Threshold Interface Magnetization Required to Induce Magnetic Proximity Effect

TL;DR

This paper investigates the relationship between proximity-induced magnetization in platinum and the temperature-dependent magnetization of an adjacent ferromagnet, revealing a non-linear scaling and the importance of magnetic susceptibilities in trilayer structures.

Contribution

It demonstrates that PIM does not linearly scale with FM interface magnetization and highlights the role of heavy metal susceptibilities in asymmetric PIM effects.

Findings

PIM vanishes before FM interface magnetization disappears.

PIM does not follow expected linear scaling with FM magnetization.

Heavy metal susceptibilities explain asymmetric PIM in trilayers.

Abstract

Proximity-induced magnetization (PIM) has broad implications across interface-driven spintronics applications employing spin-currents. We directly determine the scaling between PIM in Pt and the temperature-dependent interface magnetization in an adjacent ferromagnet (FM) using depth-resolved magnetometry. The magnetization due to PIM does not follow the generally expected linear scaling with the FM interface magnetization, as a function of temperature. Instead, it vanishes whilst the FM interface magnetization remains. The effective magnetic susceptibilities of heavy metal (HM) layers are shown to give rise to the previously unexplained asymmetric PIM found in HM/FM/HM trilayers.

Equations

$$\chi =\frac{M}{H}=\frac{{\chi }_{\mathrm{P}}}{1-Ug(E_{\mathrm{F}})}={\chi }_{\mathrm{P}}S,$$

$$\mathrm{PIM}=\chi H_{\mathrm{ex}}={\chi }_{\mathrm{P}}SJ{M}_{\mathrm{FM}},$$

$$\mathrm{PIM}=\chi \left(H_{\mathrm{ex}}-H_{\mathrm{ex}}^0\right)=\chi J\left(M_{\mathrm{FM}}-M_{\mathrm{FM}}^0\right),$$

Full text

I Introduction

Platinum, and other heavy metals (HM), are widely used for interface-driven spintronics applications. Proximity-induced magnetization (PIM) arises when these materials are placed in direct contact with a ferromagnetic (FM) material. PIM has been implicated in many spintronic phenomena including the spin-Hall effect Zhang et al. (2015a) and spin-Hall magnetoresistance Huang et al. (2012); Lu et al. (2013), the spin-Seebeck Kuschel et al. (2015) and anomalous-Nernst Guo et al. (2014) effects, the anomalous-Hall effect Shimizu et al. (2013), spin-relaxation Freeman et al. (2018), interface spin-transparency Zhang et al. (2015b); Avci et al. (2015) and spin-pumping Caminale et al. (2016), interfacial Dzyaloshinskii-Moriya interaction Rowan-Robinson et al. (2017) and chiral domain wall motion Ryu et al. (2014), and magnetization ($M$) reversal driven by spin-orbit torques Peterson et al. (2018)  and electric fields Miwa et al. (2017).

The first report of PIM in Pt suggested that it is due to interfacial hybridization between the Pt $5d$ band and the $3d$ band of FM Fe, Co, Ni, and their alloys Schütz et al. (1990). This remains the basic physical description of the PIM mechanism Nakajima et al. (1998); Liang et al. (2016); Rowan-Robinson et al. (2017). Element specific magnetometry using x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity (XRMR) have shown that PIM typically decays away from the interface over a lengthscale of $\sim 1$ nm Wilhelm et al. (2000); Geissler et al. (2001), and in some cases suggest surprisingly large amplitudes up to $\sim 0.6\text{ }\mu_{\mathrm{B}}/$atom in nominally non-magnetic materials Antel et al. (1999); Kuschel et al. (2015); Klewe et al. (2016). Pt on YIG, a ferrimagnetic oxide, may Lu et al. (2013) or may not Geprägs et al. (2012) support PIM. Despite the breadth of topics where magnetic proximity effects are implicated, little detail is known about the factors determining PIM at a HM/FM interface.

Here we demonstrate how the FM interface magnetization modifies PIM. We use a designed model structure consisting of a FM alloy with tailored Curie temperature, sandwiched between Pt layers. Complementary depth- and element-resolved magnetometries enable simultaneous extraction of the relationship between PIM and the temperature-dependent FM magnetization at both interfaces. This approach provides new insights into the phenomenology of PIM.

Pt is a paramagnet which is close to the Stoner instability, $Ug(E_{\mathrm{F}})=1$, where $U$ is the electron-electron Coulomb (exchange) interaction and $g(E_{\mathrm{F}})$ the electronic density of states at the Fermi energy. Such ‘Stoner-enhanced’ paramagnets have magnetic susceptibility

[TABLE]

where $H$ is the applied magnetic field and $\chi_{\mathrm{P}}=2\mu_{0}\mu_{\mathrm{B}}^{2}g(E_{\mathrm{F}})$ is the (approximately magnetic field- and temperature- independent) Pauli susceptibility, with $\mu_{0}$ the vacuum permeability and $\mu_{\mathrm{B}}$ the Bohr magneton. In Pt the Stoner enhancement factor $S=1/[1-Ug(E_{\mathrm{F}})]$ typically takes a value $S\approx 4$ Herrmannsdörfer et al. (1996).

The conventional description of PIM induced at the interface between a HM and a FM can be encapsulated within a simple phenomenological model Lim et al. (2013); Hase et al. (2014),

[TABLE]

whereby, e.g., through 3$d$-5$d$ hybridization the interface magnetization, $M_{\mathrm{FM}}$, in the FM and (dimensionless) interfacial exchange-coupling, $J$, produce a local ‘exchange field’, $H_{\mathrm{ex}}$ Lim et al. (2013), that results in a spontaneous equilibrium PIM in the HM. Roughness and intermixing modify $J$, intermixing of the HM into the FM modifies $M_{\mathrm{FM}}$, and intermixing of the FM into the HM modifies $\chi$. The microscopic physical structure of the interface is therefore important in determining PIM Ferrer et al. (1997); Tokaç et al. (2015); Liang et al. (2016).

Studies of the scaling between PIM and the FM interface magnetization are limited. Indirect PIM measurements on Pd/Fe/Pd multilayers (Pd is also a Stoner-enhanced paramagnet), suggest PIM vanishes despite Fe remaining strongly magnetized Cheng et al. (2004). Direct measurements of PIM for ultra-thin Fe sandwiched between Pd show PIM following the temperature dependence of a 3D FM rather than the quasi-2D behaviour of the Fe layer Hase et al. (2014). In thicker Pt/Co/Pt Rowan-Robinson et al. (2017) and Pd/Co/Pd Kim et al. (2016) trilayers the PIM at the two interfaces differs: PIM is larger at the upper FM/HM interface than at the lower HM/FM interface. In these cases Eq. 1 does not adequately describe the observed behaviour.

II Experimental Approach

Here we describe an approach to disentangle the PIM at an interface between a FM and HM using a combination of neutron and x-ray reflectivity measurements.

Polarised neutron reflectivity (PNR) is sensitive both to the physical structure of the sample via the nuclear scattering of neutrons, and enables quantitative depth-resolved extraction of the local magnetization via the interaction between the neutron spin and the local magnetic induction Ankner and Felcher (1999). As the PIM in the HM consists of small magnetic moments that are spatially concentrated close to the interface with the FM, the magnetic depth profile measured by PNR is sensitive primarily to magnetism in FM.

One the other hand, to unambiguously extract the small, spatially concentrated PIM in HM, we use x-ray resonant magnetic reflectivity (XRMR). Tuning the energy of the incident circularly-polarised x-ray beam close to an appropriate elemental absorption edge, in this case Pt $L_{3}$, provides depth-resolved element selective magnetic sensitivity — as with other x-ray techniques XRMR is sensitive to the overall physical structure via the local electron density through Thompson scattering, but most importantly, the resonant scattering interaction here is sensitive to magnetism only in Pt Macke and Goering (2014).

The combination of these approaches enables the (large) interface magnetization in FM at FM/HM interfaces to be determined quantitatively from PNR, and the (much smaller) PIM in the HM on the other side of the same interface to be determined with element specificity from XRMR. The HM magnetization (PIM) is very much smaller than the FM magnetization; so the magnetization in HM is essentially invisible to PNR while the magnetization in FM is entirely invisible to XRMR. The depth selectivity of these scattering techniques further enables us to investigate PIM and interface magnetization at multiple interfaces in a multilayered sample within a single set of measurements. By studying both interfaces as a function of temperature, we aim to determine the amplitude of the PIM on the Pt side of the interface as the FM magnetization on the other side of the same interface varies over a wide range, in a single sample.

Here, a Pt(3 nm)/Co28Fe28Ta30B14 (10 nm)/Pt (3 nm) trilayer film was used to clarify the linkage between PIM and FM interface magnetization. The subscripts represent the nominal composition of CoFeTaB (CFTB), and 30 at. % Ta reduces the Curie temperature, $T_{\mathrm{C}}$, to below room temperature. Experimental details can be found in the supplementary material sup . We have found that Ta can diffuse vertically within this amorphous alloy during film deposition, and that subtle vertical diffusion of Ta within CFTB causes variation in the local $M$ and $T_{\mathrm{C}}$ Tokaç et al. (2017). This is similar to Fe*(100-x)Tax* amorphous alloys, where $T_{\mathrm{C}}$ can be tuned from $\sim 200$ K to below 100 K by increasing $x$ from $\sim 15$ % to $\sim 30$ % Fukamichi and Gambino (1981). Here Ta diffusion produces regions of different composition through the thickness of the CFTB film where the upper and lower interfaces have different $T_{\mathrm{C}}$, further enabling independent study of PIM at each interface.

III Results and Discussion

The in-plane saturation volume $M(T)$, measured by superconducting quantum interference device (SQUID) magnetometry after field-cooling is shown in the main frame of Fig. 1. The Pt magnetization, $M_{\mathrm{Pt}}$, due to PIM is expected to be small and localized at the interfaces, so the volume magnetization is expected to be dominated by $M_{\mathrm{CFTB}}$, the magnetization in CFTB. As expected, $M$ decreases with increasing $T$. The data show that the CFTB layer does not act as a single homogeneous magnetic slab with a single $T_{\mathrm{C}}$. Instead it suggests three transitions denoted as $T_{\mathrm{C1}}\sim 215$ K, $T_{\mathrm{C2}}\sim 120$ K and $T_{\mathrm{C3}}\sim 80$ K in Fig. 1. These transitions confirm the anticipated compositional variation through the CFTB layer thickness.

This compositional variation is further confirmed by magnetic hysteresis loop measurements, made using SQUID vibrating sample magnetometry (SQUID-VSM), with examples shown in Fig. 1(a), (b) and (c). At $T<T_{\mathrm{C3}}$ a single-step reversal was observed, shown at $T=50$ K in Fig. 1(a). When $T_{\mathrm{C3}}<T<T_{\mathrm{C2}}$ a distinct two-step reversal of $M$ was observed, shown at $T=100$ K in Fig. 1(b). This indicates two magnetic regions within the CFTB layer, with different coercivities. As $T$ increased the signal amplitude from the region with smaller $H_{\mathrm{C}}$ decreased (see supplementary material, Ref. sup, ), vanishing at $T_{\mathrm{C2}}\sim 120$ K. At $T>T_{\mathrm{C2}}$ a single-step reversal was observed, shown at $T=150$ K in Fig. 1(c).

Assuming the CFTB film comprises three sub-layers each with slightly different Ta concentrations, the two-step reversal of $M$ observed for $T_{\mathrm{C3}}<T<T_{\mathrm{C2}}$ indicates that $T_{\mathrm{C3}}$ corresponds to the $T_{\mathrm{C}}$ of the sub-layer in the center of the film. At $T<T_{\mathrm{C3}}$ the film acts as a single magnetic entity, but at $T_{\mathrm{C3}}<T<T_{\mathrm{C2}}$ the upper and lower FM CFTB sub-layers are magnetically decoupled by the paramagnetic central CFTB sub-layer, similar to Ref. Magnus et al., 2016. The Ta concentration profile producing this behaviour is shown schematically inset to the upper right of Fig. 1(d) by the solid line, where we presuppose that $T_{\mathrm{C2}}$ and $T_{\mathrm{C1}}$ correspond to the $T_{\mathrm{C}}$ of the upper and lower CFTB sub-layers, respectively.

A quantitative description of the depth dependence of $M_{\mathrm{CFTB}}$ as a function of $T$ was obtained using polarised neutron reflectometry (PNR). The approach used to extract the magnetic scattering length density (mSLD) profile is described in Ref. sup, . PNR is found here to be sensitive primarily to magnetism in CFTB due to the small PIM magnetic moment in Pt. Fig. 2(a) shows PNR at $T=50$ K. The PNR spin-asymmetry in Fig. 2(b) shows the normalized difference between the reflectivity channels $R^{+}$ and $R^{-}$ as a function of scattering vector, $Q$, for different $T$. The scattering geometry is schematically illustrated in the lower left inset of Fig. 1(d). $R^{+}$, $R^{-}$, and the derived spin-asymmetry at each $T$ were fitted simultaneously using GenX software Björck and Andersson (2007), each using the same structural scattering length density (sSLD) model for the sample derived from x-ray reflectivity (XRR). Best-fits, determined from reduced-$\chi^{2}$, are shown as solid lines in Fig. 2(a) and (b). The CFTB layer was modelled as three sub-layers, as suggested by SQUID(-VSM) measurements shown in Fig. 1. This was required to describe the PNR spin-asymmetry (see Ref. sup, ), and adding further sub-layers provided no significant improvement to the fits. All reduced-$\chi^{2}$ values are below 1.4.

The mSLD profiles obtained from best-fits to the PNR data are shown in Fig. 2(c). The mSLD profile at $T=50$ K shows a uniform $M$ in the center of the CFTB layer, with larger $M$ near the upper interface, and still larger $M$ near the lower interface. At $T=100$ K the central region is paramagnetic, confirming our interpretation that $T_{\mathrm{C3}}$ corresponds to the $T_{\mathrm{C}}$ of the central CFTB sub-layer, with slightly higher Ta concentration. At $T=150$ K the upper CFTB sub-layer becomes paramagnetic, demonstrating that $T_{\mathrm{C2}}$ indeed corresponds to the $T_{\mathrm{C}}$ of the upper sub-layer. The mSLD of the lower CFTB sub-layer decreases with increasing $T$. The best-fit at $T=250$ K, i.e., above $T_{\mathrm{C1}}$ where the entire CFTB film is paramagnetic, suggests a small mSLD in the lower CFTB sub-layer. This is indicative of the uncertainty in $M_{\mathrm{CFTB}}$ extracted from PNR. Integrating each mSLD profile gives the volume $M_{\mathrm{CFTB}}$, plotted as filled square markers in Fig. 1(c); the volume $M_{\mathrm{CFTB}}$ obtained from unconstrained fitting of PNR is consistent with the measured $M(T)$ within experimental uncertainty.

The depth dependence of PIM in the Pt layers was extracted from XRMR measurements at the Pt L3 absorption edge as a function of $T$. Due to the element specificity of resonant scattering, XRMR is sensitive only to magnetism in Pt. Fig. 2(d) shows the XRMR total specular reflectivity at $T=50$ K. No variation in reflectivity with $T$ was discernible. The XRMR spin-asymmetry averaged over measurements with positive and negative (saturating) $H$ (see sup, ) is shown at various $T$ in Fig. 2(e). XRMR reflectivity and spin-asymmetry at each $T$ were fitted simultaneously using GenX, with sSLD consistent with XRR and PNR. The best-fits are shown as solid lines in Fig. 2(d) and (e).

The mSLD profiles that yield the best-fits to the XRMR data are shown in Fig. 2(f). These mSLD profiles allow direct quantitative comparisons, but do not directly yield an absolute value for $M_{\mathrm{Pt}}$ sup ; Klewe et al. (2016). At $T<T_{\mathrm{C2}}$ PIM is present in both Pt layers, and is larger in the upper Pt layer. PIM decays away from the interface with FM into the Pt layers over a lengthscale of $\sim 1$ nm at all $T$. PIM also reduces with increasing $T$. At $T=150$ K (above $T_{\mathrm{C2}}$) where the upper CFTB interface is paramagnetic, and at $T=250$ K (above $T_{\mathrm{C1}}$) where the entire CFTB layer is paramagnetic, small mSLD contributions are found at the upper and lower interfaces, respectively. These indicate the experimental uncertainty in PIM amplitude derived from XRMR.

PIM, which is strongest at the upper interface, rapidly reduces with increasing $T$ and vanishes above $T_{\mathrm{C2}}$. Although smaller at low $T$, the lower Pt/CFTB interface PIM persists to significantly higher $T$ than that at the upper CFTB/Pt interface and vanishes at $T_{\mathrm{C1}}$. This suggests that PIM does scale with $M_{\mathrm{CFTB}}$ at a given interface, similar to Eq. 1. The first important result presented here is that PIM requires the adjacent layer to have non-zero $M$, confirming that PIM in HMs does not arise solely due to interfacial charge-transfer Al Ma’Mari et al. (2015).

In the temperature region where both CFTB interfaces are ferromagnetic, the upper interface has a larger PIM but a smaller $M_{\mathrm{CFTB}}$, whereas the lower interface has a larger $M_{\mathrm{CFTB}}$ but a much smaller PIM. Such PIM asymmetry has been found in Pt/Co/Pt and Pd/Co/Pd, where $M_{\mathrm{Co}}$ should not differ significantly between the two interfaces. Such asymmetry, where different PIM is induced for similar $M_{\mathrm{FM}}$ at the HM/FM and FM/HM interfaces, is currently unexplained.

To quantitatively investigate the proposed scaling of PIM with $M_{\mathrm{FM}}$, in Fig. 3 we parametrically plot the amplitude of the XRMR mSLD (PIM) against the amplitude of the PNR mSLD ($M_{\mathrm{FM}}$) for each interface as a function of $T$. The conventional description of PIM, Eq. 1, describes a proportionality between PIM and $M_{\mathrm{FM}}$. For the lower Pt/CFTB interface the scaling is indeed linear but PIM vanishes whilst significant, non-zero, $M_{\mathrm{CFTB}}$ remains. For the upper CFTB/Pt interface there are only two measurements in the FM phase. Assuming linear scaling PIM again vanishes with similar, non-zero, $M_{\mathrm{CFTB}}$. For comparison, best fits to the XRMR data where PIM is constrained to scale with $M_{\mathrm{CFTB}}$, as described in Eq. 1, are shown in the supplementary material, Ref. sup, . This conventional model does not describe the data well. This direct measurement of the unexpected scaling of PIM with FM interface magnetization is the key experimental result presented in this manuscript.

Neglecting any $T$ dependence of the susceptibility $\chi$, which in Pt is less than 5 % between 50 K and 200 K Hoare and Matthews (1952), we can modify Eq. 1 to describe the data in Fig. 3 as

[TABLE]

where the interface magnetization in the FM required to initiate PIM corresponds to a contribution $H_{\mathrm{ex}}^{0}=JM_{\mathrm{FM}}^{0}$ ($J$ dimensionless) to the effective ‘exchange field’ $H_{\mathrm{ex}}^{\mathrm{eff}}=H_{\mathrm{ex}}-H_{\mathrm{ex}}^{0}$. Here $H_{\mathrm{ex}}^{0}$ encapsulates the more complex behaviour of the spin-polarized 3$d$-5$d$ hybridization across the FM/HM interface. $M_{\mathrm{FM}}^{0}$ does not describe a magnetic dead-layer.

This new phenomenological scaling model shows that the effective susceptibility $\chi^{\mathrm{eff}}=\chi J$, which is proportional to the slope of the linear trendlines in Fig. 3, is responsible for the PIM asymmetry. Indeed, $\chi^{\mathrm{eff}}$ is found to differ between upper and lower Pt layers. The final important result here is the demonstration that larger PIM at the upper interface results from the presence of different effective magnetic susceptibilities in the HM layers, and does not require asymmetry in the FM interface magnetization.

This asymmetry in $\chi^{\mathrm{eff}}$ may arise due to the local structure at the interfaces, via interfacial roughness and/or intermixing Ferrer et al. (1997). Intermixing should be greater at the lower HM/FM interface Lardé et al. (2009), which would enhance $\chi^{\mathrm{eff}}$ in the lower HM layer, in contrast to the observed asymmetry. Our measurements reveal no structural mechanism for $J$ to vary, showing no significant difference between the interface widths for Pt/CFTB and CFTB/Pt interfaces. As the effective susceptibility may be modified by other means beyond interfacial intermixing, $J$ does not need to differ between these interfaces for different PIM to occur. Decreasing the size of Pt and Pd nanoparticles can significantly decrease $\chi$ van Leeuwen et al. (1994), which may also apply to polycrystal grain size. Lattice strain variation between the upper and lower HM layers may modify $g(E_{\mathrm{F}})$, and hence $\chi$ Hong et al. (2007). These mechanisms may be plausible here, but cannot explain the asymmetry in strongly textured Ta/Pd/Co/Pd films with columnar grains as described in Ref. Kim et al., 2016. Our measurements reveal how the PIM asymmetry arises, but a general mechanism explaining the difference in $\chi$ between upper and lower HM layers remains elusive.

IV Conclusions

To conclude, proximity-induced magnetism in a heavy metal and interface magnetization in a ferromagnet are shown to scale in a manner inconsistent with the expected phenomenological description; a small threshold magnetization in the ferromagnet is required to begin to then induce magnetism in the adjacent heavy metal. In a trilayer, the proximity-induced magnetism is shown to be larger in the upper heavy metal layer as a result of the heavy metal layers having different effective magnetic susceptibilities. This demonstrates how asymmetric PIM arises in HM/FM/HM trilayers.

Acknowledgements

We acknowledge support from Nigerian government TETFund scheme (OI), EPSRC DTP (BN and RMR-R), Republic of Turkey Ministry of National Education (MT), EPSRC Grant Ref. EP/L000121/1, HEFCE ODA, and the Royal Society (ATH). XMaS is a UK national facility supported by EPSRC. We thank STFC for ISIS beamtime RB1620118 and access to ISIS R53 Materials Characterization Lab, and D. Atkinson, D.M. Burn, C. Cox, T.P.A. Hase, P.D. Hatton, and K. Morrison for stimulating discussions. Supporting data are available at http://dx.doi.org/10.5286/ISIS.E.86389562 and http://dx.doi.org/10.15128/r10v8380575.