Broadband ferromagnetic resonance system and methods for ultrathin magnetic films

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Broadband ferromagnetic resonance system and methods for ultrathin magnetic films Eric Montoya, Tommy McKinnon, Atieh Zamani, Erol Girt, Bret Heinrich

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S0304-8853(13)00925-6 http://dx.doi.org/10.1016/j.jmmm.2013.12.032 MAGMA58715

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Journal of Magnetism and Magnetic Materials

Received date: 13 September 2013 Revised date: 9 December 2013 Cite this article as: Eric Montoya, Tommy McKinnon, Atieh Zamani, Erol Girt, Bret Heinrich, Broadband ferromagnetic resonance system and methods for ultrathin magnetic films, Journal of Magnetism and Magnetic Materials, http://dx. doi.org/10.1016/j.jmmm.2013.12.032 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Broadband ferromagnetic resonance system and methods for ultrathin magnetic films Eric Montoya a,∗, Tommy McKinnon a, Atieh Zamanib , Erol Girta , Bret Heinricha a Surface

Science Lab, Department of Physics, Simon Fraser University, 8888 University Dr, Burnaby, BC, V5A 1S6, Canada b Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden

Abstract Spintronics requires the development of magnetic thin film structures having a wide range of magnetic properties. Ferromagnetic resonance (FMR) is a well understood experimental technique that has proven to be an invaluable tool to probe the static and dynamic magnetic properties of ultrathin films, multilayer nanostructures, and superlattices. In order to achieve a full characterization of thin film materials, one needs to carry out FMR measurements at a wide range of microwave frequencies. In this paper, we show that one does not have to use a broadband vector network analyzer; similar performance can be achieved by using a broadband microwave signal generator, a coplanar waveguide, and a broadband microwave detector. To obtain a good signal to noise ratio, one needs to employ a modulation technique in order to use lock-in detection; in this paper, we use low frequency external field modulation (105 Hz) and microwave power amplitude pulse modulation (10 kHz). The sensitivity and the performance of this broadband microwave system is demonstrated on two types of samples: molecular beam epitaxy grown single crystal GaAs(001)/Fe/Au and sputter deposited textured Si(111)/Ta/Ru/Co/Ru superlattice structures. The samples were mounted on a coplanar waveguide, allowing one a broadband measurement, ∼ 0.1-50GHz, of DC field swept FMR signals. The results are compared to traditional field swept, field modulated measurements in microwave cavity resonators. Despite the fact that the FMR signal can be very different from that obtained by standard microwave cavities, we show that the analysis of the FMR signal is fairly simple using an admixture of the in-phase and out-of-phase components of rf susceptibility and that the resulting fitted magnetic parameters are in excellent agreement. Additionally, we demonstrate that microwave power amplitude pulse modulation can be used to greatly speed up data collection times, especially for very weak and broad FMR signals. Keywords: Ferromagnetic resonance, Coplanar waveguide, Ultrathin magnetic films, Magnetic nanostructures, Magnetic anisotropy, Magnetic damping

∗

Corresponding author. Tel.: +1 778 782 8400 Email address: [email protected] (Eric Montoya) URL: http://surface-science.phys.sfu.ca (Eric Montoya)

Preprint submitted to Journal of Magnetism and Magnetic Materials

December 20, 2013

1. Introduction Spintronics requires the development of magnetic thin film structures having a wide range of magnetic properties. The bulk, interface, and exchange biased magnetic anisotropies [ 1]; the exchange stiffness [2, 3]; and interlayer exchange coupling are important for high density perpendicular magnetic recording [4, 5], magnetic tunnelling junction (MTJ) sensors [6, 7], and spin transfer torque (STT) devices [8–12]. Particularly ultrathin film structures allow one to create a controllable perpendicular anisotropy having the magnetic moment oriented perpendicular to the film surface with a variable magnetic energy. Of equal importantance are dynamic properties: the Land´e factor g and magnetic damping. STT devices utilize spin (polarized) currents to switch the magnetization of a ferromagnetic layer in a spin valve structure. The critical current at which the free layer in a STT device will switch direction is dependent upon the Gilbert damping parameter 1. Also of importance for future spintronics devices, is determining the spin diffusion length in a variety of materials. This can be done by examining additional damping in ferromagnet/normal metal and ferromagnet/normal metal/ferromagnet structures [ 13–15]. Ferromagnetic resonance (FMR) is a well understood experimental technique [ 16] that has proven to be an invaluable tool to probe the static and dynamic magnetic properties of ultrathin films and multilayer nanostructures. In order to determine the magnetic parameters, one needs to carry out FMR measurements at a wide range of frequencies. For this reason, it is of great advantage to have a broadband system where measurements can be made at many frequencies without the need to remount samples in different waveguides or cavities. Recently, techniques to measure broadband FMR signals based on transmission lines, such as coplanar waveguides, microstrips, slotted lines, etc., have been developed. The most advanced method uses vector network analyzers (VNA) [17–21]. FMR by means of VNA (VNA-FMR) has proven to be a very sensitive technique for characterizing ultrathin magnetic films and nanostructures. It has the advantages of having the signal source and detection in one box as well as the ability to extract both phases of the rf susceptibility in one measurement. Some drawbacks of VNA-FMR include the need to carefully calibrate the system, the cost of the VNA in itself, and the analysis of data can be somewhat complicated involving the calculation of the susceptibility from scattering parameters. Another method separates the components for microwave generation and detection. The most common approach is to use a broadband microwave source and a broadband microwave detector diode [ 22–24]. It has been shown that one can replace the detector diode when measuring conducting ferromagnetic samples by using the sample directly as the detector itself. In this method, the anisotropic magnetoresistance (AMR) induced microwave DC photovoltage [25, 26] allows the electrical detection of FMR (ED-FMR) in thin films. However, ED-FMR requires the sample to be patterned specifically for the measurement of DC voltage across the sample, usually in the form of a stripe, which requires additional electrical leads. The sample itself needs to be incorporated into the rf transmission line as a device. In this paper, we aim to give a detailed description of how conventional microwave sources, e.g. gun diodes, klystrons, signal generators, together with a coplanar waveguide and broadband microwave detector can be used to measure FMR signals in a broadband system and how the analysis of data can be carried out in a quite simple and straightforward manner. This paper is organized as follows: First we provide a brief introduction into the underlying theoretical background. Next, we provide a detailed description of our system. We then 1 See

Equations (2) and (3) in Katine and Fullerton[12]

2

carefully analyze the FMR signals obtained on a high quality crystalline 16 atomic layer (AL) thick Fe(001) ultrathin film deposited on a GaAs(001) template by means of molecular beam epitaxy (MBE). This test sample was also measured in a standard multimode resonance cavity to compare the role of different microwave systems on the measured magnetic properties. This is indeed an important aspect of these studies due to the fact that the coupling of ferromagnetic films is dramatically different for a coplanar microwave waveguide and a microwave cavity. We then show the sensitivity of the system for measuring structures similar to those found in industrial applications by measuring sputter deposited Co/Ru superlattices, with atomically thick Co layers. We discuss the obtained data in terms of magnetic anisotropies, the Land´e factor g, FMR linewidth, and measurement time required to obtain similar signal to noise ratios (SNR) and comment on the advantages and disadvantages of each technique. 2. Theoretical Background In the FMR experiment, the magnetization dynamics are described by the phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion, ⇀

⎛ ⎞ ⃗ ∂M ⃗ × ∂M ⎟ , ⃗ ×H ⃗eff ) + α ⎜ M = −γ ( M ∂t Ms ⎝ ∂t ⎠

(1)

⃗ is the instantaneous magnetization vector, H ⃗eff is the total effective magnetic field, α is where M the Gilbert damping parameter, M s is the saturation magnetization, and γ is the absolute value of the gyromagnetic ratio, gμB (2) γ= ̵ , h where μ B is the Bohr magneton, h̵ is the reduced Planck constant, and g is the Land´e factor . ⇀

The first term on the RHS of (1) describes the precession of the magnetization about H eff and the second term describes a viscous-like damping. The total effective field acting on the magnetic moments within a film is given by, Hieff = −

∂ F ∂Mi

(3)

⃗eff is the sum of external and internal fields. where i = x, y, z and F is the Gibbs free energy. H ⃗ and The external fields involved in the FMR experiment are the applied DC magnetic field H ⃗ the rf microwave magnetic field hrf . The internal fields are a consequence of the anisotropy of F satisfying the film’s crystalline structure (symmetry) and its shape. The individual parts of F are called magnetic anisotropies. These anisotropies arise from either the spin-orbit interaction, which leads to magneto-crystalline and magneto-elastic contributions, or from the magnetic dipole-dipole interaction which is usually treated by magneto-static approximation. A detailed overview of common crystalline symmetries and related anisotropies is given by Lindner and Farle [27] and Heinrich [28]; the magneto-elastic anisotropies by Sander [29]; and the dipolar interaction by Hurben and Patton [30]. In the FMR experiment, the microwave response signal  χ is dependent on the rf magnetic ′ ′′ susceptibility χ = χ + iχ in the direction of an applied rf field. For ultrathin films measured in 3

 Χmix

Χ



 Χmix

Χ Figure 1: The rotation of the complex plane coordinate system.

the linear response regime of (1), it can be shown that the rf signal for the in-phase component (dispersion) is given as, H − HFMR ), (4) χ′ = A (1 + 2 2 ΔH + (H − HFMR ) and for the out-of-phase component (absorption) as, χ′′ = A

ΔH ΔH 2

2

+ (H − HFMR )

,

(5)

where H is the external applied DC field, H FMR is the resonance field, ΔH is the half-width-athalf-maximum (HWHM) linewidth of the Lorentzian absorption χ ′′ , ω = 2π f is the microwave angular frequency, and BFMR A = aΔS Ms d , (6) BFMR + HFMR where BFMR and HFMR are the B and H fields at resonance, ΔS is the film surface area, d is the film thickness, and a is a proportionality factor . For more details, see Celinski et al. [ 31]. In general, one does not necessarily measure the orthogonal  χ′ and χ′′ separately, but one can measure a mixture of these components, which can be viewed as their projection onto a rotated coordinate system of the rf susceptibility complex plane given by, (

χmix cos ϕ sin ϕ ′ ′ )=( )( χ ), χ′′ − sin ϕ cos ϕ χmix ′′ 4

(7)

where ϕ is the angle of rotation in the complex plane, see Figure 1. In this paper, we have fit the FMR spectra as a mixed absorption signal, χmix ′′ = − sin ϕχ′ + cos ϕχ′′ ,

(8)

because it is more common to see the absorption data. Measuring only one signal is equivalent to having an admixture of the in-phase and out-of-phase components of the rf susceptibility signal. In systems that can simultaneously measure both projections, such as field swept VNA-FMR, one is able to measure both components of the rf susceptibility, but care must be taken to fit the correct functions to the in-phase and out-of-phase components to maintain the correct handedness under rotation.

b

3.0

0.7

2.5

0.6

Error 

Amplitude AU

a

2.0 1.5 1.0

0.5 0.4 0.3 0.2

0.5

0.1 0.0

0.0 0

2000 4000 6000 8000 10 000 12 000

0

2000 4000 6000 8000 10 000 12 000

H Oe

H Oe

′′

Figure 2: (a) The simulated data χ given by the imaginary part of (9) are shown by ● points and the black line is the fit using (5). The input parameters were similar to an Fe ultrathin film, except with an order of magnitude increase in the damping (deviations of (5) from (9) should increase with α [31]); They were Ms = 1740G, α = 0.037, and ω/γ = 12, 306.8Oe. The exact corresponding resonance field HFMR = 5528.79Oe with exact linewidth ΔH = 455.351Oe. The resulting fit parameters were HFMR = 5528.8Oe and ΔH = 455.412Oe. (b) Percent error of the fit with respect to the simulated data. The percent error is calculated by taking one hundred times the difference between the fit (black line) ′′ and the χ rf susceptibility simulated data (●) and dividing by the simulated data. In this manner positive percent error represents over estimate and negative percent error represents under estimate of the actual rf susceptibility.

Eqs. (4) and (5) are a simple expansion around the resonant field. Their validity for a wide range of fields can be tested by fitting a full equation for the in-plane rf susceptibility for a simple parallel FMR (including only perpendicular demagnetizing field) given by, χ=

Ms (H + 4πMs − ıα ωγ ) 2

(H + 4πMs − ıα ωγ ) (H − ıα ωγ ) − ( ωγ )

.

(9)

Figure 2 shows the quality of fit using (5) for simulated data generated by taking the imaginary part of (9). The error in fitting does not reach one percent even far away from the FMR peak, justifying using the simple ansatz (4) and (5) for fitting experimental data. 5

In our analysis of data we are concerned mainly with line position and shape and not total amplitude, thus we treat A as an arbitrary amplitude parameter. The line position, or resonance field HFMR , is used to determine the anisotropy fields H eff and γ. The lineshape ΔH is used to determine the Gilbert damping parameter α as it is a linear function of microwave frequency, ΔH(ω) = α

ω + ΔH(0), γ

(10)

where ΔH(0) is the zero frequency offset due to inhomogeneity induced line broadening [ 16]. 3. Experimental Setup

Microwave Generator

aux. out TTL out

pulse ref. Directional Coupler

rf output

in

GPIB

Detector 2 Attenuator

signal in B

-13dB out

signal in A

Lock-In Amplifier signal field mod. ref. out GPIB out

DC in

Magnet Power Supply

Electromagnet

DC Block Detector 1

Power Amp Sample

Coplanar Waveguide

Modulation Coils

DC out Hall Probe

Gauss Meter

Digital Voltmeter

Computer

Figure 3: Schematic of the FMR spectrometer for coplanar waveguide (CPW) with field modulation (HM) or microwave power amplitude pulse modulation (PM). The coplanar waveguide is mounted in the center of a Varian electromagnet that provides the DC field and two Helmholtz coils (Modulation Coils) that can provide HM. The rf microwave source is an Anritsu MG3696B microwave generator. The rf FMR signal is converted to a low frequency output signal, with the frequency determined by HM or PM, by means of an Agilent 8474E planar-doped barrier diode detector (0.01 to 50 GHz) (Detector 1). The SR830 Lock-in Amplifier is used to provide both the modulation reference signal and to control the Varian electromagnet to step the DC H field. CPW-HM: The 105Hz modulation signal is provided by the reference out (field mod. ref. out.) of the lock-in amplifier and is amplified by a Kepco power amp that supplies current to the modulation coils. Since the microwave track forms a conducting partial loop within the modulation coils, an Aeroflex 8179 DC Block is used to filter out signals that may arise due to electromagnetic induction from the 105Hz modulation field. CPW-PM: The 10kHz pulse modulation is supplied by the lock-in amplifier TTL out port to the microwave generator pulse reference port. The result is a on/off chopping of the microwave signal. To enhance sensitivity, a directional coupler is used to take a -13dB portion of microwave signal that bypasses the coplanar waveguide. This microwave signal is turned into a low frequency signal by a Krytar 704s planar-doped barrier diode detector (0.01 to 50 GHz) (Detector 2). The signals from Detector 1 and Detector 2 are detected by the lock-in amplifier in A-B mode.

We are going to demonstrate that one is able to create a broadband FMR system which has the sensitivity capable of detecting FMR signals in ultrathin films, even those possessing wide FMR lines. This system is not using VNA microwave signal detection, but is based on broadband, low noise components: an Anritsu MG3696B microwave generator (0.1 to 67 GHz) and an Agilent 8474E planar-doped barrier diode microwave detector (0.01 to 50 GHz). FMR measurements were carried out using two microwave spectrometers: 6

3.1 A typical microwave spectrometer based on rectangular microwave waveguides with samples inserted inside a microwave cavity. 3.2 Coaxial microwave track with samples mounted on a coplanar waveguide. Despite the different coupling between the film and microwave cavity compared to that of a coplanar waveguide, the FMR results can be analyzed in a simple manner using ( 8) and an instrumental background. The resulting magnetic properties are in a very good agreement as shown in section 4. In a typical FMR setup, measurements are made at a fixed frequency while the H is stepped through resonance. The FMR signals from ultrathin films are usually weak, for this reason it is common practice to use lock-in detection to enhance the SNR. It is most common to use field modulation (HM) to this end. In our set-up, HM was achieved by using a Kepco bipolar operational power supply/amplifier (model: BOP72-5M) to drive a set of Helmholtz modulation coils. We used a modulation frequency of 105Hz, as this system is limited by the inductive reactance of the coils. Lock-in detection is performed with a Stanford Research Systems SR830 DSP Lock-In Amplifier. 3.1. Multimode cavity In the multimode cavity with field modulation configuration (Cavity-HM), the experimental setup is the same as described by Celinski et al. [31], except with the Anritsu MG3696B microwave generator replacing the Klystron, Klystron Power Supply, and Feedback Voltage Supply. High sensitivity in this case can be achieved using a microwave cavity. The cavity used is a 25.7mm resonant section of WR-28 waveguide and is coupled to the waveguide track through a small aperture. The sample is mounted in the center of a terminating plate on the other side of the rectangular cavity. Within the WR-28 waveguide band the cavity has four resonances at f ⋍ 27.23, 31.22, 35.68, and 40.45GHz. 3.2. Coplanar waveguide The experimental setup for the coplanar waveguide configuration (CPW) is shown in Figure 3. In our case, the system is designed to be compatible with a He flow cryostat to allow FMR measurements between room and liquid He temperatures. The rf signal is brought down to the center of the electromagnet by using semi rigid coax cable. Heat losses at cryogenic temperatures are decreased by using two segments (input and output) of stainless steel cables inserted between the room temperature (inside the dewar) and cryogenic areas (below the dewar). However inside the dewar, Cu low loss non-magnetic semi rigid coax cables (UT-85C-LL) are connected to the stainless steel cables and fed into a copper box containing a coplanar waveguide located in the middle of the electromagnet. On two opposite sides of the box, the outer coax conductors are soldered to the box feedthroughs while the center conductors are soldered directly to the opposite sides of the center line of the coplanar waveguide. The system can be used in this manner; however, to increase the microwave transmission, two wires are soldered between the outer coax conductor and the outer conductors of the coplanar waveguide. This is done on both sides and is the main reason we switch from stainless steel to Cu cables. The rf transmission output is converted to a DC voltage by means of a planar-doped barrier diode detector. The increase in transmission is illustrated in Figure 4. The level of output power and frequency dependent microwave track can be improved by avoiding stainless steel coaxial cables in applications not requiring low temperature measurements. The sample filling factor for CPW is much better than that in the microwave cavity, therefore no cavity was need for CPW to achieve similar sensitivity as that obtained for the multimode 7

cavity system. FMR measurements were carried out using (i) HM and (ii) microwave power amplitude pulse modulation (PM). (i) The coplanar waveguide with field modulation mode (CPW-HM) is essentially the same as the Cavity-HM mode with the WR-28 waveguides and cavity being replace with broadband coax cables and the segment of coplanar waveguide, respectively. (ii) In the coplanar waveguide with microwave power amplitude pulse modulation configuration (CPW-PM), the low frequency square wave signal generator TTL output port of the lock-in is connected to the Pulse Trig In port on the Anritsu microwave generator. The microwave output is generally pulsed at 10kHz. This has the advantages over HM as it moves away from 1/ f noise, allowing a shorter time constant for the lock-in amplifier than that for HM. It is worth noting that ED-FMR uses a similar power modulation technique for these advantages. In ultrathin films, the FMR signal is usually very small compared to the direct transmission signal. In order to enhance the sensitivity in PM mode, a Marki C13-0150 microwave directional coupler is used to take a −13dB portion of the direct signal, before the coplanar waveguide, that is detected by a second planar-doped barrier detector diode (Krytar 704S). An attenuator is then used to nearly match the amplitude of the coplanar waveguide signal and direct signal off resonance. The additional signal is fed into the B input of the SR830 lock-in amplifier and the data collection is performed in A-B mode. A-B mode allows one to use the lock-in at higher sensitivity in order to avoid being digital noise limited. Another advantage of measuring the transmission of modulated microwave power, as opposed to the derivative of the transmission, is that one measures the total transmission signal and considering that the FMR signal is only very small fraction even of the A-B signal allows one to add both phases of the lock-in amplifier in quadrature. Simply in this case one does not have to optimize the phase of reference signal. This fact alone can greatly speed up the set up of the measurement, especially for very thin samples with wide FMR lines. 4. Results 4.1. Single Crystal Systems To compare these different FMR techniques in single crystal samples with small damping and in-plane magnetic anisotropy, a GaAs(001)/16(2.3nm)Fe/20(4nm)Au sample was prepared by means of MBE, where the integers refer to the layer thickness in atomic layers (AL). The commercially available, epi-ready GaAs(001) substrate was cleaned for 30 minutes in an atomic H-beam at 400C followed by 3hr of 650V Ar + sputter etching at room temperature. The sample was then annealed to 590C resulting in a 4x6 surface reconstruction; annealing was monitored by means of reflection high energy electron diffraction (RHEED). The Fe and Au film thicknesses were monitored by means of oscillations in the intensity of the specular spot at an anti-Bragg RHEED reflection in conjunction with a quartz crystal thickness monitor. The 4x6 reconstructed ¯ direction surface of the GaAs leads to a uniaxial anisotropy with the hard axis along the [110] (due to dangling bonds of As terminated surface), see further details in [14]. The free energy F (magnetic anisotropies) needs to follow the symmetry of the ultrathin Fe grown on the GaAs(001) reconstructed surface. The magnetic anisotropies are as follows: (i) The four fold anisotropy energy due to the cubic symmetry of Fe, K 1 (α2x α2y + α2x α2z + α2y α2z ), ⃗ with respect the Fe cube axes. A positive K 1 results where α x,y,z are the directional cosines of M with the easy axes parallel to the cube axes {100}.

8

(ii) The reconstructed GaAs(001) surface results in an in-plane uniaxial anisotropy energy √ ∥ 2 ∥ ⃗ ⋅⃗ (M n ) /M 2s , where ⃗ n = 1/ 2 (1, −1, 0) is parallel to the As dimers at the Fe/GaAs

∥ −KU

U

U

∥

interface. By this definition, a negative K U corresponds to a hard uniaxial axis. (iii) Magneto-elastic energy due to the lattice mismatch between the Fe(001) and GaAs(001) and the lack of cubic symmetry at the interfaces results in the perpendicular uniaxial anisotropy energy −KU⊥ α2z [28]. (iv) For ultrathin films, the shape leads to the demagnetization energy 2πM 2s α2z . For more details, see Kardasz et. al.[32, 33] and the references within. In the in-plane configuration, the transverse magnetic susceptibility is given by [ 28], χ=

Ms (Beff − ıα ωγ ) 2

(Beff − ıα ωγ ) (Heff − ıα ωγ ) − ( ωγ )

(11)

Resonance occurs when the denominator in ( 11) is at a minimum. Neglecting the small contributions from α, the resonance condition is, 2

ω ( ) = Beff Heff ∣HFMR , γ

(12)

where ,

Beff = H cos (φ M − φH ) +

K1 cos (3 + 4φ M ) 2Ms +

Heff = H cos (φ M − φH ) +

KU∥ cos (1 + 2 (φ M − φU )) + 4πMeff , Ms

(13)

2KU∥ cos (2 (φ M − φU )) , Ms

(14)

2K1 cos (4φ M ) Ms +

and 4πMeff = 4πMs −

2KU⊥ , Ms

(15)

where d is the film thickness, φ M is the angle of the DC magnetic moment, φ H is the angle of the applied external field H, φ U is the angle of the in-plane uniaxial hard magnetic axis, with the angles being measured from the [100] crystallographic direction. Note that in FMR experiments in thin films, one measures the effective anisotropy fields HK and not the anisotropy parameters K directly. Thus in this sample one measures H K1 = ∥ 2K1 /Ms and HK ∥ = 2KU /Ms . Note that (iii) and (iv) are both perpendicular uniaxial anisotropies U

(depend on α 2z ), therefore they enter into the rf susceptibility on an equal footing; thus, in the FMR experiment one measures an effective demagnetization field 4πM eff . Other magnetometry techniques such as superconducting quantum interference devices (SQUID) and vibrating sample 9

magnetometers (VSM) can be used to determine M s . Then from the FMR measured effective fields, one can determine the energy of crystalline anisotropies. In order to determine the in-plane anisotropy of the sample, the resonance field H FMR was measured as a function of angle φ H at 35.6802GHz. This frequency was chosen as it was the resonance closest to the center of the waveguide band for the multimode cavity and would test the sensitivity of the coplanar waveguide at higher frequency. Example FMR data for each technique together with fits using (8) and an instrumental background (2nd order polynomial) are shown in Figure 5 (a-c), the angular dependences of H FMR are shown in Figure 5 (d), and the resulting fitted anisotropy fields are listed in Table 1. Clearly all three techniques agree very well and are described well by (13) and (14). Notice that FMR measurements ′′using CPW can result in signals which are far away from measuring the microwave absorption χ (common to measurements in ′ microwave cavity), in fact Figure 5 (b-c) the measured FMR signal is very close to χ and yet fitting parameters used for FMR signals obtained in the microwave cavity ( Figure 5 (a) and using CPW Figure 5 (b-c) are identical testifying to the fact that using (8) is very reliable procedure. Table 1: GaAs/16Fe/20Au Magnetic Properties

Measurement configuration Cavity-HM CPW-HM CPW-PM

4πMeff [kOe] 16.07 16.08 16.07

HK ∥ 1 [Oe] 313 313 315

HK ∥ U [Oe] -399 -393 -384

φU [○] -44.6 -45.1 -45.3

α [10 −3 ] 3.52 3.52 3.56

ΔH(0) [Oe] 8.6 9.2 9.8

¯ Additionally, the frequency dependence of the FMR signal was measured along the [110] direction. The results of both using Cavity-HM and CPW-HM where in excellent agreement. CPW-PM proved to be slightly less well suited to measure individual FMR linewidths. This was caused by small drifts in the measured transmission amplitude as a result of the detector diode response to room temperature fluctuations. The HM techniques do not have this issue as the lineshape changes negligibly with these small drifts and thus the derivative is unchanged. This obstacle was offset by measuring CPW-PM FMR by sweeping the DC field back and forth and averaging power fluctuations. Furthermore, the broadband nature of the CPW allowed measurements at a number of microwave frequencies and the fitted Gilbert damping parameter α agrees with the field modulation techniques within 1%, see Table 1 and Figure 6 . 4.2. Polycrystalline samples Whether the films are used in granular bit patterned media, STT devices, spin torque oscillators, etc., one requires large perpendicular anisotropy to keep the magnetic moment perpendicular to the film surface. As device sizes approach very small lateral and perpendicular dimensions of tens of nanometers, a proper perpendicular anisotropy is required to compete with thermal fluctuations and maintain the stability of a device element. FMR is well suited to quickly and accurately measure the effective perpendicular anisotropy in thin films. With a broadband system it becomes possible to investigate the origin of the perpendicular anisotropy in such films. Crystalline uniaxial perpendicular anisotropy in these structures is directly associated with an angular dependent g-factor [34]. The angular dependent g can be measured by carrying out FMR measurement in a broadband frequency spectrometer in parallel and perpendicular configurations. 10

In order to show the usefulness of this technique for samples similar to those which might be found in industrial applications, Si/3nm Ta/8nm Ru/10×[d Co/8nm Ru] samples were prepared by means of sputter deposition, where d =0.6, 0.8, 1.0, 1.2, 1.4, 1.6 is the thickness in nm for the Co layer and the 10×[ ] indicates the structure in the square brackets was repeated 10 times as a superlattice. The layer thicknesses were controlled using deposition rate calibrations and verified by means of high resolution X-Ray diffraction (XRD). Note that 8nm Ru spacer layers magnetically decouple each Co layer, therefore FMR is carried out on an assembly of 10 independent ultrathin Co layers. In this thickness range, even the thinnest Co layers, d = 0.6nm (3 AL), were already ferromagnetic. However, their room temperature saturation magnetic moment M s ≃ 550G was appreciably smaller than that of bulk Co with M s = 1400G and their Currie temperature of T C ≃ 650K was lowered from the bulk value of T C = 1388K [35]. This sample represents an ultimate test for the sensitivity of our broadband FMR system for measuring samples that would be useful in material studies, spintronics, and high density memory applications. Example FMR signals for sputtered samples are shown in Figure 7 comparing the thinnest Co layers, d = 0.6nm (3AL), to the thickest, d = 1.6nm (8AL). In all of these samples the FMR lines are very broad, especially compared to the single crystal Fe samples discussed above. The FMR linewidths as a function of frequency displayed a significant contribution due to inhomogeneity with the average ΔH(0) ≃ 250Oe, see (10), and the damping parameter α on average was an order of magnitude larger than that in the Fe sample. Additionally, the benefit of CPW-PM over CPWHM for these broad lines is evident from the collection times required to obtain similar SNR. It is worth noting that the maximum modulation amplitude in our FMR spectrometer ≃ 25Oe, which is not the optimum magnitude for such wide lines. However, at large DC H fields this much modulation can already lead to vibrations in the system. Notice that even for these FMR lines with large inhomogeneity broadening, the simple ansatz (4) and (5) can be used to fit the data very well. This is indicative that the distribution of inhomogeneous internal fields is Lorentzian. Furthermore, all the FMR measurements could be fit with single FMR lines, indicating that the individual Co films within each multilayer sample have the same basic magnetic properties. In textured (0001) hcp films, the films are isotropic in-plane and therefore no in-plane anisotropy is present. However, hcp Co has a bulk uniaxial anisotropy with the easy axis parallel to the c axis (in our case perpendicular to the film surface), whose energy has the same form as (iii) and additionally: (v) a fourth order perpendicular anisotropy energy −K 4⊥ α4z which can only be detected away from the parallel configuration [36]. The corresponding effective field 4K 4⊥ /Ms looks like an additional perpendicular uniaxial field in the perpendicular configuration [ 37]. In bulk Co, −K 4⊥ < 0. In hcp systems, lattice strains result in additional uniaxial anisotropy [ 29] of the same form as (iii). These samples were measured in both the in-plane configuration (∥) with resonance condition given by, 2 ω (16) ( ) = H (H + 4πMeff,∥ ) , γ∥ and the perpendicular-to-plane configuration (⊥) with resonance condition given by, ω = H − 4πMeff,⊥ . γ⊥ 11

(17)

The differing γ’s are a consequence of the asymmetry in the orbital momentum contribution to the g-factor leading to g ∥ and g⊥ . This leads to 4πMeff,∥ = 4πMs −

2KU⊥ Ms

(18)

and

2KU⊥ 4K4⊥ − , (19) Ms Ms where 2KU⊥ /Ms is the sum of all perpendicular second order uniaxial crystalline anisotropy fields of form (iii). The magnetic properties were determined by measuring H FMR as a function of microwave frequency. Example results are shown in Figure 8 (a) and (b). The results for the magnetic parameters as a function of the film thickness are shown in Figure 8 (c) and (d). These results have not been published. We will just summarize the main results. Figure 8 shows that one can adjust 4πM eff by choosing an appropriate Co film thickness. In fact for the films d ≤ 1.0nm, the Co magnetization is oriented perpendicular to the film surface. While g∥ is relatively constant as a function of Co thickness, g ⊥ shows a large thickness dependence. In fact at d ≃1 nm it crosses the value of g ∥ indicating that in this thickness range the crystalline perpendicular uniaxial anisotropy changes its sign. It is interesting to note that where g⊥ crosses g∥ as a function of Co layer thickness is also where the films transition between in-plane and perpendicular-to-plane magnetization. Notice that in Figure 8 (c) 4πMeff,⊥ in perpendicular configuration is lower than that in parallel configuration. This is opposite to that expected for the bulk Co, see (18) and (19). This means the sign of K 4⊥ changes in the Co films thinner than 8AL. A similar behavior was found for ultrathin (d<1 nm) crystalline Fe(001) films grown on Ag(001) substrates [37]. The orientation of the magnetic moment in ultrathin Co films is given by the thickness dependence of all anisotropies discussed above. More detailed analysis require determining the saturation magnetization of all Co films and a full angular dependence (from in-plane to perpendicular-to-plane) of FMR and will be presented elsewhere. 4πMeff,⊥ = 4πMs −

5. Conclusions We have shown that one can create a broadband FMR system using a broadband microwave signal generator, coplanar waveguides, and a broadband microwave detector that is suitable for characterizing ultrathin ferromagnetic films in a wide range of applications ranging from crystalline films to sputtered films applicable to spintronics and high density memory media. The system is suitable for any sample on wafer (flip chip), extended films or patterned films, and does not require any sample modification beyond positioning above the center line of the coplanar waveguide. Furthermore, we have shown that while the signals obtained from coplanar waveguides and traditional microwave cavities can be quite different in their symmetry as a function of the applied field, the analysis of the signal is fairly simple using an admixture of the in-phase and out-of-phase components of rf susceptibility and the relevant fitted parameters are in excellent agreement. Microwave power amplitude pulse modulation can be used to greatly speed up data collection times, especially for a wide and weak FMR signals. It is also very beneficial, as compared to field modulation, for low temperature measurements because it allows one to use Cu parts (for proving a good heat conductivity inside the dewar and heat shields used for decreasing heat losses). Cu parts can substantially decrease the modulation field at the sample due to increasing eddy currents as one approaches cryogenic temperatures. 12

Acknowledgements Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. We would like to thank Dr. Georg Woltersdorf for providing the coplanar waveguides [1] J. Nogu´es, I. K. Schuller, Exchange bias, Journal of Magnetism and Magnetic Materials 192 (1999) 203–232. [2] E. Girt, W. Huttema, O. N. Mryasov, E. Montoya, B. Kardasz, C. Eyrich, B. Heinrich, a. Y. Dobin, O. Karis, A method for measuring exchange stiffness in ferromagnetic films, Journal of Applied Physics 109 (2011) 07B765. [3] C. Eyrich, W. Huttema, M. Arora, E. Montoya, F. Rashidi, C. Burrowes, B. Kardasz, E. Girt, B. Heinrich, O. N. Mryasov, M. From, O. Karis, Exchange stiffness in thin film Co alloys, Journal of Applied Physics 111 (2012) 07C919. [4] E. Girt, S. Wu, B. Lu, G. Ju, T. Nolan, S. Harkness, B. Valcu, A. Dobin, J. D. Risner, M. Munteanu, R. Thangaraj, C.-H. Chang, T. Tran, X. Wu, O. Mryasov, D. Weller, S. 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Heinrich, Spin transport in Au films: An investigation by spin pumping, Journal of Applied Physics 111 (2012) 07C512. [16] B. Heinrich, Radio Frequency Techniques, in: B. Heinrich, J. Bland (Eds.), Ultrathin Magnetic Structures II: Measurement Techniques and Novel Magnetic Properties, Springer, 2005, pp. 195–296. [17] S. S. Kalarickal, P. Krivosik, M. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, J. P. Nibarger, Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods, Journal of Applied Physics 99 (2006) 093909. [18] O. Mosendz, B. Kardasz, B. Heinrich, Dynamics studies in magnetic bilayer FeAuFe(001) structures using network analyzer measurements, Journal of Applied Physics 99 (2006) 08F303. [19] O. Mosendz, B. Kardasz, D. Schmool, B. Heinrich, Spin dynamics at low microwave frequencies in crystalline Fe ultrathin film double layers using co-planar transmission lines, Journal of Magnetism and Magnetic Materials 300 (2006) 174–178. 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[25] N. Mecking, Y. Gui, C. Hu, Microwave photovoltage and photoresistance effects in ferromagnetic microstrips, Physical Review B 76 (2007) 224430. [26] A. Wirthmann, X. Hui, N. Mecking, Y. S. Gui, T. Chakraborty, C.-M. Hu, M. Reinwald, C. Sch¨uller, W. Wegscheider, Broadband electrical detection of spin excitations in Ga0.98 Mn0.02 As using a photovoltage technique, Applied Physics Letters 92 (2008) 232106. [27] J. Linder, M. Farle, Magnetic anisotropy of heterostructures, in: H. Zabel, S. D. Bader (Eds.), Magnetic Heterostructures, volume 227 of Springer Tracts in Modern Physics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2008. [28] B. Heinrich, Basics of Nano-Thin Film Magnetism, in: E. Tsymbal, I. Zutic (Eds.), Handbook Of Spin Transport And Magnetism, Chapman and Hall/CRC, 1 edition, 2011, pp. 21–46. [29] D. Sander, The magnetic anisotropy and spin reorientation of nanostructures and nanoscale films, Journal of Physics: Condensed Matter 16 (2004) R603–R636. [30] M. Hurben, C. Patton, Theory of magnetostatic waves for in-plane magnetized isotropic films, Journal of Magnetism and Magnetic Materials 139 (1995) 263–291. [31] Z. Celinski, K. Urquhart, B. Heinrich, Using ferromagnetic resonance to measure the magnetic moments of ultrathin films, Journal of Magnetism and Magnetic Materials 166 (1997) 6–26. [32] B. Kardasz, E. A. Montoya, C. Eyrich, E. Girt, B. Heinrich, Spin dynamics and magnetic anisotropies at the Fe/GaAs(001) interface, Journal of Applied Physics 109 (2011) 07D337. [33] B. Kardasz, S. P. Watkins, E. A. Montoya, C. Burrowes, E. Girt, B. Heinrich, Interface magnetism of iron grown on sulfur and hydrogen passivated GaAs(001), Journal of Applied Physics 111 (2012) 07C115. [34] J. M. Shaw, H. T. Nembach, T. J. Silva, Measurement of orbital asymmetry and strain in Co90 Fe10 /Ni multilayers and alloys: Origins of perpendicular anisotropy, Physical Review B 87 (2013) 054416. [35] C. Kittel, Introduction to Solid State Physics, Wiley, Hoboken, 8th edition, p. 238. [36] S. Chikazumi, Physics of Ferromagnetism, Wiley series on the science and technology of materials, Oxford University Press, New York, 2nd edition, pp. 249–250. [37] B. Heinrich, J. Cochran, Ultrathin metallic magnetic films: magnetic anisotropies and exchange interactions, Advances in Physics 42 (1993) 523–639.

14

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Frequency GHz Figure 4: Microwave transmission for the broadband system configured only with the central conductor of coplanar waveguide connected to the input and output coaxial cables lines (red) and fully connected coplanar waveguide (blue). The signal was measured using pulse modulation of the microwave power without a sample mounted.

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¯ direction Figure 5: FMR measurements of GaAs/16Fe/20Au at f = 35.6802GHz along the hard uniaxial axis [110] are shown for (a) the multimode cavity with field modulation (Cavity-HM) configuration with relevant fit parameters HFMR = 7179 Oe, ΔH = 51.6 Oe, ϕ = 3.27○ , with collection time t = 240 s; (b) the coplanar waveguide with field modulation configuration (CPW-HM) with HFMR = 7170 Oe, ΔH = 52.1 Oe, ϕ = 83.7○ , t = 704 s; and (c) the coplanar waveguide with microwave power amplitude pulse modulation (CPW-PM) configuration with HFMR = 7166 Oe, ΔH = 52.9 Oe, ϕ = 88.854○ , t = 335 s. The colored dots are the collected data and the corresponding solid lines are the theoretical fit as given by (8) and a second order polynomial background (dotted black lines). From an experimental stand point, it is interesting not only to examine what parameters can be extracted from a technique, but also how quickly measurements can be performed, see the parameter t. (d) Angular dependence of HFMR for ∎ Cavity-HM, ▼ CPW-HM, and ▲ CPW-PM. Angles are measured from the [100] direction. The corresponding solid lines are the theoretical fit using (12). Fitting anisotropy parameters are shown in Table 1.. As can be seen, all three methods are in excellent agreement.

16

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Frequency GHz ¯ direction are shown Figure 6: FMR linewidth measurements of GaAs/16Fe/20Au along the hard uniaxial axis [110] for ∎ Cavity-HM, ▼ CPW-HM, and ▲ CPW-PM. The corresponding lines are the theoretical fit using (10). For both field modulation techniques all points lie on a straight line line and the fitted α are nearly identical. The CPW-PM measurements have a wider spread due to drift induced error in each measurement, however measurements at a number of microwave frequencies averages out the power fluctuations and the fitted Gilbert damping parameter α agrees with the field modulation techniques within 1%.

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Figure 7: Coplanar waveguide configuration (CPW) measurements for sputtered samples at f = 15GHz in the perpendicular to plane orientation: Si/3nm Ta/8 nm Ru/10×[0.6nm Co/8nm Ru] for (a) PM with relevant fit parameters HFMR = 4103 Oe, ΔH = 782 Oe, ϕ = 52.1○ and collection time t = 360 s and (b) HM with HFMR = 4119 Oe, ΔH = 791 Oe, ϕ = 45.3○ and collection time t = 2315 s. Si/3nm Ta/8nm Ru/10×[1.6nm Co/8nm Ru] for (c) PM with HFMR = 9094 Oe, ΔH = 357 Oe, ϕ = −6○ and collection time t = 132 s and (d) HM with HFMR = 9069 Oe, ΔH = 336 Oe, ϕ = −20○ and collection time t = 224 s. Notice that the measurements using PM require significantly a shorter time for collection of data than those using HM. The colored dots are the collected data and the corresponding solid lines are the theoretical fit as given by (8) and a third order polynomial background (dotted black lines).

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Figure 8: CPW-PM FMR results for the samples Si/3nm Ta/8nm Ru/10×[d-nm Co/8nm Ru]. (a) In-plane HFMR as a function of microwave frequency for d =∎ 0.6,▼ 1.2, ▲ 1.6. The solid lines are fits using (16) (b) Perpendicular-to-plane HFMR as a function of microwave frequency for d =∎ 0.6,▼ 1.2, ▲ 1.6. The solid lines are fits using (17). (c) 4πMeff shown for ∎ in-plane and ▲ perpendicular measurements as a function of Co film thickness. (d) Land´e factor g shown for ∎ in-plane and ▲ perpendicular measurements as a function of Co film thickness.

19