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Theory and Computation

Analytical and quasi-analytical models

As a part of the theoretical efforts within TRANSPIRE, self-oscillations in compensated ferrimagnets, induced by charge current, are studied. This is carried out, by exploiting the concept of spin-orbit torques (SOTs), which are currently playing an increasing role in the control of the magnetic degrees of freedom. The prerequisites are strong spin-orbit coupling and broken inversion symmetry. The already established zero-moment half-metal Mn2RuxGa (the prototypical candidate material studied in TRANSPIRE) exhibits all the necessary requirements for this scheme to work. It crystalizes in a tetragonal structure that has no centre of inversion. The TCD partner has previously demonstrated that the spin-orbit coupling is strong in this material, as illustrated by a rather large anomalous Hall angle (http://aip.scitation.org/doi/abs/10.1063/1.4913687).

Spin Dynamics on the Unit Sphere

Here we establish a phenomenological framework for the calculation of SOTs based on the crystallographic space-and point-group symmetries. The importance of the crystal structure is clear, as stated in the Neumann's principle [R. R. Birss, Symmetry and Magnetism (North-Holland, Amsterdam, 1966)]: "...symmetries possessed by the point group of the crystal will be inherited by any physical quantity...". Within this framework, the spin dynamics is studied, having as an input, the values of the magnetic parameters as experimentally-determined by the TCD and HZDR partners. Dynamically stable solutions (self-oscillations) are achieved, when an external energy source (the un-polarized electronic current) is able to compensate the loss of angular momentum, i.e. the magnetic damping, parametrized (usually) by the Gilbert damping parameter α. Furthermore, a non-linear feedback mechanism is required. In the case of current-induced SOTs, the effective damping can be shown to depend on the applied charge current, as well as on the azimuthal angle and strength of the dissipative SOT, thereby providing the required non-linear feedback.

 

Computational Material Science

Electronic structure of ZMHM materials

For the purposes of TRANSPIRE the Computational Spintronics group at TCD is able to compute a number of essential electronic structure and close-to-equilibrium transport parameters. The calculations are typically performed using well-established local-basis codes, such as SIESTA (for electronic structure) and in-house developed SMEAGOL (for NEGF transport).

As an example of a Density of States (DOS) calculation, informed by experiment, here we look at the example of Mn2Ga - a material previously well characterised by the experimental partners at TCD. It can be therefore assumed that a strain is carried though the thin film resulting in the MgO lattice parameter for the ab plane and 716 pm for the c lattice parameter. Under this strain Mn2Ga has the electronic structure shown below. The strain of MgO slightly changes the electronic structure reducing the width of the Mn 3d manifold. The electronic structure at the Fermi level which will be responsible for the transport is largely unchanged by the strain of MgO and we still observe a large DOS for the minority spin channel as observed in the unstrained structure. The unweighted Fermi level polarisation does not exceed about 60 %.

Computed Density of States for the case of Mn2Ga

The spin-polarised DOS for Mn2Ga, on a structure matching the one experimentally observed in thin film growth on MgO.

 

Magnonic and Phononic dispersions

The magnon dispersions can be used to evaluate the Jex integrals and the magnetic anisotropy. These quantities critical to the ability to interface the ab initio calculations with the analytical modelling of the system and the spin-dynamic simulations.

Magnon Dispersion in Mn2Ga

The calculated dispersion of the acoustic magnons in Mn2Ga.

 

Phonons and their scattering with electrons and magnons play a critical role for the limiting energy dissipation mechanisms at THz frequencies. As such, it is important that the limits for their control (for example by finite-size effects) are established well. The phonon dispersions can be calculated using, for example, the supercell finite difference approach within the Elk LAPW code.

Phonon dispersion in Mn2Ga

Phonon dispersions along the different high-symmetry directions in Mn2Ga.

 

Materials

Scientific and societal progress is driven by advances in materials science. Cross-ocean navigation was made possible by the invention of the compass, the industrial revolution depended on the control of carbon content in iron, ultra-pure silicon is at the base of the information technology we use today supported by mass-storage of information in server farms dotted around the globe relying on magnetic materials making up the spinning disks of the hard drives. On the materials front, TRANSPIRE is devoted to synthesising magnetic materials with ultra-high anisotropy fields and utilise them in spin-electronic device structures and stacks in order to enable information transmission at rates up to three orders of magnitude higher than today's standards.

 

High Anisotropy Field Materials

The key parameter of magnetisation dynamics is the magnetic resonance frequency, that is the frequency at which an out-of-equilibrium magnetic moment precesses around its equilibrium axis. The effective field driving the precession is in ferromagnets equal to the anisotropy field which is written Heff = Hk = 2Ku/Ms where Ku is the anisotropy constant and Ms the saturation magnetisation. The resonance frequency is then inferred by f = γHeff with γ = 28 GHz/T. We note from the equations above that for a given anisotropy constant Ku the anisotropy field can be increased by reducing Ms, and the natural choice to achieve high frequencies is therefore ferrimagnetic materials with two (or more) opposing magnetic sublattices. We have previously developed a number of such materials in thin film form: Mn3-xGa, Mn2FexGa as well as a very distinct material Mn2RuxGa where the two sublattices perfectly compensate to give zero net moment. This very interesting case will be discussed in more detail below. The fact that the materials we have chosen to work with are ferrimagnets has another important implication. The effective field outlined above for a ferromagnet can more generally be written as the gradiant of the magnetic free energy with respect to the magnetisation. We therefore expect in ferrimagnets to find two distinct modes, first, the mode where the two sublattices precess together without changing the angle between them. This is the ferrimagnetic equivalent to the ferromagnetic mode described above. Second, a mode where the angle between them does change. As the energy term related to this bending is the exchange, and not anisotropy, field we expect much higher effective fields and thus frequencies for this mode. From the above it is clear that in order to reach spin dynamics at several 100s of GHz or even into the THz region we need materials with high Ku's and low Ms's. The Mn-bearing Heusler alloys crystallising in the D022 crystal structure is therefore almost a prefect choice: Their crystal structure is highly tetragonal yielding Ku's as high as 2 MJ/m3 while the moments on the two Mn sites compensate each other to give net magnetisations as low as 250 kA/m. This results in anisotropy fields of order 10 T which implies a resonance frequency for the first mode described above of ~ 300 GHz. These materials furthermore all exhibit another advantage for their use in spin electronics. The most important parameter for any material to be used in spin electronics is its spin polarisation, the degree to which the current-carrying electrons have their spins aligned parallel one to the other. For traditional ferromagnets like iron or cobalt this value is about 40 %, while Mn3Ga for example, can reach 60 % (or even higher at least from a theoretical point of view). In conclusion: The D022 class of Mn-containg Heusler alloys combine properties that should make tem ideal for TRANSPIRE: high anisotropy and low moments making them almost insensitive to external fields while exhibiting extremely fast spjn dynamics. They are furthermore highly spin polarised so that all existing spin electronic devices structures should be useable: exicitation by spin transfer torque, detection by magnetoresistive effects such as tunnelling magneto resistance etc.

 

Synthetic Ferrimagnetic Stacks

To enable electrical detection of resonance below 50 GHz, i.e. in the frequency band where transport measurement facilities are already optimised at HZDR, TCD is growing different synthetic ferrimagnets, while in parallel exploring avenues for growing of tuned ferrimagnetic Heusler alloys, with anisotropies compatible with the frequency ranges of existing facilities. The generic structure of the synthetic ferrimagnets is NiFe / Ru / NiFe, with different thicknesses of the two NiFe layers. NiFe is chosen due to its high mangetoresistive response, and the Ru thickness is chosen to ensure strong antiparallel coupling of the NiFe layers. Variations of this base structure are grown, in order to obtain unbalanced and balanced ferrimagnetic structures, which model the two sublattices of ferrimagnetic Heusler-type zero-moment half-metal systems (described below), above, below and at the compensation temperature, depending on the relative thickness of the two NiFe layers.

Resonances in synthetic ferrimagnetic structures

Fitted resonance peaks from electrically detected magnetic resonance for the balanced (a), slightly unbalanced (b), and very unbalanced (c) artificial ferrimagnets. In the fully balanced system the out-of-phase mode is most difficult to detect as the contribution to the change in resistance of each layer is effectively cancelled.

 

Zero Moment Half Metals

In light of the discussion of the properties of high-anisotropy materials above the natural extention is of course to use materals with no net moment. Antiferromagnets are completely insensitive to external fields and their spin dynamics are extremely fast due to the interaction between dynamics and the exchange field. They do however come with one fundamental limitation, their spin polarisation must be zero on the lengthscale of a crystalline unit cell as the sublattices differ only be the direction of their magnetic moments. This is not the case for compensated ferrimagnets however where the two sublattices are either chemically or structurally different (or both). Such a material was envisaged about 30 years back by theoriticians Val Leuken and de Groot, who wrongly called it a "half-metallic antiferromagnet". The first experimental example of this new class of materials was found by us in 2014 and is Mn2Ru0.5Ga - MRG. In MRG the two magentic sublattices are both composed of Mn but crucially they do not occupy the same positions. We can therefore obtain perfect compensation - zero net moment - but complete spin polarisation. Our discovery has enabled a number of new studies, both of fundamental as well as applied nature. Due to the high spin polarisation, magnetic domains can be imaged in MRG as they can be in ferromagnets using fex magneto-optical Kerr effect while magnetically MRG is an antiferromagnet. Magnetoresitive effects such as anomalous Hall effect, tunnel and gian magnetoresistance can be used to read out the magnetic state (sublattice i pointing up or down) even in the case where the net moment is zero.

 

Device Stacks

The preparation of device stacks involving Zero-Moment Half-Metals, such as MRG, is an essential component to TRANSPIRE. The demonstration of sizeable TMR ratios is a pre-requisite for the use of these in STT oscillators. As Mn-diffusion is particulatly difficult to control across the active part of such structures, Al-assisted strategies are used as a starting point.

Tunnelling magnetoresistance ratios of up to 40 % are measured between 10 K and 300 K when the prototypical highly spin-polarized compensated ferrimagnet, Mn2RuxGa, is integrated into MgO-based perpendicular magnetic tunnel junctions. Temperature and bias dependences of the tunnel magnetoresistance effect, with a sign change near 0.2 V, reflect the structure of the Mn2RuxGa interface density of states. Despite magnetic moment vanishing at a compensation temperature of 200 K for x = 0.8, the tunnel magnetoresistance ratio remains non-zero throughout the compensation region, demonstrating that the spin-transport is governed by one of the Mn sub-lattices only. Broad temperature range magnetic field immunity of at least 0.5 T is demonstrated in the same sample. The high spin polarization and perpendicular magnetic anisotropy of Mn2RuxGa make it suitable to enter device stacks suitable for applications in both non-volatile magnetic random access memory cells and terahertz spin-transfer oscillators.

Demonstration of TMR in a stack based on MRG.

Room temperature (300K) TMR data of the x = 1.0 sample annealed at different temperatures. Positive TMR is observed at applied bias U = 10 mV, and negative at U =1 V. (b) TMR(U) scans at 300 K and 10 K for a chip annealed at 350 oC. The top left inset represents the spin split density of states of MRG for x = 1.0. (http://aip.scitation.org/doi/abs/10.1063/1.4948934)

MRG is a ferrimagnetic Heusler alloy, considered to be a zero-moment half-metal at its compensation temperature. Many of its properties are related to its crystal structure, a tetragonally distorted cubic L21. Due to this, the use of seed layers can alter its properties as the seed can strain the unit cell of MRG. MgO is typically used as a substrate for MRG due to close lattice matching, which allows for properties to be refined with changes in composition. We have demonstrated that MRG can successfully be grown on other materials such as TiN. We also able to deposit 20 nm thick films Mn2Ru0.7Ga on MgO substrates with a thin W seed. The W film can be deposited by either DC sputtering or by RF sputtering. In order to produce high quality W films, the MgO substrate must be annealed at 500 oC to desorb water.

MRG can be successfully grown on the following substrates and seeds: MgO, Cr, V, β-W, BTO, CoGa and TiN.

MRG on various seed layers

XRD of MRG grown directly onto substrate versus different seeds. Substrate is always MgO.

The deposition of high-quality MRG requires elevated substrate temperature in the region (250 - 400 oC), which allows for process compatibility with CMOS.

MRG grown on Si/SiO2, demonstrating CMOS compatibility.

XRD of MRG grown on SiO2//MgO/TiN/, at 330-350 oC. The black dotted line indicates the MgO (002) peak, and the blue dotted line denotes MRG (004) peak with c = 6 Å, approximately cubic.

 

Devices and Patterning

In order to investigate the spin-transfer torque effect, at high current densities, patterned GMR and TMR-type devices are required. This is achieved by a combination of e-beam and UV lithography. The smallest feature in the entire process is a 100 nm diameter nanopillar. These pillars are then used to inject high current densities into the nano- or micron- sized magnetic free layers of stacks (prepared at TCD), and correspondingly excite spin resonance and study spin-transfer-induced phenomena (such as switching and microwave precession). The samples are patterned at HZDR using its nanofabrication facilities (https://www.hzdr.de/db/Cms?pNid=550). The three essential steps of the lithography process are shown in Figure 1. The bottom and top contact layers are patterned with a UV lithography Mask Aligner 6-SÜSS Microtech. The patterning of the pillar itself is done using an Electron beam writer - RAITH 150-two. Dry etching of the stacks is performed within a Reactive Ion Beam Etcher - Roth & Rau IonSys 500 (RIBE). For SiO/SiO2 deposition, a sputter facility - Nordiko 2000 is utilized, and the final metal deposition is executed using an evaporation tool (Leybold Optics, GmbH).

Patterning of nano-pillars

Figure 1. The standard 3-step patterning process: (a) UV lithography for bottom contact, (b) E-beam Lithography for pillar, (c) UV lithography for top contact.

Pillar Formation

Figure 2. Definition of nanopillars (a), (b), (c). Captures (d), (e), (f) demonstrate pillars after ion milling, insulator deposition and lift-off.

 

STT and SOT Oscillators and FMR (up to 60 GHz)

A spin-polarized current flowing through a ferromagnet exerts a torque on the magnetization at the nanoscale, thereby providing means of manipulating it. In a nano-size magnet, spin-transfer torques can induce either magnetization reversal or steady-state precession. These phenomena have been proposed as write method for non-volatile magnetic memory devices and operating mechanism for tuneable radio-frequency nano-oscillators, respectively. Given their good scaling perspectives, spin-torque devices have recently been identified as one of the prime candidates for beyond Moore technologies. A focus of the work in TRANSPIRE is to explore the generation of magnetization dynamics in magnetic tunnel junctions and metallic spin-valve structures using spin polarized currents. To that end, we also characterize our materials using high magnetic fields (up to 90 T are available at the Dresden High Field Lab located in HZDR) as well as standard and electrically-detected ferromagnetic resonance. A first step to achieving this goal was the integration of Ruthenium-doped Mn2Ga films into magnetic tunnel junctions (http://aip.scitation.org/doi/abs/10.1063/1.4948934).

References:

V. Sluka et al., Nat. Comm. 6, 6409 (2015)

C. Fowley, et al., Journal of Physics D : Applied Physics, 48, 164006 (2015)

K. Bernert, et al., Physical Review B, 89, 134415 (2014)

C. Fowley, et al., Applied Physics Express, 7, 043001 (2014)

A. Deac, et al., Nature Physics, 4, 803-809 (2008)

 

THz Spectroscopy

THz spectroscopy is a term that meanwhile describes different techniques that allow probing the properties of matter in the so called THz frequency range. The recent 2017 Terahertz Science and Technology Roadmap defines this range to be lying between 0.1 THz and 30 THz [Dhillon2017]. The common techniques thereby range from classical THz absorption/transmission spectroscopy employing direct detectors and interferometers to ultra-fast techniques that: (i) probe the coherent response of THz driven low energy degrees of freedom by ultra-short light pulses or (ii) allow to measure re-emission of THz pulses from induced spin currents or coherently precession magnetic moments [Kovalev2018]. Different THz spectroscopic techniques are utilized within TRANSPIRE to benchmark the relevant magnetic properties of the grown thin film samples.

 

Faraday / MOKE measurements (of THz driven) coherent spin excitations

Two powerful techniques to probe magnetic resonances are transient Faraday and MOKE measurements with femtosecond lasers. Upon excitation of a magnetic material with e.g. femtosecond laser pulses or a CEP stable THz pulse of the right frequency, low energy degrees of freedom such as magnetic resonances can be coherently excited leading to subsequent phase stable precessional motion of the net magnetization. Such a precessional motion of the net magnetization can be probed sensitively by Faraday or MOKE measurements with synchronized femtosecond near-infrared laser pulses by the induced change of polarization. Different end stations in the TELBE laboratory [Green2016] are available that allow for such measurements in external magnetic fields up to 10 T and temperatures down to 3 K [Kovalev2018]. A worldwide unique feature of these set-ups is the possibility for selective THz excitation of resonances between 0.1 and 1.2 THz by means of tunable narrow-band THz pulses from a superradiant undulator source. Faraday/MOKE spectroscopy is one of the key techniques within TRANSPIRE to determine the magnetic resonance frequencies of the grown thin film samples.

 

THz Emission Spectroscopy

THz emission spectroscopy is another powerful technique to probe the precessional motion of magnetization or spin currents. The technique is based on the fact that ultra-fast charge movements or changes of the magnetization direction leads to the emission of an electromagnetic wave. In the case of spin currents the emitted wave form is a single-cycle broadband pulse, the bandwidth of which is directly related to the timescale of the charge movement. In the case of precessional motion of magnetization the center frequency of the emitted THz wave corresponds to the resonance frequency while the damping can be directly deduced from the decay time of the emitted THz transient. Within TRANSPIRE THz emission spectroscopy is the key technique not only for characterizing the magnetic modes in the magnetic thin films, but also to study and understand the most optimal design of the films for efficient THz emission [Awari2016].

References:

[Dhillon2017] S. S. Dhillon et al, J. Phys. D: Appl. Phys. 50, 043001 (2017)

[Kovalev2018] S Kovalev et al 2018 J. Phys. D: Appl. Phys., accepted

[Green2016] B Green et al, Sci. Rep. 5, 22252 (2016)

[Awari2016] N. Awari et al, Appl. Phys. Lett., 109, 032403 (2016)

 

Microwave Characterisation and Applications (60 - 300 GHz)

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Contact: stamenov.plamen@tcd.ie
Last updated: Feb 08 2018.
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