# Presentation: 694462

## Determination of Magnetic Directions in Multiferroic BiFeO3 Thin Films  

***Determination of Magnetic Directions in Multiferroic BiFeO******3 ******Thin Films ***

- Mikel Barry Holcomb
*Department of Materials Science and Engineering & Department of Physics, University of California, Berkeley*
*Lawrence Berkeley National Laboratory*

**Supported by LBL-LDRD & SRC-NRI**

## Introduction to Multiferroics 

- Multiferroic  Materials possess two or more of the following
- (Anti-)Ferromagnetism, (Anti-)Ferroelectricity, 		(Anti-)Ferroelasticity

***Introduction to Multiferroics****** ***

- Before applied field

- During and after applied field

- field

- Coupling between order parameters

**Notes:**
My group is predominately interested in multifunctional materials which possess multiple order parameters. We focus on multiferroics—materials which are at least two of the following: ferromagnetic, ferroelectric, and ferroelastic. A ferroelectric has a spontaneous polarization, which can be changed by an applied electric field; A ferromagnet has a spontaneous magnetization, which can be changed by an applied magnetic field; and a material with ferroelasticity has a spontaneous deformation, which can be changed by an applied stress.

There may be coupling between the order parameters, so if you had a multiferroic that was both a ferroelectric and a ferromagnet you might be able to change the magnetization of this material with an electric field or change the polarization with a magnetic field. Why care?

[Ferroelectrics are interesting because they often have unusually high and temperature dependent values of the dielectric constant, the piezoelectric effect, pyroelectric effect, and electro-optical effects (such as optical w doubling). They come in two types: order-disorder (paraelectric displacements about some multi-well configuration of sites, ordered subset) and displacive (paraelectric oscillations about a nonpolar site, then after displacive transistion about a polar site).] 
[Magnetic response slow because due dipoles, not monopoles. Response fades away above 100 GHz.]

## BiFeO3 ; only room temp multiferroic

**Polarization points in one of 8 possible <111> directions.**
**Magnetic plane is perpendicular to the polarization direction.**

***BiFeO******3****** ; only room temp multiferroic***

**T****C**** ~ 1103K**

**T****N**** ~ 643K**

**Ederer and Spaldin, PRB 71(2005)**

**Notes:**
I will show you that Bismuth ferrite is an excellent example and model system to analyze the coupling between magnetism and ferroelectricity. It is the only single phase room temperature multiferroic that is known today.  Bismuth ferrate is a ferroelectric with large polarization for thin films as demonstrated in this hysterisis curve. The polarization directions point in one of the 8 111 body diagonal directions. It is also a G-type antiferromagnet. Ederer and Spauldin used Density functional theory calucations to tell us that the energy is minimized when the AFM vector points somewhere in the plane perpendicular to our polarization. There are six preferred axes per plane, but none of these is energetically favorable over the other five for bulk films. 
And by changing the polarization direction,

Transition: How do we grow these materials? 

[Origin of FE is 6s2 is involved in the hybridization which causes FE, Nicola. Origin of M from superexchange mediated by O. All superexchange leads to AFM; BFO no exception.]

## Probing ME coupling

**Parameters:**
**Film orientation**
**Variants**
**Strain **

_**AFM**_
**X-ray dichroism & PEEM**

_**Ferroelectricity**_
**Piezoelectric force microscopy**

**Notes:**
A lot of groups focus on single crystals, which from my experience are basically impossible to get. Therefore, we’ve decided to use epitaxial thin films grown by pulse laser deposition. Not only are these films easy to grow, but the growth technique allows a wide range of parameters to vary. 
My group has gotten really good at selectively growing only some polarization directions, growing different orientations, and varying the strain of our samples with both thickness and substrate dependence. 
Though it might seem counterintuitive, I’ve focused on the 001 orientation, because its complexity due to having multiple polarization directions is actually what allows the ability to distinguish between different magnetic possibilities. 

We want to look at this ME coupling, so we need to be able to probe both ferroelectricity and AFM. One of these order parameters is well understood through piezoelectric force microscopy. PFM gives 3D mapping of ferroelectric domains with high resolution and accuracy; it also allows the manipulation of domains by using a bias on the tip. 
Since this is so well understood already, my focus is on studying the AFM and probing the coupling. 
I’ve decided to focus on a new and unexplored combination of x-ray dichroism and PEEM, which allows direction determination and imaging of AFM domains. 
To do this

## Absorption Studies of AFMs

**A**

**B**

**B/A**

**6 ********m**

***Absorption Studies of AFMs***

**XMLD**

**Ratio image: Magnetic contrast**

- A. Scholl, Science 287 1014 (2000)

**Element Specific**

**Intensity map**

**Before**

**After**

- X-rays

**LaFeO****3**

**Notes:**
I probe the Fe magnetic moments of BFO. The magnetic properties of transition metals are largely determined by the 3d valence electrons. These d-shell properties are best probed by L-edge absorption studies, or 2p to 3d transitions. 
There are differences in the L-edge spectra depending on what direction we measure the sample from. Why is this? Polarized xray absorption can sense the charge anisotropy of the valence states involved in the excitation process. For magnetic materials, the alignment of the local atomic spins can cause an anisotropy in the charge through the spin-orbit coupling. For example, in a cubic material the charge is highly isotropic in the atomic sphere, but in the presence of a magnetic interaction it shows a small ellipse-like distortion about the magnetic direction. This charge anisotropy leads to an asymmetry of the xray absorption signal, called XMLD. The intensity of the multiplet peaks at the absorption edge depends on whether the electric field vector is aligned parallel or perpendicular to the AFM axis, as shown for antiferromagnetic lanthium ferrate. This signal follows a cosine squared function, where cosine theta would just the be projection of the magnetic direction on the electric field direction.

So, what do we see when we look at multiferroic films? Let’s take a look at some BFO films we grew.
Xas spect

## Electrical Control of AFM in BFO

***E***

***E***

**AFM is controlled by FE!**

**OP PFM**

**Matching domains**
**Same temperature dependence of both as grown and poled areas**

- T. Zhao, M. Barry et al., *Nat Mat* **5**, 823 (2006)

**PEEM**

**PFM**

**Notes:**
We used this (PEEM) technique to compare the imaged domains to ferroelectric domains taken by PFM, where the colors in the polarization images tell you up/down or horizontal directions. It is clear that the PEEM images in grey show domains that match up exactly with the in-plane projection of the ferroelectric domains. 

We see only two dominate colors in the linear images. The contrast will reverse if we rotate the sample by 90 degrees, which tells us what we observe is a real dichroism. 
What happens if we use our PFM to switch the polarization domains out of plane, as shown by the OOP PFM like I mentioned before. The in plane domains of the polarization change, as do the magnetic domains. This matching and the temperature dependence measurements we’ve done both before and after poling tell us that our AFMism does in fact couple to the ferroelectric domains. So, we’ve proven what theory guessed, but can we learn any more about the AFMism of this system? We know that it’s coupled, but what is its nature? Theory predicts a degenerate magnetic plane for bulk. Does this happen in thin films as well? So, in order to determine this, we want to use the linear light that we used here and also an additional polarization. 

## Expected signal for XMCD

***Expected signal for XMCD***

- Top view

- E

- xrays

**RCP**

- 1

- 2

- 3

- 4

**Sample Rotation**

- 1,3

- 2

- 4

- 1,3

- 2

- 4

- Intensity for Easy **Axis**

- Intensity for Easy **Plane**

***I=p***** (cos****2**** ********PH**** + cos****2**** ********PV****)**
***+q***** (cos****2**** ********MH**** + cos****2**** ********MV****)**

**Linear**

**Linear**

**65****°**

**Notes:**
Forumlas

For example let’s look at the expected signal for all four of our downward polarization directions in the case of an easy plane and one particular easy axis. I’ve started here with linear curves, which look the same since these intensities are scaled by an unknown factor. The two shades of blue overlap. Now let’s see how these split up for circular light. (click) If we are clever about what angle we measure at we will go to an angle like 65 degrees, where we would expect a different result between the two cases; two of the domains would share the same grey color for the easy plane. We don’t see that for an easy axis. 

There is a reason I colored these different shades of red and blue. Experimentally, we can only compare our images taken with these two light polarizations. So, we need to see how the domains from these two sets of images split up. So, for an easy plane at 65 degrees, some of the bright and dark domains from linear images would appear the same color in circular images. This would not happen for an easy axis. The bright XMLD domains would stay bright in the other images. Now let’s take a look at the data. 

## Split into darker & medium grey in RCP

- 65°

- -25°

- RCP

***Split into darker & medium grey in RCP***

- 90° rotation

- 65°

- -25°

**E**

**There may be a preferred magnetic axis in BFO thin films!**

**Notes:**

As we saw before, we observe two main colors in linear images. This shows the contrast reversal with a sample rotation of 90 degrees.

When we instead measure with circularly polarized light, though the contrast is reduced, we can clearly still see the stripes. This does not fit with what we were expecting from an easy plane at this angle. This set of stripes should not be distinguishable.

I actually have a library of angles from which I’ve collected data and everything seems consistent with an easy axis—either 110 or 112 type depending on the sign convention I use in the dichroism formula. Well, this is exciting, but it would be really nice to figure out which axis we have.

## Determining Which Axis with Grazing Studies

***Determining Which Axis with Grazing Studies***

- 

- <110>

- <112>

- P

- plane

-  First observation of an easy axis in BFO
-  Choice of axis is controllable by strain

- Expected 110 Expected Plane Expected 112 Thin STO  Thick STO Thick DSO

**Notes:**
We will need grazing incidence studies to determine this. Here is a sample with only 2 polarization directions. So, I can measure the angle dependence of my spectroscopy signal as I rotate the light polarization from horizontal to vertical. We should see a maximum or minimum in of our signal when the incoming light is polarized parallel to the averaged projection of our magnetic and ferroelectric vectors. We expect the resulting solid curves for 110, 112, and the easy magnetic plane. We find that we have a 110 type magnetic easy axis for thin samples and a plane type for thicker samples.  

This is a pretty big deal. This is the first observation of a preferred axis in a very popular film that was long thought to have an easy plane. And, if we choose to use a substrate with the opposite kind of strain, we get the opposite axis. 
So of course, my working hypothesis involves strain. The degeneracy of the magnetic plane occurs in rhombohedral BFO (R3c). This degeneracy is lifted if BFO becomes monoclinic, even slightly, as would occur due to strains caused by the substrate. The strain squeezes the 111 plane horizontally and allows it to stretch vertically. Even our 200nm thick films show evidence of this relaxation from thicker films. 

## Summary

**Dichroism is rich for exploration in probing AFM properties in magnetoelectric materials **

**Multiple order parameters can be separated by taking advantage of temperature and crystallography**

**Epitaxial BFO (001) has an easy magnetic **_**axis**_**, instead of the easy plane predicted for bulk**

**Notes:**
In summary, dichroism is a new and mainly unexplored way to probe magnetoelectric coupling. The ferroelectric and magnetic contributions to dichroism can be studied by temperature, angle dependence, and by measuring different orientations.

I used angle dependent PEEM and spectroscopy to show that  BFO thin films have a preferred magnetic axis. What’s next?

##  Many Applications

**AFM/FE**

**FM**

**Physics of AFM**
**(Optical Studies)**

**Exchange Bias**
**FM/AFM**

**MagnetoelectricCoupling**
**AFM/FE**

-  ***Many Applications***

**Notes:**
The portion of my work that I’ve shown you today was predominately focused on the physics of AFM in BFO. 

Though this is interesting on its own, it is also useful for understanding two types of coupling. I already spoke a little bit about magnetoelectric coupling.

Another popular type of coupling is called exchange bias, which pins ferromagnetic directions with antiferromagnetic thin films. This is used in modern memory devices. Exchange bias is still not totally understood and the extra electric order parameter in BFO gives new control and insight into this coupling. And, since BFO is both an antiferromagnet and a ferroelectric, we might have the possibility to combine all of these directions by electrically controlling ferromagnetism... even at room temperature!  

##  Many Applications

**AFM/FE**

**FM**

**Physics of AFM**
**(Optical Studies)**

**Exchange Bias**
**FM/AFM**

**MagnetoelectricCoupling**
**AFM/FE**

- Elke Arenholz
- Cinthia Piamonteze
- Joe Orienstein & Group
- Andrew Doran
- Andreas Scholl

- Aranta Fraile
- Lane Martin
- Eddie Chu
- Martin Gajek
- Jan Seidel
- Ramesh

- Tong Zhao
- Kilho Lee
- Florin Zavaliche

- S.Y. Yang
- Chan-Ho Yang

**Notes:**
I have been collaborating with a large group of people to realize the possibility of electrical control. But, this is just one of many exciting possibilities for multifunctional systems, but in order to understand how to best use BFO or other magnetoelectric materials in these multifunctional devices, it’s vital that we understand this AFM in detail. This is my part in this much larger picture.  

## Thick BiFeO3

**XMLD**

**At least 3 colors**
**No unique axis for each polarization direction**
**Whole plane?**
**Why different?  Epitaxial strain?**
- Migloiri, Millis, JAP,** 83** (3), 1588

**Black**

**White**

**Grey**

**Another Color?**

**5 ********m**

- 15	Micky Barry Holcomb

**Notes:**
My working hypothesis involves strain. The degeneracy of the magnetic plane occurs in rhombohedral BFO (R3c). This degeneracy is lifted if BFO becomes monoclinic, even slightly, as would occur due to strains caused by the substrate. The strain squeezes the 111 plane horizontally and allows it to stretch vertically. Even our 200nm thick films show reciprocal space mapping evidence of a large difference in the relaxation in-plane from thicker, more bulk-like film. 
Fix

So what? AFM in BFO comes from superexchange mediated through the Fe-O-Fe bonds. The exchange constant is thought to depend strongly on distance, and therefore these small changes might have a drastic effect.

(This choice of a preferred axis is not unheard of. Contraction of AFM NiO which has been used to study exchange bias, also picks an axis, in fact the same one.)

What happens if we relax the strain? Here is a PEEM image of a very thick sample, 1.5 micron. The ferroelectric domains are about 2.5 times larger than for thinner films. Not only do we see at least three colors, but it looks like we can make out tiny domains. This data is consistent with the easy plane/tiny domains case. What is clear is that we don’t see only two colors as we should if we had an easy axis. Grazing incidence studies also show clearly different behavior for the thicker films. This thick film data is a strong indication that strain plays an important role in the magnetic behavior. 

## Temperature Dependent PEEM

***Temperature Dependent PEEM***

- T. Zhao, M. Barry et al., *Nat Mat* **5**, 823 (2006)

- 8	Micky Barry Holcomb

**We get roughly equal contributions from both magnetic and ferroelectric prop.**
**Can decouple the contributions with temperature dependence**
**Angle dep. also allows separation and can determine magnetic behavior.**

**Notes:**
Recall that I told you that for a pure AFM, the contrast should disappear above the Neel temperature. Actually is goes at the square of the magnetic moment, shown here. 
And if our signal was only from polarization, since the polarization does not change much over this temperature range, as observed by the Bi displacement [diffraction/absorption synchrotron scattering, Tong], we expect very little change with temperature. What do we see?

Well, kind of both. [Here are the results of nearly a year’s worth of data. We plot the contrast for five similar BFO samples to show reproducibility.] There is a strong temperature dependence up until the Neel temperature, but then it mostly flattens out at nearly half of the room temperature value. So, the temperature dependence reveals that our linear dichroism comes not only from magnetic contrast. But, we also see a ferroelectric contribution, which on its own is a exciting result. And, we can use temperature dependence to decouple the two effects. 

Another method for decoupling the two effects is angle dependence. It’s a little complicated, but it’s extremely powerful because it also gives information about the magnetic behavior. But, in order to determine what angle dependence to expect, we need a better idea of the possible magnetic behaviors.

## Angle Dependence of AFM

**Pure AFM XMLD**
***I= (3 cos******2****** ******θ******M****** -1)<M******2******> ***
**	****+**background
_**At given temperature**_***:***
***I=p***** cos****2**** ********P ****+ *****q***** cos****2**** ********M ****+**background, *******p*********+*********q*********=1**
- *p*=percentage polarization contribution
*p* and *q* can be positive or negative cos2x+sin2x=1

- Alders, PRB, **57** 11 623

- E

- L

**X-rays**

- 10	Micky Barry Holcomb

**Notes:**
Alders first showed that the sample rotation angle dependence of the intensity at the absorption edge of an AFM depends on a cosine squared function. Cosine theta is just the projection of L onto the electric field direction of the incident x-rays.

There currently is no equation for dichroism of a multiferroic because I’m one of the first people to look at a multiferroic with PEEM. The ferroelectric contribution is not well understood yet. But, based on expectations and preliminary measurements, it seems to follow the simplest picture: behaving just like the magnetism. So, I used an equation with two terms, one for magnetism and one for ferroelectricity. (Since the rest of the measurements I will show you today are done at a given temperature, I will lump all other constants into the background.)

The absolute value of p represents the percentage of the dichroism that comes from the polarization. Though I have considered many p values, the following analysis has been done with p=55%, which agrees with the temperature dependence I presented before. (However, the conclusions do not change even with large changes in this p value. (check graphs) Since p and q can be either positive or negative, the angle dependence may appear more like sine squared than cosine squared because of this identity. This depends on the symmetry of the crystal. And, determining which is very tricky both experimentally and theoretically, so for now we need to consider both.)

## Expected signal for XMLD

***Expected signal for XMLD***

- xrays

- 1,3

- 2,4

**e****-**

****

- p

- s

***I=p***** cos****2**** ********P**** + *****q***** cos****2**** ********M**

- 11	Micky Barry Holcomb

**1**

**2**

**3**

**4**

**Notes:**
Fix

So experimentally, linearly polarized x-rays with a horizontal E vector give the in plane projection of the contributing vectors. Thus, for a sample with four variants as shown here we should see two colors for two of the magnetic cases we discussed in the last slide, one when the polarization projection is parallel to the E vector and the other when it is perpendicular. And according to the formulas before, the angle dependence of this goes as cosine squared (or sine squared) with the angle. High intensities mean the domains should appear bright in the PEEM images. 

(Since circular light is a superposition of horizontal and vertical, right) circularly polarized light is part this horizontal signal we considered just now and part (click) the projection onto the vertical when we come in from this direction. The bright red vectors have the same out of plane component for this angle, so they have the same intensity in circular images. But the other two split. 

Let us look at the sample rotation angle dependence of circular intensity for different magnetic behaviors.

## Expected magnetic behavior

**P**

**P**

**Ferroelectric domain**

**Easy Magnetic Axis**

**Look similar in XMLD images**

**AFM domain**

**Might there be a preferred axis?**

- 9	Micky Barry Holcomb

**Notes:**
Well first of all,what antiferromagnetic nature are we expecting for BFO? Theory predicts a degenerate magnetic plane for bulk. Does this happen in thin films as well? This could manifest itself in one of two manners. First, the domains could be tiny (much less than our resolution of 50nm), and be randomly distributed over the appropriate 111 plane for that polarization domain. Second, the domains could be the size of the FE domain and randomly pick from the six possible axes for each polarization. There would be lots of these large domains so we would see all of these axes in the plane. Or maybe it doesn’t even limit itself to this theory-predicted plane. In each of these cases, there should be a distribution over myriad magnetic directions. For large domains, we would be able to make out many colors in the XMLD images because of all of the magnetic directions. For tiny domains, however, there should be an averaging over the plane. There is another magnetic possibility; that instead of the polarization picking randomly, it picks only one of these axes. Now averaging and one magnetic axis should look very similar using linearly polarized x-rays.

Once we have an expected magnetic behavior, how do we determine its expected angle dependence?

## FM-AFM coupling/switching with BFO

**OOP PFM**

**In plane PFM**

- 10 

**20x20 ******

**10x10 ******

- 18	Micky Barry Holcomb

**Notes:**
Here, we poled BFO 001 with the PFM once upward and then again downward in the center obtaining these in plane and out of plane polarization images. We know the magnetism of BFO follows these domains. We grew CoFe on top, and then studied the sample with PEEM. We observe that the Co magnetic domains match quite nicely with the BFO ferroelectric domains of the first poled box. Both inside and outside of this box, we can not see the stripes. Note that the ferroelectric domains are much larger in the first poled box. So, is this a resolution problem or does the Co not couple to the smaller domains. Let look at some more images. 

CoFe magnetic domains couple to double poling patterns
Due to geometry, stripes not as clear for some domain directions.
Possibility of electrical control of CoFe at room temperature
Lack of resolution or coupling when BFO FE domains get smaller?

Plans in the works to do this poling after the growth of the FM, but as you may realize, this is a bit trickier. 

## Thank you!

- _Publications_:
- T. Zhao, A. Scholl, F. Zavaliche, K. Lee, **M. Barry**, A. Doran, M.P. Cruz, Y.H. Chu, C. Ederer, N.A. Spaldin, R.R. Das, D.M. Kim, S. H. Baek, C.B. Eom, R. Ramesh, “Electrical control of antiferromagnetic domains inmultiferroic BiFeO3 films at room temperature,” Nature Materials 5 823 (Oct 2006).
- T. Zhao, A. Scholl, F. Zavaliche, H. Zheng, **M. Barry**, A. Doran, K. Lee, M.P. Cruz, R. Ramesh, “Nanoscale x-ray magnetic circular dichroism probing of electric-field-induced magnetic switching in multiferroic nanostructures,” APL 90, 123104 (2007).
- R. Ramesh, N. Spaldin, **M. Barry** ... “Thin film multiferroics: Progress and prospects”
**M. Barry**, ...”First observation of Easy Magnetic Axes in BiFeO3 Thin Films,” Nature Physics, near submission
- L.W. Martin, Y.H. Chu, **M. Barry**, S.J. Han, Q. Zhan, P.L. Yang, K. Lee, A. Scholl, S.X. Wang, Z.Q. Qiu, R. Ramesh, Science, near submission
- K. Lee, **M. Barry**, “Magnetic Anisotropy and Exchange Coupling in Multiferroic BiFeO3 Thin Films,” PRL, near submission

- 19	Micky Barry Holcomb

**Notes:**
Thank you for your time.

## Magnetoelectric Multiferroics Equations

- Contributions to the ME effect are obtained from a material’s free energy
- Differentiations lead to both polarization:
- and to magnetization:

***Magnetoelectric ******Multiferroics****** Equations***

- Fiebig, J. Phys. D Appl Phys. 38 (2005) R1123-R152

- 1	Micky Barry Holcomb

**Notes:**
What is magnetoelectricity? It is the coupling between the electric and magnetic fields in matter. We expect it in all materials, but it is typically very small. The contributions to the ME effect are determined by the free energy of a material. Differentitiations of the free energy give both the polarization and magnetization, where Ps and Ms are the spontaneous polarization and magnetizations. You’ll notice this shared term here that is the linear magnetoelectric tensor. There are higher order terms as well, but they are generally much smaller. 

What are some of these materials with a large ME effect?

[According to BFO’s symmetry, can’t have linear effect, quadratic due to symmetry.]
[Insert more here as backup from Fiebig paper]

## Imaging Ferroelectric domains in BiFeO3 

***Imaging Ferroelectric domains in BiFeO******3 ***
***Piezoelectric Force Microscopy***

| OOP 
Contrast | IP Contrast |  | Possible Orientations |
| --- | --- | --- | --- |
|  | [010] | [0-10] |  |
| Dark (up) | Dark (left) | Light (right) | [-111], [-1-11] |
| Light (down) | Light (right) | Dark (left) | [1-1-1], [11-1] |

**White**
**Black**
**Brown**

- 5	Micky Barry Holcomb

**Notes:**
Piezoelectric force microscopy measures both the out of plane force and the torque of the PFM tip caused by the polarization of the sample when the tip has an oscillating voltage applied to it. So, the out of plane mode will tell us whether we have one of the four up or down body diagonal directions. And the in plane mode distinguishes between these four. From these two modes, we can distinguish which polarization direction we have. Here we see that when our PFM tip comes in from the 110 direction, we see black, white (check) and brown depending on whether our tip is torqued left, right or not. Now how would one look at the antiferromagnetism?

[Locking in tip oscillation to deformation of crystal.]
[why domains? Not much anisotropy]

## Electrical Control

**Bi**
**Fe**
**O**

- * F. Kubel, H. Schmid, *Acta Cryst.* **B46**, 698 (1990)

**8 possible polarization variants **
**3 types (180°, 71° and 109°)** **of ferroelectric polarization switching**

- T. Zhao, M. Barry et al., *Nat Mat* **5**, 823 (2006)

**BiFeO****3**

**SrRuO****3**

**SrTiO****3**

- 1	Micky Barry Holcomb

**Notes:**
We see here BFO polarized in a particular direction. We can apply a vertical electric field using our PFM, which works by applying a DC voltage [around 12V] between the tip of the PFM and a bottom electrode of Strontium Ruth. When we do this, the polarization can choose to go in one of four directions. A change of 180 degrees requires no magnetic switching of the perpendicular plane. However, any other change does. This is how one could electrically control the magnetism. Now how would one look at this antiferromagnetism?

## Magnetoelectric Multiferroics Materials

**Cr****2****O****3**** **
- Prototypical ME, first discovered
***P*** and ***M*** are field induced
- αZZ = 4.13 ps m-1 @ ***E*** = 106 V
- Corresponds to the magnetization observed after reversal of only 5 of every  106 spins in the AFM lattice!!
**Other ME Materials**
- Ti2O3
- GaFeO3
- Boracites and Phosphates
- PbFe0.5Nb0.5O3
- Garnet films
- ~80 total materials have ME effects

**Top Performers **
- LiCoPO4 (αYX = 30.6 ps m-1)
- Y3Fe5O12 films (α ~ 30 ps m-1)
- TbPO4 (αAA = 36.7 ps m-1)
- 	Principal weakness of ME Effect  Perturbative nature of the microscopic mechanisms driving ME behavior
- and ME response is limited by
***α******ij******2****** < ******χ******ii******e****** ******χ******jj******m***
- Where χiie and χjjm are the magnetic susceptibilities

- _[Back](slide3.xml)_

## Devices

-  Permanent Magnets
-  Magnetic recording media or domain stabilizers in recording heads based on anisotropic MR
-  GMR systems--reduction of the saturation fields to observe GMR

## Total Electron Yield

-  X-rays are absorbed by exciting a core electron
-  Recombination of the core hole leads to emission of an Auger electron
- As they leave the sample, the primary Auger electrons inelastically scatter creating secondary electrons which dominate the total electron yield intensity.
-  The sampling depth is typically a few nanometers.

- 1	Micky Barry Holcomb

**Notes:**
In our total electron yield detection, instead of directly measuring the absorbed x-ray intensity, the photoelectrons that are created by the absorbed x-rays are observed. Absorption takes place when the core electrons are excited to empty states above the Fermi level. These excited photoelectrons recombine with the core states by emitting an Auger electron. Following the Auger electron emission, the photoelectron and Auger electron lose energy through inelastic scattering due to their small mean free path. A large number of secondary electrons are created for each photoelectron; these secondary electrons dominate the TEY intensity. Electrons formed deep in the sample lose a lot of energy from many scattering events and will not contribute to the TEY. Thus, the sampling depth for PEEM is only a few nanometers. 

[In short, the incident photon creates a photoelectron which recombines to make an Auger electron, which on their journey to the surface, scatter a bunch of secondary electrons which we measure. Energy is lost in this scattering, so we only sample the top few nanometers. ]
[Auger excitation conserve orbital momentum? There are some spatial and QM things to consider. Wavefunctions must overlap.]

## Why does XMCD tell us about magnetism? 

**Photon**
****** **
**Photoelectron**
****
**Spin**
****
***d *****holes**

**Absorption Intensity ******** angle between *****E***** and *****FM ********** *****number of *****d***** holes with a certain spin**

**Transfer of angular momentum**

**3*****d***

**2*****p*****3/2**

**2*****p*****1/2**

**Back**

**Notes:**
In the last slide, I explained some about why we see dichroism in XMLD. XMCD is a little easier to understand the details behind it and it’s extremely similar to linear dichroism, so let’s consider it. 

[Magnetic properties of transition metal elements are largely determined by the 3d valence electrons. Since x-ray absorption spectra are governed by dipole selection rules, L-edge absorption studies (2p to 3d transitions) best determine the d-shell properties. The two spectra peaks originate from the spin orbit interaction of the 2p core shell, and their total intensity is proportional to the number of empty 3d valence states. Oxides (like what we are studying) exhibit considerable fine structure in their spectra, called multiplet structure. The reason for this is that the empty oxide states are more localized than metal states and their energies are determined by crystal field and multiplet effects. Origins of multiplet effects are the spin and orbital momentum coupling of different 3d valence holes or electrons in the electronic ground state and the coupled states formed after x-ray absorption between the 3d valence holes and the 2p core hole. ]

## Two Magnetic Axes

**[110]**

**[110]**

**-**

**Notes:**
Let’s take a look at these axes. There are two for BFO 001, one for the four polariation directions for the yellow plane and another for the four on the red plane. Thus, we should only change the magnetic axis when the polarization goes between these two planes. We should keep this in mind for any devices we might want to make out of this.

## The Linear Magnetoelectric Effect

- Polarization and magnetization of a medium:

_*with:*_

- Relativistic equivalence of electric and magnetic fields requires	"**magneto-electric**" cross-correlation (~ ) in matter:

- Covariant relativistic formulation:

**Back**

## Future Work

**Physics of AFM**
**(Optical Studies)**

**Focus 1:**
**Thickness Dependence**

**Focus 2:**
**Orientation Dependence**

- 1	Micky Barry Holcomb

**Notes:**
The portion of my work that I’ve shown you today was predominately focused on the physics of AFM in BFO. 
I would like to understand both the mechanism that chooses the observed easy axis and the robustness of this axis. There are three ways I would like further probe this, thickness, substrate and orientation dependence. I showed you a thick sample before. I would like to better understand the magnetism involved in this case and how it differs from the thin films. Also, what happens when we go to really thin films? Say, 20nm or even 2nm. Is BFO even AFMic at a few monolayers? We can learn more about both thick and thin a full investigation of the angle dependence, much like I already discussed. [Grazing incidence spectroscopy is also clearly important.] 

I’m also interested in looking at different orientations of BFO. (next slide)

Oxy edge, XAFES, Ext Fine Structure

## OP

**OP**

**1.5μm**

****

**(001)**

**P****1****-**

**(110)**
**plane**

**P****1**** ****-**

**P****2**** ****-**

**[1-10]**

**[001]**

**(111)**
**plane**

**P ****-**

**1.5μm**

**(111)**

**(110)**

**IP**

**IP**

**IP**

***Piezoforce Microscopy of  FE Domain Structure***

- 1	Micky Barry Holcomb

**Notes:**
Here are shown the in-plane polarization domains of three orientations of BFO, 001, 111, and 110 and their preferred polarization directions.  A number of measurements have been done on BFO 110, and so far things seem consistent with the 110 easy axis, which is shared between the two polarization directions so it wouldn’t switch with poling unlike BFO 001. How about the case of BFO 111, where only one polarization direction is present and can be switched by 180 degrees? Do we still retain the easy axis even though the substrate-induced strain for this orientation should be symmetrical over the 111 plane? 

Similar modeling a clever choice of experimental geometry while varying temperature will allow us antiferromagnetic determination of directions in these orientations where strain pushes on the 111 plane in different ways. 
In the end, I plan to have a clear understanding of how strain or some yet-unidentified factor controls the magnetism of BFO`? 

## Future Work

**Physics of AFM**
**(Optical Studies)**

**MagnetoelectricCoupling**
**AFM/FE**

**Focus 1:**
**Thickness Dependence**

**Focus 2:**
**Orientation Dependence**

- 1	Micky Barry Holcomb

**Notes:**
Though the AFM of BFO interesting on its own, it is also useful for understanding two types of coupling. I already spoke a bit about magnetoelectric coupling, but I haven’t showed you any proof of its existence in BFO so far. 

[Oxy edge, XAFES, Ext Fine Structure]

## Electrical Control of AFM in BFO

***E***

***E***

**AFM is controlled by FE!**

**OP PFM**

**Matching domains**
**Same temperature dependence of both as grown and poled areas**

- T. Zhao, M. Barry et al., *Nat Mat* **5**, 823 (2006)

- 1	Micky Barry Holcomb

**Notes:**
We’ve established now that our PFM and PEEM images show the same domains as grown. What happens if we use our PFM to switch the polarization domains out of plane, as shown by the OOP PFM like I discussed before. The in plane domains of the polarization change, as do the magnetic domains. This matching and the temperature dependence both before and after poling tell us that our AFMism does in fact couple. Spin lattice coupling and dielectric anomalies around the Neel temperature also suggest this coupling. These measurements lay the groundwork for studying magnetoelectric coupling.