# Password similarity using probabilistic data structures

Davide Berardi, Franco Callegati, Andrea Melis, Marco Prandini  Dipartimento
di Informatica Scienza e Ingegneria (DISI)
Università di Bologna
Bologna, Italy
{davide.berardi6, franco.callegati, a.melis<EMAIL_ADDRESS>
###### Abstract

Passwords should be easy to remember, yet expiration policies mandate their
frequent change. Caught in the crossfire between these conflicting
requirements, users often adopt creative methods to perform slight variations
over time. While easily fooling the most basic checks for similarity, these
schemes lead to a substantial decrease in actual security, because leaked
passwords, albeit expired, can be effectively exploited as seeds for crackers.
This work describes an approach based on Bloom filters to detect password
similarity, which can be used to discourage password reuse habits. The
proposed scheme intrinsically obfuscates the stored passwords to protect them
in case of database leaks, and can be tuned to be resistant to common
cryptanalytic techniques, making it suitable for usage on exposed systems.

###### Index Terms:

password, Bloom filters, hash functions, text analysis

##  1 Introduction

Text-based passwords are still the most common way to authenticate users
against services[14]. According to a typical classification for authorization
mechanisms, they fall in the “what you know” category. The other categories,
“what you are” and “what you have”, are most commonly used only as a second
factor for the so-called _MFA_ multiple factor authentication schemes[13]. An
example of MFA is a one time password available only on a personal device
(e.g. smartphone) at each login attempt into a critical service. Passwords
should be easy to remember, but hard to guess. In a long game of cops and
robbers, users try to base them on dictionary words[16], and system
administrators write policies to block these attempts. As a common reaction,
users make simple variations to hide the base, easy-to-remember common word.
This makes the password harder to remember, so users try to stick to the same
one forever, but system administrators add expiration times to their policies.
Users then adapt by making the smallest possible change at each password
update. This is still an insecure behavior, making life much easier to
malicious actors trying to guess current passwords, because old ones are often
available through leaked databases. The countermeasure to discourage this
behaviour is to prevent choosing a password too similar to the previous
one(s). The problem with the simplest approaches to similarity estimation —
for example based on the Levenshtein distance[9] between two clear-text
strings — is that passwords are sensitive and personal data. Storing them to
enable similarity checks exposes users to unacceptable risks of breaches that
may result in unauthorized access to some of their accounts. To overcome this
problem, in this paper we propose a system to calculate the similarity of
passwords over obfuscated data, based on Bloom filters. The tuning of the
filter is thoroughly analyzed to determine the values of parameters that
ensure password secrecy, yet allow achieving an effective detection of
similarity. The scheme natively allows the integration of a cryptographic
access control method, which will be investigated in a future work. The paper
is structured in the following way: section 2 discusses a list of previous
works and state-of-the-art tools that employ similar techniques to evaluate
similarity between data. The details of password similarity, design of our
system and a possible attack on this kind of data analyzers are introduced in
section 3. Our scheme was implemented in C language for the Linux operating
system, and a performance analysis is presented in section 4. We illustrate
some application scenarios and propose future improvements for our work in
section 5.

##  2 State of the art

The foundations for this work can be traced back to Schnell’s (et alii) paper
[15], which describes a method for querying private data over a Bloom filter
structure. Another work presented in [1] describes the application of privacy
methods like differential privacy to probabilistic data structures such as
Bloom filters. While the described approach is vulnerable to an attack called
the “Profile Reconstruction Attack”, this is due to use of differential
privacy methods (which are not exploited in our work) and not to the filter
itself. Anonymized datasets, using techniques such as differential privacy,
purposely introduces errors and noise in the data in order to hide the
presence of specific information or to ensure that links between users and his
correspondant data cannot be established. This controlled errors are
compensated in large dataset: the errors do not effect the quality of such
evaluations. In our use cases, users - even if forced to change password
regularly - can’t generate a password dataset big enough to compensate the
introduced noise. That is, anonimization techniques can affect the quality of
password similarity queries, with several false positives compared to the
proposed bloom filter approach. We still did not provide an experimental
analysis of this statement which is planned to be implemented in future works.
RAPPOR[6] is a system used by Google to get data from the Chrome browser. The
data is hashed in a Bloom filter, anonymized by introducing a perturbation on
the values, and then retrieved and reconstructed at server side. This approach
is similar to the one we propose in this work, but it explicitly does not
apply to passwords, to avoid sending potentially sensitive data from the
device to a cloud system. To the best of our knowledge, in the literature
there is not a use case for a password scenario. For this reason the aim of
this paper is to study it, illustrate the advantages it brings, and discuss
the security-related issues that it introduces.

##  3 Password similarity

It is widely known that password reuse is a common behaviour which can turn
into a threat if passwords get leaked online[8]. Password leaks are a common
form of information leak that happens
regularly111https://us.norton.com/internetsecurity-emerging-threats-2019-data-
breaches.html. A similar threat appears when a user is forced to a password
change and (especially for corporate passwords that must be changed quite
often), he can insert a different password with little variations from the
last one (e.g.  password2020 changing password from  password2019). This can
make brute force attacks very effective, since the new password is easily
computed by a limited number of mutations starting from a dictionary of leaked
ones. We can describe the password mutation as a perturbation of the password
with slight variants. Tools such as password crackers or word-lists generators
like cupp222A password generator based on personal and open source data:
https://github.com/Mebus/cupp or johntheripper333Johtheripper is a common
password cracker and generator https://www.openwall.com/john/ implements
various methods for password generation, the passwords can also be generated
by neural-based techniques such as adversarial generation[10]. With these
approaches, choosing a similar password is almost as insecure as choosing a
dictionary password[17]. For the purpose of this work, password similarity can
be informally defined as the structural similarity of the text composing two
password being compared, i.e. it has nothing to do with the possible
underlying meaning of the string. This definition of password similarity can
be used to guarantee that a user is not reciclying what, in terms of actual
entropy, can be considered the same password every time. Common methods to
guide users to choose “robust” passwords are focused on avoiding the direct
use of dictionary words. These methods have two shortcomings: users resource
to variations that are easily discovered by mutation by the aforementioned
tools, and there is no detection of password similarity when a password change
is mandated. A straightforward method to detect password similarity over a
meaningful time span would require saving old passwords in clear-text into a
database, which is obviously a despicable approach. We propose a solution
based on Bloom filters that overcomes this shortcoming.

###  3.1 Bloom filters for text similarity

A Bloom filter is a probabilistic data structure which can be used to cache
data and speed up operations such as lookup in databases[2, 11]. It is
composed by:

  * •

a bucket which can be an array of bits initially set to the false value ($0$);

  * •

a set of hash functions which will be used to insert and check values.

An insertion operation ($Insert(\beta,s)$) of a value in a Bloom filter is
performed according to the following steps:

  * •

the value that must be inserted into the bucket is hashed using the set of
hash functions; The hash functions output must be re-mapped to provide indexes
in the co-domain of cardinality $\kappa$.

  * •

every bucket slot indexed by the keys got using the hash functions is set to
the true value ($1$).

This operation therefore insert the hashed value into the filter, setting the
correspondent hash values to the true value. This is described in figure 1
which pictures an insertion of the strings $password1234$ and $password123!$.

000100100000101000password1234password123! Figure 1: Insertion procedure with
two strings. The strings $password1234$ and $password123!$ are hashed
independently. This Insertion procedure process the passwords as single items,
leading to different hashed values.

The verification process of the value presence in the filter
($Check(\beta,s)\to Boolean$) is analogous to the insertion case:

  * •

The element which is checked is hashed against all the functions to get a list
of indexes;

  * •

If any index points to a false value, then the element is not present in the
filter for sure. The Bloom filter never exhibits false negatives.

  * •

Otherwise the value can be present in the filter, but due to the collision
possibility of the hash functions, the result can be a false positive.

This procedure is described in figure 2.

000001100010101000password1234 $\to$ Maybe presenthelloworld $\to$ Not Present
Figure 2: Check procedure with two strings. The strings $password1234$ and
$helloworld$ are hashed independently and the resultant indexes from the hashe
functions are checked in the bucket. If the lookup lead to a $0$ value, the
string is not present in the filter. Otherwise, it can be a value that is
present in the filter or can be a collision (a false positive).

Bloom filters can be used for text similarity using an n-gram approach. This
techniques divides the string in n-grams and hashes every resultant n-gram
with the hash functions present in the set:

011101100111101001$pa$$ss$$wo$$rd$$12$$34$password1234$pa$$ss$$wo$$rd$$12$$3!$password123!
Figure 3: n-gram insertion procedure with two strings. The strings are divided
into $n-grams$ (in this case bi-grams) and hashed using an $Insert$ operation
for every $n-gram$.

The hashing procedure to enable the measure of distance is presented in figure
3. By extending the check procedure to get the number of n-grams which are the
same in the two strings, independently of the order, the similarity of the two
sets can be calculated by using various distance definitions. The similarity
distance of two Bloom filters is commonly expressed using the Jaccard
coefficient[3] and is defined as:

$\delta(\beta_{1},\beta_{2})=\dfrac{2\gamma_{\beta_{1},\beta_{2}}}{k_{\beta_{1}}+k_{\beta_{2}}}$
(1)

With $\gamma_{\beta_{1},\beta_{2}}$ as the common number of true values in the
sets of the two Bloom filters $\beta_{1}$ and $\beta_{2}$. $k_{\beta_{1}}$ and
$k_{\beta_{2}}$ are the number of true values of, respectively, the
$\beta_{1}$ filter and $\beta_{2}$ filter. Therefore the relevant operations
on a filter to measure similarity are:

  * •

$Create(\Gamma,\kappa)\to\beta$ which generate a Bloom filter $\beta$ using
the hash functions present in the set $\Gamma$ with a bucket of size $\kappa$.

  * •

$Insert(\beta,s)$ which insert the value $s$ in the Bloom filter.

  * •

$Check(\beta,s)\to Boolean$ which check if the value $s$ is not present in the
filter or if it collides with a present value.

  * •

$QInsert(\beta,s,\nu)$ that insert the string $s$ splitting it in $\nu$-grams.

  * •

$Distance(\beta_{1},\beta_{2})\to Real$ that returns the distance between two
Bloom filters. To be comparable, two Bloom filters must have the same bucket
size $\kappa$, and need to use the same set of hash functions $\Gamma$.

The effectiveness of the filter is strictly tied to the choice of the hash
function set $\Gamma$ and the size of the bucket $\kappa$. The tuning of these
parameters is essential to achieve a satisfactory trade-off between the
utility of the query and the number of false positives. A wrong sizing of
buckets or a choice of low-randomness hash functions can easily lead to a
vulnerable filter (as detailed in section 3.4) or to an unstable filter that
leads to too many false positives.

###  3.2 Privacy guarantees

To size the filter there are some criteria which can be derived from the
following formulas:

$fpp=\left(1-\left(1-\dfrac{1}{m}\right)^{kn}\right)^{k}$ (2)

Where $fpp$ is the false positive probability of the filter. This can be
calculated a-priori from the variables $m$, $k$ and $n$, defined as:

  * •

$m$, the cardinality of the set on which the filter is built;

  * •

$k$, the number of different hash functions that are used to hash values into
the filter;

  * •

$n$, the number of elements which will be inserted into the filter.

From this formula we can derive the optimal values for the filter size and the
number of hash functions to use for a specific number of elements that will be
inserted in the filter. The optimal value for $m$ can be calculated as:

$m^{\prime}=\left\lceil{-\dfrac{n\ln fpp}{(ln2)^{2}}}\right\rceil$ (3)

The optimal number of different hash functions is derived from the optimal
size of the Bloom filter internal set:

$k^{\prime}=\left\lceil{\dfrac{m^{\prime}}{n}\ln 2}\right\rceil$ (4)

with $m^{\prime}$ being the optimal value for $m$ calculated as in 3. The
rationale behind this sizing formula comes from the observation that as the
size of buckets increases, the probability of collisions decreases. Using this
approach, a Bloom filter with a controllable number of false positives can be
tuned to fit any specific scenario. Conversely, as it is useful for the
proposed application in order to enhance password confidentiality, a Bloom
filter can be designed in such a way to have a big number of false positives,
thus obfuscating data by forcing collisions. Password confidentiality could be
protected also by adopting privacy-preserving approaches, such as
$\delta$-presence[12] or differential privacy[5], exist. These approaches take
in consideration the amount of data stored into a database, or the filter in
this case, and try to anonymize the data between many false positives. In this
case the approach is directly applicable to the filter which can gain a lot of
advantages in terms of privacy from this approach.

###  3.3 Analysis of the hash function family

Another key component of the filter which impacts on confidentiality is the
distribution of the values returned by the chosen hash function family. In
this kind of probabilistic data structures, it may be necessary to deploy a
huge number of hash functions. Using a different algorithm for every index can
be unfeasible, and in any case a large variability within the hash function
set hinders a precise analysis of the randomness of the generator. To overcome
these problems, the hash function set can be generated by using the well-known
salt approach, as described in figure 4. When a value has to be inserted, many
random numbers (salts) are generated. Prepending these numbers to the value,
and using a fixed hash function, the effect is analogue to having adopted
different, random hash functions. In our implementation we used $MD5$ as the
base hash function. The salts are saved in the same location as the filter
set, to allow reloading the state in subsequent invocations of the algorithm.
We acknowledge that this trivial solution is vulnerable to attacks if the file
is saved in clear-text form, like the one described in section 3.4.

Saving salts in a more secure way seems not too challenging, and is the
subject of current and future investigation aimed at making the filter immune
to this kind of attacks. For example, the salt can be generated using a cipher
like AES using an user provided key and a fixed payload similarly to AES-CTR
mode, extending the functions applicable on the filter with a function
$GenerateHashes(key)\to\Gamma$ which generate the set of hash functions
$\Gamma$ starting from the key $key$. Using this technique, the filter set can
be saved without specific protections, since it can be verified only using the
chosen secret key. An in-depth analysis of the security of the encryption
scheme, particularly concerning the peculiarity of having very short payloads
due to the division in n-grams, will be the focus of ongoing research work.
These approaches to the generation of hash functions are described in figure
4. In the first hash set we can see that $h1$ and $h2$ are two functions
generated with a random padding applied to the $MD5$ hash function. In this
scenario we suppose to have a $Random(n)$ function that can generate a random
string of length $n$. This generation, when re-applied will lead to a totally
different set of hash functions, making the distance function inapplicable.
That is the concept of the construction of $h1^{\prime}$ and $h2^{\prime}$.
These functions can return different results from the functions $h1$ and $h2$
described before. Reusing the same value for the salt applied to the functions
will lead to the same set of results, making the distance calculation
possible. This is the concept of the third figure, which describes how,
applying a fixed salt to a symmetric cipher using a secret key $k$ the filter
will lead to the same set of results.

$h1(s)=MD5(Random(10)+s)$$h2(s)=MD5(Random(10)+s)$$Insert(\beta,^{\prime}password1234^{\prime})\to\\{6,15\\}$000000100000001000

$h1^{\prime}(s)=MD5(Random(10)+s)$$h2^{\prime}(s)=MD5(Random(10)+s)$$Insert(\beta^{\prime},password1234)\to\\{9,14\\}$000000001000010000

$h1^{\prime\prime}(s)=MD5(fixedsalt_{1}+s)$$h2^{\prime\prime}(s)=MD5(fixedsalt_{2}+s)$$Insert(\beta^{\prime\prime},password1234)\to\\{3,11\\}$001000000010000000

$\widehat{h1}(s)=MD5(AES(k,fixedsalt_{1}),s)$$\widehat{h2}(s)=MD5(AES(k,fixedsalt_{2}),s)$$Insert(\widehat{\beta},password1234)\to\\{5,9\\}$000010001000000000

Figure 4: Different hash functions generation. These functions will lead to
different use-cases. In the first two figures we have a fully random
generation which leads to different cases every time as we cannot predict the
output got from $Random$ function. The fourth case employes a cryptographic
function and a set of fixed strings ($fixedsalt_{n}$) to generate the same set
of hash function based on a secret key $k$.

###  3.4 Anagram attack

The system as described in the previous sections is vulnerable to an attack
which exploits the order of the discovered n-grams. This attack aims to
reconstruct the password as the anagram of the various n-grams. The attack is
composed of four steps:

  1. 1.

Generate all the hashes for a specific n-gram;

  2. 2.

Hash the n-grams into a Bloom filter;

  3. 3.

Analyze the Bloom filter and get the position of bits set to the true value;

  4. 4.

Compose the various n-grams to create a password.

This scenario can be disruptive and can lead to the full disclosure of hashed
password in no time. Also, this kind of attack can be enhanced with the help
of a word dictionary similar to the one used in classical password attacks:
the search tree can be pruned by excluding the words which do not contain the
n-gram. For instance, let us imagine that a user inserts the password
“password!!” in the filter with $\nu=2$. Accordingly, the attacker will
generate all the possible bi-grams. This, using an alphabet $\Delta$ will
result in a generation of $|\Delta|^{2}$ bi-grams which, for the ASCII case,
is $(127-32)^{2}=9025$ bi-grams, an operation which requires at most a couple
of milliseconds on any modern CPU. After this step, the attacker will hash the
bi-grams inserting them into the filter, which requires $\Theta(n)$ insertions
with $n$ as the number of bi-grams. Subsequently, the attacker can create all
the possible combinations in the search space generated by the pruned alphabet
of bi-grams $\Delta_{II}$. The research can be conducted by using an
incremental number of repetitions. Therefore, the number of combinations which
can be generated using the corresponding Bloom filter are:

${\Delta_{\nu}\choose\dfrac{n}{\nu}}$ (5)

with $n$ as the length of the searched string and $\nu$ the grade of the
n-grams. In the case of a common password of $8$ ASCII characters and a Bloom
filter constructed with bi-grams the formula will result to:

${9025\choose\dfrac{8}{2}}\approx 2.76\times 10^{14}$ (6)

combinations. If we consider the worst case with repetitions the formula
become

${\Delta_{\nu}+\dfrac{n}{\nu}-1\choose\dfrac{n}{\nu}}$ (7)

which, in this example, will result to ${9025+4-1\choose 4}$ which is almost
the same as the non-repetition case. Passwords can be longer than $8$ char to
provide enough security against brute-force or dictionary attacks. For a
password varying from $n$ characters to $N$ the number of combinations are:

$\sum^{N}_{i=n}{\Delta_{\nu}+\dfrac{i}{\nu}-1\choose\dfrac{i}{\nu}}$ (8)

In our data-set the average password size was 11.56, therefore, limits between
8 and 14 can be evaluated resulting in:

$\sum^{14}_{i=8}{9025+\dfrac{i}{2}-1\choose\dfrac{i}{2}}\approx 9.96\times
10^{23}$ (9)

The crypto-analysis of the attack should include the details of the filter
like the size of the bucket or the number of hash functions used.

##  4 Experimental analysis

The specified method to check password similarity has been implemented in C
language. The hash functions used was the standard
OpenSSL444https://www.openssl.org/ implementations of hash functions, in this
case MD5. The system was checked on a Ubuntu 18.04 system running in a
VirtualBox virtual machine with 2 virtual CPUs and 1 GB of memory. The
hypervisor runs over an Intel core i7-8700 cpu which clock frequency runs at
3.2GHz, and the host is used exclusively to run the test VM. The random data
was provided by  /dev/urandom to avoid blocking behaviour[7] and read to
generate random hash functions. We used the following queries used to check
the filter:

  1. 1.

$\beta\leftarrow Create(\Gamma,\kappa)$

  2. 2.

$Insert(\beta,AAAA)$

  3. 3.

$Insert(\beta,BBBB)$

  4. 4.

$Check(\beta,AAAA)$

  5. 5.

$Check(\beta,CCCC)$

  6. 6.

$Check(\beta,BBBB)$

Figure 5: Creation time of the filter changing the size of the salt strings.

In this case the hash dimension seems not to influence the performances of the
filter. The computational load is dominated by the generation of the salt
string. The performance of the salt string generation presented in figure 5
are the averaged results of 5 runs of experiments, in which the size of the
salt changes from 1 (really easy to brute-force) to 1000 (really hard to
brute-force). As shown in the graph, the performance decreases linearly when
the salt size increases. This happens because a single random character of the
salt must be multiplied by the number of hash functions present in the filter.
The $QInsert$ and $Distance$ performances has been evaluated using the
following querying pattern:

  1. 1.

$\beta_{1}\leftarrow Create(\Gamma,\kappa)$

  2. 2.

$QInsert(\beta_{1},thisismypassword,2)$

  3. 3.

$\beta_{2}\leftarrow Create(\Gamma,\kappa)$

  4. 4.

$QInsert(\beta_{2},thisismyp4ssword,2)$

  5. 5.

$\beta_{3}\leftarrow Create(\Gamma,\kappa)$

  6. 6.

$QInsert(\beta_{3},thisismypassw0rd,2)$

  7. 7.

$Distance(\beta_{1},\beta_{2})$

  8. 8.

$Distance(\beta_{1},\beta_{3})$

In this test run, as in the Insert evaluation, the computational load is
dominated by the filter generation. This system was also tested using c.a.
5000 credentials from real-world leaked institutional logins. Data were
clustered and analyzed using the filter, to observe which values are correctly
identified as similar.

Figure 6: Performances of the filter compared to the edit distance applied to
the password data set

The graph in figure 6 represent the analysis of the filter’s precision. The
graph also shows the edit distance between the various strings.

##  5 Application scenarios

In this work, we described a technique to analyze password similarity
maintaining a good trade-off between utility and privacy. The proposed use
case presents a system that can notify if a new password is not different
enough from a previous one. The typical application could be a browser’s plug-
in that issues a warning when the distance between a new password chosen by
the user and the strings saved in the plug-in is below a pre-declared
threshold. The application can be exploited both to discourage the use of
similar passwords over time and to prevent their use over different domains as
pictured in figure 7. The application can be instrumented to report the
results of equations in section 3 regarding not only the similarity check
result, but also the various parameters characterizing the filter, to evaluate
the quality of the classification process.

Service 1P4ssword123!Service
2P4ssw0rd123!Browser$\square\square\square\square\square\square\square\square\square$$\beta$
Figure 7: Application scenario: The browser can insert the passwords
$P4ssword123!$ and $P4ssw0rd123!$ into the Bloom filter, checking if they are
similar enough to trow a warning of password similarity.

###  5.1 Future works

We are actually working on several improvements of the proposed password
similarity algorithm:

  * •

As stated in the section 3, the filter can be generated using encrypted salts
in conjunction with a strong cryptographic hash function555For example SHA3..
This approach can be employed to ensure that data inserted in the structure
are analyzable only by the owner of the secret key. The crypto-analysis of the
resultant system should be explored to create secure Bloom filters.

  * •

A comparison with deep-learning based techniques can be introduced. This
comparison should therefore include an analysis of the resistance against
data-set reverse engineering. We argue that a neural network-based system
needs a bigger data-set than our Bloom filter-based one, and that the former
approach can be difficult to analyze using black-box classifiers.

  * •

The analysis of the crypto-system can be improved with a more in-depth
comparison with privacy preserving techniques, such as $\delta$-presence or
differential privacy. As stated in section 5, these approaches can suffer from
the same issues affecting the deep-learning based one, i.e., the user cannot
provide a data-set big enough to make the analysis valuable.

  * •

Analysis of homomorphic encryption could lead to devise an encryption scheme
to compute distances between encrypted strings using algorithms present in
literature[4].

We claim that these analyses can lead to the creation of an useful password
checker, which, while respecting user experience guidelines and security best-
practices, can signal to them dangerous similarities between their passwords.

##  6 Conclusion

In this paper we proposed a system which can help the analysis of similar
passwords keeping them obfuscated or saved in a secure enclosure. This
proposal tries to advise against the behaviour of password reuse, acting from
an application point of view, using a controllable method which is otherwise
difficult to achieve. The system we proposed uses Bloom filters, a family of
probabilistic data structures, as the core elements of its design. This choice
is driven by two properties of these artifacts: the predictability of their
behavior, and the deterministic cryptanalysis that can be executed over them.
In conclusion, we claim that the proposed method can be integrated as a
modular component in any kind of authentication system, to discourage the use
of vulnerable passwords.

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# Influence of structure and cation distribution on magnetic anisotropy and
damping in Zn/Al doped nickel ferrites

Julia Lumetzberger<EMAIL_ADDRESS>Phone: +43-732-2468-9651; FAX:
-9696 Johannes Kepler University Linz, Institute for Semiconductor and Solid
State Physics, Altenberger Strasse 69, 4040 Linz, Austria  Martin Buchner
Johannes Kepler University Linz, Institute for Semiconductor and Solid State
Physics, Altenberger Strasse 69, 4040 Linz, Austria  Santa Pile  Johannes
Kepler University Linz, Institute for Semiconductor and Solid State Physics,
Altenberger Strasse 69, 4040 Linz, Austria  Verena Ney  Johannes Kepler
University Linz, Institute for Semiconductor and Solid State Physics,
Altenberger Strasse 69, 4040 Linz, Austria  Wolfgang Gaderbauer  Christian
Doppler Laboratory for Nanoscale Phase Transformations, Johannes Kepler
University Linz, Center for Surface and Nanoanalytics, Altenberger Strasse 69,
4040 Linz, Austria  Niéli Daffé  Swiss Light Source (SLS), Paul Scherrer
Institut, 5232 Villigen PSI, Switzerland  Marcos V. Moro  Department of
Physics and Astronomy, $\mathrm{\SIUnitSymbolAngstrom}$ngström Laboratory,
Uppsala University, Box 516, SE-751 20 Uppsala, Sweden  Daniel Primetzhofer
Department of Physics and Astronomy, $\mathrm{\SIUnitSymbolAngstrom}$ngström
Laboratory, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden  Kilian
Lenz  Helmholtz-Zentrum Dresden – Rossendorf, Institute of Ion Beam Physics
and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany  Andreas
Ney  Johannes Kepler University Linz, Institute for Semiconductor and Solid
State Physics, Altenberger Strasse 69, 4040 Linz, Austria

###### Abstract

An in-depth analysis of Zn/Al doped nickel ferrites grown by reactive
magnetron sputtering is relevant due to their promising characteristics for
applications in spintronics. The material is insulating and ferromagnetic at
room temperature with an additional low magnetic damping. By studying the
complex interplay between strain and cation distribution their impact on the
magnetic properties, i.e. anisotropy, damping and g-factor is unravelled. In
particular, a strong influence of the lattice site occupation of
Ni${}^{2+}_{\text{Td}}$ and cation coordination of Fe${}^{2+}_{\text{Oh}}$ on
the intrinsic damping is found. Furthermore, the critical role of the
incorporation of Zn2+ and Al3+ is evidenced by comparison with a sample of
altered composition. Especially, the dopant Zn2+ is evidenced as a tuning
factor for Ni${}^{2+}_{\text{Td}}$ and therefore unquenched orbital moments
directly controlling the g-factor. A strain-independent reduction of the
magnetic anisotropy and damping by adapting the cation distribution is
demonstrated.

## I. Introduction

In spintronics one aims to obtain pure spin currents as an additional degree
of freedom in logic circuits aside from electric charges WA01 . By spin
pumping TBB02  it is feasible to induce a spin current from ferromagnetic
materials into adjacent non-magnetic layers. To ensure pure spin currents and
exclude charge currents ferromagnetic insulators are the materials of choice.
However, ferromagnetic insulators with low intrinsic magnetic damping are
sparse HE15 . The most commonly used material is yttrium iron garnet (YIG)
OKK14 ; CLZ14 . YIG has two major drawbacks, i.e. the complex garnet
structure, which is almost exclusively grown on gadolinium gallium garnet
(GGG) substrates and its weak magnetoelastic response. It could be replaced by
cubic Zn/Al doped nickel ferrite (NiZAF) thin films grown on
MgAl${}_{\text{2}}$O${}_{\text{4}}$, which were reported to have comparably
favorable magnetic properties E17  as YIG: ferromagnetic at room temperature
and a low intrinsic damping. Furthermore, the static magnetic analysis shows a
soft magnetic behavior with a low coercive field, which makes the material
relevant for high frequency applications. The combination of these properties
makes it especially suitable for applications in magnetoelectric and acoustic
spintronics.
NiZAF is based on nickel-ferrite NiFe${}_{\text{2}}$O${}_{\text{4}}$, which
ideally grows in the cubic inverse spinel crystal structure, i.e. Ni occupies
octahedral (Ni${}_{\text{Oh}}$) lattice sites and Fe is located in a $1$ : $1$
ratio either at tetrahedral (Fe${}_{\text{Td}}$) or octahedral
(Fe${}_{\text{Oh}}$) lattice sites. This is explained in more detail in
section VI [see Fig. 5(a)]. Thin film growth of NiZAF on a MgAl2O4 (001)
substrate with a normal spinel crystal structure gives rise to disorder
between the tetrahedral A (Ni2+) and octahedral B (Fe3+) sites. Therefore Ni
and Fe with a valency of 2+ (Ni${}^{2+}_{\text{Td}}$ and
Fe${}^{2+}_{\text{Oh}}$) are introduced into the lattice. Previous work on the
single ion model of ferrite magnetism D11  shows a negative impact of
tetrahedrally coordinated Ni${}^{2+}_{\text{Td}}$ on the magnetic damping due
to unquenched orbital moments. This effect has not been found for octahedrally
coordinated Ni${}^{2+}_{\text{Oh}}$. Additionally, Fe${}^{2+}_{\text{Oh}}$
increases the magnetic damping due to hopping. Thin film growth of co-
sputtered NiFe${}_{\text{2}}$O${}_{\text{4}}$ on the same substrate confirms
the presence of Fe${}^{2+}_{\text{Oh}}$ in this system K14 .
The structural and magnetic properties can be controlled by doping with Zn and
Al, which predominantly substitute Ni and Fe, respectively. Since Zn2+ prefers
the tetrahedral coordination it prevents Ni2+ from occupying these sites and
therefore, predominantly Ni${}^{2+}_{\text{Oh}}$ is formed N67 . Growth of
highly strained NiFe${}_{\text{2}}$O${}_{\text{4}}$ thin films K14  showed an
increase in damping caused by defects. Thus, to reduce the strain, smaller
Al3+ cations are added to substitute for Fe3+. A doping percentage of 0.8 was
reported to be the best compromise between magnetostriction and saturation
magnetization for bulk polycrystalline NiZAF L13 .
Substituting ferromagnetic with non-ferromagnetic elements in NiZAF results in
a reduced saturation magnetization $M_{\text{S}}\sim$
$110\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ and Curie temperature
$\sim$ $450\text{\,}\mathrm{K}$ E17  compared to undoped
NiFe${}_{\text{2}}$O${}_{\text{4}}$ with $M_{\text{S}}$ up to $300$
$\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ and a significantly higher Curie
temperature of $T_{\text{C}}=860$ $\mathrm{K}$ H12 . In turn, NiZAF exhibits a
smaller ferromagnetic resonance (FMR) linewidth down to $\sim$
$0.82\text{\,}\mathrm{mT}$ resulting in a Gilbert damping parameter of
$\alpha\sim 3\times 10^{-3}$ E17  in comparison to a linewidth $\mu_{0}\Delta
H_{\text{pp}}=35$ $\mathrm{mT}$ of NiFe${}_{\text{2}}$O${}_{\text{4}}$H12 .
Furthermore, in contrast to a coercivity of $H_{\text{c}}=100$ $\mathrm{mT}$
K14  for undoped NiFe${}_{\text{2}}$O${}_{\text{4}}$ a reduced coercive field
of $\sim$ $0.2\text{\,}\mathrm{mT}$ E17  has been reported. Zn/Al doping of
NiFe${}_{\text{2}}$O${}_{\text{4}}$ is, therefore, an advantageous trade-off
since low damping and coercivity are desired for applications in spintronics.
NiZAF was studied for the correlation between composition, strain, cation
distribution, magnetic anisotropy and intrinsic damping. This manuscript is
structured as follows: in section II the experimental details of the sample
fabrication are provided together with the experimental details of the various
techniques used throughout this work. At first the structural characterization
is discussed in section III followed by the static and dynamic magnetic
analysis in section IV. In section V the cation distribution in the material
is studied in detail by comparing the experimental spectra with multiplet
ligand field simulations. A comparison to a sample with intentionally altered
stoichiometry is given in section VI to highlight the governing mechanism in
the material system. Finally, a short conclusion is given in section VII.

## II. Experimental Details

In this work NiZAF was fabricated using reactive magnetron sputtering (RMS)
with a nominal target composition of
Ni${}_{\text{0.65}}$Zn${}_{\text{0.35}}$Al${}_{\text{0.8}}$Fe${}_{\text{1.2}}$O${}_{\text{4}}$
as suggested in Ref.E17 , in which pulsed laser deposition (PLD) was used. The
epitaxial thin films were grown in an ultra high vacuum (UHV) chamber with a
base pressure of $2\times 10^{-9}$ $\mathrm{mbar}$. A doubleside polished
single crystalline spinel [MgAl${}_{\text{2}}$O${}_{\text{4}}$(001)] was
chosen as a substrate. The data of the growth optimization including
temperature, Ar : O2 ratio and thickness variation and annealing can be found
in the data repository LBN19-S . The best results were achieved with the
highest possible heater temperature corresponding to a sample temperature of
$\sim$ $525\text{\,}\mathrm{\SIUnitSymbolCelsius}$, an Ar : O2 ratio of ($10$
: $0$) $\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ to ($10$ : $0.1$)
$\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, a magnetron power of
$30\text{\,}\mathrm{W}$ and a working pressure of $4\times 10^{-3}$
$\mathrm{mbar}$. Additionally, a sample with an adjusted composition, i.e.,
increased Zn while maintaining the Al concentration was fabricated. During
that growth a sample temperature up to $\sim$
$600\text{\,}\mathrm{\SIUnitSymbolCelsius}$ could be achieved.
The structural characterization of the samples was done by X-ray diffraction
(XRD) measurements with a Pananalytical X’Pert MRD and a Seifert XRD3003
recording $\omega-2\theta$ scans and symmetric as well as asymmetric
reciprocal space maps (RSM). The surface roughness was characterized with an
atomic force microscope (AFM). The interface on an atomic scale was checked by
transmission electron microscopy (TEM) using a Jeol JEM-2200 FS. Furthermore,
the chemical composition was obtained with energy dispersive X-ray
spectroscopy (EDX) in the TEM system. Additionally, the composition was
determined more accurately by ion beam analysis, i.e. Rutherford
backscattering spectrometry (RBS) using $2\text{\,}\mathrm{MeV}$ He+ and
$10\text{\,}\mathrm{MeV}$ 12C3+ primary beams at the Tandem Laboratory at
Uppsala University. To disentangle the element specific contributions, the
spectra were analyzed using the SIMNRA software M97 . Details of the
experimental setup are described elsewhere M19 . The static magnetic
properties were measured with integral superconducting quantum interference
device (SQUID) magnetometry by a Quantum Design MPMS-XL5 system applying the
magnetic field in the film plane (IP) as well as out-of-plane (OOP). The
magnetic behavior in a field range of $\pm 5$ $\mathrm{T}$ from room
temperature (RT) down to $2\text{\,}\mathrm{K}$ and the temperature dependence
of the magnetization up to $400\text{\,}\mathrm{K}$ were measured. The data
were background corrected for the contribution of the diamagnetic substrate
and known artefacts were carefully avoided SSA11 ; B18 .
The dynamic magnetic properties were analyzed with a broadband vector network
analyzer ferromagnetic resonance (VNA-FMR) setup at room temperature at the
HZDR, researching the polar and azimuthal angular dependence of resonance
position and linewidth. Furthermore, the frequency dependence was measured to
verify the g-factor and disentangle the different contributions to the
magnetic damping. The angular dependence was cross-checked with a conventional
X-band FMR setup and the data can be found in LBN19 .
Finally, X-ray absorption (XAS) and X-ray magnetic circular dichroism (XMCD)
spectra at the Ni and Fe L3,2 edges were measured at the X-Treme beamline at
the Swiss Light Source (SLS) PFS12 . The XMCD spectra were obtained in total
electron yield (TEY) with $20\text{\,}\mathrm{\SIUnitSymbolDegree}$ grazing
incidence at RT and a field of $6.8\text{\,}\mathrm{T}$. The XMCD(H) curves
were measured in a field range of $\pm$ $6.8\text{\,}\mathrm{T}$ in total
fluorescence yield (TFY) at normal incidence, RT and at the maximum of the
XMCD peaks sensitive to the site occupancy of the cation in the
crystallographic structure. The raw data of the measurements can be found in
the data repository LBN19 .

## III. Structural Properties

Figure 1: Structural properties of NiZAF measured with XRD on a
$70\text{\,}\mathrm{nm}$ sample. (a) shows a symmetric $\omega-2\theta$ scan
in comparison to a $16\text{\,}\mathrm{nm}$ sample, (b) symmetric RSM along
($004$) and (c) asymmetric RSM along ($\bar{1}\bar{1}5$).

The crystalline structure of the material is routinely analyzed by symmetric
$\omega-2\theta$ scans using XRD. Results for two samples with different
thicknesses are shown in Fig. 1(a). Both samples have the (004) reflection at
$42.67$ $\mathrm{\SIUnitSymbolDegree}$ with respect to the substrate and show
Laue oscillations. The film reflection with a small full width at half maximum
(FWHM) around $0.13$ $\mathrm{\SIUnitSymbolDegree}$ for the
$70\text{\,}\mathrm{nm}$ sample corresponds to a perpendicular lattice
parameter of $a_{\perp}=(8.47\pm 0.01)$ $\mathrm{\SIUnitSymbolAngstrom}$. The
symmetric RSM along the ($004$) plane and the asymmetric RSM along the
($\bar{1}\bar{1}5$) plane are shown in Figs. 1(b) and 1(c), respectively. The
reflection from the MgAl${}_{\text{2}}$O${}_{\text{4}}$ substrate corresponds
to a lattice parameter of $a_{\text{sub}}=8.08$
$\mathrm{\SIUnitSymbolAngstrom}$, which has a lattice mismatch of $\sim$
$2\text{\,}\mathrm{\char 37\relax}$ to bulk NiZAF ($a_{0}=8.24$
$\mathrm{\SIUnitSymbolAngstrom}$) L13 . The asymmetric scan reveals an in-
plane lattice parameter of $a_{\parallel}=(8.09\pm 0.01)$
$\mathrm{\SIUnitSymbolAngstrom}$, i.e. fully strained with respect to the
substrate. A calculation of the tetragonal distortion yields $c/a=1.047\pm
0.003$ confirming a clearly strained material. Additionally, the unit cell
volume of the strained material is $a_{\parallel}^{2}\cdot a_{\perp}=(554\pm
2)$ ${\mathrm{\SIUnitSymbolAngstrom}}^{3}$, which is equal to a reduction of
the unit cell volume by only $\sim$ $1\text{\,}\mathrm{\char 37\relax}$ with
respect to the bulk $a_{0}^{3}=$
$559.5\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}$. Even though the samples
are significantly strained, they maintain an excellent crystal quality
evidenced by the well pronounced Laue oscillations visible in the line scan as
well as the RSM indicating a fully strained homogeneous crystal growth for a
thickness of up to $70\text{\,}\mathrm{nm}$.

Figure 2: Surface and interface properties of a $70\text{\,}\mathrm{nm}$ NiZAF
sample. (a) a high-resolution cross section TEM image showing the interface of
film and substrate on an atomic scale, (b) the film on a larger scale. The RBS
spectrum from a $2\text{\,}\mathrm{MeV}$ He+ beam to determine the chemical
composition analysed by SIMNRA is depicted in (c). (d) shows an AFM scan of
the surface.

In Fig. 2(a) the high resolution cross-section TEM image along the
$\left\langle 100\right\rangle$ direction shows a sharp interface transition
between film and substrate on an atomic scale. No indication for dislocations
or defects can be found in the measurements on various length scales, further
proving the excellent structural quality of the coherently strained material.
A clear separation between film and substrate is visible at the sample
interface on a larger scale, depicted in Fig. 2(b). However, the film exhibits
a clearly enhanced strain contrast, which corroborates the findings of the RSM
[see Fig. 1(b)]. Additional annealing had no influence on the structural
quality nor the magnetic properties further supporting a low-defect material,
in contrast to previous works on epitaxially grown spinel ferrite thin films
H12 ; S01 .
The analysis of the chemical composition with EDX in the TEM system (not
shown, see repository LBN19 ) revealed a ratio of
($\text{Fe}:\text{Ni}:\text{Zn}$) ($1:0.55:0.22$). In comparison to the
nominal values of ($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$)
($1:0.54:0.29:0.66$) (all values are normalized with respect to the Fe amount
in the material) a clear reduction of Zn content is observed. The deficiency
in Zn can be explained by its high volatility, which is even more enhanced by
the high growth temperatures ASY16 . The aluminium content cannot be reliably
determined by EDX due to the difference in atomic number in comparison to the
other metals. Therefore, the elemental composition was refined by an in-depth
ion beam analysis using RBS with $2\text{\,}\mathrm{MeV}$ He+ primary
particles, which makes an accurate determination of the concentration depth
profile of lighter elements like Al feasible. From these measurements a
chemical composition of ($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$)
($1:0.62:0.26:0.71$) is determined [see Fig.2(c)]. The Zn deficiency is less
than suggested from EDX, however the amount of Ni is increased compared to the
nominal values from the composite target. The Al content is slightly
increased, indicating only a small deviation from the nominal values. These
findings suggest that the stoichiometric transfer for this composition by RMS
is comparable to PLD E17  since both results are in reasonable agreement with
the target composition. Note that the Al content cannot be correlated due to
the lack of data from the PLD samples in Ref. E17 . Furthermore, by analyzing
the sample with a $10\text{\,}\mathrm{MeV}$ 12C3+ ion beam, a more reliable
result for the heavier elements of ($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$)
($1:0.6:0.23:0.83$) could be obtained due to the better mass separation. Thus
confirming previous results, i.e. a good incorporation of Ni with a slight
deficiency in Zn. The increased Al content is confirmed from this measurement.
From the spectrum in Fig. 2(c) no drastic gradient is visible in the element
concentration. This behavior is supported for Ni, Zn and Fe by the C ion beam
LBN19 .
In Fig. 2(d) an AFM image of the surface of a $550\times 550$
${\mathrm{nm}}^{2}$ area is shown. A flat surface with neither cracks nor
holes and a low average maximum roughness peak height $R_{pm}=40$
$\mathrm{pm}$ as well as a root mean square roughness of $R_{q}=24$
$\mathrm{pm}$ is found. This is further supported by the maximum height
deviation of $2\text{\,}\mathrm{nm}$ within the image, which corresponds to
only 2 monolayers of NiZAF. The smooth surface is ideal for growing
heterostructures making NiZAF a perfect choice for spin pumping devices with
an insulating ferromagnetic material.

Figure 3: Static magnetic properties obtained from integral SQUID
magnetometry. (a) shows the hystereses at exemplary temperatures between
$300\text{\,}\mathrm{K}$ and $2\text{\,}\mathrm{K}$ with an inset giving a
detailed look at the coercive field in this temperature range. (b) depicts the
temperature dependence of the magnetization from
$2\text{\,}\mathrm{K}400\text{\,}\mathrm{K}$ at $10\text{\,}\mathrm{mT}$. An
estimation of the Curie temperature is given in the inset. In (c) the XMCD (H)
of Fe${}_{\text{Oh}}$, Fe${}_{\text{Td}}$, Ni and an average of all three in
comparison with the integral IP $\left\langle 100\right\rangle$ and OOP
$\left\langle 001\right\rangle$ SQUID measurements are plotted.

## IV. Magnetic Properties

The static and dynamic magnetic behavior of the material is measured by SQUID
magnetometry and FMR, respectively. In Fig. 3(a) the magnetic hystereses at
selected temperatures are shown. The inset depicts the dependence of the
coercive field for all investigated temperatures between
$300\text{\,}\mathrm{K}$ and $2\text{\,}\mathrm{K}$. A small coercive field of
$H_{\text{c}}=1.2$ $\mathrm{mT}$ at $300\text{\,}\mathrm{K}$ is determined,
which is further evidence for a material devoid of pinning centers. A steady
increase from $H_{\text{c}}=1.2$ $\mathrm{mT}$ at $300\text{\,}\mathrm{K}$ up
to $H_{\text{c}}=40$ $\mathrm{mT}$ at $2\text{\,}\mathrm{K}$ was determined,
as can be seen in the inset of Fig. 3(a). For low temperatures the typical
increase of remanence and coercivity is observed.
The volume of the film is taken into account for the magnetization values by
thickness determination from the Laue oscillations [see Fig. 1(a)] and the
area of the used sample piece. Accordingly, a saturation magnetization of
$M_{\text{S}}=(118\pm 12)$ $\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ is
obtained from the SQUID data at RT. This value matches the bulk value of
$\sim$ $120\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ L13  and
previous values for thin films $\sim$
$120\text{\,}\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ E17 . The Curie
temperature of $T_{\text{C}}=(375\pm 2)$ $\mathrm{K}$ was estimated from the
$M(T)$ curve at $10\text{\,}\mathrm{mT}$ shown in the inset of Fig. 3(b).
Compared to PLD samples with $T_{\text{C}}=$ $450\text{\,}\mathrm{K}$ E17  the
Curie temperature is slightly reduced. Nevertheless, it is well above
$300\text{\,}\mathrm{K}$ making ferromagnetic applications at RT feasible.
In addition, the directional dependence of the static magnetic properties was
studied. In Fig. 3(c) the difference in saturation field between IP
$\left\langle 100\right\rangle$ and OOP $\left\langle 001\right\rangle$ $M(H)$
curves measured by SQUID is shown in comparison with XMCD (H) curves of
Fe${}_{\text{Oh}}$, Fe${}_{\text{Td}}$, Ni and an average of all three. For
now, only the comparison of the different contributions to the average with
respect to the SQUID data is of importance and the XMCD spectra will be
discussed in more detail further below. A large uniaxial OOP anisotropy field
of $\mu_{0}H_{\text{k}}>3$ $\mathrm{T}$ is obtained, which cannot be solely
explained by shape anisotropy, which is $\mu_{0}M_{\text{S}}=$
$0.15\text{\,}\mathrm{T}$. Furthermore, the high OOP anisotropy field of more
than $3\text{\,}\mathrm{T}$ is evident in the XMCD(H) curves. The average of
the element selective hystereses shows the same behavior as the OOP $M(H)$
curve of the integral SQUID measurements. Fully strained
NiFe${}_{\text{2}}$O${}_{\text{4}}$ with lower crystal quality, on the other
hand shows no contribution to the OOP anisotropy field except for shape K14 .
The large $\mu_{0}H_{\text{k}}$ presumably originates from the
magnetocrystalline anisotropy of the highly strained inverse spinel crystal
structure. This is supported by previous work on less-strained Zn/Al doped
nickel ferrite ($c/a=1.035$) with a smaller out-of-plane anisotropy
($\mu_{0}H_{\text{k}}>1$ $\mathrm{T}$) in Ref. E17 . At first sight the major
change in anisotropy from $\mu_{0}H_{\text{k}}>1$ $\mathrm{T}$ E17  to
$\mu_{0}H_{\text{k}}>3$ $\mathrm{T}$ seems to be caused by a change in the $c$
lattice parameter from $a_{\perp}=8.36$ $\mathrm{\SIUnitSymbolAngstrom}$ E17
to $a_{\perp}=8.47$ $\mathrm{\SIUnitSymbolAngstrom}$ for the present film. The
fact that, in the present sample the Al content is slightly higher than
nominal together with the lack of knowledge about the actual Al content in
Ref. E17  indicates that another factor could play a decisive role for the
increased damping.

Figure 4: Dynamic magnetic properties including (a) the polar angular
dependence from
$-20\text{\,}\mathrm{\SIUnitSymbolDegree}90\text{\,}\mathrm{\SIUnitSymbolDegree}$
and (b) the azimuthal angular dependence from
$0\text{\,}\mathrm{\SIUnitSymbolDegree}360\text{\,}\mathrm{\SIUnitSymbolDegree}$
with an anisotropy fit (red line) for the resonance position in both
dependences. The inset in (a) depicts the smallest FMR line measured with a
conventional setup at $f=9.5$ $\mathrm{GHz}$ in the easy axis. (c) shows the
frequency dependence of the resonance position as well as linewidth (inset) in
a range from $5\text{\,}\mathrm{GHz}40\text{\,}\mathrm{GHz}$.

Angle- and frequency-dependent FMR measurements have been performed at RT to
obtain accurate values for magnetic anisotropy and damping. The FMR spectra
were fitted by Lorentzians to obtain the resonance field ($\mu_{0}H$) and
peak-to-peak linewidth ($\mu_{0}\Delta H_{\mathrm{pp}}$). Figure 4(a) shows
the polar angular dependence measured at $f=9.5$ GHz by VNA-FMR, where
$\theta_{H}=0^{\circ}$ denotes the out-of-plane direction, i.e. the hard axis
[see Fig. 4(a)]. The resonance field in this direction was larger than the
available field range of the electromagnet. Hence, no resonance could be found
around the hard axis. The inset shows a typical FMR spectrum taken for field
in-plane, i.e., $\theta_{H}=90^{\circ}$, using a conventional X-band resonator
with field-modulation technique. The fit reveals a resonance field of
$\mu_{0}H=(36.2\pm 0.2)$ $\mathrm{mT}$ and a peak-to-peak linewidth of
$\mu_{0}\Delta H_{\mathrm{pp}}=(12.0\pm 0.2)$ $\mathrm{mT}$. Compared to that
the linewidth of the bulk material is four times higher, i.e., $\mu_{0}\Delta
H_{\mathrm{pp}}=43$ $\mathrm{mT}$ L13 . Figure 4(b) shows the corresponding
azimuthal angular dependence clearly indicating a cubic (fourfold)
magnetocrystalline anisotropy with easy axes along the $\left\langle
110\right\rangle$ directions. A comparison with bulk shows that the IP easy
axis switches from $\left\langle 111\right\rangle$ to $\left\langle
110\right\rangle$ directions for thin film growth in agreement with E17 .
To fit the angular dependences in order to determine the cubic IP
($K_{4||}/M_{\mathrm{s}}$) and OOP ($K_{4\perp}/M_{\mathrm{s}}$) anisotropy
fields as well as the intrinsic uniaxial OOP ($K_{2\perp}/M_{\mathrm{s}}$), IP
($K_{2||}/M_{\mathrm{s}}$) and shape contributions, the following free energy
density function was used F98 :

$\displaystyle F=$ $\displaystyle-
M_{\mathrm{s}}H_{0}[\sin\theta\sin\theta_{H}\cos(\phi-\phi_{H})+\cos\theta\cos\theta_{H}]$
$\displaystyle-(2\pi M_{\mathrm{s}}^{2}-K_{2\perp})\sin^{2}(\theta)$
$\displaystyle-K_{2\parallel}\sin^{2}(\theta)\cos^{2}(\phi)$
$\displaystyle-\frac{K_{4\perp}}{2}\cos^{4}(\theta)$
$\displaystyle-\frac{K_{4\parallel}}{8}[3+\cos(4\phi)]\sin^{4}\theta\quad.$
(1)

Here $\theta,\theta_{H}$ and $\phi,\phi_{H}$ denote the OOP and IP angles of
the magnetization and external magnetic field, respectively. To account for a
possible deviation from the cubic system due to the high strain in the
material the free energy density of the lower-symmetric tetragonal crystal
structure was used. The fits of the experimental polar and azimuthal angular
dependences to the resonance condition [red curves in Figs. 4(a) and 4(b)]
result in the following anisotropy fields: The effective magnetization is
$\mu_{0}M_{\mathrm{eff}}=\mu_{0}M_{\mathrm{s}}-\frac{2K_{2\perp}}{M_{\mathrm{s}}}=2.5$
$\mathrm{T}$. Using $M_{\mathrm{s}}$ determined by SQUID the uniaxial OOP
anisotropy field $2K_{2\perp}/M_{\mathrm{s}}$ can be calculated as
$2.35\text{\,}\mathrm{T}$, which correlates well with the anisotropy field
estimated from SQUID [see Fig. 4(b)]. This is in agreement with the
expectation that a strong hard axis in a material with a low saturation
magnetization has to stem from a strain induced perpendicular uniaxial
anisotropy component. The uniaxial IP anisotropy field
$K_{2\parallel}/M_{\mathrm{s}}$ is disregarded, since the visible scatter of
the data points makes potential contribution not significant. Furthermore, the
fits reveal that $K_{4\parallel}$ and $K_{4\perp}$ are the same. Hence, the
uniform cubic anisotropy field is $2K_{4}/M_{\mathrm{s}}=-4$ $\mathrm{mT}$.
Previous work showed an even stronger preference for the $\left\langle
110\right\rangle$ easy axis with an in-plane anisotropy of $\sim 10$
$\mathrm{mT}$ for a less-strained material ($c/a=1.035$) grown by PLD E17 .
The $g$-factor of $g=2.18\pm 0.19$ was obtained from the frequency-dependence
of the resonance field depicted in Fig. 4(c) by using the Kittel equation Z07
. This infers to a lower contribution of the orbital momentum in comparison to
Ref. E17 , where $g=2.29\pm 0.09$ was reported. The inset of Fig. 4(c) depicts
the frequency dependence of the linewidth. A monotonic non-linear dependence
is visible, which is a clear sign for a two-magnon scattering (TMS)
contribution to the damping in addition to the intrinsic Gilbert damping L03 ;
L06 , which is linear in frequency. The fit (red line) includes both
components resulting in a Gilbert damping parameter of $\alpha=1\times
10^{-2}$ and a TMS factor of $\Gamma_{100}=0.04\times 10^{-8}$ s-1,
respectively. Even neglecting the TMS contribution, the pure Gilbert damping
is still higher by an order of magnitude than previously reported E17 .
Additionally, an inhomogeneous contribution of $B_{\text{inhom}}=$
$7.8\text{\,}\mathrm{mT}$ is apparent from the linewidth dependence. Since the
material and substrate are both insulating and without additional cap layers,
broadening by eddy current damping and/or spin pumping can be excluded.
In a first evaluation of the magnetic properties in comparison to the
structural analysis the following observation is made: The higher strained RMS
material ($c/a=1.047\pm 0.001$) has a lower cubic anisotropy
$2K_{4}/M_{\mathrm{s}}$ of $4$ $\mathrm{mT}$, yet shows a significant increase
in magnetocrystalline anisotropy evidenced by the high
$2K_{2\perp}/M_{\mathrm{s}}$ of $2.35\text{\,}\mathrm{T}$. In turn, this leads
to a broadening of the linewidth and increased damping with a non negligible
contribution of TMS at higher frequencies. Even though, the structural
analysis shows an excellent crystal structure with a low amount of defects at
least on a local scale, a significant inhomogeneous component is detectable by
sensitive magnetic measurements.

## V. Cation distribution

Figure 5: (a) Sketch of the inverse spinel crystal structure of
NiFe${}_{\text{2}}$O${}_{\text{4}}$ as the underlying structure for NiZAF.
Total electron yield XAS and XMCD spectra in grazing incidence of
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$ at RT and simulations done with
CTM4XAS SG10  are depicted at (b) the Ni L3,2 and (c) the Fe L3,2 edges. (d)
shows the cation distributions of the simulated weighted linear combination of
the XMCD at the Fe L3,2 edges.

To verify if strain is causing the increased damping, the cation occupation is
studied in more detail, since it reportedly E17 ; D11  has a strong influence
on the intrinsic damping. The possible coordination in the case of an ideal
inverse spinel crystal structure, as it is given for undoped bulk
NiFe${}_{\text{2}}$O${}_{\text{4}}$, is shown in Fig. 5(a). Half the Fe3+
occupies octahedral, the other half tetrahedral sites, whereas Ni2+ only sits
at octahedral sites. Ideally, the dopant Zn2+ would substitute for Ni2+ and
the smaller Al3+ goes to octahedral Fe3+ sites according to the nominal
composition of
Ni${}_{\text{0.65}}$Zn${}_{\text{0.35}}$Al${}_{\text{0.8}}$Fe${}_{\text{1.2}}$O${}_{\text{4}}$
maintaining the inverse spinel. However, due to thin film growth on a normal
spinel substrate MgAl2O4 a mixed spinel crystal structure leading to a small
degree of A/B disorder, is most likely.
For experimental evidence, total electron yield XAS and XMCD spectra in
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$ grazing incidence at the Ni and Fe
L3,2 edges shown in Fig. 5 are recorded. Respective simulations are done with
CTM4XAS SG10  using multiplet ligand field theory. The chosen parameters are
adapted from nickel ferrite PLH11 , which shows similar XAS spectra and
resulting XMCD curves. Scaling the percentages for the $F_{\text{dd}}$,
$F_{\text{pd}}$, and $G_{\text{pd}}$, Slater integral reductions of
$70\text{\,}\mathrm{\char 37\relax}$ and $80\text{\,}\mathrm{\char 37\relax}$,
respectively, are used to consider interatomic screening and mixing. For the
octahedral coordination a crystal field splitting of $10Dq=$
$1.2\text{\,}\mathrm{meV}$ and a positive exchange field of $J=$
$48\text{\,}\mathrm{meV}$ is used to fit the obtained Curie temperature of
$T_{\text{C}}=(375\pm 2)$ $\mathrm{K}$ [see Fig. 3(c)] PMG09 . The tetrahedral
coordination is simulated with a splitting of $10Dq=$
$-0.6\text{\,}\mathrm{meV}$ and a negative exchange field $J=$
$-48\text{\,}\mathrm{meV}$. Charge transfer is not taken into account, because
no influence on the absorption spectra has been found SG10 . Furthermore, the
instrumental and intrinsic broadening is included by a Gaussian function of
$\sigma=$ $0.25\text{\,}\mathrm{eV}$ and a Lorentzian function with a range of
$\Gamma$[$0.3\text{\,}\mathrm{eV}0.5\text{\,}\mathrm{eV}$], respectively. Note
that the simulation is shifted in photon energy to fit the experimental
spectra.
A comparison between the experimental and simulated XAS and XMCD spectra at
the Ni L3,2 edges [see Fig. 5(b)] suggests percentages of
$94\text{\,}\mathrm{\char 37\relax}$ Ni${}^{2+}_{\text{Oh}}$, and
$4\text{\,}\mathrm{\char 37\relax}$ Ni${}^{2+}_{\text{Td}}$, showing a slight
deviation from the inverse spinel crystal structure. The assumption of A/B
disorder is supported by evaluation of the simulation matching the
experimental XAS and XMCD spectra of Fe [see Fig. 5(c)]. The Fe contributions
are more complex, since not only Fe3+ occupying Oh and Td sites but also
typical spectroscopic signatures of Fe${}^{2+}_{\text{Oh}}$ were identified in
the experimental data. The best match between experiment and simulation was
determined by relying on the main peaks of the XMCD at the L3 edge as shown in
Fig. 5(d). Percentages of $33\text{\,}\mathrm{\char 37\relax}$
Fe${}^{2+}_{\text{Oh}}$, $45\text{\,}\mathrm{\char 37\relax}$
Fe${}^{3+}_{\text{Oh}}$ and $22\text{\,}\mathrm{\char 37\relax}$
Fe${}^{3+}_{\text{Td}}$ are obtained as best fit. From this, a mixed state
between the inverse and normal spinel crystal structure is apparent, as has
been evidenced for thin film nickel ferrites in earlier works E17 ; K14 ; H15
. The element selective magnetic contributions from Ni and Fe indirectly infer
the occupation of Zn and Al. According to the single ion model of ferrites D11
, Ni${}^{2+}_{\text{Oh}}$ does not enhance the damping, but
Ni${}^{2+}_{\text{Td}}$ contributes by an unquenched orbital momentum. A non-
negligible amount of $4\text{\,}\mathrm{\char 37\relax}$
Ni${}^{2+}_{\text{Td}}$ can be correlated with the reduced amount of Zn2+ D11
as evidenced by EDX and RBS. Additionally, the strong imbalance between
octahedral and tetrahedral coordinated Fe as well as the high amount of
Fe${}^{3+}_{\text{Oh}}$ suggest a deficiency of Al. This is further supported
by the findings of bulk NiZAF reported by Ref. L13  since a higher amount of
Al doping lowers the saturation magnetisation and the magnetic damping.
However, the concentration of Al relative to Fe determined from RBS fits
rather well with the nominal values. Therefore the difficulties of Fe
incorporation cannot solely be explained or solved with the Al concentration.
Additionally, the large amount of $\sim$ $33\text{\,}\mathrm{\char 37\relax}$
Fe${}^{2+}_{\text{Oh}}$ has a negative impact on the damping due to hopping
[Fe2+ $\rightarrow$ Fe3+ \+ e-] E17 ; D11 .
The results are in good agreement with the previous analysis of the material
system and give an explanation on the atomic level for the increased intrinsic
damping. The main cause being a non-negligible amount of
Ni${}^{2+}_{\text{Td}}$ due to a low incorporation of Zn2+ and large amounts
of Fe${}^{2+}_{\text{Oh}}$. The role of Ni${}^{2+}_{\text{Td}}$ is even more
important, since it directly influences the g-factor by orbital momentum. In
addition, the strong A/B disorder promotes scattering centers resulting in the
TMS contribution to magnetic damping. Furthermore, the imbalance between
tetrahedral and octahedral coordinated Fe3+ supports the assumption of a mixed
spinel structure as suggested by growth and chemical composition.

## VI. Governing Mechanism

Figure 6: Analysis of a Zn-rich NiZAF showing the TEY XAS and XMCD spectra in
grazing incidence of $20\text{\,}\mathrm{\SIUnitSymbolDegree}$ at RT and
simulations done with CTM4XAS SG10  at (a) the Ni L3,2 and (b) the Fe L3,2
edges. The inset in (a) depicts a symmetric $\omega-2\theta$ scan. (c) the
$M(T)$ curve at $100\text{\,}\mathrm{m}\mathrm{T}$ from
$2\text{\,}\mathrm{K}390\text{\,}\mathrm{K}$ with an inset magnifying the high
temperature range. (d) shows hystereses at exemplary temperatures between
$300\text{\,}\mathrm{K}$ and $2\text{\,}\mathrm{K}$ with an inset giving a
detailed look at the coercive field in this temperature range.

To evidence the crucial role of the Ni${}^{2+}_{\text{Td}}$ in conjunction
with the Zn deficiency a sample with a different composition of
($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$) ($1:0.43:0.39:0.71$) was
fabricated. The composition was determined using RBS with a
$2\text{\,}\mathrm{MeV}$ He+ beam in analogy to Fig. 2(c). For this purpose
the Al content was kept constant to maintain strain and directly see the
influence of the Zn dopant. By comparing the composition with the previous
sample a strong change in the ($\text{Ni}:\text{Zn}$) ratio from ($0.62:0.26$)
to ($0.43:0.39$) relative to Fe is apparent. Furthermore, the higher energetic
$10\text{\,}\mathrm{MeV}$ 12C+ ion beam analysis of
($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$) = ($1:0.48:0.42:0.76$) revealed an
even more drastic change of the Ni-to-Zn ratio to ($0.48:0.42$). However,
structural analysis shows a comparably excellent crystal quality with well
pronounced Laue oscillations and a (within error bars similar or even slightly
increased) perpendicular lattice parameter of $a_{\perp}=(8.49\pm 0.01)$
$\mathrm{\SIUnitSymbolAngstrom}$ instead of $a_{\perp}=(8.47\pm 0.01)$
$\mathrm{\SIUnitSymbolAngstrom}$ [see inset of Fig. 6(a)]. Thus a tetragonal
distortion of $c/a=1.049\pm 0.003$ is determined.
In Fig. 6(a) a comparison between data and simulation of the XAS and XMCD
spectra at the Ni L3,2 edges is depicted resulting in percentages of
$2.5\text{\,}\mathrm{\char 37\relax}$ Ni${}^{2+}_{\text{Td}}$ and
$97.5\text{\,}\mathrm{\char 37\relax}$ Ni${}^{2+}_{\text{Oh}}$. A reduction of
almost $50\text{\,}\mathrm{\char 37\relax}$ in tetrahedrally coordinated Ni
either suggests an improved incorporation of Zn2+ or an overabundance of Zn in
this sample leading to less possibilities for Ni2+ to occupy Td sites.
Furthermore, the correlation between data and simulation of the XAS and XMCD
spectra at the Fe L3,2 edges shown in Fig. 6(b) confirms the results obtained
for Ni. The simulation is fitted with respect to the primary peaks of the XMCD
at the L3 edge, since the magnetic information of the material is mainly
contained in the XMCD spectra. Percentages of $28\text{\,}\mathrm{\char
37\relax}$ Fe${}^{2+}_{\text{Oh}}$, $28\text{\,}\mathrm{\char 37\relax}$
Fe${}^{3+}_{\text{Oh}}$ and $44\text{\,}\mathrm{\char 37\relax}$
Fe${}^{3+}_{\text{Td}}$ are calculated indicating a more even distribution of
Fe in the inverse spinel crystal structure in contrast to previous values [see
Fig. 5(c)]. From this a better incorporation of the Al3+ in the crystal
structure can be inferred, even though the analysis of the chemical
composition revealed the same amount of Al relatively to Fe. This further
highlights the sensitivity of Fe to disorder in the crystal lattice.
Additionally, the reduction of Fe${}^{2+}_{\text{Oh}}$ suggests a positive
impact on the intrinsic magnetic damping due to reduced hopping. This
interpretation is confirmed by the improved magnetic properties of the
material indicated by an increase in Curie temperature by
$10\text{\,}\mathrm{K}$ up to $T_{\text{C}}=(385\pm 2)$ $\mathrm{K}$ at
$100\text{\,}\mathrm{mT}$ as shown in the inset of Fig. 6(c). Furthermore, the
hystereses at exemplary temperatures in a range of
$300\text{\,}\mathrm{K}2\text{\,}\mathrm{K}$ shown in Fig. 6(d) indicate a
transition to an even softer magnetic material than previously determined [see
Fig. 3(a)]. From a closer look at the coercive fields dependence on the
temperature depicted in the inset, a coercive field of $H_{\text{c}}\sim 0.2$
$\mathrm{mT}$ at $300\text{\,}\mathrm{K}$ is determined. At temperatures as
low as $100\text{\,}\mathrm{K}$ similar values for the coercivity as in
previous samples of $H_{\text{c}}=1.2$ $\mathrm{mT}$ are reached, increasing
up to $H_{\text{c}}=4$ $\mathrm{mT}$ at $2\text{\,}\mathrm{K}$. Additionally,
an increase of the saturation magnetization to $M_{\text{S}}=(195\pm 20)$
$\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ at RT (not shown, see repository
LBN19 ) in comparison to $M_{\text{S}}=(118\pm 12)$
$\mathrm{k}\mathrm{A}\mathrm{/}\mathrm{m}$ was measured.

Figure 7: Dynamic magnetic properties including (a) the polar angular
dependence from
$-20\text{\,}\mathrm{\SIUnitSymbolDegree}90\text{\,}\mathrm{\SIUnitSymbolDegree}$
and (b) the azimuthal angular dependence from
$0\text{\,}\mathrm{\SIUnitSymbolDegree}360\text{\,}\mathrm{\SIUnitSymbolDegree}$
with an anisotropy fit (red line) for the resonance position in both
dependences. The inset in (a) depicts the smallest FMR line at $f=9.5$
$\mathrm{GHz}$ in the easy axis. (c) shows the frequency dependence of the
resonance position as well as line-width (inset) in a range from
$5\text{\,}\mathrm{GHz}40\text{\,}\mathrm{GHz}$.

In Fig. 7 the VNA-FMR analysis is shown. In the inset of Fig. 7(a) the FMR
line at $f=$ $9.5\text{\,}\mathrm{GHz}$ is shown indicating an increased
resonance position of $\mu_{0}H=(57.8\pm 0.2)$ $\mathrm{mT}$ and a reduced
linewidth of $\mu_{0}\Delta H_{\text{pp}}=(4.4\pm 0.2)$ $\mathrm{mT}$
confirming the improved magnetic properties. Since the resonance position
depends on the magnetocrystalline anisotropy this coincides with the decreased
anisotropy of $2K_{2\perp}/M_{\mathrm{s}}=1.53$ $\mathrm{T}$ determined by the
polar angular dependence. Additionally, a lower effective magnetization of
$\mu_{0}M_{\text{eff}}=$ $1.78\text{\,}\mathrm{T}$ is calculated from the fit
to the angular dependences. The azimuthal angular dependence confirms the
cubic (fourfold) symmetry of the crystal. The easy axis in the $\left\langle
110\right\rangle$ direction coincides with NiZAF [see Fig. 4(b)], however the
cubic in plane anisotropy has two components
$2K_{4\perp}/M_{\mathrm{s}}=-(420\pm 100)$ $\mathrm{mT}$ and
$2K_{4\parallel}/M_{\mathrm{s}}=-1.2$ $\mathrm{mT}$, indicating a slight shift
towards a tetragonal crystal symmetry. Additionally, a slight uniaxial in
plane anisotropy component of $2K_{\parallel}/M_{\mathrm{s}}=-1.4$
$\mathrm{mT}$ is needed to fit the data. The frequency dependences of the
resonance position and the linewidth are shown in Fig. 7(c) and its inset,
respectively. Due to the larger FMR signal, the g-factor could be determined
with high precision yielding $g=2.109\pm 0.002$. A comparison with previous
work E17 , where values of $g=2.29\pm 0.09$ are obtained, shows a drastic
change in orbital momentum. These findings match the decreased
Ni${}^{2+}_{\text{Td}}$, since these contribute to damping by unquenched
orbital momentum. Furthermore, the frequency dependence of the linewidth shows
that in the Zn-rich sample no two magnon scattering is apparent, resulting in
a Gilbert damping of $\alpha=6.8\times 10^{-3}$. Additionally, the lack of an
inhomogeneous contribution suggests an excellent crystal growth without any
defects.
Although the strain has slightly increased, by improving the cation
distribution and deviating from the reported best stoichiometry E17 ; L13  the
magnetic anisotropy and the linewidth broadening effects could be reduced
remarkably. These results demonstrate the relevance of the cation
distribution, in particular the amount of Ni${}^{2+}_{\text{Td}}$ and
Fe${}^{2+}_{\text{Oh}}$ as another major criteria for the optimisation of the
magnetic properties. In particular, the reduction of Ni${}^{2+}_{\text{Td}}$
and A/B disorder, lowered the g-factor and magnetic damping and eliminated the
TMS contribution.
So far, only the influence of Al on bulk NiZAF L13  has been studied
systematically. The present investigation shows the importance of tuning both
the Al and the Zn content. Therefore, for a full understanding of this complex
material system the determination of the whole parameter space of Al and Zn
concentration together with the site occupancy in NiZAF thin films is
required.

## VII. Conclusion

In this work the growth of Zn/Al doped nickel ferrite thin films with
excellent crystal quality was achieved by reactive magnetron sputtering from a
target with nominal composition of
Ni${}_{\text{0.65}}$Zn${}_{\text{0.35}}$Al${}_{\text{0.8}}$Fe${}_{\text{1.2}}$O${}_{\text{4}}$.
The chemical composition of ($\text{Fe}:\text{Ni}:\text{Zn}:\text{Al}$)
($1:0.62:0.26:0.71$) obtained by RBS evidenced a rather good stoichiometric
transfer with a slight Zn deficiency. The material is highly, but coherently
strained and no indication for defects or dislocations can be observed from a
structural analysis. A comparison with bulk L13  shows a shift of the in-plane
magnetic easy axis from $\left\langle 111\right\rangle$ to the $\left\langle
110\right\rangle$ in agreement with the thin films in E17 . Furthermore, the
frequency dependence revealed a reduced g-factor, an increased damping and
additional contributions from two magnon scattering and inhomogeneity compared
to Ref. E17  indicating a lower amount of orbital momentum.
These changes are caused by the cation distribution, which has a significant
influence on the magnetocrystalline anisotropy and the intrinsic magnetic
damping. A comparative sample with increased Zn content shows a reduction of
Ni${}^{2+}_{\text{Td}}$, which infers a better incorporation of Zn2+ leading
to a decrease in coercivity, anisotropy and damping. Due to the reduction in
orbital momentum the g-factor is lowered significantly. Furthermore, less
Fe${}^{2+}_{\text{Oh}}$ resulted in a smaller linewidth and an even lower
magnetic damping. By improving the A/B disorder, the contributions of two
magnon scattering and inhomogeneity could be eliminated.
To conclude, in contrast to initial assumptions, strain is not the sole
mechanism to control the magnetic properties in this complex material system.
In addition, the cation distribution, i. e. the amount of
Fe${}^{2+}_{\text{Oh}}$ and Ni${}^{2+}_{\text{Td}}$ was found to have a major
impact on the magnetic anisotropy and damping independent of strain. The
influence of the doping can be divided into two aspects: To first order the
Ni:Zn ratio controls the magnetic damping and g-factor and the Fe : Al ratio
the strain. Secondly, the resulting A/B disorder promotes the formation of
scattering centers leading to TMS contributions and inhomogeneity. While
previous work on bulk NiZAF have already evidenced the importance of the Al
concentration, the present work demonstrates that for future optimization the
crucial role of the Zn concentration has to be taken into account.

## Acknowledgement

The authors gratefully acknowledge funding by FWF project ORD-49. The X-ray
absorption measurements were performed on the EPFL/PSI X-Treme beamline at the
Swiss Light Source, Paul Scherrer Institut, Villigen, Switzerland. In
addition, support by VR-RFI (Contract No. 2017-00646_9) and the Swedish
Foundation for Strategic Research (SSF, Contract No. RIF14-0053) supporting
accelerator operation at Uppsala University is gratefully acknowledged. The
financial support by the Austrian Federal Ministry for Digital and Economic
Affairs and the National Foundation for Research, Technology and Development
in the frame of the CDL for Nanoscale Phase Transformations is gratefully
acknowledged. Further the authors thank Werner Ginzinger for TEM sample
preparation.

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