# Cu-substituted Fe2P: An emerging candidates for magnetic RAM application

Enamullah  S. Bhat  Seung-Cheol Lee<EMAIL_ADDRESS>S.
Bhattacharjee<EMAIL_ADDRESS>Indo-Korea Science and
Technology Center (IKST), Bangalore 560065, India

(August 27, 2024)

###### Abstract

We propose that Cu-substituted Fe2P, (Fe1-xCux)2P ($x\sim 0.16$), to be an
outstanding contender for the STT-MRAM application. Using first principles
based calculations in the framework of density functional theory and through
Monte Carlo simulations, we demonstrate that this material can be used as
ferromagnetic electrode in the magnetic tunnel junction (MTJ) of STT-MRAM due
to its moderate perpendicular magnetic anisotropy (PMA), large tunnel magneto-
resistance (TMR), good thermal stability and high ferromagnetic transition
temperature. We point out that the simplicity in the synthesis, huge
abundance, and non-toxicity make this material a very good candidate to
replace the current MTJ materials for STT-MRAM such as FePt, FeCo or FeCoB.

##  1 Introduction

In the current years, heaps of considerations are given to Spin-transfer-
torque magnetic random access memory (STT-MRAM) due to its high density, low
power consumption, non-volatility and considered to be one of the promising
candidate for next-generation universal memory [1]. The basic unit of a STT-
MRAM consists of a magnetic tunnel junction (MTJ) with perpendicular magnetic
anisotropy (PMA) [2, 3]. The MTJ is constructed with a thin non-magnetic
insulating layer sandwiched between two ferromagentic layers. One of the
layers has a fixed magnetization while the other layer’s magnetization can be
rotated [4, 5]. The bits are recorded in terms of the magneto-resistance of
the MTJ. The MTJ has a low resistance if both the ferromagnetic layers have
same polarity and usually represents a logical ”0” state while the MTJ has a
high resistance if the ferromagnetic layers have opposite polarity and is
represented by a logical ”1” state [6, 7]. Typically MgO-based MTJ films with
ferromagnetic L10 ordered electrodes such as FeCo,FeCoB or FePt are used due
to their strong interfacial PMA, large tunnel magneto-resistance and thermal
stability[8, 9].

In the present study, we propose another contender for the ferromagnetic
electrode, which can be utilized as a part of MTJ of the STT-MRAM. We show
here that (Fe1-xCux)2P can be used as alternative to FeCo or FePt. This
material fulfils all the essential requirements to act as component in MTJ.

Stoichiometric Fe2P is a ferromagnet with Curie temperature (TC) of 216 K
[10], exhibiting large Magnetocrystalline anisotropy energy MAE of about 500
$\mu$eV/f.u. [11]. Due to its low TC, Fe2P is impractical for room temperature
applications. However, earlier studies have shown great enhancement in TC, by
alloying Fe2P with Ni, Co, Si and B [10, 11, 12, 13, 14], making them useful
for room temperature applications. Interesting magnetic behaviour have been
reported for Mn, Cr, Co and Ni substitutions of Fe2P using Mossbauer
spectroscopy techniques [10, 15, 16, 17, 18, 19]. Very small substitutions of
Mn (Fe1-xMnx)2P (for $x<$ 0.015) induce metamagnetism and for $x>$ 0.03 it is
antiferromagnetic. Similar results are reported for Cr substitution [10, 18].
Contrarily, for Co substitution TC increases with $x$ to a maximum of 480 K at
$x$ = 0.3 [17]. Similar behaviour is observed for (Fe1-xNix)2P compounds with
TC reaching to maximum (342 K) at about $x$ = 0.1 [18, 20]. Also, presence of
very small amount of Cu impurities are found to greatly enhance the TC [21].

All the above mentioned studies were intended to make the metal substituted
Fe2P to be useful for permanent magnet applications. However no efforts have
been made so far to in a direction where non-stoichiometric Fe2P may find a
”softer” magnetic applications [22, 23, 24, 25] such as switching component in
magnetic devices. In the present investigation, we rationalize the
attainability of such application.

We explored systematically the the effect of Co, Ni, Cu and Zn substitution on
the various magnetic properties of Fe2P, particularly the magnetic moments,
Magnetocrystalline anisotropy energy, the ferromagnetic transition
temperature. Such screening shows Cu substituted Fe2P is the most suitable
candidate for the MRAM application which we have further verified through the
calculation of TMR. We discuss our findings following a brief outline of the
computational methods.

##  2 Computational methods

We performed first-principles calculations using the projector-augmented wave
(PAW) method [26] in the framework of DFT as implemented in VASP code [27,
28]. The exchange-correlation energy of electrons is treated within a
generalized gradient approximated functional (GGA) of the
Perdew−Burke−Ernzerhof (PBE) [29] parameterized form. Interactions between
ionic cores and valence electrons are represented using PAW pseudo-potentials,
where 4$s$, 3$d$ electrons for transition metals (Fe, Co, Ni, Cu and Zn) and
3$s$, 3$p$ electrons for P are treated as valence. Plane-wave basis set with
kinetic energy cutoff of 500 eV and an energy convergence criteria of
$10^{-6}$ eV are used. Uniform mesh of 9x9x15 k-points used for Brillouin zone
sampling of the unit cell, provided sufficient accuracy. MAE is calculated
using force theorem which treats the change in the band energy as a result of
the variation of the angle of magnetization axis with respect to the easy axis
[30].

The Heisenberg exchange coupling constants $(J_{ij})$ are calculated using
spin-polarized relativistic (SPR) Korringa-Kohn-Rostoker (KKR) Green’s
function method, as implemented within SPRKKR package[31]. Using Heisenberg
model, exchange Hamiltonian is given by,

$\hat{H}=-\sum_{i\neq j}\hbox{}J_{ij}\hat{e}_{i}\hbox{}\hat{e}_{j},$

where, $\hat{e}_{i}$ and $\hat{e}_{j}$ are the unit vectors along the
direction of local magnetic moment on atomic site $i$ and $j$ respectively.
The exchange parameters can be obtained from the energy difference between two
different magnetic configurations using the formulation of Liechtenstein et
al.[32]. An angular momentum cutoff of $l_{max}$=3 and 30 complex energy
points was used for the expansion of Green’s function. The energy convergence
criteria of 10-5 is used for self-consistence cycles. Equilibrium lattice
parameters obtained from the ab-initio simulation are used to calculate
exchange interaction parameters.

Once the exchange coupling constants are calculated from SPRKKR package, one
can estimate the Curie temperature either using simplified mean filed
approximation or via more sophisticated Monte Carlo simulation as implemented
in VAMPIRE software package[33, 34]. We have used VAMPIRE code to obtain the
magnetization versus temperature data and hence the estimation of Curie
temperature. The Curie temperature $(T_{C})$ can be obtained using the
following expression,

$T_{C}=\frac{\epsilon zJ_{ij}}{3k_{B}},$

where, $J_{ij}$ is the pair wise exchange energy either between same or
different species of atoms within nearest neighbor approximation, $z$ is the
coordination number (number of nearest neighbors), kB is the Boltzmann
constant and $\epsilon$ represents a correction factor to account for spin
wave fluctuations in different crystal lattices.

##  3 Results and Discussions

Initial structure of Fe2P is taken from the experimental data [35] and is
optimized by full relaxation of the unit cell and atomic positions. Fe2P
crystallizes in hexagonal C22 structure with space group $P\bar{6}2m$ (#189).
The unit cell is composed of three formula units with three Fe atoms (say
Fe${}_{\text{I}}$) occupy 3$f$, other three Fe atoms (say Fe${}_{\text{II}}$)
occupy 3$g$, two P atoms occupy 2$c$ (P${}_{\text{I}}$) and one P atom
occupies 1$b$ Wyckoff sites (P${}_{\text{II}}$). Fe${}_{\text{I}}$ atom is
surrounded by four P atoms, whereas Fe${}_{\text{II}}$ atom is surrounded by
five P atoms, and so referred as tetrahedral and pyramidal sites respectively.
The structure can be expressed as Fe3 triangles in the $ab$ plane, with P
occupying the alternate layers (see Fig. 1). Computed lattice constants ($a$ =
5.81 and $c$ = 3.43 $\AA$) agree well with the reported experimental values
($a$ = 5.87, and $c$ = 3.46 $\AA$) [35].

An early X-ray diffraction experiment on (Fe1-xMx)2P alloys (where M is the
transition metal) by Fruchart et al. [10] revealed Fe2P-type hexagonal
structure for $x$ $\leq$ 0.2. Therefore, we took the optimized Fe2P structure
and one out of six Fe atoms, either from Fe${}_{\text{I}}$ site or
Fe${}_{\text{II}}$ site is substituted by transition metal resulting in the
formula (Fe1-xMx)2P, with $x$ = 0.16 and M = Co, Ni, Cu and Zn.

###  3.1 Site preference

To examine the site preference of the solute M atoms in Fe2-xMxP, we compared
the total energies for both cases, i.e. with M atom at Fe${}_{\text{I}}$ and
Fe${}_{\text{II}}$ sites, and the energy differences $\Delta
E^{\text{Fe}_{\text{I}}-\text{Fe}_{\text{II}}}$ is listed in Table 1. For
(Fe1-xCox)2P, total energy is lower by 67 meV/f.u. when Co occupies
Fe${}_{\text{I}}$ site. This is in agreement with the earlier
M$\ddot{o}$ssbauer studies [10, 36] which disclosed the preferential filling
of tetrahedral site. Same trend is obtained for Ni substitution where the
energy difference is 21 meV/f.u., which is in accordance with the experimental
finding, where Ni atoms occupy Fe${}_{\text{I}}$ site preferentially, for $x$
in the range 0 $\leq$ $x$ $\leq$ 0.3, but Fe${}_{\text{II}}$ site for $x>0.7$
[10, 16, 37]. In case of (Fe1-xCux)2P and (Fe1-xZnx)2P, our calculations
predict that Cu and Zn substitutes Fe preferentially at pyramidal site, for
which there are no previous data available for comparison.

###  3.2 Magnetic moment

Table 2 presents the total and local magnetic moments calculated for 3$f$ and
3$g$ sites for Fe2P and (Fe1-xMx)2P alloys. Calculated total magnetic moment
(3.01 $\mu_{\text{B}}$/f.u.) for Fe2P agrees well with the experimental value
(3.27 $\mu_{\text{B}}$) [38]. The local magnetic moments computed for 3$f$ and
3$g$ sites (0.83 and 2.23 $\mu_{\text{B}}$) are also in accordance with
earlier reports (0.96 and 2.31 $\mu_{\text{B}}$/f.u.) [38]. For Co
substitution total magnetic moment decreases to 2.71 $\mu_{\text{B}}$/f.u.,
which can be compared with the experimental value of 2.47
$\mu_{\text{B}}$/f.u. reported for (Fe0.70Co0.30)2P measured at 12 K [19]. For
Ni case, computed value is 2.43 $\mu_{\text{B}}$/f.u., which can be compared
to experimental value of 2.14 $\mu_{\text{B}}$/f.u. measured at 4 K for
(Fe0.75Ni0.25)2P [16]. The agreement between our calculation and experimental
values are acceptable as magnetic moments are found to decrease monotonically
with increase in $x$, for Co and Ni substitutions [16, 17, 18]. Calculated
$\mu_{\text{total}}$ for Cu and Zn substitution is 2.07 and 1.75
$\mu_{\text{B}}$/f.u., respectively, where Cu has negligible magnetic moment
and Zn has negative magnetic moment.

Fig. 3 illustrates the variation of MAE and total magnetic moment for stable
low energy structures of (Fe1-xMx)2P alloys. It is evident form the figure
that the total moment decreases linearly as we move from Fe to Zn. Also, MAE
decreases for all the transition metal substituted Fe2P cases with respect to
the pristine alloy. Further, for all the studied cases, decrease in
$\mu_{\text{total}}$ is more pronounced when M occupies pyramidal site. That
is, substituting at Fe${}_{\text{I}}$ site produces little change in magnetic
moment, whereas magnetic moment changes significantly for Fe${}_{\text{II}}$
substitution.

###  3.3 Magnetic anisotropy

Table 3 shows the MAE estimated for Fe2P and (Fe1-xMx)2P alloys. For Fe2P,
computed MAE is 496 $\mu$eV/f.u., which is very close to experimentally
determined value of 500 $\mu$eV/f.u. measured at low temperature [11].
Further, our calculation reproduces the observed $c$-axis as the magnetization
easy axis. From Table 3 it is evident that for all M substitutions, the
calculated MAE is lower than that of Fe2P. Kumar et al. [17] reported the
decrease in MAE for Co substitution up to 10$\%$ in hexagonal phase and then
progressive increase with increasing Co in the orthorhombic phase. For Ni
substitution, Fujii et al. [18] through their experiments revealed a monotonic
decrease in MAE with increase in $x$ and dropping to zero at $x$ = 0.3. Thus,
our results are in accordance with these experimental findings. For Cu and Zn
substitutions there are no previous experimental reports available and our
calculations predict their MAE to be 266 and 134 $\mu$eV/f.u., respectively.

Similar to Fe2P, lower energy structures of Co, Cu and Zn substituted Fe2P
also have [001] as magnetization easy axis. Since these alloys have TC above
room temperature and magnetic easy axis oriented along the [001] direction,
they can be used in perpendicular magnetic recording applications. For Ni
substitution it is reversed, i.e., the magnetic easy axis is along [100]
direction. Further, it shows lowest MAE (97 $\mu$eV/f.u.) among all the alloys
under consideration (see Fig. 3). Note that the decrease in MAE is substantial
($\sim 80\%$) for small substitution of Ni, while the decrease in magnetic
moment is marginal ($\sim 20\%$). As mentioned earlier, TC is maximum for
(Fe1-xNix)2P alloys at $x\sim$0.1, and thus it can be useful for high
temperature applications, where high magnetization and low MAE are the desired
requirements.

##  4 Cu-substituted Fe2P as magnetic memory material

From the above, it is quite evident that the Cu-substituted Fe2P satisfies all
the necessary requirements. In the following we further investigate its
competence as for the same from the calculation of TC and TMR calculations.

###  4.1 Exchange interaction constants and Curie temperature

Here, we demonstrate the results of interatomic exchange constants for
pristine Fe2P and Cu-substituted Fe2P obtained using SPR-KKR package and the
corresponding Curie temperature as presented in Table 4. In order to calculate
the Curie temperature accurately beyond the simplified mean field
approximation, Monte Carlo simulation is used via VAMPIRE software package[33,
34]. For the simulation, we construct a 12$\times$12$\times$7 super cell with
periodic boundary condition. To calculate thermal equilibrium magnetization at
each temperature, we use 5000 equilibrium time steps. In order to get fast
relaxation to thermal equilibrium, the Hinzke-Nowak combinational algorithm is
used in Monte Carlo simulations[39]. The simulated temperature dependent
normalized magnetization plot for Fe2P and Cu-substituted Fe2P data are fitted
using the Curie-Bloch equation within classical limit[40],

$m(T)=\left(1-\frac{T}{T_{C}}\right)^{\beta},$

where, m(T) is normalized magnetization as a function of temperature (T), TC
is the Curie temperature and $\beta$ is the critical exponent. In case of
Fe2P, $\beta$ is 0.501 whereas, for Cu-substituted Fe2P it is 0.497. The
fitted values of TC for both Fe2P and Cu-substituted Fe2P are shown in Table3.
The simulated TC for Fe2P is 230K which is in good agreement with the
experimental value of 217K, where as in case of Cu-substituted, TC reaches to
792K. We have also calculated the TC with the lower concentration of Cu
(8.11%) and got the value 502K.
To further understand the origin of large TC in the Cu-substituted Fe2P, we
show in the Fig.4, the calculated exchange constants as a function distance.
In the topmost panels (a) and (b) we show the calculated exchange constants
for pure Fe2P while in the bottom panels (c), (d) and (e), the exchange
constants for the Cu-substituted Fe2P are shown. It can be seen that for the
pure case, the strongest interaction is FeII-FeII type and is about 14.44 meV.
While n the case Cu-substituted Fe2P, there are three irons, among which the
most prominent interaction is among the FIII sites (21.6 meV). It is to be
noted that in both the cases, intra-sublattice interaction plays dominant
role.

###  4.2 Tunnel Magnetoresistance of (Fe1-xCux)2P (001)/MgO
(001)/(Fe1-xCux)2P(001) trilayer structure

The magnetic tunnel junction(MTJ) composed of Cu-substituted Fe2P having
different number of insulating layers of MgO is shown in Fig.5. In the figure,
different thickness of MgO(001) layers sandwhiches between the four layers of
Cu-substituted Fe2P(001). Top two and bottom two layers of MTJ have been
treated as bulk and remaining layers are fully relaxed using VASP. After
getting the spin polarization of both the ferromagnetic slab, the tunnel
magnetoresistance(TMR) ratio has been calculated using the following formula,

$TMR=\frac{2P_{L_{1}}P_{L_{2}}}{1-P_{L_{1}}P_{L_{2}}}\times 100\%$

where, $P_{L_{1}}(P_{L_{2}})$ is depicts spin polarization value of
ferromagnetic layer, $L_{1}(L_{2})$. The variation of TMR with different
number of insulating layer has been shown in Table4. The maximum TMR achieved
for 8.11% of Cu-substituted Fe2P having two layers of MgO (94$\%$) which is
considerably large and makes the material suitable for STT-MRAM applications.

##  5 Summary

In summary, we have studied the magnetic properties of Fe2P and
$M$-substituted Fe2P ($M$ is the transition metal) using first-principles
calculations based on DFT. Our calculations show that Co, Ni substitutes Fe
preferentially at tetrahedral site, whereas Cu and Zn substitutes at pyramidal
site. For all studied alloys, total magnetic moment is less than that of Fe2P
and decreases linearly as we move from Co to Zn substitution. Further,
decrease in magnetic moment is more pronounced for substitution at pyramidal
site. Computed MAE for Fe2P is 496 $\mu$eV/f.u., with magnetic easy axis
oriented along the [001] direction, which is in excellent agreement with the
experimental results. The MAE of Fe2P is found to decrease for all
substitutions. Co, Cu and Zn substituted Fe2P retains [001] as magnetization
easy axis, thus can be used in perpendicular magnetic recording applications.
Interestingly, Ni substituted Fe2P has [100] as easy axis with lowest MAE of
97 $\mu$eV/f.u. For Cu -substituted Fe2P, we show that due to its moderate
perpendicular magnetic anisotropy, large TMR, it has significant potential to
be used as component for a magnetic RAM.

## Acknowledgement

We acknowledge support from the Convergence Agenda Program (CAP) of the Korea
Research Council of Fundamental Science and Technology (KRCF) and Global
Knowledge Platform (GKP) program of the Ministry of Science, ICT and Future
Planning. Enamullah, as a research associate acknowledges IKST for providing
financial support.

References:

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Table 1: Calculated total energy difference $\Delta
E^{\text{Fe}_{\text{I}}-\text{Fe}_{\text{II}}}$ along with preferred site for
M occupation
|  $\Delta E^{\text{Fe}_{\text{I}}-\text{Fe}_{\text{II}}}$ (meV/f.u.) | Preferred site
---|---|---
Co | -67 | Fe${}_{\text{I}}$
Ni | -21 | Fe${}_{\text{I}}$
Cu | 117 | Fe${}_{\text{II}}$
Zn | 268 | Fe${}_{\text{II}}$

Table 2: Calculated local and total magnetic moment for Fe2P and (Fe1-xMx)2P,
x=0.16. $\mu_{\text{Fe}_{\text{I}}}$ and $\mu_{\text{Fe}_{\text{II}}}$ are
average local magnetic moment at Fe${}_{\text{I}}$ and Fe${}_{\text{II}}$
sites, respectively. $\mu_{\text{M}_{\text{I}}}$ and
$\mu_{\text{M}_{\text{II}}}$ represents local magnetic moment of M atom
substituted at Fe${}_{\text{I}}$ and Fe${}_{\text{II}}$ sites, respectively.
| Site |  $\mu_{\text{Fe}_{\text{I}}}$ ($\mu_{\text{B}}$) |  $\mu_{\text{M}_{\text{I}}}$ ($\mu_{\text{B}}$) |  $\mu_{\text{Fe}_{\text{II}}}$ ($\mu_{\text{B}}$) |  $\mu_{\text{M}_{\text{II}}}$ ($\mu_{\text{B}}$) |  $\mu_{\text{total}}$ ($\mu_{\text{B}}/$f.u.)
---|---|---|---|---|---|---
Fe2P | – | 0.83 | – | 2.23 | – | 3.01
(Fe1-xCox)2P | Fe${}_{\text{I}}$ | 0.75 | 0.37 | 2.13 | – | 2.71
Fe${}_{\text{II}}$ | 0.88 | – | 2.30 | 0.87 | 2.66
(Fe1-xNix)2P | Fe${}_{\text{I}}$ | 0.59 | 0.12 | 2.03 | – | 2.43
Fe${}_{\text{II}}$ | 0.88 | – | 2.18 | 0.28 | 2.39
(Fe1-xCux)2P | Fe${}_{\text{I}}$ | 0.42 | 0.004 | 1.90 | – | 2.15
Fe${}_{\text{II}}$ | 0.82 | – | 1.93 | 0.04 | 2.07
(Fe1-xZnx)2P | Fe${}_{\text{I}}$ | 0.27 | -0.04 | 1.75 | – | 1.88
Fe${}_{\text{II}}$ | 0.77 | – | 1.53 | -0.12 | 1.75
Table 3: Calculated MAE along with magnetic easy and hard axis for Fe2P and
(Fe1-xMx)2P with x=0.16
| Site | Easy Axis | Hard Axis | MAE ($\mu$eV/f.u.)
---|---|---|---|---
Fe2P | – | 001 | 100 | 496
(Fe1-xCox)2P | Fe${}_{\text{I}}$ | 001 | 100 | 199
Fe${}_{\text{II}}$ | 001 | 100 | 188
(Fe1-xNix)2P | Fe${}_{\text{I}}$ | 100 | 010 | 97
Fe${}_{\text{II}}$ | 001 | 100 | 146
(Fe1-xCux)2P | Fe${}_{\text{I}}$ | 100 | 001 | 266
Fe${}_{\text{II}}$ | 001 | 100 | 182
(Fe1-xZnx)2P | Fe${}_{\text{I}}$ | 100 | 001 | 134
Fe${}_{\text{II}}$ | 001 | 100 | 157

Table 4: Calculated exchange interaction constants ($J_{ij}$ in meV/link) and
Curie temperature ($T_{C}$ in $K$) for Fe2P and Cu-substituted Fe2P.
$J_{ij}$’s are considered only between Fe atoms. In Fe2P, there are two
inequivalent sites for Fe-atom, whereas, in Fe2-xCuxP ($x$=16.67%), there are
three inequivalent sites. The indices, I,II and III represent FeI, FeII and
FeIII atoms respectively.
System | $J_{I-I}$ | $J_{I-II}$ | $J_{I-III}$ | $J_{II-II}$ | $J_{II-III}$ | $J_{III-III}$ | $T_{C}$
---|---|---|---|---|---|---|---
Fe2P | 5.13 | 9.39 | – | 14.44 | – | – | 230
Fe2-xCuxP | 9.84 | 1.18 | 8.10 | -0.05 | 3.41 | 21.60 | 792
Table 5: TMR for Cu-substituted Fe2P MTJ with different number of MgO
insulating layers.
layer | TMR for $x$=8.33$\%$ | TMR for $x$=16.67$\%$ |
---|---|---|---
2 layer | 94$\%$ | 58$\%$ |
4 layer | 13$\%$ | 74 $\%$ |
6 layer | 2$\%$ | 15$\%$ |

Figure 1:  (color online). Fe2P crystal structure. Fe${}_{\text{I}}$
tetrahedral sites (brown), Fe${}_{\text{II}}$ pyramidal sites (blue) and P
atoms (yellow).

Figure 2: (color online) Variation of Curie temperature (TC) and MAE versus Cu
concentration $x$. Plot depicts that increasing the doping concentration
increases TC and decreases MAE.

Figure 3:  (color online). Calculated MAE and magnetic moment for pristine and
Co, Ni, Cu and Zn substituted Fe2P. Dashed and solid lines represent magnetic
moment and MAE respectively.

Figure 4: Calculated exchange constants for the pure Fe2P and Cu-substituted
Fe2P

Figure 5: (color online) Magnetic Tunnel Junction (MTJ) with Cu-substituted
Fe2P and MgO