This document summarizes a review article on exchange bias in ferromagnetic-antiferromagnetic systems. Exchange bias is a phenomenon where cooling a system through the Neel temperature of an antiferromagnet in the presence of a ferromagnet induces an anisotropy (exchange bias) in the ferromagnet. The key findings of the review are: 1. Exchange bias was first discovered in 1956 when studying cobalt particles embedded in cobalt oxide. 2. It has since been observed in small particles, inhomogeneous materials, ferromagnetic films on antiferromagnetic single crystals, and thin films. 3. Various theoretical models have been proposed to explain exchange bias based on interface coupling, anisotropies, and domain formation.

1. Review Report
by
Ashok Ranjan
(106031891)
NTHU-MSE, Taiwan

2. Exchange bias [Journal of Magnetism and Magnetic Materials, 192, (1999) 203-232]
J. Nogues, Ivan K. Schuller

3. When materials with ferromagnetic (FM)-antiferromagnetic (AFM) interfaces are cooled
through the Neel temperature of the AFM (with the Curie temperature of the FM larger than
Neel temp.) an anisotropy (exchange bias) is induced in the FM.
Discovered in 1956 by MeikleJohn and Bean
when studying Co particles embedded in
their native antiferromagnetic oxide (CoO)
1. Material Used : Co as a Core and CoO as a Shell
2. Method : Electrodeposition
3. Particle Size : ~200Å
4. The material is cooled from the paramagnetic state of the
oxide to the antiferromagnetic state in a saturating
magnetic field. Since the Neel temperature of cobaltous
oxide is 293K, the material was cooled from 300K to 77K
in a magnetic field.
Ref : W.H. Meiklejohn, C.P. Bean, Phys. Rev. 102 (1956) 1413.
Definition:

4. Other Systems in which this anisotropy discovered
1. Small particles
2. Inhomogeneous materials
3. FM films on AFM single crystal
4. Thin films
Phenomenology:
Ref : J. Nogues, T.J. Moran, D. Lederman, I.K. Schuller, K.V. Rao, Phys. Rev. B
• Static magnetic field from a temperature above TN but below TC to temp.
T<TN
• After T<TN Field cooling procedure shifts the hysteresis loop in opposite
direction
• Absolute value of coercive field for decreasing and increasing field is
different
• This loop shift is normally called as Exchange Bias, HE
• Coercivity increased after field cool procedure
• Both effect disappear at (or) close to Neel Temp.

5. FM
AFM
FM
AFM
FM
AFM
FM
AFM
FM
AFM
Field Cool
M
H
Intuitive Picture:
TN < T < TC
H
T < TN
(i)
(ii)
(iii)
(iv)
(v)

6. Techniques
Magnetization Torque
Ferromagnetic
resonance
Neutron
Diffraction
Brillouin Scattering
Magnetic
Dichroism
Mossbauer Effect Magnetoresistance AC-Susceptibility
Domain
Observation

7. Materials:
1. Small Particles:
• Parameter exhibited by most fine particles:
1. Non-vanishing rotational hysteresis
2. Increase of coercivity below TN.
• These properties related to surface layer of the particle which due to the
changes in the atomic coordination form a layer of disordered spins.
• Particles behaves as a two magnetic system.
Disadvantage:
• Difficult to compare results quantitatively
• Non ideal for Exchange Bias:
1. Distribution of particle shapes and size is always present
2. Difficulty to identify the nature of interface.
3. Stoichiometry
4. Crystallinity
Ref : W.H. Meiklejohn, C.P. Bean, Phys. Rev. 102 (1956) 1413.

8. Ref : Review: J.S. Kouvel, J. Phys. Chem. Sol. 24 (1963) 795.
2. Inhomogeneous materials: (materials without well defined interfaces)
Spin glass and some ferrimagnets
Example:
1. Cu1-xMnx
2. Ag1-xMnx
3. Ni1-xMnx
(Au1-xFex)
Exchange bias is an intrinsic property of material rather than a sample preparation artifact.
(Which has been observed)
 Polycrystalline
 Single crystal
 Thin film form
Amorphous materials
• Fe1-xZrx
• Ni1-xMnx
• P16B6Al3
Other example of inhomogeneous materials: (multiple FM-AFM interface)
• Co sputtered in low O2 pressure atm.
• Co-sputtered CoCr or NiO with NiFe2O3 precipitates.

9. 3. Coated antiferromagnetic single crystals:
1. Role of spin configuration at the interface (by selecting different crystallographic directions)
2. Role of the roughness (by controllably damaging the AFM surface before depositing the FM)
(two important aspect of Exchange bias)
Exchange bias exhibited ay all three systems are substantially smaller than the one obtained in small particles
or thin films.
1. AFM surface is contaminated before transferring the single crystal to the deposition chamber.
2. Very little dependence of the Exchange bias on the spin configuration of the AFM at the interface.
(Why?)
Compensated AFM surface Uncompensated AFM surface
Ref: J. Nogue, I.K. Schuller / Journal of Magnetism and Magnetic Materials 192 (1999) 203-232

10. 4. Thin films:
• Interface can be quite effectively controlled and characterized
• Most of the device application are in thin film form
Some interesting phenomenon:
• AFM thickness
• Interface disorder or Orientation dependence
• The magnitude of Exchange bias is described in terms of an
interface energy per unit area
∆𝑬 = 𝑴 𝑭𝑴 𝒕 𝑭𝑴 𝑯 𝑬
1. Oxide AFM
2. Metallic AFM
3. Ferrimagnets
4. Other AFM
(Types)
Saturation magnetisation
Thickness of Ferro-magnet
This kind of samples are difficult to compare
Oxide layer can measured accurately
Film oxidized through grain boundaries
Increasing the interface surface
Antiferromagnetic oxides have been
sputtered directly from the oxide or in a
reactive oxygen atmosphere.
Surprisingly, well oriented AFM oxides can exhibit smaller exchange bias than oxidized metallic layers or polycrystalline
AFM layers, probably due to oxidation through grain boundaries, increasing the effective interface area or other magnetic
or microstructural factors.
Problems
Solution
Ref: J. Nogue & I.K. Schuller / Journal of Magnetism and Magnetic Materials 192 (1999) 203-232

12. Metallic AFMs
Others

13. Applications:
• Permanent magnet materials
• High density Recording media
• Perpendicular Recording media
• Magnetic Recording Media
• Domain Stabilizer
(In recording media heads based on
anisotropic magnetoresistance. An AFM layer
is deposited on the edge of the FM layer, to
avoid closure domains and thus reduce the
Barkhausen noise of the devices.)
Recently Exchange Bias became part of new class of ‘spin-valve’ devices, based on GMR.
This type of device consists of two FM layers separated be a non magnetic layer.
FM
FM
AFM
Free
Pinned
Ref: B. Dieny, V.S. Speriosu, S.S.P. Parkin, B.A. Gurney, D.R.Wilhoit, D. Mauri, Phys. Rev. B 43 (1991) 1297.
Low to high resistance occurs at rather low fields.
GMR in Exchange Bias
Read heads
Magnetic sensors
Magnetoresistive memories

14. Theoretical models:
𝑬 = −𝑯𝑴 𝑭𝑴 𝒕 𝑭𝑴 𝐜𝐨𝐬 𝜽 − 𝜷 + 𝑲 𝑭𝑴 𝒕 𝑭𝑴 𝒔𝒊𝒏 𝟐
𝜷 + 𝑲 𝑨𝑭𝑴 𝒕 𝑨𝑭𝑴 𝒔𝒊𝒏 𝟐
𝜶 − 𝑱 𝑰𝑵𝑻 𝐜𝐨𝐬(𝜷 − 𝜶)
Applied magnetic field
Saturation magnetization
Thickness of the FM layer
Anisotropy of the FM layer
Interface coupling constant
𝜽 − 𝒂𝒏𝒈𝒍𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒂𝒑𝒑𝒍𝒊𝒆𝒅 𝒇𝒊𝒆𝒍𝒅 𝒂𝒏𝒅 𝑭𝑴 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒚 𝒂𝒙𝒊𝒔
𝜷 − 𝒂𝒏𝒈𝒍𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒛𝒂𝒕𝒊𝒐𝒏 𝒂𝒏𝒅 𝑭𝑴 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒚 𝒂𝒙𝒊𝒔
𝜶 − 𝒂𝒏𝒈𝒍𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝑨𝑭𝑴 𝒔𝒖𝒃𝒍𝒂𝒕𝒕𝒊𝒄𝒆 𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒛𝒂𝒕𝒊𝒐𝒏 𝒂𝒏𝒅 𝑨𝑭𝑴 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒚 𝒂𝒙𝒊𝒔
MAFM
α
β
θ
KAFM, KFM
MFM
H
Ref: Review: W.H. Meiklejohn, J. Appl. Phys. 33 (1962) 1328.

15. 𝑬 = −𝑯𝑴 𝑭𝑴 𝒕 𝑭𝑴 𝐜𝐨𝐬 𝜽 − 𝜷 + 𝑲 𝑭𝑴 𝒕 𝑭𝑴 𝒔𝒊𝒏 𝟐 𝜷 + 𝑲 𝑨𝑭𝑴 𝒕 𝑨𝑭𝑴 𝒔𝒊𝒏 𝟐 𝜶 − 𝑱 𝑰𝑵𝑻 𝐜𝐨𝐬(𝜷 − 𝜶)
Effect of applied field on FM layer Effect of FM anisotropyEffect of AFM anisotropy Effect of interface coupling
Condition: 1
𝐊 𝐅𝐌 𝐭 𝐅𝐌 ≪ 𝐊 𝐀𝐅𝐌 𝐭 𝐀𝐅𝐌
𝑬 = −𝑯𝑴 𝑭𝑴 𝒕 𝑭𝑴 𝐜𝐨𝐬 𝜽 − 𝜷 + 𝑲 𝑨𝑭𝑴 𝒕 𝑨𝑭𝑴 𝒔𝒊𝒏 𝟐
𝜶 − 𝑱 𝑰𝑵𝑻 𝐜𝐨𝐬(𝜷 − 𝜶) 𝑯 𝑬 =
𝑱 𝑰𝑵𝑻
𝑴 𝑭𝑴 𝒕 𝑭𝑴
𝐊 𝐀𝐅𝐌 𝐭 𝐀𝐅𝐌 ≫ 𝐉𝐈𝐍𝐓
𝐊 𝐀𝐅𝐌 𝐭 𝐀𝐅𝐌 ≪ 𝐉𝐈𝐍𝐓
System is minimized by keeping α small independently of β.
It is energetically more favourable to keep (β-α) small, i.e. AFM-FM spins rotates together
The AFM spins follow the motion of FM layer, thus no loop shift should be observed, only an increase in coercivity.
Condition: 2

16. If JINT is taken to be similar to the ferromagnetic exchange, HE is predicted to be several orders of magnitude
larger than the experimental result.
1. Formation of domains in the AFM or FM layer
2. Field effect on AFM layer
3. Grain size distribution
4. Induced thermoremanent magnetization in the AFM layer
5. Non-collinearity of AFM-FM spins
6. Random anisotropy in the AFM layer or uncompensated surface spins
Important parameter in Exchange Bias which
are not considered in basic formula.
Ref :
• R. Jungblut, R. Coehoorn, M.T. Johnson, J. aan deStegge, A. Reinders, J. Appl. Phys. 75 (1994) 6659.
• K. Takano, R.H. Kodama, A.E. Berkowitz, W. Cao, G.Thomas, Phys. Rev. Lett. 79 (1997) 1130.
• A.A. Glazer, A.P. Potapov, R.I. Tagirov, Y.S. Shur, Sov. Phys. Sol. State 8 (1967) 2413.
• E. Fulcomer, S.H. Charp, J. Appl. Phys. 43 (1972) 4190.

17. • In a recent model in which quantum mechanical Hamiltonian is solved for spin compensated AFM surfaces,
HE arises from spin waves transmitted across the interface.
• This model assumes unidimensional and collinear spins.
Another model:
AFM Domains Perpendicular coupling
• The formation of AFM domains perpendicular to the
interface plane due to the random field created by
roughness and it is contribution of energy difference
between the different random domains which produce
Exchange Bias.
• Other model claims that formation of AFM domains
parallel to the interface when the FM layer rotates can
also cause Exchange Bias.
Ref:
1. A.P. Malozemoff, Phys. Rev. B 35 (1987) 3679.
2. A.P. Malozemoff, J. Appl. Phys. 63 (1988) 3874.
3. D. Mauri, H.C. Siegmann, P.S. Bagus, E. Kay, J. Appl.Phys. 62 (1987) 3047.
4. N.C. Koon, Phys. Rev. Lett. 78 (1997) 4865.
• For a compensated surface the interfacial energy
is minimized for perpendicular coupling between
the FM and AFM layers.
Ref: N.C. Koon, Phys. Rev. Lett. 78 (1997) 4865.
Ref: H. Suhl, I.K. Schuller, Phys. Rev. B 58 (1998) 158.

18. Unsolved Issues:
1. Thickness dependence
FM Thickness AFM Thickness
𝑯 𝑬 ∝
𝟏
𝒕 𝑭𝑴
Ref: Review: F.S. Luborsky, Electro-Technology (Sept. 1962)107.
• As the AFM thickness is reduced HE decreases abruptly
and finally for thin enough AFM layers HE becomes zero.
• Exchange bias requires the condition:
• As tAFM is reduced condition is violated.
𝐊 𝐀𝐅𝐌 𝐭 𝐀𝐅𝐌 ≫ 𝐉𝐈𝐍𝐓
2. AFM orientation
Compensated – Uncompensated:
1. Net spin averaged over a microscopic length scale is zero Zero magnetization.
2. If the spin arrangement is such that the surface magnetization is non zero the surface is uncompensated.
3. For compensated surfaces the spin pinning of FM layers cancel giving rise to a net zero HE.
4. A compensated surface remains compensated in the presence of unit cell random roughness however
more complicated roughness could result in uncompensated surfaces.
5. All compensated surfaces exhibit Exchange Bias.
Ref: T.J. Moran, J.M. Gallego, I.K. Schuller, J. Appl. Phys. 78(1995) 1887., A.E. Berkowitz, J.H. Greiner, J. Appl. Phys. 36 (1965)3330.

19. Out of the plane spins:
An intuitive explanation for this effect comes from the FM-AFM spin-spin interaction strength,
𝑺∗
𝑨𝑭𝑴. 𝑺∗
𝑭𝑴 = 𝑺 𝑨𝑭𝑴 𝑺 𝑭𝑴 𝒄𝒐𝒔𝜶
If FM spins lay in the interface plane due to shape anisotropy α is the angle between the AFM spins and the interface
plane. Therefore for in plane AFM spins:
α = 0° cosα = 1 HE maximum
and for out of plane spins:
α = 90° cosα = 0 HE = 0
Another possible explanation assumes that the dominant factor in HE is AFM domain formation.
𝑯 𝑬 ∝ 𝑲 𝑨𝑭𝑴 𝑨 𝑨𝑭𝑴
Thus in case of out of plane AFM spins, the effective AFM in plane anisotropy Keff and stiffness Aeff would play a
mojor role.
Due to angle of AFM spins, effective anisotropy and stiffness at the interface plane should scale with cosα.
𝑯 𝑬 ∝ 𝑲 𝑬𝒇𝒇 𝑨 𝑬𝒇𝒇 = 𝑲 𝑨𝑭𝑴 𝑨 𝑨𝑭𝑴 𝒄𝒐𝒔𝜶
Ref: D. Mauri, H.C. Siegmann, P.S. Bagus, E. Kay, J. Appl.Phys. 62 (1987) 3047, A.P. Malozemoff, Phys. Rev. B 35 (1987) 3679.

20. 3. Interface disorder
Roughness
Magnitude of HE decreases with
increasing roughness.
This behaviour appears to be independent
of the interface spin structure i.e.
compensated, uncompensated or out of
plane.
Magnitude of HE increasing with
increasing roughness has been observed
for FM coated AFM single crystal
indicating that microstructure may
play an important role.
HE for samples with polycrystalline AFM
layers appear to be less sensitive to
roughness.
Ref:
K. Takano, R.H. Kodama, A.E. Berkowitz, W. Cao, G.
Thomas, Phys. Rev. Lett. 79 (1997) 1130.
A.P. Malozemoff, J. Appl. Phys. 63 (1988) 3874.
Crystallinity
The crystallinity may be determined using
XRD from the FWHM of rocking curve
however some information can be
obtained from θ-2θ scans and TEM.
If AFM is textured in single orientation HE
increases with increasing texture.
If the sample has a wider rocking curve
the different grains will have a wider
range of coupling FM-AFM angles thus
reducing HE
Ref:
R.P. Michel, A. Chaiken, Y.K. Kim, L.E. Johnson,
IEEE Trans. Magn. 32 (1996) 4651.
C.M. Park, K.I. Min, K.H. Shin, J. Appl. Phys. 79
(1996) 6228.
Grain Size
Role of grain size in Exchange bias
remains unclear.
AFM grain size are expected to be
similar to thickness effects i.e. HE
and TB should decrease with reduced
AFM grain size.
The role of grain size is related not
only to the change in its size but
also to the degree of the texture,
the spin structure and AFM
anisotropy.
Ref:
C.H. Lai, T.C. Anthony, R. Iwamura, R.L.
White, IEEE Trans. Magn. 32 (1996) 3419.
C.H. Lai, H. Matsuyama, R.L. White, T.C.
Anthony, IEEE Trans. Magn. 31 (1995) 2609.

21. Anisotropy
• The Exchange bias should be larger for larger AFM anisotropy.
• The main difficulty in analysing these results rises from the fact that they involve mixtures or dilution of AFM materials,
therefore the absolute value of anisotropy is usually unknown.
• It is important to consider that different materials have different blocking temperature thus HE should be considered at the same
reduced temperature T/TB.
• The anisotropy of AFM materials and HE depend on microstructure of AFM layer, Exact quantitative analysis is
difficult.
Ref: M.J. Carey, A.E. Berkowitz, Appl. Phys. Lett. 60 (1992) 3060, C.H. Lai, W.E. Bailey, R.L. White, T.C. Anthony, J. Appl. Phys. 81 (1997) 4990.
Blocking Temperature
• Exchange bias vanishes above a temperature often denoted as blocking temperature, TB.
• The origin of this effect is seems to be related at least in part to the grain size and thickness of the AFM layer, through finite
size effects.
• Other size effect are caused by the fact that the anisotropy of the AFM depends on its dimension and that the condition
• Other factors influencing TB include stoichiometry or presence of multiple phases of certain thin film systems.
Ref: Y. Tsuchiya, K. Kosuge, S. Yamaguchi, N. Nakayama,Mater. Trans. JIM 38 (1997) 91. , M. Tsunoda, Y. Tsuchiya, M. Konoto, M. Takahashi, J. Magn. Magn.
Mater. 171 (1997) 29.
𝐊 𝐀𝐅𝐌 𝐭 𝐀𝐅𝐌 ≫ 𝐉𝐈𝐍𝐓

22. Training Effect:
• It is well known that in many Exchange biases film systems, HE depends on the number of measurements, a property often
called a Training Effect.
• If several consecutive hysteresis loops are measured, the shift of these decreases. This phenomenon has also been observed
using others techniques such as torque measurement.
• It is important to note that this phenomenon is more important in polycrystalline AFM, and very small or non-existent
in system based on single crystal.
• This effect is seems to be related to partial reorientation of the AFM domains with each FM magnetization reversal.
Ref: D. Paccard, C. Schlenker, O. Massanet, R. Montmory, A.Yelon, Phys. Stat. Sol. 16 (1966) 301., T.J. Moran, J.M. Gallego, I.K. Schuller, J. Appl. Phys. 78 (1995)
1887
Coercivity:
• The coercivity usually increases below TB, which is probably linked to the anisotropy of the AFM layer.
• In the case of an AFM with small anisotropy, when the FM rotates it ‘drags’ the AFM spins irreversibly, hence increasing
the FM coercivity.
• For a large AFM anisotropy the FM decouples because it can not drag AFM spins, consequently the coercivity is reduced.
Ref: M.J. Carey, A.E. Berkowitz, Appl. Phys. Lett. 60 (1992)3060., C.H. Lai, H. Matsuyama, R.L. White, T.C. Anthony, G.G. Bush, J. Appl. Phys. 79 (1996) 6389.

23. Perpendicular Coupling:
• Several system exhibit a perpendicular coupling at the interface between the FM and AFM spins.
• Perpendicular coupling has been observed in compensated and uncompensated AFM surfaces.
• This effect has been theoretically predicted for AFM-FM systems when the FM has a low anisotropy.
• Some degree of non collinear coupling has been observed in others systems by torque magnetometry and domain observation.
• The lowest energy configuration for a compensated surface is with the FM orientated perpendicular to the two AFM
sublattices.
• This reasoning can be extended to uncompensated surfaces if due to the fluctuations, e.g. roughness, domain formation, etc., the
AFM spins arrange themselves antiparallel at the interface.
Ref: T.J. Moran, I.K. Schuller, J. Appl. Phys. 79 (1996)5109., T.J. Moran, J. Nogue«s, D. Lederman, I.K. Schuller, Appl. Phys. Lett. 72 (1998) 617.,
C. Schlenker, Phys. Stat. Sol. 28 (1968) 507.0