Coercivity enhancement near blocking temperature in exchange biased Fe/Fe
xMn
1−xfilms on Cu(001)
Wei Pan, Nai-Yeou Jih, Chein-Cheng Kuo, and Minn-Tsong Lin∗ Department of Physics, National Taiwan University, Taipei 106, Taiwan
Exchange bias is found in the Fe/FexMn1−x/Cu(001) bilayer films. The coercivity (Hc) is en- hanced at blocking temperature (Tb) for 0.25 < x < 0.35, but not for 0.1 < x < 0.25. A simple model based on the discrepancy of the N´eel temperature (TN) and Tbis proposed, which may reveal the physical origins of these two temperature points.
Exchange bias is a unidirectional anisotropy, which is found at the interface between ferromagnetic (FM) and antiferromagnetic (AF) materials1. It has been applied in magnetic sensors and magnetic data storage as magneto- resistive materials with a spin-valve structure2. Two sig- nificant phenomena observed in an exchange biased sys- tem are the shift of magnetic hysteresis loop along the field axis, exchange bias (Hex) and the increase of the loop width, coercivity (Hc) enhancement, which is usu- ally found to reach the maximum when the bias field Hex
is zero2,4, e.g. Hc reaches maximum at the Tb where Hex
is zero. However, this Hcenhancement at Tbdoes not oc- cur in all exchange biased systems2,4. Models accounted for the exchange biased system are e.g. the random-field associated with the imperfect interface, the domain of AF layer, spin-flop model, and etc1,14–16. Although a full understanding for the exchange bias is not available, the Hex and Hc are affected by interfacial roughness or frustration, cooling field, domain walls in the FM or AF materials in some degree of agreement3.
In bilayer ultrathin films of 15 ML Fe/17 ML FexMn1−x/Cu(001), the Fe overlayer exhibits various magnetic properties depending on the composition x5. For the films with x above 0.35, the Fe overlayer is face- centered cubic structure and no MOKE signal is observed in the temperature ranging from 110 K to 330 K un- der the field of 1200 Oe. For the x below 0.35, the Fe overlayer is body-centered cubic structure, which is cat- egorized into three regimes: (I) x < 0.1, FM without exchange bias, (II) 0.1 < x < 0.25, FM with exchange bias, whose Hc decreases monotonically along with the increase of the temperature, and (III) 0.25 < x < 0.35, FM with exchange bias, whose Hc enhances at Tb. In this article, we focus on the films with exchange bias and propose a partial-coherent model to interpret this phe- nomena by the discrepancy between TN and Tb, which might indicate the different physical origins of the tem- perature points.
The experiment was performed in an ultra high vac- uum (UHV) chamber with a base pressure below 2 × 10−10 mbar. The surface of the substrate Cu(001) was cleaned by Ar+ sputtering and examined by Auger elec- tron spectroscopy (AES) for the cleanliness. The crys- talline structure was rebuilt by annealing and checked by low energy electron diffraction (LEED) for the sharp 1 × 1 pattern. The films were prepared by co-deposition of Fe (99.995 %, at. %) and Mn (99.95 %, at %) on Cu(001)
at 300 K and followed by deposition of Fe at 150 K. The composition x of the FexMn1−x alloy films was adjusted by the individual deposition rate of Fe and Mn monitored by medium energy electron diffraction (MEED) and cal- ibrated by AES. The films were cooled from 300 K to 90 K with an magnetic field of 350 Oe and measured by in situ magneto-optical Kerr effect (MOKE) both at in-plane and out-of-plane orientation at the temperature increasing from 110 K to 330 K. For details of the exper- iments, see Ref.6,7.
The temperature dependence of the Hc and Hex for these films are shown in the Fig. 1. For the films in regime (II) and (III), the Hex decreases along with the increase of the temperature and Tb are found to be about 270 K.
The significant difference is the temperature-dependent Hc behavior. For the Fe film grown on FexMn1−x with x = 0.2, the Hc decreases monotonically along with the increase of the temperature. For the Fe film grown on FexMn1−xwith x = 0.3, the Hc decreases but is strongly enhanced while the Hex approaches zero.
The coherent rotation model accounts that the ex- change bias arises from the AF layer, which ”pins” the magnetization of the FM layer after field cooling2,11. The energy per unit area is written as1,2
E = − HMF MtF Mcos(θ − β) + KF MtF Msin2β + KAFtAFsin2α − J cos(β − α) (1) where H is the applied field, MF M the saturated mag- netization, tF M the thickness of the FM layer, tAF the thickness of the AF layer, KAF the anisotropy of the AF layer, and J the interface coupling constant. β, α, and θ are the angles between the magnetization and the FM anisotropy axis, the AF sublattice magnetization (MAF) and the AF anisotropy axis, and the applied field (H ) and the FM anisotropy axis, respectively (see Fig. 2).
For simplicity, θ is set to be zero that the external field is applied along the easy axis of the FM layer. The hys- teresis loop is obtained by minimizing the energy with respect to the angle α and β.
For understanding the origin of the loop shift Hex, a hard AF approximation is introduced that assumes the spins in AF layer are completely fixed during the rotation of the magnetic moments in the FM layer, i.e. setting α to be constant (e.g. zero). The Hc and Hex can be obtained.
E = −HMF MtF Mcos β + KF MtF Msin2β − J cos β (2)
2
Hc=2KF MtF M
MF MtF M
Hex = − J MF MtF M
(3)
The exchange bias is ascribed to the interlayer coupling J between FM and AF layers. The Hcremains the same as that without exchange bias coupling.
In order to understand the origin of the Hc enhance- ment, a soft AF approximation is introduced by assuming the spins in the AF layer rotate with the spins in the FM layer coherently, i.e. α is set to be as β. The Hc and Hex can be obtained.
E = −HMF MtF Mcos β+(KF MtF M+KAFtAF) sin2β−J (4)
Hc=2(KF MtF M+ KAFtAF) MF MtF M
Hex= 0
(5)
The Hc is enhanced by 2(KAFtAF)/MF MtF M. Real exchange biased systems would be in between the hard and soft AF approximation.
In this model, Hex originates from the interlayer ex- change coupling, J cos(β − α). It disappears when J is zero or α = β, i.e. spin decoupled at FM/AF interface or the AF spins rotate completely with FM spins, re- spectively. The Hc enhancement is ascribed to the AF spins rotates coherently with the FM spins. Thus the more coherent-rotated spins in the AF layer, the larger Hc enhancement.
Here we propose a model that assumes that a ratio ² (<1) of the spins rotates coherently, i.e. ² ratio of the AF spins aligning along β and the ratio κ remains along α.
Additionally, the interlayer exchange coupling becomes smaller. Eq. 1 is modified as:
E = − HMF MtF Mcos(θ − β) + KF MtF Msin2β + κKAFtAFsin2α + ²KAFtAFsin2β
− J0cos(β − α) where
κ, ² < 1 J0 ∝ (1 − ²)J
(6)
The Hex and Hc are obtained as:
Hc= 2KF MtF M
MF MtF M + ²2KAFtAF
MF MtF M
Hex= − J0 MF MtF M
(7)
Temperature is as an indication of the thermal fluc- tuation that reduces the exchange coupling between the
spins in the FM, AF, and the interlayer exchange cou- pling at the FM/AF interface. It is reasonable to assume that more spins in AF layer are ”dragged” by the spins in FM layer at higher temperature but they decoupled above Tb. Therefore temperature effect is introduced in
², which would increase with the temperature until Tb. For J’, it would decrease with the increase of the tem- perature and approaches zero at Tb. By setting h0 as 2KF MtF M/MF MtF M, hk as 2KAFtAF/MF MtF M, and j ’(T) as J0(T )/MF MtF M, Eq. 7 is modified as:
hc = h0+ ²(T )hk
hex = −j0(T ) set t ≡ T
Tc, tb≡Tb
Tc, tN ≡ TN
Tc
=⇒ h0= (1 − t)a
²(t) =
½ (tt
N)b, t < tb
(ttb
N)b(1 − (t − tb))a, t ≥ tb
j0(t) =
½(1 −tt
b)c, t < tb
0, t ≥ tb
(8)
where a, b, and c are positive real number.
The function of the temperature governing the spin coupling is formulated in the form of Curie-Weiss law13, which may need further modification.
A numerical result of this model is plotted in Fig. 3.
For the curve with tN equals to tb, the increase of hcnear tb is the largest (see the curve for tN = 0.5 in Fig. 3).
For the curve with tN much larger than tb, this increase is insignificant (see the curve for tN = 0.9 in Fig. 3).
In Fig. 1, the Tb for both films are close that 275 K for the film with x = 0.2 and 270 K for the film with x
= 0.3. From this model, the TN of 17 ML FexMn1−x
for the x = 0.2 would be higher than that for the x = 0.3, which agrees with the TN for bulk FexMn1−x(TN 0.2
= 425 K and TN 0.3 = 375 K9). Note that the TN for the FexMn1−x film is reduced by the finite size effect.
The parameters such as a, b, and c require more detail analysis on the temperature dependence in Hc and Hex
to obtain these quantities.
For the exchange biased system with or without this increase of Hcat Tb might indicate the different effect of the thermal fluctuation on spin coupling in the AF layer and at the FM/AF interface.
This work was supports by National Science Coun- cil in Taiwan (Grant No. NSC-92-2112-M-002-028) and MOEA Program (Grant No. 92-EC-17-A-08-S1-0006).
∗ Author to whom correspondence should be addressed.
Email address: [email protected]
1 W. H. Meiklejohn and C. P. Bean, Phys. Rev. 102, 1413
3
100 150 200 250 300 350
0 20 40 60 80 100 120 140
-20
Magnetic field (Oe)
Temperature (K) -Hex
Hc
Hc -Hex
0.2 0.3 x
FIG. 1: Hexand Hc as a function of temperature for 15 ML Fe/17 ML FexMn1−x/Cu(001) with x = 0.2 and 0.3. The Tb
is about 270 K. For the films with x = 0.2, the Hcdecreases monotonically along with the temperature. For the films with x = 0.3, the Hc reaches the maximum at Tb. The lines are guides for the eyes.
KFM, KAF MAF
MFM H
FIG. 2: Schematic illustration for the spatial relation among external field (H), magnetization (MF M and MAF) and anisotropy (KF M and KAF) of FM and AF layers in an ex- change bias system.
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h
hex
0.2 0.4 0.6 0.8
-1.0 -0.5 0.0 0.5 1.0 1.5
t ho
t = 0.75
N
t = 0.5
N
t = 0.9
N
FIG. 3: Numerical results of the partial coherent model. The curves shown are deduced from the setting of a, b, and c are 0.5, 4, and 0.6, respectively, and tb is set to be 0.5. The increase of hc near tb is more obvious in the curve with tN
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