Exchange bias is a special type of magnetic anisotropy that can manifest in a ferromagnet when interfaced with an antiferromagnet [1]. An (over)simplified depiction of this phenomenon is shown in Figure 1(a). In general, there is no net magnetization associated with an antiferromagnet, as neighboring spins align antiparallel, canceling each other out. However, if an antiferromagnet is cooled through it’s ordering point (Neel temperature, *T _{N}*), in the presence of a modest external magnetic field, symmetry breaking near an imperfect interface can lead to a relatively small number of spins that are uncompensated and aligned in the same direction. Because these interfacial spins are still very strongly coupled to the antiferromagnetically ordered bulk, they are

Despite the widespread utilization of exchange bias, basic questions of the underlying mechanisms are still being explored, including efforts to understand the role of magnetic order in the bulk of the antiferromagnet [2] and the ferromagnet [3], as opposed to just at the interfaces. Here, we consider the case of an exchange biased ferromagnet with *T _{C}* that varies with distance away from the antiferromagnet / ferromagnet interface. Specifically, we will examine an exchange biased

The biasing antiferromagnet is IrMn, while the ferromagnetic material is Py_{x}Cu_{1-x}, an alloy of permalloy, Ni_{80}Fe_{20} (abbreviated Py) with non-magnetic Cu to control *T _{C}*. The layer closest to the antiferromagnet is the

To investigate this phase transition, we will use the PBR beamline to perform specular polarized neutron reflectometry (PNR), a technique sensitive to the depth profiles of the nuclear composition and magnetization [6]. Using a narrowly collimated, monochromatic (wavelength 0.475 nm) neutron beam, we will measure measure the spin-dependent reflectivities as a function of wavevector transfer along the sample growth direction (*Q _{z}*) using a

The *Q _{z}*-dependent reflectivity is determined by the depth dependence of the scattering length density, which has both nuclear and magnetic components. The nuclear scattering length density is defined

$$\rho_{N} = \sum_{i} N_{i}b_{i},\tag{Eq. 1}$$

where *N* is the number density, *b* is the nuclear scattering length corresponding to a particular isotope [7], and the summation is over each isotope present in the scattering volume, and provides information about the chemical composition of the sample. For our purposes here, the magnetic scattering length density is defined as a vector quantity,

$$\overrightarrow{\rho_{M}} = C\overrightarrow{M} ,\tag{Eq. 2}$$

where \(\overrightarrow{M}\) is the sample magnetization (magnetic moment per unit volume) and the constant *C* = 2.91 x 10-9 for \(\rho_{M}\) in units of Å^{-2} and *M* in units of kA m^{-1} (or emu cm^{-3}). The non spin-flip reflectivities *R ^{++}* and

$$ R^{\pm \pm}(Q_{z}) = \frac{16 \pi^{2}}{Q_{z}^{2}} \left |\int_{-\infty}^{+\infty}e^{iQ_{z}z} \left[ \rho_{N}(z) \pm \rho_{M}(z) \cos \phi_{M}(z)\right]dz\right |^{2} \tag{Eq. 3 } $$

where \(\phi_{M}\) is the angle between \(\overrightarrow{M}\) and \(\overrightarrow{H}\).

The spin-flip scattering tells us about the in-plane magnetization perpendicular to *H*. We can usually [8] assume that* R ^{-+}*and

$$ R^{+-}(Q_{z}) = R^{-+}(Q_{z}) = \frac{16 \pi^{2}}{Q_{z}^{2}} \left |\int_{-\infty}^{+\infty}e^{iQ_{z}z} \left[ \rho_{M}(z) \sin \phi_{M}(z)\right]dz\right |^{2} \tag{Eq. 4 } $$

Thus, measurement of all four polarization states allows us to determine the structural and in-plane *vector *magnetization depth profiles. While the Born Approximation is useful for providing a simple qualitative picture of the relationship between reflectivity and scattering length density, it fails catastrophically near total external reflection. Fortunately, it is straightforward to use the optical transfer method to exactly calculate the reflectivity corresponding to any any arbitrary sld profile [6]. As such, we can determine the depth profiles via model fitting of the reflectivity data. We will do this using the Refl1D software package [9].

The reflectivity measured for our sample in a 500 mT saturating field parallel to the bias direction at 40 K is shown in the top panel of Figure 3, while the profile determined from the fit to this data is shown in the bottom panel.

We see features in \(\rho_{N}\) corresponding to each of the expected layers, and non-zero \(\rho_{M}\) for the three ferromagnetic layers. This is because all competing fields (i.e. the biasing and applied magnetic fields ) are oriented in the same direction (and the applied magnetic field is strong enough to align the magnetizations of all the ferromagnetic layers anyway). For the bulk of the antiferromagnetic IrMn \(\rho_{M}\) should be zero, as the ordered spins should perfectly cancel, and (while certainly good enough to see the contributions from the ferromagnet) the statistical quality and *Q _{z}*-range of the data are insufficient for us to reasonably distinguish any weak \(\rho_{M}\) corresponding to the pinned interfacial magnetization [10]. Thus the data are modeled well with a IrMn layer featuring zero \(\rho_{M}\). We will use this model as the basis for modeling our temperature-dependent data.

For our experiment, we will start with the sample at 300 K, and will apply a 700 mT saturating field (enough to align the magnetization of all layers except for the pinned spins of the IrMn) antiparallel to the IrMn bias direction (marked on the sample). The field will then be reduced to a near remanent 1 mT. This should result in an antiparallel alignment of the pinned and free layers, similar to what is shown in Fig. 2. We will then take PNR measurements as a function of decreasing temperature in order to examine the evolution of the magnetic depth profile as ferromagnetism emerges in the Py_{0.4}Cu_{0.6} spacer layer.

[1] J Nogués, and Ivan K Schuller. Journal of Magnetism and Magnetic Materials , **192**, 203 (1999).

[2] R. Morales, Zhi-Pan Li, J. Olamit, Kai Liu, J. M. Alameda, and Ivan K. Schuller, Physical Review Letters **102**, 097201 (2009)

[3] R. Morales, Ali C. Basaran, J. E. Villegas, D. Navas, N. Soriano, B. Mora, C. Redondo, X. Batlle, and Ivan K. Schuller. Physical Review Letters **114**, 097202 (2015).

[4] A. F. Kravets, A. N. Timoshevskii, B. Z. Yanchitsky, M. A. Bergmann, J. Buhler, S. Andersson, and V. Korenivski. Physical Review B **86**, 214413 (2012).

[5] Here we are concerned with direct exchange between layers, which should provide the dominant contribution to any interlayer coupling for this system. However there are means of indirect exchange (e.g. RKKY coupling) which can play significant roles in metallic magnetic multilayers.

[6] C. F. Majkrzak, K.V. O’Donovan, and N.F. Berk. “Polarized Neutron Reflectometry.” In Neutron Scattering from Magnetic Materials, 397–471. Elsevier, 2006.

[7] https://ncnr.nist.gov/instruments/magik/Periodic.html

[8] There are special (and interesting!) situations where this would not be the case for this scattering geometry (e.g. helical magnetism).

[9] http://refl1d.readthedocs.io/en/latest/

[10] However, while challenging, you can distinguish those pinned spins with PNR! see M. R. Fitzsimmons, M, B. J. Kirby, S. Roy, Zhi-Pan Li, Igor V. Roshchin, S. K. Sinha, and Ivan K. Schuller. Physical Review B **75**, 214412 (2007).

Created May 31, 2018, Updated June 7, 2018