Influence of spin reorientation on magnetocaloric effect in NdAl
2
: A microscopic model
P. J. von Ranke,
1,
* N. A. de Oliveira,
1
C. Mello,
1
D. C. Garcia,
1
V. A. de Souza,
1
and A. Magnus G. Carvalho
2
1
Instituto de Física, Universidade do Estado do Rio de Janeiro—UERJ, Rua São Francisco Xavier, 524, 20550-013,
Rio de Janeiro, Brazil
2
Instituto de Física ‘Gleb Wataghin,’ Universidade Estadual de Campinas—UNICAMP, Caixa Postale. 6165, Campinas 13 083-970, São
Paulo, Brazil
Received 23 May 2006; published 21 August 2006
We report a theoretical investigation about the influence of the spin reorientation from easy magnetic
direction 001 to the applied magnetic field direction 111 on the magnetocaloric properties of NdAl
2
. This
compound was fully investigated using a model Hamiltonian which includes the Zeeman-exchange interactions
and the crystalline electrical field, which are responsible for the magnetic anisotropy. All theoretical results
were obtained using the proper model parameters for NdAl
2
, found in the literature. The existence of a
minimum in magnetic entropy change below the phase transition was predicted and ascribed to the strong jump
on the spin reorientation.
DOI: 10.1103/PhysRevB.74.054425 PACS numbers: 75.30.Sg, 75.10.Dg, 75.20.En
INTRODUCTION
In the last ten years much efforts have been dedicated to
the development of new magnetocaloric materials due to the
broad interest which runs from technologic applications,
such as magnetic refrigeration that is based on the magneto-
caloric effect, to the pure physical theoretical interest, such
as several types and nature of phase transitions.
1
The mag-
netocaloric potential in given magnetic material is character-
ized by the two main thermodynamics quantities, namely
S
mag
the isothermal magnetic entropy change and T
ad
the adiabatic temperature change, which are observed upon
changes in the external magnetic field. The experimental dis-
covery of giant magnetocaloric effect around room tempera-
ture in some magnetic materials such as Gd
5
Si
x
Ge
1-x
4
,
2
MnFeP
0.45
As
0.55
,
3
MnAs
1-x
Sb
x
,
4,5
and LaFe
1-x
Si
x
13
,
6,7
and
its hydrides enhanced the interest in magnetocaloric effect
due to the potential applications of these materials to work as
refrigerant materials in magnetic refrigeration at room tem-
perature. The potential application of a near-room tempera-
ture magnetic refrigerator was firstly reported by G. V.
Brown.
8
The first theoretical descriptions, using a phenom-
enological model and in which the magnetic state equations
were solved self-consistently and applied to the giant mag-
netocaloric materials Gd
5
Si
x
Ge
1-x
4
, MnFeP
0.45
As
0.55
, and
MnAs
1-x
Sb
x
, were reported by some of us Refs. 9–11. The
signature of giant magnetocaloric materials is the abrupt
change in the order parameter, magnetization, at Curie tem-
perature first-order magnetic phase transition, which is
coupled to crystallographic phase transition or a high change
in lattices parameters. More recently the experimental and
theoretical investigations led to the discovery of the colossal
magnetocaloric effect where the lattice entropy plays funda-
mental role in order-disorder magnetic process due to the
magnetoelastic interaction.
12–14
Another important aspects of magnetocaloric materials is
concerned with the magnetic anisotropy effects which leads,
for example, to different behaviors for temperature and mag-
netic field dependence of the magnetization for different
choices of applied magnetic field direction in crystallo-
graphic referential frame. Since the magnetocaloric potential
quantities, S
mag
and T
ad
, depend on the magnetization re-
sponse to the applied magnetic field change, the choice of the
applied magnetic field direction in the crystal, in an aniso-
tropic magnetic material, leads to different values for S
mag
and T
ad
. We are interested in the anisotropy caused, in rare
earth intermetallic compounds due to the crystalline electri-
cal field CEF interaction. In rare-earth the CEF interaction,
in general, destroys the magnetic symmetry due to the total
or partial break of 2J +1-times degenerated 4 f Hund’s
ground states. As a consequence, some interesting physical
effects can appear—for example, the pure paramagnetic
PrNi
5
compound cools down when submitted to external
magnetic field in an adiabatic process below 14 K for mag-
netic field change from 0 to 5 T the so-called anomalous
MCE. Therefore, as far as we know, PrNi
5
is the only para-
magnetic system that has its magnetic entropy increased with
the magnetic field, and this anomaly could be quantitatively
explained by the CEF anisotropy effects.
15,16
Recently, ex-
perimental measurements of ferromagnetic single-crystal
DyAl
2
showed anomalous magnetocaloric effect when the
external magnetic field change is considered along the 111
crystallographic direction,
17
confirming the previous theoret-
ical prediction
18
based on the study of CEF anisotropy of this
material.
In this paper, we present the theoretical results of a full
investigation on the magnetic and magnetocaloric properties
of NdAl
2
considering the magnetic field change along the
three main crystallographic directions, namely 001the
easy magnetic direction, 101, and 111. We started with
the microscopic model where the interactions included in the
magnetic model Hamiltonian are i the Zeeman interaction,
ii the exchange interaction in the molecular field approxi-
mation, and iii the cubic CEF anisotropic interaction. The
lattice entropy was treated in the Debye assumptions. From
the Hamiltonian, the magnetic state equation is obtained and
the temperature and field dependence of magnetization are
calculated, self-consistently, in the three main directions.
When the magnetic field is applied in the 111 direction, a
predicted critical temperature T
R
50 K, is calculated at
PHYSICAL REVIEW B 74, 054425 2006
1098-0121/2006/745/0544256 ©2006 The American Physical Society 054425-1
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