertex satisfying the ice rule constraint [2], allowing to reach efficiently any desired spin microstate using a field demagnetization protocol. This concept will be demonstrated both numerically and experimentally, and we will show how we can access all predicted phases of the dipolar kagome ice [3, 4, 5].References: [1] I. A. Chioar, B. Canals, D. Lacour, Phys. Rev. B 90, 220407(R) (2014) [2] J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933) [3] W. R. Branford, S. Ladak, D. E. Read, Science 335, 1597-1600 (2012) [4] B. Canals, I. A. Chioar, V. D. Nguyen, Nature com. 7, 11446 (2016) [5] G.-W. Chern, P. Mellado and O. Tchernyshyov, Phys. Rev. Lett. 106, 207202 (2011). 

Bypassing Dynamical Freezing and Accessing Low-energy Microstates in Artificial Kagome Ice

The nearest neighbour antiferromagnetic Ising model on the kagome lattice is well known for its high frustration and macroscopic ground state degeneracy [1,2]. Recently, new experimental realizations of Ising-like spin systems have been developed - so-called artificial spin systems - based on mesoscopic structures of chirally coupled nanomagnets [3]. On the square lattice, such systems have proven to behave as nearest neighbour Ising antiferromagnets. Because of frustration, realizations of kagome lattice Ising antiferromagnets with these mesoscopic structures (Fig.1) are much more challenging to study. From the theoretical side as well, such models still present some difficulties [4,5]. I will describe how to tackle classical frustrated spin systems using Monte Carlo techniques [5] and tensor network methods [4,6,7] (Fig.2), focusing on the kagome lattice nearest neighbour Ising antiferromagnet in an external magnetic field, and I will compare the experimental and numerical results.References: [1] K. Kanô and S. Naya, Prog. Theor. Phys., Vol. 10, p. 158 (1953) [2] A. Sütö, Z. Phys. B, Vol. 44, p. 121 (1981) [3] Z. Luo et. al., Science, Vol. 363, p. 1435 (2019) [4] B. Vanhecke, J. Colbois, L. Vanderstraeten, et. al., arXiv:2006.14341 (2020) [5] G. Rakala and K. Damle, Phys. Rev. E Vol. 96, 023304 (2017) [6] V. Zauner-Stauber, L. Vanderstraeten, et. al. Phys. Rev. B Vol. 97, 045145 (2018) [7] L. Vanderstraeten, B. Vanhecke, and F. Verstraete, Phys. Rev. E Vol. 98, 042145 (2018) 


New Approaches to the Nearest Neighbour Ising Antiferromagnet on the Kagome Lattice

Excitation by light pulses enables the manipulation of phases of quantum condensed matter. Here, we photoexcite high-energy holon-doublon pairs as a way to alter the magnetic free energy landscape of the Kitaev-Heisenberg magnet α-RuCl3,[1,2] with the aim to dynamically stabilize a proximate spin liquid phase. The holon-doublon pair recombination through multimagnon emission [3] is tracked through the time-evolution of the magnetic linear dichroism originating from the competing zigzag spin ordered ground state. A small holon-doublon density suffices to reach a spin disordered state. The phase transition is described within a dynamic Ginzburg-Landau framework, corroborating the quasistationary nature of the transient spin disordered phase. Our work provides insight into the coupling between the electronic and magnetic degrees of freedom in α-RuCl3 and suggests a new route to reach a proximate spin liquid phase in Kitaev-Heisenberg magnets.[4]References: [1] A. Banerjee et al., Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet, Nat. Mater. 15, 733-740 (2016). [2] H. Takagi et al.,Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264-280 (2019). [3] Z. Lenarcic et al., Ultrafast charge recombination in a photoexcited Mott-Hubbard insulator, Phys. Rev. Lett. 111, 016401 (2013). [4] R.B. Versteeg et al. Nonequilibrium quasistationary spin disordered state in the Kitaev-Heisenberg magnet α-RuCl3, arXiv:2005.14189 [cond-mat.str-el] (2020) 


Nonequilibrium quasistationary spin disordered state in the Kitaev-Heisenberg magnet α-RuCl3

One dimensional spin S = 1/2 chain systems provide a perfect platform to explore many of the quantum phenomena and the related excitations. We report here the discovery of a stimulating magnetic ground state in a tetragonal compound Ti4MnBi2 that contains perfectly linear chains of Mn-ions with dMn-Mn = 2.49 Å running along the crystallographic c-axis and which are separated from each other by a large interchain distance dchain ≈7.4 Å. Our electrical transport measurements and electronic structure calculations establish that compound is metallic. Curie-Weiss fit to the susceptibility data suggests that Mn moments are in low-spin S = 1/2 configuration. The results show that despite the presence of a sizable antiferromagnetic (AFM) interaction [Jc = 18(6) K], the full-moment long range magnetic ordering is not achieved down to 50 mK. Neutron diffraction measurement performed on an assembly of aligned single crystals detect a weak AFM order within the Mn chains, with a further evidence of the reduced-moment ordering coming from heat capacity data. Apparently, strong quantum fluctuations overcome the magnetic order and the material enters into a state at low temperatures which can be best described as a ``quantum admixture" of a quantum spin liquid and a long-range magnetically ordered states, resulting into a highly reduced value of the ordered moment μ << 1 μB.References: A. Pandey, P. Miao, M. Klemm, H. He, H. Wang, X. Qian, J. W. Lynn, and M. C. Aronson, Phys. Rev. B in press (2020). 

Incipient antiferromagnetic order in metallic Ti4MnBi2 containing linear Mn chains of spin S = 1/2

The realization of energy efficient spin-current based electronics relies on the existence of low-loss magnetic insulator thin films capable of generating spin currents without an accompanying charge current. Currently, the number of such materials is extremely limited, with the only candidates being the garnets Y3Fe5O12 (YIG) [1] and Lu3Fe5O12 (LuIG) [2] along with the recently discovered spinels Ni0.65Zn0.35Al0.8Fe1.2O4 (NZAFO) [3] and MgAl0.5Fe1.5O4 (MAFO) [4,5]. Bulk phase Li0.5Fe2.5O4 (LFO) is well known to have the lowest Gilbert damping parameter (α ≈ 0.002) among the spinel ferrites, but thus far LFO thin films have not lived up to these expectations. In this talk, we demonstrate the realization of epitaxial ultra-thin (~3 nm) LFO thin films on MgAl2O4 substrates with an ultra-low damping parameter of α ≈ 0.0013 and an FMR linewidth of 1.17 mT at 20.6 GHz. Such a damping value rivals those of YIG and is comparable to the lowest damping previously reported in sub-10-nm magnetic films [2]. LFO also offers distinct advantages over YIG such as smaller external field requirements and thinner interfacial magnetic dead layers due to the low growth temperature, making it ideal for magnetic switching applications. Our results show the promise of LFO as a new candidate for spin-current based spintronics. This work was supported by the U.S. Department of Energy, Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DESC0008505.References: [1] B. M. Howe, S. Emori, H. Jeon, IEEE Magnetics Letters., Vol. 6, p. 1-4 (2015) [2] C. L. Jermain, H. Paik, S. V. Aradhya, Applied Physics Letters., Vol. 109, p. 192408 (2016) [3] M. T. Gray, S. Emori, B. A. Gray, Physics Review Applied., Vol. 9, p. 064039 (2018) [4] S. Emori, D. Yi, S. Crossley, Nano Letters., Vol. 18, p. 4273-4278 (2018) [5] J. J. Wisser, S. Emori. L. Riddiford, Applied Physics Letters., Vol. 115, p. 132404 (2019) 


Ultra-low Magnetic Damping in Epitaxial Li0.5Fe2.5O4 Thin Films

High magnetostriction and low damping are two crucial properties for voltage tunable high frequency devices using magnetostrictive ferromagnet-piezoelectric hybrid structures to achieve low microwave loss [1, 2]. FeGa is a promising candidate for such devices as it is free of rare earth elements and has a large magnetostriction [3]. We grew epitaxial FeGa films on MgO (100) substrates using off-axis sputtering technique. Broadband ferromagnetic resonance (FMR) is used to investigate the magnetization dynamics of the epitaxial FeGa thin films. The resonance field Hres versus frequency f data is fitted using the Kittel equation to extract the reduced gyromagnetic ratio γ′, the effective magnetization Meff, and the four-fold magnetic anisotropy H4. The frequency dependence of the linewidth data is used to extract the effective damping αeff and residual linewidth ΔH0 due to inhomogeneities in the film. We report ultra-low residual linewidth, ΔH0 = 13±1 [Oe] – indicative of the high quality of the epitaxial films- significantly lower than reported previously [4]. The effective damping parameter αeff is found to be as low as 0.0065(+0.0005 -0.0001), as shown in figure 1, which is one order magnitude lower than previously reported values [5, 6]. In-plane angular dependence of resonance field Hres clearly demonstrates a four-fold in-plane anisotropy arising from the crystal symmetry. The four-fold anisotropy extracted from the Kittel plot H4 = -786±15 [Oe] is in good agreement with the value determined from fitting of in-plane rotation data H4 = -795±1 [Oe] as shown in figure 2.References: 1) V. Novosad et al., Journal of applied physics 87, 6400 (2000). 2) J. Lou et al., Applied Physics Letters 92, 262502 (2008). 3) A. E. Clark et al., Materials transactions 43, 881 (2002). 4) B. K. Kuanr et al., Journal of Applied Physics 115, 17C112 (2014). 5) D. Parkes et al., Scientific reports 3, 2220 (2013). 6) D. B. Gopman et al., IEEE transactions on magnetics 53, 1 (2017). 


Low damping and linewidth in magnetostrictive epitaxial FeGa thin films using ferromagnetic resonance

Identifying the origins of ferromagnetic resonance (FMR) linewidth broadening is essential for the fundamental understanding of magnetic relaxation, often discussed in terms of “damping”. It is not yet well understood how inhomogeneity and structural disorder contribute to magnetic relaxation in polycrystalline thin films, even though they are widely used in device applications. In this presentation, we systematically examine the impact of inhomogeneity and disorder on the FMR linewidth of sputter-grown polycrystalline Fe and Fe80V20 films with thickness 2-25 nm and different seed layers. A highly nonlinear frequency dependence of FMR linewidth is observed for Fe films on Cu/Ti seed layers. As shown in Fig. 1, all linewidth vs frequency data are quantitatively reproduced with a two-magnon scattering model [1, 2, 3] that accounts for a random distribution of the effective anisotropy field among grains in the polycrystalline film. The fit results indicate that a larger grain size is correlated with stronger two-magnon scattering, which – somewhat counterintuitively – may be accompanied by a lower Gilbert damping parameter. Films with the strongest two-magnon scattering contribution (cf. 10-nm-thick Fe/Cu/Ti, Fig. 1) exhibit the highest coercivity, pointing to a connection between magnetic inhomogeneity and the observed non-Gilbert relaxation. In addition, it is found that two-magnon scattering is reduced by changing the seed layer or alloying Fe with V (Fig. 2). We will discuss the possible mechanisms that lead to narrower FMR linewidths in polycrystalline Fe(V) films. The fundamental understanding gained from our study enables a coherent approach to develop low-loss polycrystalline magnetic media for power-efficient spintronic devices.References: [1] R. McMichael and P. Krivosik, IEEE Trans. Mag., Vol. 40, p.2 (2004) [2] S. Kalarickal, P. Krivosik and J. Das, Phys. Rev. B, Vol. 77, p.054427 (2008) [3] W. Peria, T. Peterson and A. McFadden, Phys. Rev. B, Vol. 101, p.134430 (2020) 


Two-magnon Scattering in Polycrystalline Fe and FeV Alloy Thin Films

Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades. This is the case even for some of the simplest and most technologically relevant ferromagnetic metals, such as pure Fe. Here, we experimentally identify intrinsic Gilbert damping that increases with decreasing electronic scattering in thin films of BCC Fe [1]. We directly compare the temperature dependence of Gilbert damping and electronic transport in pristine epitaxial films (Figure 1). Our observation of “conductivity-like” damping, which cannot be accounted for by classical eddy current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering (often understood in terms of the “breathing Fermi surface” model) [2,3], as shown in Figure 2. While this fundamental damping mechanism was originally proposed more than 40 years ago [4], our study is the first to confirm it unambiguously for thin films of a pure ferromagnetic metal. Our results also reveal – somewhat counterintuitively – that disorder can reduce intrinsic damping in ferromagnetic metals particularly at low temperatures. This suggest that optimally disordered films may exhibit enhanced spin coherence required for cryogenic and quantum information devices.References: [1] B. Khodadadi, A. Rai, A. Sapkota, et al. Phys. Rev. Lett., Vol. 124, 157201 (2020). [2] K. Gilmore, Y. U. Idzerda, and M.D. Stiles, Phys. Rev. Lett., Vol. 99, 27204 (2007). [3] S. Mankovsky, D. Kodderitzsch, G. Woltersdorf, and H. Ebert, Phys. Rev. B, Vol. 87, 14430 (2013). [3] V. Kamberský and Czechoslov. J. Phys., Vol. 26, 1366 (1976).

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Higher-order contribution to perpendicular anisotropy and interfacial damping of Co/Ni multilayers

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THz Magneto-Optical Investigation of Quadrupolar Spin-Lattice Effects in Magnetically Frustrated Tb2Ti2O7

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Bypassing Dynamical Freezing and Accessing Low-energy Microstates in Artificial Kagome Ice